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5l08 KIProj/AocaPrelelRC/DateDue.indd

EVOLUTION OF NUCLEAR SHELL STRUCTURE: fi-DECAY AND
ISOMERIC PROPERTIES OF NUCLEI IN AND NEAR THE fp
SHELL
By

Heather Lynn Crawford

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Chemistry

2010

ABSTRACT

EVOLUTION OF NUCLEAR SHELL STRUCTURE: fl DECAY AND ISOMERIC
PROPERTIES OF NUCLEI IN AND NEAR THE fp SHELL

By

Heather Lynn Crawford

One of the fundamental questions in nuclear structure science is how the nucleon
single-particle energies evolve with changing proton-to-neutron ratio. The nucleon
magic numbers, correctly described by the shell model near the valley of U stability,
do not appear to be static across the nuclear landscape. The shifting energies of
single-particle orbitals, resulting from variations in nucleon-nucleon interactions such
as the tensor monopole interaction, lead to the erosion of some magic numbers, and
the appearance of new subshell closures as the driplines are approached.

Near the borders of, and within the f p shell, relatively low single-particle level
densities lead to a number of distinct regions of changing shell structure. The low-
energy structure of nuclei near N 232 and Z220 are stabilized by the presence of a
subshell closure at N232, a result of an energy gap between the 1/2123 /2 level and
the higher-lying 1/2p1/2 and V1f5/2 levels. An open question, however, is whether
or not the continued upward shift of the 1/1 f5 /2 orbital in the Ca isotopes leads to
another subshell closure at N234. At slightly higher masses, the migration of the
1499/2 orbital leads to the erosion of the expected N240 subshell closure, and the
apparent development of a new region of deformation in the Cr, Mn and Fe isotopes.
The question in this region is how quickly collectivity develops as a function of Z,
as the 1499/2 orbital drops in energy with decreased occupancy of the proton 1f7/2
orbital below Z228.

The U decay and isomeric properties of nuclei in and on the border of the f p shell

have been studied at the National Superconducting Cyclotron Laboratory (NSCL)
using the combined experimental set-up of the NSCL fl Counting System and 16
detectors from the Segmented Germanium Array. The nuclei studied, 53"54Ca, 54568c,
50K, and 61Cr, were produced in two separate experiments, through the fragmentation
of a 76Ge primary beam by a 9Be target. Nuclei were implanted into a double—sided
Si microstrip detector, and correlated with subsequent fl decays on an event-by-event
basis. Detection of 7 rays in coincidence with the implant events permitted observation
of [1.8 isomeric states, while those detected in coincidence with decay events permitted
elucidation of the populated levels in daughter nuclei.

The low-energy level structures of the neutron—rich 53"(’4’568c isotopes were inves-
tigated and compared with the expectations of the extreme single-particle model, as
well as with more advanced shell-model calculations using the GXPFl, GXPFIA and
KBBG effective interactions. The results confirm the N232 subshell closure, but sug-
gest a compression of the V2191 /2-V1 f5 /2 spacing relative to that assumed in current
effective interactions, which may preclude formation of a N234 subshell closure in
the Ca isotopes. The low-energy structure of 61Mn was probed through the ,8 decay of
61Cr. The structure was investigated for signs of developing deformation, but results
suggest that the effects of the approaching deformation—driving 1/199/2 orbital are not
yet significant at N236 for the Mn isotopes. The observation of an isomer in 50K
permitted investigation of the changing shell structure just below the f p shell. The
isomeric structure in 50K suggests that the inversion of the 7r1d3/2 and «281/2 orbitals
which is known in 47K may persist above N > 28, which is at present unexpected in

sd— f p cross—shell interactions.

ACKNOWLEDGMENTS

First, I want to thank my advisor, Paul Mantica. Thank you for providing the
guidance, and having the patience to see me through my Ph.D. I know I sometimes
made it more difficult than was necessary, but thanks for understanding that at times
that was what I needed to do. You were always, as you say, my cheerleader, and I am
grateful for that. Thank you for everything.

I also want to thank Dave Morrissey, Michael Thoennessen, Alexandra Cade and
Abby Bickley for serving on my guidance committee, and to acknowledge NSERC of
Canada for funding support.

Thank you to my fl group-mates, Jill, Josh, and most recently Andrew and Sophia.
In particular, Jill and Josh, you led the way for me, and forced me to become a better
person in order to meet the standards you set. Thank you for your friendship, and for
making graduate school feel more like fun than work. Thanks also to Kei and Geoff,
for always being sounding boards, and gamely answering all of my random questions.
Nothing that I’ve accomplished would have been possible without my group.

In my four years here, I’ve made friends I’ll have for life, better friends than I
deserve. Thank you for all of the happy-hours, the softball (even if I was terrible!),
and the random conversations over the last four years. In particular, I’d like to thank
a few very good friends - you know who you are. Thank you for believing in me when I
couldn’t seem to believe in myself, and for pointing out the pitfalls with my umbrella
factory back-up plan. You cannot know what your friendship and support has meant
to me.

Finally, I have to thank my family. Mom, you wanted credit for a small piece of
this work, but you deserve so much more than that. My family is my rock, and even
2301 miles away, I knew you were always right there with me. Thank you for always

listening and for your blind faith in me.

iv

Contents

1.1.1 Evolution of nuclear shell structure ...............

1.2 Describing the structure of nuclei ....................

1.2.1 Structure near closed shells ...................

1.2.2 Collective structures and nuclear deformation .........

1.3 Experimental observation of shell closures and nuclear structure . . .

1.3.1 E(2?) and B(E2 : 2?" ——> 01*) in even-even nuclei ........

1.3.2 Tracking single-particle energies and the extreme single—particle

model ...............................

1.4 Re—ordering of single-particle states in neutron-rich f p shell nuclei . .

1.4.1 N232 and N 234 subshell closures ...............
1.4.2 N240 shell closure and intrusion of the neutron 1g9/2 orbital

1.5 Motivation for the measurement .....................

1.6 Organization of Dissertation .......................

2 Experimental Techniques ...................... . . .
2.1 fl decay ..................................
2.1.1 fl-decay half-lives .........................

2.1.2 ,B-delayed neutron emission ...................
2.1.3 Selection rules and log f t .....................
2.2 7-ray decay ................................
2.2.1 Selection rules and lifetimes ...................
2.2.2 Isomeric 7-ray transitions ....................
2.2.3 Internal conversion ........................
2.3 Summary of the decay of exotic nuclei .................

3 Experimental Setup ...........................
3.1 Isotope production and identification ..................
3.1.1 NSCL experiment 05101 .....................

3.1.2 NSCL experiment 07509 .....................

3.2 Detector apparatus for fl-decay experiments ..............
3.3 6 Counting System ............................

20
22
22
25
31
32

37
39

46
46
49
50
52
52

3.3.1 Electronics ............................. 55

3.3.2 BCS calibrations ......................... 60
3.4 Segmented Germanium Array ...................... 62
3.4.1 Electronics ............................. 62
3.4.2 SeGA Calibrations ........................ 64
3.5 Data analysis: Correlations and data fitting .............. 69
3.5.1 Implantation-decay correlations ................. 70
3.5.2 Decay curve fitting methods ................... 76
4 Experimental Results .......................... 80
4.1 Low-energy structure of neutron-rich 218C isotopes ........... 81
4.1.1 6 decay of 53Ca to 53Sc ..................... 83
4.1.2 ,6 decay of 54Ca to 54Sc ..................... 86
4.1.3 B decay and isomeric structure of 54 Sc ............. 89
4.1.4 6 decay of 5680 .......................... 97
4.1.5 Isomerism in 5680 ......................... 104
4.2 Isomeric Structure of 50K ........................ 109
4.3 Structure of 61Mn from [3 decay of 61Cr ................ 113
5 Discussion ................................. 121
5.1 Interpretation of the low-energy levels in neutron-rich 2180 ...... 121
5.1.1 Low—energy structure of odd-A 53Sc ............... 122
5.1.2 Low—energy structure of even-A Sc isotopes ........... 123
5.2 Re-ordering of proton single-particle states in neutron-rich K isotopes 131
5.2.1 Systematics of the 19K isotopes around N228 ......... 131
5.2.2 Comparison to shell-model calculations using sd— f p cross-shell
interactions ............................ 138
5.3 Onset of collectivity in the 25Mn isotopes ................ 139
5.3.1 Systematics in odd-A Mn .................... 140
5.3.2 Even-A Mn isotopes ....................... 143
5.3.3 Deformation in comparison to neighboring 24Cr and 25Fe iso—
topic chains ............................ 145
6 Conclusions and Outlook ........................ 147
6.1 Conclusions ................................ 147
6.2 Outlook .................................. 149
6.2.1 Open questions in the f p shell .................. 149

6.2.2 The NSCL 6 Counting System with Digital Data Acquisition .’ 151

Bibliography ................................. 154

vi

List of Tables

2.1
2.2
2.3
3.1
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
5.1

5.2

Classification of fl-decay transitions ................... 38
7-ray selection rules ............................ 40
Weisskopf single-particle lifetime estimates for 7 decay ........ 42
y-ray Transitions Used in the Recalibration of SeGAll ........ 67
fi-delayed 'y rays assigned to the decay of 5" Sc ............. 90
568C fi—delayed 'y rays ........................... 98
fl and fin contributions to the decay of 568C .............. 104
Prompt 568C 7 rays ............................ 105
Weisskopf half-life estimates for prompt 5680 7-ray transitions . . . . 109
'y rays observed in coincidence with 50K implantation events ..... 110
Weisskopf half-life estimates for prompt 50K 7-ray transitions . . . . 113
fl-delayed 7-raygtransitions in the decay of 61Cr ............ 116

Application of the Pandya transform relating neutron particle and hole
states in 50’52Sc .............................. 126

Calculated transition probabilities for the 31” —+ 4? transition in 54Sc 130

vii

List of Figures

1.1
1.2
1.3
1.4
1.5
1.6
1.7

Observables for atomic and nuclear shell closures ........... 2
Evolution of the nuclear shell model ................... 5
Single—particle states in Egnglg—g .................... 11
Illustration of parameters in j-j coupling ................ 15
Parabolic rule for p—n multiplets ..................... 16
Systematics of E (2?) across isotopic chains ............... 19
Monopole shift of the V1f5/2 orbital with increasing 7r1f7/2 occupancy 23

1.8 Systematics of E(2f) and B(E2 : 2? —+ 01+) across isotopic chains

around N 232, N 234 ........................... 24
1.9 Systematics of E(2i’") around Z240, N254 and N240, Z228 ..... 27
1.10 Nilsson Diagram for 502N , Z 220 .................... 30
3.1 Schematic of the NSCL Coupled Cyclotron Facility .......... 47
3.2 Particle Identification Plots for NSCL Experiments 05101 and 07509 . 51
3.3 Schematic of the Beta Counting System Detectors ........... 53
3.4 Schematic of DSSD Electronics ..................... 55
3.5 Schematic of SSSD Electronics ...................... 57
3.6 Schematic of PIN Detector Electronics ................. 58
3.7 Schematic of Trigger Electronics ..................... 59
3.8 228Th and 908r DSSD Calibration Spectra for Illustrative Front and

Back Strip ................................. 61
3.9 Schematic of the Geometric Layout of the SeGA Detectors ...... 63
3.10 Schematic of Electronics for SeGA Detectors .............. 64

viii

3.11
3.12
3.13
3.14
3.15
3.16

4.1
4.2

4.3
4.4
4.5
4.6
4.7
4.8
4.9

4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20

Residuals for Energy Calibration of Individual SeGA Detectors . . . . 66

Residuals for Total SeGA Array Energy Calibration .......... 66
Recalibration of SeGA 11 ........................ 68
SeGA Efficiency Calibration ....................... 69
Position dependence of rates in NSCL experiment 07509 ....... 74
Comparison of 55Ti ,B-delayed 7-ray spectra and half-life curves for

analysis including pixels at the edge and over the full DSSD ..... 75
7-ray spectrum collected within 20 ,us following a 54Ca implantation . 82

fi-delayed 7-ray spectrum in the range 0-3 MeV following the decay of

53Ca .................................... 84
Decay curves for the B decay of 53Ca .................. 85
Decay scheme for decay of 53Ca to states in 53Sc ............ 86
fi-delayed 7-ray spectrum following the decay of 54Ca ......... 87
Decay curves for the decay of 54Ca ................... 88
Decay scheme for the decay of 54Ca to states in 54Sc ......... 89
fl-delayed 7-ray spectrum for the decay of 54Sc ............. 90
fl-decay curves for the decay of 5480, with and without the requirement

of a coincident decay 7 ray ........................ 92
Decay Scheme for the decay of 54Sc to states in 54Ti ......... 93

77 coincidence spectra for fi-delayed 7 rays following the decay of 54Sc 94

Prompt 7-ray spectrum following implantations of 548C ........ 96
Decay curve for 110—keV isomeric transition in 5480 .......... 96
fi-delayed 7—ray spectrum following the decay of 56Sc ......... 98
7-gated decay curves for the decay of 5680 ............... 100
Decay scheme for 5680 to states in 56Ti ................. 101
77 coincidence spectra for the decay of 568C .............. 102
7-ray spectrum following implantation of 568C ............. 105
Decay curve for the 7-decaying isomeric state in 56Sc ......... 106
77 coincidences for prompt 7 rays in 568C ............... 107

ix

4.21
4.22
4.23
4.24
4.25
4.26
4.27
4.28
5.1

5.2

5.3

5.4

5.5

5.6

5.7
5.8
5.9
6.1

Decay curves for the 6 decay of 568C .................. 108
7—ray spectrum following 50K implantation events ........... 111
77 coincidence spectra for isomeric decay of 50K ............ 112
Proposed low-energy level scheme for 50K ............... 114
Decay curve for the decay of 61Cr to states in 61Mn .......... 115
B—delayed 7-ray spectrum following the decay of 6’Cr ......... 116
Decay scheme for the decay of 61Cr to states in 61Mn ......... 118
77 coincidence spectra for decay of 61Cr ................ 119
Level structure of 53Sc and schematic of coupling to states in 52Ca . . 123
Experimental level scheme for 50’52’54’5680 ............... 125
Shell model calculations for the even-A Sc isotopes using the GXPFl,

GXPF 1A and KB3G effective interactions ............... 127
Energy separation of the 3 / 2+ and 1 /2+ states in the odd-A K isotopes

from N220 to N230 ........................... 133
Known states in 48K, and their interpretation within the independent

particle model framework ......................... 135
Low-energy structure of 50K known from decay of the 172-keV isomeric

state .................................... 137
Comparison to shell model results for theodd-A 25Mn isotOpes . . . . 142
Low-energy level structure of the even-A 60’62’64Mn isotopes ..... 144
Sgn values for the isotopes surrounding Fe near N 240 ......... 145
Resolution of 228Th spectrum collected using DDAS vs. analog data

acquisition ................................. 153

Chapter 1

Introduction

1.1 Nuclear shell structure

The periodicity in the chemical nature of the elements has been represented on the
periodic table for more than a century, and is now understood with the essential con-
cept that the electrons surrounding the atomic nucleus are arranged in discrete energy
levels, or shells. One of the most direct indicators of this electron shell structure in
atoms can be seen by considering the first ionization energy, the energy required to
remove an electron from the neutral atom, as a function of atomic number, Z. Shown.
in the top panel of Fig. 1.1, the observed trend of ionization energy has discontinuities
at specific values of Z. These discontinuities are understood as arising from the un-
derlying electron shell structure. After filling a given energy orbital, the next electron
is placed in a higher energy orbital, and the energy required to remove it decreases
substantially.

Analogous to the observed trend in atomic ionization energies, systematic ex-
amination of many physical properties of nuclei has revealed periodic trends. Near
the valley of stability, bulk properties related to the nuclear mass are suggestive of
enhanced relative stability for nuclei with “magic” numbers of protons or neutrons,

corresponding to 2, 8, 20, 28, 50, 82, and 126. One can consider, for instance, the one-

 

 

 

 

 

 

 

302

E 710

E3 , 18 34

320,1 54 86

ES 1 i l

8 15a 1

'5 10

s i

.3 5 ,' . .

.2 ‘NeiK. RbCF
0 20 40 60 80 100

Atomic Number (Z)

9 9? 20

0» 8§- 128

5 7E— i 50 82

ms: 6; ,1 l l 126

<1 5E— i\
. ll,
43” "Wit
3%- "1” “:2, ..
15+..11111411.1...111111111..11...1
0 20 40 60 80 100120140160

Neutron Number (N)

Figure 1.1: (Top) Systematics of the first ionization energies of the atomic elements
from hydrogen (Z21) to nobelium (Z2102). Data were taken from Ref. [1]. Discon—
tinuities correspond to atomic electron shell closures. (Bottom) Systematics of the
difference in neutron separation energy for even-even nuclei 9X N and their even-odd
neighbors. Data were taken from Ref. [2]. Solid lines connect isotopic chains. Dis-

continuities provide evidence for nuclear shell structure, representing closed neutron
shells.

neutron separation energy for a nucleus with mass number A, and atomic number Z,

which is defined as follows:

‘n(N) = B(éXN)—B(A‘IZX~_1)

= [MM-12m-» — M<§XN> + Mac? (1.1)

Here, B (9X N) represents the nuclear binding energy,
B(ZXN) = [ZMH + N412 — MVz‘XNHCQ, (1-2)

where M H is the atomic mass of hydrogen, Mn is the neutron mass, M (QX N) is the
atomic mass of the given nucleus, and contributions from the differences in the elec-
tron binding energies are neglected. The neutron separation energy is analogous to
the atomic ionization energy, representing the energy required to remove one neutron
from the nucleus. The systematics of the neutron separation energy show periodicity
suggesting an underlying shell structure of the nucleus. These shell effects are en-
hanced by considering the difference in Sn values between even N nuclei and their

N + 1 neighbors, defined as follows:

A5,, = 5,,(N) — STAN +1)

= [M(A"IZXN_1 + M(A+IZXN+1) — 2M(§XN)]C2. (1.3)

The neutron separation energy differences, AS", are plotted in the bottom panel of
Fig. 1.1 as a function of neutron number for the isotopes with even numbers of protons
and neutrons up to fermium (Z2100). The discontinuities corresponding to neutron
‘magic numbers’ are apparent; an analogous examination of proton separation energy
systematics similarly highlights the same ‘magic numbers’ for protons.

Given the success in describing atomic structure in terms of electron shells, a simi-
lar approach has been employed in nuclear physics to describe the structure of nuclei.
However, in the atomic case, electrons move in an “external” field created by the well-
understood Coulomb force. As such, the Schr6dinger equation for the atomic system
can be solved exactly, and electron orbital energies accurately calculated, reproduc—
ing the experimentally observed shell closures. The picture is more complicated in the

nuclear case, as nucleons move within a field created by the surrounding nucleons,

and the analytical form of the force involved, namely the strong force, is not defined
at present [3].

The success of the nuclear shell model rests primarily with the choice of the po-
tential assumed to confine the protons and neutrons within the nucleus. Historically,
a starting point has been the harmonic oscillator potential. The energy levels aris-
ing from the solution of the Schr6dinger equation assuming a harmonic oscillator
potential are shown in Fig. 1.2(a). This simple potential reproduces the lowest shell
closures, at 2, 8 and 20, however, the higher closures are not in agreement with obser-
vation. A more realistic potential, bounded at r212, is considered to provide a better
approximation.

The Woods-Saxon potential has a shape intermediate between a square well and

a harmonic oscillator, and takes the form

__V0

VT 2 ,
U 1+exp1512—‘01

 

(1.4)

where the parameter R is the mean nuclear radius, 0. represents the diffuseness of
the nucleus, and V0 is the depth of the potential well, usually adjusted to a value of
approximately 50 MeV. Solution of the Schr6dinger equation assuming this potential
again reproduces the lowest shell closures at 2, 8 and 20 but still fails to accurately
describe the higher lying magic numbers [see Fig. 1.2(b)].

The missing piece of the puzzle was put in place in the 1940’s, when the inclusion
of a spin-orbit potential was shown to properly separate subshells and reproduce the

experimentally observed magic numbers [5,6]. The spin-orbit potential takes the form:
[V30 = V30(r)l-.' g, (1.5)

where l represents the orbital angular momentum, and s? the intrinsic nucleon spin.

The I: 5" term accounts for the interaction of the nucleon spin and its orbital motion,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2f
........ 1117972
1h =:::::j: 1h
35 ,,,,,,,,,,,,,,,,, 3511/12/2
33, 2d, 1g 2d -=:::::::ZZII:::: 333/2
.......... ‘lsifi
18—53:: ............. [Igg/Z
..____J40 2191/2
2p,1f 2p -====333.I.I£l-I-I-I- ''''' "fi 1f5/2
If =22: ~~~~~~~ \2p3/2
1f7/2
23,1d 23 ...... .. Ids/2
1d .............. 131572
11’ 1 ------------- 1P1/2
@ p @ """"""" 1P3/2
IS IS """""""""" 151/2
Harmonic Woods-Saxon

Oscillator Woods-Saxon + Spin-Orbit

(a) (b) (C)

Figure 1.2: Evolution of the nuclear shell model to represent the experimentally ob—
served nucleon “magic” numbers. The first approximation with a harmonic oscillator
potential evolved to the more physical Woods-Saxon potential, and finally the in-
clusion of a spin—orbit potential to reproduce the experimental observations. Figure
adapted from Ref. [4].
and leads to a removal of the l-degeneracy of states, or a splitting of states with l > 0,
based upon the total angular momentum (3’ 2 f’+ 5) projection. This reordering of
the subshell states is shown in Fig. 1.2(c), and the shell closures that develop agree
fully with observations of the magic numbers near the valley of 6 stability.

The nuclear shell model has been further developed and extended to include more

subtle aspects of nuclear structure. The basic tenets discussed here, which assumes a

spherically symmetric potential, remains the starting point for understanding the level

structures of spherical nuclei near closed shells. However, recent experimental evidence
suggests that the shell structure of nuclei, i.e. the ordering and energy separation of
single-particle states, is not static across the nuclear landscape, but rather evolves
with varying proton-to—neutron ratios. The nature and origins of this re-ordering of

single-particle states is the topic of the following section.

1.1.1 Evolution of nuclear shell structure

Across the nuclear chart, as progressively more exotic nuclei are probed, there is
increasing evidence for an evolution of shell structure. The ordering of single—particle
levels as shown in Fig. 1.2(c) has been observed to change slightly with proton-to-
neutron ratio, or isospin projection, T2 2 (N — Z ) / 2, which can change the observed
nuclear properties.

At Z24, in the relatively light isotopes, breakdown of the N28 shell closure
has been observed in the neutron-rich nucleus liBe [7]. The last two neutrons in
12Be are expected to occupy the 1191/2 orbital. However, spectroscopic factors for
the removal of a neutron from 1”Be provide direct evidence of significant sd—shell
intruder contributions to the ground state wavefunction, and the disappearance of
the N 28 shell closure in this isotope. At slightly heavier masses, the so—called ‘island
of inversion’ at N 220 away from stable nuclei, also gives evidence of evolving shell
structure. Nuclear ground states have been shown to be dominated by 1/(sd)‘2(fp)2
intruder configurations, suggesting the breakdown of the N 220 shell closure [8,9] for
neutron—rich nuclei with 10 3 Z s 12 and 20 S N g 22. Shell evolution is also seen in
the apparent erosion of the N 228 shell closure in the neutron rich 168 isotopes [10],
and the development of a new subshell closure in neutron-rich 20Ca [11,12], 22Ti [13]
and 24Cr [14] isotopes at N 232. At even higher masses, however, the shifting of
single-particle levels is less likely to result in a change in the position of the major
shell closures, due to the higher single-particle level densities. None the less, the

evolution still occurs — in the region of N 250-82, and Z 240-50 there is a reordering

of neutron single-particle levels as the 197/2 orbital rapidly drops in energy between
91Zr and 1318m [15,16].

These examples highlight the ubiquity of evolving shell structure over the nuclear
landscape. It is clear from these instances that there are effects and interactions be—
yond the scope of the simple shell model which can greatly alter single-particle level
energies and ordering. Understanding the origins of and accounting for experimen-
tally observed changes in shell structure are critical for the development of nuclear
theory models — an understanding of the phenomena already observed will enhance
the reliability of theoretical predictions. One nucleon-nucleon interaction, believed to

be a possible cause of shell evolution, is discussed next.

Proton-neutron monopole interaction

One of the suggested reasons for the evolution of nuclear shell structure is the spin-
isospin dependent part of the nucleon-nucleon interaction [17]. This is a tensor monopole
force, which is additional to the spin-orbit interaction discussed previously, and can
alter the effective nucleon single—particle energies (ESPEs). These ESPEs account for
the mean effects from all other nucleons, on a nucleon in a given single-particle orbital.
The single-particle energy of an orbital j is determined by its kinetic energy, and
the interaction with the nucleons in the core that produce the mean field [18]. When
nucleons are added to a different orbit j’, the single—particle energy of the original j
orbital is altered. The nucleons in j’ and j will couple to form states with different
total angular momentum, J, but in considering changing shell structure, it is the
shift of single-particle orbitals irrespective of the details of the coupled J states that
is interesting. Thus, the J dependence is averaged out, and only monopole effects are
considered. The monopole component of a nucleon-nucleon residual interaction V for

the effect of the nucleons in j' on the orbital j takes the form:

2 1 . ., . ./ r
VT, = 2J( J + )< .7] IVIJJ >JF, (1.6)
.7] 2J(2J +1)

 

where < jj'IVIjj’ >JT is the matrix element for j and 3" coupling to a state with spin
J, and isospin T. With this interaction, it is possible to evaluate, for example, the
effect of nn(j’) neutrons in the orbital j’ on the single particle energy of the proton
orbital j. The shift in the single-particle energy of the proton orbital j, denoted
Aep(j), resulting from the presence of 12,, neutrons in the j’ orbital is given by [18]:
AW) = g 13.370 + 1957117222). (1.7)
With the inclusion of the tensor monopole shift, a new effective single-particle energy
can be defined, which is dependent on the nucleon configuration, and thus changes
with proton-neutron ratio. The same arguments hold for the inverse case, the effect of
protons in a given orbital on neutron single-particle energies. It should be noted that
protons (neutrons) in an orbital j will also affect the energy of protons (neutrons) in
another orbital 3". However, only T 2 1 interactions, which are weaker than T 2 0
interactions [18], are relevant in proton-proton or neutron-neutron interactions. Thus,
these effects are less significant than those arising from proton-neutron interactions.
As discussed by Otsuka et al. [18], there is a general rule for the way in which the
proton-neutron tensor monopole force affects the single-particle energies. An attrac-
tive interaction is observed between opposite isospin particles (protons and neutrons)
in j< 21—1/2 and j") 2 l’+1/2 orbits (and vice versa, j> 2 l+1/2 and j’< 2 l’—1/2
orbits), while the interaction between protons and neutrons in j< 2 l — 1 / 2 and
j’< 2 l’ — 1 / 2 orbits (and similarly j> 2 l+ 1 / 2 and 3") 2 l’ + 1 / 2 orbits) is repulsive.
The strength of the interaction is also maximized for I ~ 1’, so a stronger attractive
interaction between protons and neutrons in spin-orbit coupling partner orbitals is
expected [17].
Nearly all of the examples of evolving nuclear shell structure discussed previously
can be partially explained in the framework of the proton—neutron tensor monopole

interaction. The disappearing N 28 shell closure in 1gBe results from the low occu-

pancy of the 7r1p3/2 orbital that causes the u1p1/2 orbital to migrate higher in energy,
eroding the N 28 gap. The island-of-inversion nuclei can be largely explained by the
decreasing attractive interaction between the u1d3/2 orbital and the 7rld5/2 orbital as
protons are removed from the 7rld5/2 level. This reduction causes the V1d3/2 orbital
to rise in energy, eroding the N 220 shell closure, and producing a N216 subshell
closure for the lightest nuclei in the region. The region surrounding N 234, Z220 also
experiences changes in neutron level ordering driven largely by a reduced monopole
interaction between the 7r1f7/2 orbital and the u1f5/2 orbital, while the heavier nu-
clei near N250 show evidence of shell evolution arising from the changing monopole

interaction between the 2199/2 orbital and the spin-orbit partner 11197/2 orbital.

1.2 Describing the structure of nuclei

While one of the goals of nuclear science is to create a single theoretical framework to
adequately describe the entire nuclear landscape, the variation in nuclear structure
across the chart of the nuclides is significant. The nuclear shell model provides a basis
for understanding the overall structure of all nuclei, but important simplifications can
be made in certain regions of the nuclear chart. The most basic shell model interpre-
tation, the independent particle model, provides an excellent qualitative description
of the low-lying states in nuclei one nucleon from closed shells [19]. A few nucleons
from a closed shell, this model can be extended, and residual nucleon-nucleon inter-
actions taken into account, to successfully describe the low-energy structure of nuclei.
However, for nuclei far from closed shells, these types of microscopic shell model cal-
culations become intractable. Geometric models provide a better description of the
growing collective behavior of mid-shell nuclei, as macroscopic deformations play an

increasingly important role in determining the relevant nuclear structure.

1.2.1 Structure near closed shells
The independent particle model

The so—called “independent particle model” describes a nucleus in terms of non—
interacting particles orbiting within a central spherically symmetric potential, which
is itself produced by all the nucleons. Within this model, nucleons are assumed to
sequentially fill the single-particle levels generated by this nuclear potential, in much
the same way that electrons are assumed to fill atomic energy levels. Also in anal-
ogy to the atomic picture of valence, in which filled electron shells do not contribute
to the chemical properties of an element, filled nucleon orbitals are assumed to be
inert within the structure of the nucleus. A closed shell will always contribute a to-
tal angular momentum and parity, J 7' 2 0+ in the nuclear case, and so the ground
state angular momentum of a nucleus with only one valence particle in a shell n1 j is
determined entirely by the single valence nucleon as J 2 j , with parity 7r2(-1)‘ [19].
The independent particle model provides a framework for predicting the ground
state spin and parity of nuclei one nucleon removed from a closed shell, and has
also proven successful in predicting the low-lying excited states in these nuclei. Low-
energy levels in such nuclei are formed by simply elevating the valence particle from
the ground state orbital to a higher single-particle state. An example of the success of
this approach can be found in the structure of 2gng127, as shown in Fig. 1.3. With
one valence neutron above the N 2126 shell closure, the ground state in 209Pb is of»
served to have J “29/ 2+, as expected with a (12299/2)1 configuration. The other six
levels corresponding to promotion of the single valence neutron to the other single-
particle levels above the N 2126 shell closure are all evident in the low-energy struc-
ture [see Fig. 1.3(b)]. The neutron spectroscopic factor is near unity for each of these
seven states. The spectroscopic factor is a measure of the contribution of a given
single-particle configuration to a nuclear state, as determined by comparison of ex-

perimental reaction cross-sections with calculations assuming pure single-particle con-

10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ll
8, 8
3d 5
4s??? /2g7/2 E ___._...=3/2+ 1.09
1:71:15/2’ :395/2 3; _____7/2+ 1.05
89/2" ‘ ll11/2 "4 +
m2. ——-————-1/2 0.98
-. a
”1113/2 +§ ___5/2+ 0.98
1 .45 15/2- 0.58
~ .. N
1h ml’ ——11/2+ 0.86
11/2‘""".""’f - .
, ~ - 0- ———9/2+ 0.83
2 9
7‘ V 821319127

(a) (b)

Figure 1.3: (a) Schematic representation of the nucleon configuration for the one-
valence neutron nucleus 209Pb. (b) Experimentally observed levels of 209Pb below
3 MeV [2]. Black levels correspond to single-particle states arising from occupation of
the seven single-particle levels above the N 2126 shell gap. The purity of these single
particle configurations is supported by the near-unity spectroscopic factors. Grey
levels correspond to levels with configurations beyond the scope of the independent
particle model.

figurations [20]. Thus, spectroscopic factors near 1 indicate the relative purity of the
single-particle states in 209Pb.

Strictly speaking, the independent particle model is applicable only to nuclei with
one valence particle (or hole) outside of a closed shell. However, the fundamental ideas
of this model can be extended to nuclei with a few valence particles (or holes) outside
of a closed shell inert core. The low-energy structures of such nuclei can be understood

by including a residual nucleon-nucleon interaction between valence nucleons above

the inert core.

11

Few nucleon configurations

A few nucleons outside of a shell closure, the independent particle model can be
extended to provide an adequate description of the low-energy states within a nucleus.
The simplified idea of the nucleus as consisting of valence nucleons occupying single-
particle states above an inert core of closed shells provides a basis for interpreting
the structure solely in terms of the interactions among valence particles. However,
with more than one valence particle, it is important to consider the residual nucleon-
nucleon interaction, which largely determines the observed structure of few-nucleon
systems.

Two nucleons occupying orbitals with quantum number nllljl and 7121ng can
couple, in the most general case, to produce a multiplet of states with [j] — jg] S J g
I j1 + jg]. If the nucleons are identical and occupy the same orbital, the requirement
of an antisymmetric wavefunction limits J to values from 0 to (2j-1), and without
a residual nucleon-nucleon interaction, all J states in a multiplet are expected to be
degenerate in energy. Under the effect of a residual interaction, V12, this degeneracy

is broken, and each state J experiences an energy shift AE(j1j2J), given by [19]:

. . 1 . . . .
A13(31J2J) = \/—2J;+_1: < J1J2J||V12||J192J >, ' (1-8)

where the double-bar indicates summation over all M states.

The exact form of the residual nucleon-nucleon interaction, V12, is not known,
although it is expected to have a strong attractive short-range component, as well
as a long-range component which is of particular importance in producing collective
nuclear properties [19]. One example of a commonly used interaction is the so—called

‘pairing plus quadrupole’ interaction, which takes the following form:

Vppq 2 Vim-7. + nr¥r3 P2(cos 9), (1.9)

12

where 0 represent the angle between the radius vectors to each particle (F1 and F2),
and n represents the strength of the quadrupole interaction. me-r represents the
short-range attractive pairing interaction, while the quadrupole component is a first
approximation to the long-range component. An even simpler approximation for the
residual nucleon-nucleon interaction is a simple delta-function interaction, which only
represents the short-range interaction and has been shown to reproduce many of the
results from more realistic interactions. The relative spacing of states within proton-
proton (p-p) or neutron-neutron (n-n) multiplets, for example, can be well-described
by assuming a delta-function residual interaction. Taking the form of the residual
interaction to be V12 2 V06(F1 — F2), where F1 and F2 are the radial coordinates of

the two nucleons, and V0 is the strength of the interaction, Eqn. 1.8 becomes [19]:

2
. . . . J1 J2 J _
AE(]1]2J) 2 —V0FR(2]1+1)(2]2 +1) 1 1 1f 11 + l2 — J even
2 ‘2‘ 0
2 0 if l1 + l2 — J odd, (1.10)

where F3 is a function of the radial coordinates (i.e. 7111111212) only. Thus, only half
of the states in a given p—p or n—n multiplet will be shifted under the influence of a
delta-function residual interaction. Further information can be gained by considering
that the isospin portion of the nuclear wavefunction for a p-p/n-n configuration is
symmetric (T21), which means that the Pauli principle requires the wavefunction
to be antisymmetric in either spin or space. A symmetric spin configuration 821
thus requires the spatial wavefunction to be antisymmetric. However, a delta-function
interaction between two nucleons vanishes if F1 2 F2, and so will not alter the energy
of states with S21, and will only affect S20 states. Given that only half of the states
of a p-p or n—n multiplet will be affected by a delta-function residual interaction, as
indicated from Eqn. 1.10, a general rule arises describing the splitting of energy levels

in p—p and n-n multiplets. If the parity is positive, even J value are lowered in energy,

13

with the extreme J value (Jmin 2 Ijl — jg] or Jmam 2 | j1 + jgl) lowered the most,
while for negative parity, odd J values are lowered. If jl 2 jg, as in the case of even-
even nuclei, the parity of the expected states is positive, and this interaction results
in a dramatic lowering of the 0+ state. This interaction is, in fact, the underlying
explanation in this model for the fact that even-even nuclei have 0+ ground states [19].

The residual interaction in p-p/n-n multiplets is restricted to T21 interactions,
which simplifies the possible effects of the residual interaction on the relative spacing
of states in a multiplet. Proton-neutron (p—n) multiplets however can also include
T20 interactions, which have been observed to be stronger than the T21 interac-
tions [19]. Thus, a different approach is more appropriate for describing the energy
splitting of states within a p—n multiplet under the effect of the nucleon-nucleon resid-
ual interaction. Insight into the effect of a residual interaction on the relative ordering
of low-lying levels in few nucleon systems can be gained by considering a multipole
decomposition of the interaction. Any interaction that depends on the separation be—
tween two particles, as the residual interaction is expected to, can be expanded in
terms of multipoles [19]. Such a decomposition allows, among other important re-
sults, the derivation of the parabolic rule [21] to describe the energies of states in two
particle p—n multiplets.

Within a decomposition, each multipole, It has an angular dependence, Pk(cos 6),
where Pk(x) are the Legendre polynomials, and 0 is the angle between the angular

momentum vectors for each particle, as shown in Fig. 1.4, and given by the following:

 

J(J+1)—j1(j1 +1) —2202 +1).

2¢jirj1+1>1202 +1) (1.11)

cos0 2

 

The monopole component, k20, is constant, and thus affects all states equally, sim-
ply giving an overall energy shift to the entire multiplet of states. This monopole
interaction is in fact the same effect discussed previously in Section 1.1.1.

The quadrupole component, [£22, is proportional to P2(cos 9) 2 915(3 cos2 0), and is

14

 

 

Figure 1.4: Schematic representation of the coupling of two nucleon angular momenta
(jl, jg) values in a geometric representation to a final J, and the definition of the
angle 0 between them.

maximized for 0 2 0° and 180°, which corresponds to the alignment or antialignment
of the angular momentum vectors of the two constituent particles. Thus, the attractive
particle-particle quadrupole interaction lowers the energies of extreme J values the
most, and raises intermediate spins. The J dependence on the energy splitting between
states in a given p—n multiplet is given by the following expression [19], which arises

from the Pg(cos 0) proportionality of the 1:22 multipole combined with Eqn. 1.11 for

the angle 6:
[J(J + 1) moi +1) — 1202 +1112

42101 +1)j2(j2 + 1)
oc A[J(J +1)]2 + BJ(J + 1) + C, (1.12)

 

13501227 ) 0‘

where A, B and C are independent of J. This relationship takes the form of a parabola
in J (J + 1), and despite the omission of higher multipoles of the residual interaction,
has been shown to provide a good first approximation to experimental data. Figure 1.5
illustrates the parabolic rule applied to the proton-neutron (Half/21112], /2) multiplet

in 122Sb, and the proton-neutron hole (7r f71/21/ f7712) multiplet in 48Sc. The multiplet

15

J J
0.1??4§§Z$2 012.311???
0’ (a) 2’ 0’) 485C (“fi/2Vf2i2)

 

 

 
   

Relative Excitation Energy (keV)

 

 

 

 

 

 

Relative Excitation Energy (MeV)

1 1
’2sz (“87/2Vh11/2) 0_ ,
-300» . . . . 1 . . . . . .
0153045607590 0102030405060
J(J+1) J(J+1)

Figure 1.5: Examples of the qualitative success of the parabolic rule describing the
level ordering of p—n multiplets. (a) illustrates the p—n particle—particle parabola in
122Sb [22], while (b) illustrates the p-n particle-hole parabola in 48Se [23]. Dots rep—
resent experimentally measured energies, while the solid line is a best fit parabola.
under consideration in the case of 488C is actually a particle-hole p—n multiplet. The
residual interaction in this case is repulsive, and thus the extreme J values corre-
sponding to high p—n overlap are pushed higher in emery, while the intermediate
spins are lowered.

Moving beyond the case of two valence particles, within the single—particle model
it can be assumed that nucleons in a partially filled single-particle orbital will pair to
.17'20+ where possible [19]. Under this assumption the low-lying states of any nucleus
near a closed shell can be interpreted, in the independent particle model, as arising

from either a single valence nucleon configuration, or a p—n multiplet outside a core

of fully paired nucleons.

1.2.2 Collective structures and nuclear deformation

The description of nuclei that are more than a few nucleons away from closed shell con-
figurations becomes progressively less practical purely within the shell model frame-

work. These calculations rapidly become intractable for mid—shell nuclei due to the

16

large numbers of valence nucleons. Additionally, the simplifications made by assum-
ing inert closed shell cores become less appropriate. Significantly more complex ex-
citations develop in these nuclei, which are better described in a more macroscopic
framework [19].

Collective interactions between nucleons typically lead to quadrupole (oblate or
prolate) deformation of the overall shapes of mid-shell nuclei. The extent of defor-
mation is denoted by a quadrupole deformation parameter, fig. fig 2 0 in the case of
spherical nuclei, while this deformation parameter takes on positive values for pro-
late deformations, and negative values for oblate deformation. Models which attempt
to describe deformation of the nuclear shape, such as the Nilsson model, provide a
framework in which to understand the structures of such deformed mid-shell nuclei.
The Nilsson model is, in many ways, similar to the spherical shell model discussed
earlier, but follows the variation of the energies of the spherical shell-model orbitals in
a deformed nuclear potential - it is the single-particle model applicable to deformed
nuclei [19].

While the previous sections have discussed a theoretical framework for under-
standing the structure of nuclei near shell closures, the shell-model framework re—
quires knowledge of the location of shell closures, and the ordering of single-particle
states. The following section discusses some of the experimental observables which

can provide such information.

1.3 Experimental observation of shell closures and
nuclear structure

One of the most critical pieces of information needed to allow development of nuclear
structure models and theory is the location of shell and subshell closures across the
nuclear landscape. As discussed previously, the location of shell closures is not static

across the nuclear chart, and an ongoing experimental focus in nuclear physics is to

17

locate these shell closures in previously unknown nuclei, and track the migration of
single-particle orbitals which lead to this dynamic shell structure.

A number of experimental observables are sensitive to the presence of shell closures
across the nuclear landscape. Nuclear masses and binding energies provide the most
fundamental mapping of structural evolution across the nuclear landscape. Changes
in the trends of neutron-separation energies across isotopic chains, for example, can
indicate the presence of neutron shell closures, or the development of deformation,
depending on the nature of the observed change. Ground state nuclear moments are
also good indicators of shell closures. The nuclear quadrupole moment provides a
measure of the nuclear charge distribution, and thus the nuclear shape. Near closed
shells, nuclei are expected to be spherical, and ground state quadrupole moments
should be small. Away from shell closures, nuclei may be axially deformed, and have
large magnitude quadrupole moments. Another indicator for shell closures comes from
the excited states of nuclei. Certain characteristics of excited state configurations are
expected near closed shells, and such states can be used to identify shell closures,
when compared with the systematic behavior in neighboring nuclei. The properties of
the first 2+ excited state in even-even nuclei, for instance, are sensitive to the presence

of shell closures, as is discussed in the following section.

1.3.1 E 2+ and B E2 : 2+ —> 0+ in even-even nuclei
1 1 1

Across the nuclear landscape, there are certain pervasive structural patterns that
emerge — the near-spherical shape of nuclei near closed shells and the dominance of
quadrupole collective nucleon excitations near midshell, for instance. Thus, experi-
mental quantities that are related to the amount of quadrupole collectivity can be
good probes of nucleon shell closures. One such measure of quadrupole collectivity in
even-even nuclei is the energy of the first 2+ excited state, E(2f). The first 2+ excited
state in an even-even nucleus is understood as arising from the breaking of a pair of

nucleons and excitation of one nucleon of the pair into a higher-lying level. At closed

18

 

\l

 
 
  

E01) (MeV)

@

 

”it.

    

 

 

 

0 ' 100120 140
Neutron Number (N)

Figure 1.6: Behavior of E (21") across isotopic chains. Data were taken from Ref. [25].
Solid lines connect isotopic chains. The trend of increased values of E (2?) near neu-
tron closed shells is very clear; a similar trend is seen for E (2?) along isotonic chains

for closed proton shells. The same magic numbers seen in the variation of the neutron
separation energies in Fig. 1.1 are apparent.
shells there is an observed peak in E (2]) relative to neighboring nuclei. This reflects
the fact that the energy required to break a pair of nucleons and promote one across
a shell gap would be significant, while away from the shell closures, multi-state mix-
ing lowers the collective quadrupole states [24]. Macroscopically the curvature of the
potential energy surface is lessened, deformation requires less energy, and the energy
of the first 2+ state is reduced. Thus, the value of E(2f) in even-even nuclei, relative
to the neighboring even-even nuclei is a good indicator of nuclear shell structure and
shell closures. Figure 1.6 illustrates the systematic variation of E(2f') for even-even
nuclei across the nuclear chart, and the appearance of the characteristic peaks in this
quantity at closed shells.

Based on the observed trends in the energy of the first 2+ state in even-even

nuclei, Grodzins [26,27] derived an empirical relation some time ago between E(2f)

19

and the quadrupole deformation parameter fig:

1225
f) — —— MeV. (1.13)

E(2 _ 147/332

At closed shells, E (21*) values are high, and according to Eqn. 1.13, fig is small, indi-
cating the near-spherical nature of magic nuclei. Moving away from closed shells, fig
increases as E (21*) drops, representative of the increasing collectivity and developing
deformation of mid—shell nuclei.

A related indicator of quadrupole collectivity, and hence shell closures, in the
nuclear chart is the reduced transition matrix element for the E2 transition between
the first 2+ excited state and the 0+ ground state in even-even nuclei, B(E2 : 21+ —1
0;”). With an inverse relation to the energy of the first excited 2+ state according
to the Grodzins rule [26], the B(E2 : 2f —» 0?) value peaks near midshell, and
reaches minimum values near closed shells. These two quantities, E(2f) and B(E2 :
2f —» 01+) are among the most readily accessible in nuclei far from stability. Trends
observed in these two independently measured values have served as indicators for

shell closures at the far reaches of the nuclear chart (e.g. [13,14,28]).

1.3.2 Tracking single-particle energies and the extreme single-

particle model

Tracking the evolution of nucleon single-particle energies requires more information
than simply the location of shell gaps in the nuclear chart. It is desirable to have a
measure of the changing single-particle energies between closed shells. This involves
not only identifying states within a nucleus, but also determining the nucleon configu-
rations that contribute to these states. Elucidation of the contributing configurations
permits a better appreciation of the shifting single-particle energies that lead to the
observed nuclear structure.

One method to obtain information on the wavefunctions contributing to nuclear

20

states is analysis of nucleon transfer reactions. Stripping reactions and the inverse,
nucleon pickup reactions, are direct reactions which are constrained to the nuclear
surface, and thus excite specific and limited nucleon degrees of freedom. The cross-
sections for such reactions are dominated by the wavefunctions of the transferred nu-
cleons [29]. This property makes single-particle transfer reactions uniquely powerful in
characterizing the single-particle character of a nuclear state. Cross-section measure-
ments can be compared to expectations assuming single-particle configurations, and
experimental spectroscopic factors can be extracted [30]. These spectroscopic factors
provide a measure of the single—particle character of nuclear states, as was mentioned
above in the case of 209Pb (see Fig. 1.3).

While other techniques, including fi decay, do not provide access directly to the
wavefunctions of nuclear states, information regarding parentage of states can be ac—
cessed indirectly by taking advantage of the predictions of the single-particle shell
model. Within the framework of this model the spin and parity of the ground state
should be representative of the single-particle orbital occupied by the last unpaired
nucleon(s). The extreme single-particle model can be extended and predicts certain
multiplet configurations corresponding to specific combinations of single-particle lev-
els for nuclei with two unpaired nucleons. The spin, parity and relative energy of
low-lying nuclear states can provide guidance for assignment of states as probable
members of specific multiplets, and thus insight into the configuration leading to the
states. While these inferences are not as robust as the spectroscopic factors from
transfer reactions, such interpretations can serve as first steps in understanding the
underlying nuclear structure, and relative single-particle energies. It is possible, in
this way, to qualitatively track the relative ordering of single-particle orbitals. Lid-
dick et al. [31] relied on such qualitative observations in the region of N 234, and

gained insight into the 1r1f7/2-1/1 f5/2 monopole migration.

21

1.4 Re-ordering of single-particle states in
neutron-rich f p shell nuclei

The previous sections have discussed the general usefulness of the shell model in
describing the structure of the atomic nucleus, as well as the nucleon-nucleon forces
which are believed to drive the evolution of this structure across the nuclear chart.

Specific regions of evolving structure within the f p shell are highlighted in this section.

1.4.1 N 232 and N 234 subshell closures

As discussed in Section 1.1.1, the proton-neutron tensor monopole interaction has a
strong influence on evolving shell structure across the nuclear landscape. One region
mentioned previously is that near Z 220 and N 234. The monopole interaction in this
region is that between the 1f5/2 (l— 1 / 2) neutron orbital and the 1f7/2 (l +1 / 2) proton
orbital. The low-energy structures of neutron-rich nuclei with neutrons occupying the
1f7/2, 2113/2, 2111/2 and 1f5/2 orbitals are strongly influenced by the occupation of the
proton 1f7/2 orbital, as illustrated in Figure 1.7. With increasing 7r1 f7 /2 occupancy in
moving from 20Ca to 28N i, the energy of the 5 / 2" level, which has a large contribution
from the u1f5/2 orbital, drops, moving much closer to the 3/2— (V2193 /2) ground state.

Along with the sizeable spin-orbit splitting between the V2113 /2 and V2111 /2 states,
the monopole migration of the u1f5/2 orbital suggests that, for nuclei with low occu-
pancy of the 7rlf7/2 orbital, e.g., the 20Ca, ggTi and g4Cr isotopes, there is a sufficient
gap in energy between the V2p3/2 and V2191 /2 states to produce an N 232 subshell
closure. This expectation has been borne out experimentally in the 20C& [11, 12],
ggTi [13] and g4Cr [14] isotopes in the systematic variation of the E(2[’) as a func-
tion of neutron number, shown in Fig. 1.8(a). The rise in E(2f) at N 232 relative
to the nearest even-even neighbors for the even-even Ca, Ti and Cr isotopes is clear.
Further support for the N 232 subshell closure below Z 228 comes from the small

B(E2 : 2]" 20;”) transition probabilities measured for 33Ti3g [28] and ggCI‘gg [32] [see

22

 

 

9 4.01
0.)
a 3.5' _‘
g6 30
‘12 2.5- ; 7/2‘
m ‘— I
c, 2.0 —‘ 1, '.
.2 ‘s “ '
B 1.5‘ \‘_ :“‘—- . —o -
.8 1.0. _“ s -- ‘ "— 1/2
iii ‘~ ,7— 5/2'

0.51 ‘—-~ . _'

OJ - _ - - o - - — 3/2'

 

 

 

49 51 - 53 55 57 -

Figure 1.7: Evolution of the low-energy states in the N229 isotones from Z 220 to
Z 228. The monopole shift of the u1f5/2 orbital with increasing occupation of the

7r1 f7 /2 orbital is suggested by the decreasing energy of the 5/2‘ state along the
chain.

Fig. 1.8(b)]. The high-spin structures of 50’52’54Ti [13] are also indicative of a sizeable
N 232 gap. The separation between the 6? and the closely space 81*, 9? and 101’“
levels in 54Ti has been interpreted as an indication of the substantial cost to promote
a V2113 /2 neutron across the N 232 gap to either of the V2191 /2 or V1 f5 /2 orbitals [13].

The experimentally-confirmed N 232 subshell closure has been well-reproduced by
shell-model calculations in the f p shell using several effective interactions [33—35]. Be-
yond N 232, the GXPFl interaction [33] further predicts a subshell closure at N 234
for the gOCa and ggTi isotopes, arising from the continued upward monopole shift
of the V1 f5 /2 orbital [33]. Experimental evidence, however, is inconsistent with the
prediction of N 234 as a subshell closure in the ggTi isotopes. Measurement of E(2‘1f)
for 56Ti34 by Liddick et al. [36] placed the first 2‘L level at 1127 keV, nearly 400 keV
drop lower than the E(2'1f)21495 keV observed for 54Ti3g [13] [see Fig. 1.8(b)]. This
result, at odds with the expectation of a N 234 subshell closure for the ggTi isotopes,
spurred the development of the new GXPF 1A effective shell model interaction [34].

To improve the description of the low-energy structure of 56Ti, five of the two—body

23

 

 

 

 

 

9 4000- -
£4: (a) ’ " 20(23—
".Z - Ti —
:N/ 3500 22
m 24Cr —
3000-
2500- g—Zflca
2000-
1500 —. _:'.j—‘_ .——.
__ — ‘9: 3' ‘1— Ti
1000 4 ‘ .'—: 9—" .——~. 22 C
~ .._3 — 24 r
500
22 24 26 28 30 32 34
Neutron Number
’7 30 '
D. (b) zoCa°
E 25 . I: \ 22T1 .
f; " o' \ CI‘ 0
E 'r 24
T 20. 1| 3‘ i‘
+—-« , , . .
N II ‘ ‘\
6i 15‘ '0’ ‘1 .4, '. 24Cr
% ’ ‘I ' ' f I “ "
.1 "..--| i. ’ ‘ s“ "o .
10 i ‘\‘ “\ x, “f L a" 22T1
5- ’ 1' '
0 ~ i . . T “O zoca
22 24 26 28 30 32 34
Neutron Number

Figure 1.8: Behavior of (a) E(2if) and (b) B(E2 : 21* —> 01*) across the 20Ca, ggTi
and g4Cr isotopic chains in the region of N 232,34.

24

matrix elements were altered to reduce the strength of the monopole interaction in nu-
clei with N >32. These modifications produced an effective interaction that provides
improved agreement with experimental data for isotopes in the region, and continues
to predict a N 234 subshell closure for the goCa isotopes, which have no protons in the
7rlf7/2 orbital and thus a maximum separation between the 1/1f5/2 and 7rl f7 /2 [34].
The most direct method of addressing the possible N 234 subshell closure in the Ca
isotopes would be to measure E (21*) for 33Ca34 directly. Low production yields have

kept such a measurement elusively out of reach at the present time.

1.4.2 N 240 shell closure and intrusion of the neutron lgg/g

orbital

According to the shell model orbital ordering shown in Fig.1.2(c), the 199/2 single-
particle orbital is well-separated from the 197/2, 2d5/2, and other higher-energy or—
bitals, giving rise to a well-established N ,Z 250 shell closure. A less pronounced shell
closure at N ,Z 240, arising from an energy separation between the 199/2 orbital and
the lower-lying f p shell levels is also expected within the simple spherical shell-model
framework.

Near N ~Z however, there is little evidence of the suggested magicity at N or
Z240. The self-conjugate nucleus 282nm, for example, shows no evidence of magicity,
as it has a rotational-like yrast structure [37], and a large quadrupole deformation,
fig20.39 [38], suggestive of a highly collective structure. This structure is similar to
that of EggSr38, which again has a rotational-like yrast structure, and a large quadru-
pole deformation, with fig >0.4 [39]. The dominance of a deformed structure rather
than the expected spherical ‘doubly-magic’ structure of §8Zr40 is explained by the
shape-polarizing effect of a well-stabilized deformed shell gap at N, Z238 [40]. At
large prolate deformation (fig 2 0.4) a significant gap forms at N238 between Nils-

son orbitals arising from the 199/2 orbital. Energetically, unless stabilized by a large

25

spherical shell gap (for instance at N, Z 2 28 or 50), it is preferential for a nucleus
to assume a quadrupole deformation and occupy the local energy minimum at nu-
cleon number 38. These deformed shell gaps strongly stabilize the highly deformed
N 2Z 238 76$r core, and lead to a situation in which the 80Zr deformed configura-
tion is more stable than the spherical configuration, even with a subshell closure at
N , Z 240. The stability of the deformed 768r core is also believed to be responsible
for the particle stability of the proton-rich nucleus §3Y38 [41].

Except for the collectivity at N N Z, the expected shell gap at nucleon number
40 is evident for both protons and neutrons in the neutron-rich nuclei. Figure 1.9(a)
shows E(2'1”) for the neutron-rich 4OZr isotopes relative to their nearest neighbor even-
even isotones over a range of neutron numbers from N 250 to N258. 90Zr50, 96Zr56
and 98Zr58 all show evidence of an increase in E(2f’) relative to the nearest isotonic
even-even neighbours, supporting the presence of a Z240 subshell gap. However, this
quasi-magic gap is eroded with the addition of neutrons beyond N258, due to the
attractive monopole interaction between 111 97 /2 neutrons and 7r199/2 protons [15].

The bulk of evidence for the expected N 240 subshell gap comes from studies
of ggNim and its nearest—neighboring isotopes. As is shown in Figure 1.9(b), the
energy of the first 2+ state in 68Ni is 2.033 MeV [45], significantly higher than in the
neighboring 66Ni and 70N i isotopes, providing an experimental signature indicative of
a subshell closure at neutron number N 240. Further evidence for the N 240 subshell
closure in the Ni isotopes comes from the E(4f)/E(2f) ratio, which reaches a local
minimum at 68Ni, and the low transition probability [46,47] for excitation to the first
excited 2+ state.

While in the Ni isotopes there are numerous indicators for the goodness of the
N 240 subshell closure, with the addition or removal of protons away from the magic
number Z228, the N 240 closure is rapidly washed out. Figure 1.9(b) shows the
systematics of E(2'1") for the even-Z g4Cr through 32Ge isotopic chains surrounding

N 240. The E(2f) values for the g4Cr, ggFe, 30Zn and 32Ge isotopes all decrease with

26

E01) (keV)
B
8
Z
LIL
A

1000 - 1'-

 

 

34 36 38 40 42 44 46
(Se) (Kr) (Sr) (Zr) (Mo) (Ru) (Pd)

 

 

Proton Number
9 Ge (2:32)
5‘: (b) — Zn (2:30)
+2 2000 - —" Ni (2:28) .—,
8 —— Fe (2:26) .
m — Cr (2:24)
. .' —-—Ni
—’
1000-—,==:——’—:—‘:
— __ :3 _~. =,
s‘ —‘ ‘:‘— Zn
‘ ’-——- Ge
— Cr Fe

 

 

30 32 34 36 38 4O 42
Neutron Number

Figure 1.9: Systematic variation of E(2i’") for the (a) isotonic chains in the region of
2:.40, and (b) neutron-rich g4Cr, ggFe, 28Ni, 302n and 32Ge isotopic chains in the
regron around N 240. Data were taken from Refs. [14,25,42—44].

27

increasing neutron number, even through N 240. Deformation of the ground state
is well-known in the case of the higher-Z 3gGe isotopes. As discussed by Leenhardt
et al. [48], systematics of B(E2: 2720?) support the trends seen in E(2'1"), and
suggest that the gem isotopes are a transitional region between the spherical 28Nl
isotopes and the well-deformed ggGe isotopes.

Collectivity has also been observed to develop near N 240 for the isotopes below
Z 228. Hannawald et al. [42] identified the first 2+ state in 66Fe40 at E(2f)2573 keV
following fi decay from 66Mn. This low excitation energy was taken to be an indication
of collectivity near the ground state, and a quadrupole deformation parameter of
fig20.26 was obtained from the Grodzins relation [26]. A recent measurement has
extended the data for the 26Fe isotopes past N 240, identifying the first excited state
in 68Fe4g at 517 keV in a 2p knockout reaction [43]. This is the most neutron-rich Fe
isotope studied, and shows that the decreasing trend of E(2f) for the 25Fe isotopes
continues past N 240.

The systematic decrease of E(2f) is even more pronounced in the g4Cr isotopes
[see Fig. 1.9(b)]. The low E(21+) values in 60Cr36 and 62Cr3g are indicative of defor-
mation, leading to deduced values of fig20.27 and 0.31 respectively [44]. Deformation
is also suggested by the reported large quadrupole deformation lengths for 60’62Cr
obtained in the analysis of proton inelastic scattering [49,50]. While data are not yet
available for the low-energy structure of 64Cr40, the trend of lowering E(2f) values
is predicted [51] to continue at and beyond N 240, as observed already in the 26Fe
isotOpes.

Understanding the origin of collectivity, which apparently develops in the region
0f N =40 in nuclei above and below Z 228, requires a knowledge of the interactions
at Work. The strength of the N 240 subshell closure is dependent on the energy
separation between the 1f5/2,2p1/2 neutron orbitals and the higher-lying 199/2 orbital.
The strong repulsive monopole p-n interaction between protons in the 7rlf7/2 (l + 1 / 2)

orbit and neutrons in the 1/1 99 /2 (l + 1 / 2) orbit decreases with the removal of 7rlf7/2

28

protons (Z <28), as does the attractive 7rlf7/2 (l + 1 / 2) - u1f5/2 (l — 1 / 2) interaction,
which causes a narrowing of the V199/2-V1f5/2 energy separation. This effectively
weakens the N 240 subshell closure, which may only manifest itself in 68Ni due to
reinforcement by the spherical Z 228 closed shell [52].

In addition to the weakening of the spherical N 240 subshell closure by the
monopole interaction, the first two Nilsson substates of the V1 99 /2 orbital are steeply
downsloping in energy with increasing quadrupole deformation, as is shown in Fig. 1.10.
The reduced energy gap at N 240 is insufficient to maintain the nucleus in a spherical
configuration [48], as occupation of the deformed levels is energetically preferential,
and collective deformed ground states develop, further eroding the N 240 subshell
closure. Thus, the 199/2 neutron orbital plays a strong role in determining collectiv-
ity near N 240, as its approach to the Fermi surface permits development of ground
states with significant quadrupole deformation. The decrease in energy of 9/ 2+ states
in odd-A Cr isotopes approaching N 240 [53—55] offers further evidence of the 199/2
orbital approaching the Fermi surface.

Considering Figure 1.9(b) in more detail, the decrease in E(2if) suggests an onset
of deformation in the g4Cr isotopes beginning at N 236, while in the 26Fe isotopes,
such evidence for deformation first appears at N 238. The point at which collectivity

sets in in this region will add to the understanding the effect of the neutron 199/2
orbital on the structure of nuclei at the extremes of the f p shell. The neutron-rich
24Cr and 26Fe isotopes have been investigated, but scant data are available for the
neighbouring odd-Z g5Mn isotopes near to N 240. An understanding of the onset of
deformation for the g5Mn isotopes would contribute significantly to the understanding

of the evolving structure in the region near N 240.

29

7/2[404]
5/2[413]

 

 

 

 

s " .64 ‘74
../2 a 2 4
5 i391 1/2 440 1ng2 9’ 7/21413l 31-
93 ‘ 5/2 422 112199} 4
mm 5.0 413 - .

 

 

 

 

 

 

 

Figure 1.10: Nilsson diagram for the neutron orbitals between 20 and 50. The Nilsson
substates arising from the 199/2 orbital are highlighted in bold red, and with increasing
deformation, the lowest two substates are observed to be steeply downsloping. Figure

adapted from Ref. [2].

30

1.5 Motivation for the measurement

The motivation for the present study was to more fully understand the evolution of
the single particle energies in the neutron—rich nuclei of the f p shell. Within the f p
shell, and at its upper and lower borders, the evidence of evolving single-particle level
ordering has been described. Further experimental data are required to constrain
nuclear theory, and help in the development of cross-shell interactions, which are
believed to be critical for the description of nuclei on the border of major shells.

Near N 232,34, fi decay of the 53’33Ca isotopes was investigated to gain insight

53’3‘[Sc isotopes. Isomeric decay 0f

into the low-energy structures of the daughter
states in 541563c provided additional information for these isotopes. The odd-Z 218C
nuclei are nuclei with a few nucleons more than a closed shell, and, as discussed
previously, the low-energy level schemes can be described in terms of proton-neutron
multiplets. Within this simple framework, insight into the neutron configurations in
the Sc isotopes can be gained. An improved understanding of the situation in the
218C isotopes may shed light on the case of the 20C& isotopes, and the open question
of a N 234 subshell closure at 54Ca.

At higher Z, the onset of deformation for nuclei with Z <28 approaching N 240
is also interesting. As discussed, 26Fe and g4Cr isotopes have been well studied, but
the location of the onset of deformation for the intermediate g5Mn isotopes is not
clear. While extensive level schemes up to high—spin have been deduced for the lighter
57-ggMn isotopes [56], no level structures are available for Mn isotopes with N >38.
In-beam 7 rays have been recently observed for neutron-rich 59“‘63Mn produced by

multinucleon transfer between a 70Zn projectile and a 238U target [57]. For the most
neutron-rich 63Mn only a single 7 ray was assigned. Five 7 rays were assigned to
62Mn, completing the low-energy level scheme proposed previously from fi decay [58],

a Structure which is complicated by the presence of two fi-decaying states. 7 rays

have been assigned from both fi decay [59] and in-beam work [57] in the case of

31

61Mn. Transitions identified in the former fi decay by Sorlin et al. were not placed in
a level scheme, while only yrast states have been identified in the latter in-beam work.
The present work studied the fi decay of 61Cr to states in 61Mn to produce a more
complete level scheme for this nucleus. Comparison with shell model calculations in
different valence spaces were found to provide insight into the onset of collectivity, and
the monopole migration of the deformation inducing V199 /2 orbital with decreasing
occupancy of the 7r1f7/2 orbital.

The low-energy isomeric structure of §3K31 was also studied, and provided insight
into the evolution of the proton single particle 1d3/2 and 131/2 states just below the
f p shell. The insight gained in this region of the nuclear chart does not clarify current
open questions, but rather adds to mounting evidence for structural evolution outside

the predictions of current theoretical treatments.

1.6 Organization of Dissertation

An introduction to the concepts of nuclear shell structure and the need for studying
neutron-rich nuclei was presented in this chapter, including the motivation for the
present measurement. The principles of the measurement techniques of fi and 7 decay
are presented in Chapter 2, as well as an explanation of how they pertain to nuclear
structure. Details of the experimental setup are presented in Chapter 3, including a
description of the detectors. The results for the low-energy level structures of 50K,
53’54’5630 and 61Mn are presented in Chapter 4, and the implications of these results
discussed in Chapter 5. Chapter 6 includes a summary of this work, and a discussion
0f the possibilities for future studies using both fi decay and other complementary

techniques.

32

Chapter 2

Experimental Techniques

fi-delayed 7—ray spectroscopy is a powerful method to probe the structure of the
most exotic nuclei, including short-lived nuclei near the driplines. A highly sensitive
technique, fi decay itself can provide valuable information on half-lives, decay Q
values, and branching information, even in cases with very few events. The branching
of the fi-decay process populates states in a daughter nucleus selectively, based on the
relative angular momenta and parities of the parent and daughter states. The excited
states populated in a daughter nucleus most often de—excite by the emission of 7 rays.
The-energy of the emitted 7 rays provides information on the excitation energy of the
states populated in the fi decay, another key observable in nuclear structure studies.
This chapter details the relevant processes of fi and 7 decay, and outlines how their

combined use permits access to details of the structure of exotic nuclei.

2. 1 fi decay

fl decay, in the most qualitative sense, describes the process of the conversion of a
proton in the nucleus into a neutron, or vice versa. During this process, the atomic
number (Z) and neutron number (N) of the nucleus is changed, but the mass number

(A) remains the same. Thus, fi decay moves nuclei along isobaric chains towards

33

stability. One of the earliest observed radioactive decay modes, fi decay is governed

by the weak force, and encompasses three distinct decay processes:

fi‘ : g‘XN 22313;“ 0‘ +v+ Q}, (21)
6+ : g‘XN 224’ 1,7,, + 8+ + z/ + and (2.2)
Electron Capture : Z AXN + e‘ 494 Y1?“ + V + Qfl, (2.3)

where e’ is an orbital electron, fii is a beta particle, l/ is a neutrino, '17 is an anti-
neutrino, and Q [3 represents the characteristic amount of energy released for a given
fi decay process [3]. The energy released, Q73, must be greater than zero for fi decay
to occur. On the neutron—rich side of stability fi" decays occur, driving nuclei towards
stability along an isobaric chain by converting neutrons to protons within the nucleus.
On the neutron-deficient side of the line of stability, both fi+ and electron capture
processes can occur, though fi+ is only observed in nuclei with a sufficiently large Q ,3,
due to a 1.022 MeV threshold for the creation of an e—-fi+ pair.

Electron capture is the process in which an orbital electron is captured by the nu-

cleus, and combines with a bound proton to achieve the transformation of a nucleus
éXN into Z—f’YNH' The Q3 for electron capture is given by QEC 2 [m(/Z’XN) —
m(Z_’14YN+1)]c2 — Bn, where Bn is the binding energy of the captured n—shell elec-
tron [3]. Only one particle, a neutrino, is emitted in the electron captures process. Due
to the extremely small neutrino mass, and the fact that neutrinos have no charge, it
is nearly impossible to observe this particle directly. Thus, electron capture processes
are typically observed by monitoring secondary radiation. The captured electron is
111081? often an inner shell (i.e. K or L shell) electron, and its capture during the de-
cay process creates a vacancy, which is filled by electrons from higher shells. These
downward transitions result in emission of characteristic X rays or Auger electrons,
Which can provide a signature for the electron capture process.

The other possibility for neutron-deficient nuclei to move towards stability along

34

an isobaric chain is fi+ decay. The Q 5 value for fi+ decay is given by Q W” 2
[m(’§XN) — m(z_14YN+1) — 2me]c2, and thus there is an energy threshold for fi+ de-
cay, requiring an atomic mass difference of at least two electron rest masses, 1.022 MeV,
between the parent and daughter species. As was the case in electron capture, a neu-
trino is emitted during the decay, but a second particle, a fi+, is also emitted. It is
very diflicult to detect the neutrino, but it is possible to detect the fi+, either directly,
through its interaction with atomic electrons in a detection medium, or by detection
of the two 511-keV 7 rays which result when the positron thermalizes and annihilates
with an electron.

On the neutron-rich side of stability, the relevant fi—decay process is fi‘ decay.
The Q [3 value for this decay is the simplest case, given by the difference in the atomic
masses of the parent and daughter, Q ,6— 2 [m(’§X N) — m( Z +’1’YN_1)]C2. As was the
case in fi+ decay, this process involves emission of two particles, an anti-neutrino and
a high-energy electron or fi‘ particle. The fi— can be detected directly through its
interaction with atomic electrons in the detection medium. It is this decay mode that

is of interest in the present study of neutron-rich nuclei.

2.1.1 fi-decay half-lives

One of the most fundamental quantities describing a fi-decay process is the rate at
which the decay occurs. fi decay is governed by first-order rate law, and the number

of nuclei, N, in a sample at a time t is given by:
N(t) = Noe-M, (2.4)

Where No is the number of nuclei originally in the sample, and A is the decay constant
Characteristic of the decay. Physically, A represents the probability per unit time for

the decay of a given nucleus [3]. The decay constant, A, is closely related to the more

35

often quoted half—life, T1/2 as:

T,,=_(_> (2.5)

The half—life corresponds to the average time required for half of the nuclei in a
sample to decay. Governed by the weak interaction, the half-life of fi-decay processes
ranges from a few milliseconds to seconds or even longer. The longest-lived fi—decaying
nuclei have half-lives in excess of 1018 years. The half-life of a fi-decay process depends
strongly on the energy of the decay processes, and differences (i.e. spin and parity)
between the parent initial state and the final state in the daughter. The dependence
on the initial and final state structures can be qualitatively understood, and relates to
the selection rules for fi decay, which are discussed in Section 2.1.3. The next section
addresses the process of fi-delayed neutron emission, a decay mode which can be a

significant part of the decay of neutron-rich nuclei.

2.1.2 fi-delayed neutron emission

Neutron emission is a decay process involving direct emission of a neutron from a

nucleus according to the following equation:
’2sz —>”‘IZ XN—l + n + Q... (2.6)

where 62,, represents the mass-energy difference between the initial and final states.
When the daughter nucleus, A-IZXN_1, is left in its ground state, Qn 2 -Sn, where Sn
is the neutron separation energy, a measure of how much energy is required to remove
a neutron from a given nucleus, as discussed in Chapter 1 (see Eqn. 1.1). In general
the neutron separation energy becomes lower with the addition of neutrons along an
.iSOtOpic chain. Thus, for the most neutron-rich nuclei, neutron separation energies are
(mite low, and in fact when the separation energy reaches zero, the nucleus is said to
be at the neutron dripline. Not being subject to the Coulomb force, and thus without

a C'Oulomb barrier, the last neutron is simply not confined within a nucleus at the

36

neutron dripline.

While the ground state of a fi-decay daughter nucleus may be bound with respect
to neutron emission (i.e. Sn > 0), there are many cases in fi‘ decay in which the decay
populates states in the daughter which are above the neutron separation energy, or
neutron threshold. When this occurs, the emission of a neutron from the excited state
of the daughter can proceed rapidly, as neutron emission is mediated by the strong
force and competes favorably with 7-ray emission mediated by the electromagnetic
interaction. Following neutron emission, excited states in the fin daughter may be
populated, and further de—excite through emission of 7 radiation characteristic of
that nucleus. It is possible to identify fi-delayed neutron emission in the decay of

neutron-rich nuclei through the detection of these characteristic 7 rays.

2.1.3 Selection rules and log ft

fi“ decay involves the emission of two particles, a fi‘, or high energy electron, and an
anti-neutrino. These emitted particles are leptons with intrinsic spin S21 / 2, and can
carry additional orbital angular momentum. If the spins of the two emitted particles
are antiparallel, they are coupled to S g20, and the system undergoes what is called
Fermi decay [3]. The other possibility, that the spins of the electron and neutrino
are aligned parallel, coupling to S [321, is called Gamow-Teller decay. The orientation
of the electron and anti-neutrino spins provides the first classification of fi decay —
whether the electron and/or neutrino carry additional angular momentum further
divides the fi-decay process.

The so—called allowed fi decay describes the situation in which the electron and
neutrino carry no orbital angular momentum (120). With Sfi20, an allowed Fermi
decay has no change in the nuclear spin, AJ 2 [Ji - J f] 2 0. Additionally, with l20,
there is no change in parity between the initial and final states, 7r 2 (-l)’ in this
Case. $321 for allowed Gamow-Teller decays, and one unit of angular momentum

is Ca«I‘ried by the electron and neutrino, even with zero additional units of orbital

37

Table 2.1: fi decay selection rules for allowed and forbidden transitions. Table adapted
from Ref. [4].

 

 

Transition Type Arr Al Al logft

 

Superallowed No 0 0 2.9 — 3.7
Allowed No 0 0, 1 4.4-6.0
First forbidden Yes 1 0, 1, 2 6 - 10
Second forbidden No 2 1, 2, 3 10 - 13
Third forbidden Yes 3 2 3 4 2 15

’ 3

 

 

angular momentum (I20). Allowed Gamow-Teller decays thus have J; 2 if + 1, and
so [Jf — 1] 2 J,- 2 [Jf + 1], or AJ20,1. Again, with l 2 0, there is no change in
parity between final and initial states in allowed Gamow—Teller decay. Since AJ20 is
allowed in both cases, most transitions are mixed Fermi and Gamow-Teller decays,
except when Ji 2 J f 2 0, in which case only Fermi decay is possible [3]. This special
case is called a “super-allowed” decay.

Allowed fi-decay transitions are among the fastest, although other transitions

in which the electron/neutrino carry non-zero orbital angular momentum (l > 0)
are possible. These so—called ‘forbidden’ transitions are not completely forbidden as
the name suggests, but are slower and thus much less likely to occur than allowed
transitions. The degree of forbiddenness increases with l - first forbidden decays have
the electron and neutrino emitted with 121, while l22 corresponds to second forbidden
decays, etc. Table 2.1 summarizes the selection rules for fi decay up to third forbidden
decays.

The comparative half-life, or ft value provides a method for comparing the fi-
decay probabilities in different nuclei. The dependence of the fi-decay rate on specific
nuclear properties such as the Coulomb interaction based on the atomic number
0f the daughter, Z, and the maximum energy of the fi transition are incorporated
into the value of f, the Fermi integral [3]. With these well-understood dependencies
r emOved, differences in ft, or the more commonly reported log f t, represent differences

betvWeen the initial and final nuclear states. Values for the Fermi integral are tabulated

38

for ranges of Z and the maximum fi energy, Emu, but approximate values can be

obtained using the empirical expression for log f [3‘ [60]:
log f5_ 2 4.010g Emaa: + 0.78 + 0.02Z — 0.005(Z — 1) log Emax. (2.7)

The value of t in log f t is the partial half-life for the decay to a specific state in the

daughter nucleus. If the parent nucleus has a total halflife T3301, then the partial

half-life for decay populating a specific state i in the daughter is given by [3]:
total

partial,i _ 1/2
T1/2 _ BR,’ (2.8)

 

where BB,- is the branching ratio to the state i in the daughter.

2.2 7-ray decay

Following fi decay, the daughter nucleus may be left in an excited state. Internal
transition or colloquially, 7—ray decay, is the process by which an excited nucleus can
release excess energy in the form of electromagnetic radiation, or a photon. From
a schematic perspective, the emitted electromagnetic radiation connects two states
within the nucleus, each of which have definite spin, J, and parity, 7r. The emitted
photon must connect the states in energy, and conserve both spin and parity. This

results in strict selection rules for 7-ray transitions.

2.2.1 Selection rules and lifetimes

Photons have no intrinsic spin, and thus the orbital angular momentum, A, carried
by a photon is constrained by the spins of the initial (J,) and final (J f) nuclear states
as:

[Ji—Jfl SA S (Ji+Jf)h. (2.9)

39

Table 2.2: 7-ray decay selection rules and multipolarities up to A23. Table adapted
from Ref. [4].

 

 

 

Radiation Type Name A2AJ Arr
E1 Electric dipole 1 Yes
Ml Magnetic dipole 1 No
E2 Electric quadrupole 2 N 0
M2 Magnetic quadrupole 2 Yes
E3 Electric octupole 3 Yes
M3 Magnetic octupole 3 No

 

 

While there may be a number of possible A values, or multipolarities for 7—rays con-
necting two nuclear states, the transition rate is strongly dependent on A, and the
lowest possible 7-ray multipolarity will be favored. However, the required conserva-
tion of parity plays a significant role in determining the type of 7-ray transition which
occurs.

Each nuclear state corresponds to a distinct distribution of matter and charge,
and thus an electromagnetic transition connecting two nuclear states necessarily cor-
responds to a change in the distribution of protons and neutrons within that nu-
cleus [4]. A shift in the charge distribution produces an electric field, while a shift
in the distribution of current gives rise to a magnetic field. Thus, de—exciting 7-ray
transitions can be classified as either electric or magnetic in nature. Electric transi-
tions are characterized by a parity dependence on A of A7r2(-1)A, while for magnetic
transitions, the parity change is A7r2(-1))‘+1. Combined with the angular momentum
requirements, the resulting 7-ray selection rules are summarized in Table 2.2.

Based upon the type and multipolarity of a de—exciting 7-ray transitions, estimates
can be made for the expected lifetime of the parent state. The decay constant for the
emission of a photon from a well—defined single state with excess energy is given by

what is known as Fermi’s golden rule [4]. The transition rate, T(EA) or T(M A), for

40

a 7-ray transition with energy E, can be written as follows [4]:

 

 

_ 87r(A+1) E 2"“1

T(EA) _ amA[(2/\+1)H]2(fi) EB(EA), (2.10)
_ h 2 87r(A+1) E 2"“1

TM“) — Ghee—777,5) A[(2A+1)11]2('EZ') 718(EA)’ (2'11)

where a is the fine structure constant, 5 is Plank’s constant divided by 27r, c is the
speed of light, mp is the mass of the proton and B(EA) and B(MA) are the reduced
electric and magnetic transition probabilities respectively, which contain all of the
nuclear wavefunction information.

To obtain useful estimates of the transition rates for 7-ray transitions, estimates
of the reduced transition probabilities are required. However, these values depend
strongly on nuclear models. A commonly-used value was derived for the extreme
single-particle model, discussed earlier in Section 1.2.1. Assuming that the transition
involves the change of a single particle in a uniform density nucleus, then the so-called
Weisskopf single-particle estimates for the reduced transition probabilities are given

by the following [4]:

 

2
BW(EA) = (1:72” (£3) A2V3e2(fm)2*, (212)

10 _ 3 2 _ h 2 _
BW(MA) = #12)” 2(fi‘3’) A<2A W3 (51;) (rm)2A 2. (2.13)

Combination of the Weisskopf single-particle transition probability estimates with
the expressions for the 7-ray transition rates yields the so-called Weisskopf estimates
for 7-ray decay transition rates. The Weisskopf estimates for the lifetimes of certain

types of 7-ray transitions are given in Table 2.3.

41

Table 2.3: Weisskopf single-particle lifetimes estimates for electric and magnetic 7
transitions up to multipolarity 3 [4]. A represents the mass number of the nucleus,
while E7 is the 7 energy in MeV.

 

 

Radiation Type Weisskopf Estimate for Transition Lifetime (3‘1)

 

E1 1.0 x 1014/12/3Ei,3
M1 5.6 x 1013153
E2 7.3 x 107A4/3E2
M2 3.5 x 107A2/3E§
E3 3421215;

M3 16/14/313;

 

 

2.2.2 Isomeric 7-ray transitions

The possibility exists in nuclei for excited states to be relatively long-lived, or isomeric.
Isomeric states are those which have unexpectedly long lifetimes compared to other
nearby states in the nucleus. While there is no clear lifetime cut-off for classifying a
nuclear state as isomeric, for example states with lifetimes > 10‘9 s can be considered
isomeric, particularly in comparison to the typical lifetime for nuclear states of order
10‘15 3.

When low-lying states in a nucleus have very different angular momenta and
there are no intermediate states, the 7-ray decay from the higher-lying state will
be hindered due to the large change in angular momentum, a result predicted even
by the Weisskopf single-particle estimates. This leads to long-lived nuclear excited
states, or isomeric states. When this long lifetime arises due to a large change in
angular momentum between the excited state and lower-lying states, this is known
as spin isomerism. Also evident from the expressions for the Weisskopf single-particle
lifetime estimates is a strong 7—ray energy dependence. Low-energy 7-ray transitions
may be long-lived, particularly in heavy nuclei with large mass number.

There are other sources of hindered 7-ray transition probabilities which can lead
to nuclear isomerism. As an example, in highly-deformed nuclei, the projection of the

total angular momentum onto the nuclear symmetry axis, K, is an approximately

42

conserved quantum number. As such, selection rules emerge for transitions allowed
based on AK, and K isomerism is possible when transitions are inhibited by a large
AK [19].

Aside from large changes in quantum numbers hindering 7-ray transitions, isomers
can arise when transitions to lower states involve a significant change in nucleon con-
figuration, even without a large change in angular momentum. The overlap between
initial and final states can be poor, and thus hinder the transition. These are called
structural isomers and are analogous to the molecular isomers in chemical systems.
As such, the presence (or absence) of nuclear isomers can provide critical insight into

nuclear structure.

2.2.3 Internal conversion

A competing process to 7-ray decay, internal conversion, occurs when an excited
nucleus de-excites by interacting electromagnetically with an orbital electron, and
ejecting it [3]. This process involves no direct electromagnetic radiation (no photons
are involved), and the ejected electrons will have discrete energies, related to the

transition energy according to:

EIC = Etransition _ electron binding energy- (2-14)

Since orbital electrons occupy discrete shells, within a conversion electron spectrum,
separate lines will appear corresponding to ejection of K, L, M, etc. shell electrons.
To quantify the process of internal conversion, and its competition with 7-ray

decay, an internal conversion coefficient (a) is defined as follows:

 

a _ number of internal conversion decays _ A12 (2 15)
_ number of 7-ray decays — A7 ’ '

As there are contributions to the internal conversion process from electrons in a

43

number of electron shells, the total probability of decay, atotal is given by summing a
for all possible atomic electrons. However, atom) is usually dominated by contributions
from ejection of inner (i.e. K and L) shell electrons.

Compilations for internal conversion coeflicients are available [61], which provide
the internal conversion coefficient for each atomic electron shell, as well as the total
value. Internal conversion is expected to compete most strongly with 7-ray decay for

heavy elements (high Z), and low transition energies (low E) [3].

2.3 Summary of the decay of exotic nuclei

Governed by the selection rules presented in Table 2.1, the allowed fi decay of a
state in the parent nucleus selectively populates states in the daughter according to
AJ 2 0,1. Usually the fi-decaying state is the ground state, though isomeric states
may also undergo fi decay. If the spin and parity of the decaying state is known, the
selectivity of the fi-decay process immediately provides limitations for the possible
J7r values of the states populated in the decay.

Following the fi-decay process, excited states populated in the daughter will de-
excite by 7-ray emission to the ground state, or if the populated state is above the
neutron separation threshold for the nucleus, by neutron emission to states in the
fin daughter. fi-delayed neutron emission can be identified and quantified by moni-
toring the 7—rays emitted when states in the fin daughter de—excite, as discussed in
Section 2.1.3. Emitted 7 rays provide information not only on the energy of states in
the daughter, but can also limit spin and parity values, when combined with other
information. The most intense 7-ray transitions will, in general, correspond to low
multipolarity transitions, usually limiting non-isomeric transitions to AJ 2 1, 2. This
requirement can further constrain possible J ’r values for states populated in the de-
cay based on the observed 7-ray transitions connecting to other states. Considering

energetics, 7 rays may de—excite a state directly to the nuclear ground state, in which

44

case the 7-ray energy is equal to the excitation energy of the state. Alternatively,
7 rays may occur in cascade, through an intermediate state. Level energies can be
determined by looking for 7 energy sums in the case of 7-cascades. Often, there is
more than one possible cascade, and identifying 7-ray transition sums can help in
building up nuclear level schemes. 7-7 coincidence measurements also provide invalu-
able information in determining 7-ray cascades, while 7-ray transition intensities can
additionally constrain the possibilities.

Prompt, or isomeric 7-rays can be similarly used to determine low-energy level
schemes of parent nuclides. Summing relationships and 7-ray intensities provide valu-
able input for assembling level structures from prompt 7-ray data.

The very powerful techniques of fi-delayed 7-ray spectroscopy and prompt 7—ray
spectroscopy were used to study the low-energy level structures of neutron-rich nuclei
in the fp shell in the present work. The next chapter will detail the experimental

set-up used for the present study.

45

Chapter 3

Experimental Setup

The motivation for nuclear structure studies of exotic neutron-rich radioactive iso-
topes was presented in Chapter 1, focusing on important cases in the f p shell. The
second chapter presented the fundamentals of fi and 7 decay, discussing the selec-
tivity of these processes and the utility of fi-delayed and prompt 7-ray spectroscopy.
This chapter focuses on the more practical aspects of the experimental set-up used
in two fi-decay experiments that studied neutron-rich f p shell nuclei at the National
Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. Pro-
duction and separation of the short-lived isotopes of interest using fragmentation and
in-flight separation is discussed. The details of the experimental end-station detectors,
including the fi counting system (BCS) and Segmented Germanium Array (SeGA)
are presented, including a description of the readout electronics and calibrations per-
formed for each detector system. Details of the procedure for implantation-decay

correlations and elements of data analysis are also included.

3.1 Isotope production and identification

Only a handful of very long-lived radioisotopes are naturally abundant on Earth.

Thus, to study unstable nuclei, it is necessary to produce these species in an artificial

46

RT-ECR

 

 
 
 

final
focus
A1900 \
stripping _
foil . "
, image 2
. _ , (dispersive
7"}?49'5-‘83/71 " “ = " ' lane
.7 1%,, ‘3 -- p )

      

41'

fi'KIZOO

target

Figure 3.1: Schematic of the NSCL Coupled Cyclotron Facility, showing the K500
and K1200 cyclotrons and the A1900 fragment separator.

way. At NSCL, secondary beams of exotic rare isotopes are produced using the pro—
jectile fragmentation technique. The fragmentation process involves the interaction of
a medium-energy primary beam (100—160 MeV / nucleon) on a stationary target. The
primary beam is a stable isotope that is first ionized in one of the NSCL’s electron
cyclotron resonance (ECR) ion sources. The primary beam of ions is then accelerated
by the coupled K500 and K1200 cyclotrons, shown schematically in Fig. 3.1. After
extraction out of the K1200 cyclotron, the primary beam has an energy in the range
100 to 160 MeV/ nucleon. The beam is then impinged on a production target. Typi-
cally the production targets are thin 9Be foils with thicknesses of order hundreds of
mg/cm2. Beryllium is used because of its high number density and robust physical
properties. Fragmentation of the primary beam in the production target, in which a
range of nucleons is abraded from the heavy beam, results in the production of nuclei
between the A and Z of the primary beam and hydrogen. As fragmentation reactions
are mostly peripheral reactions, there is a relatively small momentum transfer [4],
and the surviving larger-mass fragments emerge from the thin production target with
energies close to that of the primary beam. These secondary beam components are

forward focused and continue into the A1900 fragment separator [62].

47

Given the large variety of ions produced in the fragmentation process, and the low
production rates for the most exotic nuclei, it is critical to efliciently separate the ions
of interest from all others produced. This is accomplished at NSCL using the A1900
fragment separator [62]. The A1900 separator is a large acceptance, achromatic, high
resolution separator. Fragments entering the separator after the production target
are separated by a combination of magnetic selection and energy loss (Bp—AE—Bp).
Ions of a single magnetic rigidity, Bp 2 mv/ q, are selected in the first stage of
the separator. Since ions emerge from the production target with approximately the
same velocity (7)), this first separation selects ions with nearyly the same mass / charge
(m/ q) ratio. At the second intermediate image of the separator, the dispersive image
(image 2, or I2), maximum horizontal dispersion of the beam is present and the ions
pass through a wedgeshaped energy degrader. The ions entering the wedge have the
same Bp, but experience an energy loss proportional to Z2 in the wedge material,
and thus exit the wedge degrader with different energies, and different momenta. A
second B p separation stage in the second half of the separator then provides isotopic
resolution [63].

The rate and purity of the secondary beam are determined by the composition
and thickness of the production target and wedge degrader, as well as the momen-
tum acceptance settings. Variably-adjustable slits are located at each of the three
intermediate images of the separator, and can be narrowed to limit the momentum
acceptance of the separator below the maximum Ap/p ~5%.

The A1900 is a versatile device, and can be tuned to accommodate the needs of
a wide variety of experiments. Many experiments require a high level of purity in
the secondary beam, while others have more stringent requirements in terms of the
overall fragment rate. The two experiments discussed in this dissertation made use of
so-called “cocktail beams”, with multiple component nuclei, as the overall beam rate,
and not beam purity, was most important.

Regardless of the specific requirements of a given experiment, a critical experi-

48

mental necessity is particle identification. Nearly all experiments at NSCL use the
combination of energy loss in a thin detector and time—of—flight (TOF) to identify
secondary beam particles. The general requirement for particle identification is thus
two detectors separated by some distance over which to measure a time of flight. The
BCS set-up measures energy loss in a silicon PIN detector, which is a part of the BCS
detector telescope, described in detail in the following section. The time-of-flight mea-
surement with the BCS uses the signal from the energy-loss PIN as a start, and either
the cyclotron RF signal, or a signal from a plastic scintillator at image 2 of the A1900,
as a stop signal. The plastic scintillator can also be used to provide an event-by-event
momentum correction to the time-of-flight for those experiments in which the A1900
is operated with a large momentum acceptance. The 12 scintillator is read out by two
photomultiplier tubes, one on each end, permitting determination of the approximate
position of fragments in the scintillator. The position information is used to correct
time-of-flight measurements for the differing path lengths and velocities of ions when
a large momentum acceptance is used. Such time-of-flight corrections were necessary
for both experiments discussed in this dissertation.

This section has described in general terms the production, separation and iden-
tification of exotic nuclei at NSCL. The following subsections present the specific
details for production of the cocktail beams used in NSCL experiments 05101 and

07509, the experiments discussed in this dissertation.

3.1.1 NSCL experiment 05101

The main focus of NSCL experiment 05101 was the study of neutron-rich gOCa iso—
topes, and settings of the A1900 magnetic rigidities were optimized for 54Ca and 54K
production. Some data, however, were taken with an incorrect target setting, which
resulted in a secondary beam of isotopes in the region of 60V. The fragmentation pro-
cess used to produce these neutron-rich nuclei was the interaction of a 76Ge beam with

a Be target. The primary beam of 76Ge was ionized to 12+ in the room—temperature

49

ECR ion source and accelerated to 11.6 MeV/ nucleon in the K500 cyclotron. Follow-
ing foil stripping to a charge state of 30+, the 7’6Ge primary beam was accelerated to
a full energy of 130 MeV/ nucleon by the K1200 and impinged on a 47-mg/cm2 9Be
target, located at the object position of the A1900 separator. Secondary fragments
were separated through the A1900 with magnetic rigidity settings of Bp24.403 Tm
before the wedge, and Bp24.134 Tm following a 300 mg/cm2 Al wedge located at
the intermediate image of the separator. The full momentum acceptance of the A1900
(Ap/p~5%) was used for fragment collection. Given the large momentum acceptance
used in the experiment, the plastic scintillator at the dispersive image of the A1900
(12) was used for event-by-event momentum correction, and as the stop for the time—
of—flight measurement. The start of the TOF measurement was provided by the signal
of the most upstream PIN detector in the BCS silicon telesc0pe, PIN01, described in
the next section. The secondary cocktail beam consisted of ~10 isotopes, including
60V, delivered to the experimental end-station of the BCS + SeGA located in the N3

vault. The particle identification plot for this setting is shown in Fig. 3.2(a).

3.1.2 NSCL experiment 07509

The isotopes of interest in NSCL experiment 07509 were those centered only around
54Ca. The primary beam of 7"’Ge was accelerated to 130 MeV/ A in the same man-
ner as in NSCL experiment 05101, which was detailed in section 3.1.1. The beam
was impinged on a 352-mg/cm2 thick Be production target, and the projectile-like
fragments entered into the A1900 fragment separator. The first half of the separator
was set to a magnetic rigidity of 4.103 Tm. A thin 45 mg/cm2 Al wedge was placed
at the A1900 intermediate image to provide differential energy loss. The second half
of the separator was set to a magnetic rigidity of 4.030 Tm to optimize production
and separation of 54Ca. The A1900 was operated with a maximum momentum accep-
tance of ~5%. In total 24 isotopes, including 54Ca, were directed to the experimental

end station set up in the S2 vault. As was the case in experiment 05101, the TOF

 

DJLHUJUJ
NAOOO
COCO

(21)

Mb)
000
CO

Energy loss (arb. units)

N
O\
O

 

850 .~
800 : ; _
750

\‘I
O
O

650 ‘:-- .‘ :';‘
(b) 550/ ,
50095:: " ,, -' 33:;-
4502 ‘35
660 700 740 780 820
Time of flight (arb. units)

 

Energy loss (arb. units)
8
O

 
 

 

 

Figure 3.2: Particle identification plots for the relevant experimental settings in NSCL
experiment (a) 05101, and (b) 07509. In both cases, time of flight measurements were
started by the signal from the most upstream PIN detector of the BCS, and stopped
by a signal from the 12 scintillator. Energy loss was measured in the upstream PIN
detector of the BCS. The particle groups were identified by their subsequent decay.

51

measurement was started by the signal from the upstream PIN detector of the BCS,
PIN01, and stopped by the delayed signal from the 12 scintillator. The 12 scintilla-
tor was also used to provide event-by-event momentum correction for the TOF. The

particle identification plot for experiment 07509 is shown in Fig. 3.2(b).

3.2 Detector apparatus for fi-decay experiments

The experimental apparatus for both experiments discussed here consisted of the
NSCL fi counting system (BCS), and detectors from the SeGA. Secondary beam
fragments were implanted into the detectors of the BCS, which provided triggers for
both implantation and fi-decay events. 7 rays were detected in the SeGA detectors,
and 7-ray events were recorded for both implantation and decay processes. The fol-
lowing sections describe the end-station systems in detail for NSCL experiments 07509
and 05101. The end-station set-ups for these two experiments were nearly identical.

However, the minor differences between the set-ups will be noted when present.

3.3 fi Counting System

The NSCL fi counting system (BCS) [64] consists of a stack ’of Si detectors. A
schematic of the BCS detectors as set-up in NSCL experiment 07509 is shown in
Fig. 3.3. The centerpiece of the system is a highly-segmented double-sided Si mi-
crostrip detector (DSSD), into which the secondary beam is implanted. The high
segmentation of the implantation detector permits event-by-event correlation of frag-
ment implantations with their subsequent fi decays. The detectors of this system as
set-up for NSCL experiment 07509 are described in this section. The readout elec-
tronics, calibration procedures and calibration results are also described.

The central detector of the BCS was a 4 cm by 4 cm, 40x40 DSSD, manufactured

by Micron Semiconductors. The segmentation of the detector with 40x1 mm strips

52

 

 

PINOI PIN03 SSSDl SSSD3 SSSDS
[ PIIIIOZ SSSD2 SSSD4 SSSD6
l w ‘1 y
l [ [l I z
l [ l 20 mm 1 7mm ‘ ) . -
\\\ 12 mm 1 mm -

\‘\ . 7 Beta Counting System /
’ \\ ,,,,, ,.,.. ,»/.I

- 1.l..L.l33_
Figure 3.3: Schematic diagram of the silicon detectors which constitute the NSCL fi
Counting System. The arrangement of detectors for experiments 07509 and 05101 were
as pictured; for details regarding detector thicknesses, see the text. Figure adapted

from Ref. [65].

53

on the front and 40x1 mm perpendicular strips on the back resulted in electrical
segmentation into 1600 individual pixels, each of which act as an individual detec-
tor. Fragments were continuously implanted in this detector, and implantations were
correlated with decays on an event-by—event basis. The correlation requirements are
described in detail in Section 3.5 at the end of this chapter. A DSSD detector thick-
ness of 995 mm was used in NSCL experiment 07509, while the implantation detector
used in experiment 05101 had a nominal thickness of 979 ,um.

Downstream of the implantation detector were six 5 cm by 5 cm, 16-strip single-
sided silicon strip detectors (SSSD3), which constituted the fi calorimeter. Segmented
in only one direction, the orientation of strips in the SSSDs was alternated between the
horizontal (51:) and vertical (y) directions for adjacent detectors, as is shown in Fig. 3.3.
This arrangement of detectors allowed for two-dimensional position information for
any particles moving downstream of the DSSD. The thicknesses of SSSDl through
SSSD6 for NSCL experiment 07509 were 975 pm, 981 pm, 977 pm, 989 pm, 988 ,um,
and 985 pm respectively. For experiment 05101, the thicknesses were 981 pm, 977 pm,
975 pm, 988 pm, 989 pm, and 985 pm for SSSDl-SSSD6 respectively.

A stack of three silicon PIN detectors were placed upstream of the DSSD, which
acted as active energy degraders and provided the energy loss and timing information
required for particle identification. The thicknesses of the three PIN detectors were
297 pm for PIN01, 297 pm for PIN02, and 488 pm for PIN 03, during NSCL experiment
07509. Experiment 05101 had thicknesses of 991, 997 and 309 pm for PIN01, PIN02,
and PIN03, respectively.

A passive aluminum energy degrader was placed upstream of the PIN detectors
to ensure fragments were stopped near the center of the DSSD implantation detector.
A 7.5 cmx7.5 cm Al degrader foil was held on a rotating mount, that was used to
adjust the angle, and thus the effective thickness, of the foil with respect to the beam.
The Al degrader thickness for experiment 07509 was 4 mm, while experiment 05101

only required a degrader with a thickness of 2.3 mm.

54

 

MCS CPA 16
Preamp
Grounding” Non-inverting Lgvv Impedance+CAEN V785

Board (Inverting) Gam Matching ADC
for FRONT
(BACK)
.Hish

Gain

P' s t
5153820 Fast 1C0 ys ems 812w CAEN V785

3 _ Sh./ Disc. .-
D . . .
chler (ECL t)Isc (Nmmveflmg) (1:3? ADC

Fast disc.
'16—channel
OR

CAEN V977
F I /O t Dela 9»-
’ an n u ’+ Y Coinc. Reg.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘

 

 

 

 

 

 

 

 

 

 

 

OR (of all FRONT,
all BACK strips)

Figure 3.4: Schematic diagram of the signal processing electronics for the DSSD of
the BCS.

3.3. 1 Electronics

A schematic diagram of the signal processing electronics for the DSSD is shown in
Figure 3.4. Signals for the front and back segments were carried from the detector
within the vacuum chamber to feedthroughs on a backplate by separate ungrounded
50-pin ribbon cables. Outside the vacuum, 50-pin ribbon cables carried signals for
the front and back of the DSSD to a grounding board. On the ground board, signals
from each strip were paired with ground signals, and were grouped in units of 16 to
match the input channel density of the conventional analog electronics. The grouping
performed on the ground board created blocks with F1-16, F17-32, F33-40, B1-16,
Bl7—32 and B33-40, where F and B represent front and back strips respectively, and
numbers refer to the strip number of the detector.

One of the challenges of using a single detector to detect both implantation events
and fi decays is the dynamic range required to measure both types of events. Ion

implantation deposited energies of order several GeVs, while fi decays deposited much

55

lower energies, of order a few hundred keVs. The BCS overcomes this challenge by
using dual-gain preamplifiers from Multi Channel Systems (MCS). The 16—channel
preamps have a high-gain amplification for the lower-energy fi signals of 2 V/pC, and
a low-gain amplification for the high-energy implantation signals of 0.1 V/pC. The
50 Q low-gain signals from the MCS preamps were impedance matched to the 1 k5)
inputs of 32-channel CAEN 785 VME analog-to—digital converters (ADCs). The high-
gain signals from the preamplifiers required further signal processing to amplify the
small signal. The high-gain outputs of the MCS preamps were sent into PicoSystems
programmable CAMAC shaper/discriminator modules. These l6—channel modules
have programmable discriminator thresholds and gains, and analog energy and digital
timing outputs for each channel. A logical OR of the discriminator output of all 16
channels is also available from each module. Analog energy signals were sent to VME
CAEN 785 ADCs, where each block of 16 high-gain signals and the corresponding low—
gain signals were digitized in a single ADC module. The digital timing outputs were
sent to SIS 3820 VME scaler modules for rate monitoring on a channel-by—channel
basis. The logical OR of the 16 channels was used to define the master trigger logic, as
discussed at the end of this section, and also sent to a VME CAEN V977 coincidence
register for sparse readout. A given 32-channel ADC contained both high- and low-
gain signals from one block of 16 DSSD channels. The coincidence register reduced
the event size by allowing restriction of the ADC digitization to those modules that
had data above threshold.

Shown in Fig. 3.5 is a schematic of the electronics for the six SSSDs downstream
of the implantation DSSD. Signals from each of these 16—strip detectors were carried,
with paired grounds, by 34-pin ribbon cables from the detector to the backplate
feedthroughs, and from the backplate to MCS preamps identical to those used with
the DSSD. However, in the case of the SSSDs, only high-gain signals were processed.
Similar to the DSSD electronics, the SSSD signals were amplified and discriminated

using PicoSystems shaper/ discriminator modules. Analog energy signals were sent to

56

 

 

 

 

 

SSSD MCS CPA 16Hggh Pico Systems 319W CAEN V785
Preamp Gam Sh./ Disc. (Lmear ADC

vFast disc. out)
l6-channel

OR

CAEN V977
Fa In/O t Dela +—
Ln ’1’» y Coinc. Reg.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

OR (of 16 strips for
a given SSSD)

Figure 3.5: Schematic diagram of the signal processing electronics for the SSSD5 of
the BCS.

VME CAEN 785 ADCs, with two SSSDS worth of signals in a single ADC, in pairs of
SSSDs 1 and 2, 3 and 4, and 5 and 6. The individual channel discriminator outputs
were not monitored in sealers. However, the OR of the 16 discriminator. outputs was
sent to the VME CAEN V977 coincidence register allowing sparse readout of the
ADCs, as was the case in the DSSD electronics. Additionally, for NSCL experiment
07509, a logical OR was taken of the ORs of the discriminator signals from SSSD5 and
SSSD6. This signal was used to veto the master gate trigger against light particles
that did not stop in the DSSD, and increase the data acquisition live time. Such a
veto was not required in NSCL experiment 05101.

The electronics for all three upstream PIN detectors were essentially identical. The
signal from each detector was sent through a four-channel Tennelec TC178 preampli-
fier, and then a Tennelec TC248 shaping amplifier. The slow unipolar output from
the shaping amplifier was then sent to a VME CAEN 785 ADC, while the fast timing
output was analyzed by a Tennelec TC455 constant fraction discriminator (CFD).
One of the CFD outputs from PIN01 was sent to a coincidence register. The set bit
for PIN01 was used to control the readout of the ADC containing the signals from
all three PIN detectors, as well as signals derived from the PIN detectors, including
those from time-to-amplitude converters (TACs) used to measure time-of-flight. Tim-

ing signals from the CFDs of all three PIN detectors were distributed to VME SIS

57

 

 

Tennelec Tennelec 810 C
_ AEN V785
TC178 Quad."" TC248 (Unipd’lar) ADClO

Preamp Amplifier
VEast
utput

Tennelec
TC 4 5 5 S§S3820
Quad.CFD ca er

i
200 ns CAEN V977 PINOI

Delay Coinc. Reg. only

i
CAEN V775 Common

TDC (“09) HESS?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.6: Schematic diagram of the signal processing electronics for the three PIN
detectors used in NSCL experiments 07509.

3820 scaler modules for rate monitoring, and to time—to—digital converters (TDCs) as
a stop signal, where the module was gated with a common start derived from the
master trigger of data acquisition. Figure 3.6 is a schematic of the electronics for the
PIN detectors.

The master-gate trigger (MG) for data readout was derived using the discriminator
signals from the implantation detector, the DSSD. The MG for experiment 07509 was
generated in hardware by taking a logical OR of all of the front strips logically ANDed
with a logical OR of all of the back strips of the DSSD. The MG was vetoed by the
logical OR of signals from SSSD5 and SSSD6. The MG was more complicated in
the case of NSCL experiment 05101. The MG was generated by a logical OR of: (1)
DSSD front AND back, as described for 07509, (2) signal above threshold in any
of the 16 strips of the most upstream SSSDOl, and (3) signal above threshold in
the most upstream PIN01. A master gate live (MGLive) signal was derived in both
experiments from MG by requiring a hardware logical AND with a signal from the
data acquisition computer indicating not-busy. The MGLive signal was used to trigger

data acquisition, as well as to generate digitization gates for all ADCs, TDCs, and

58

 

 

MG NIM-ECL 8183820
Fan In/ Out Converter Sealer

 

 

 

 

 

 

 

 

 

 

CAEN V977
Coinc. Reg. Gate

 

 

 

 

CAEN V775 TDC
Common Start
DSSD CAEN V785
Gate/ Delay DSSD
MGLive f Generator ADCs Gate

Fan III/Out [ SSSD CAEN V785
Gate/ Delay SSSD
Generator ADCs Gate

ADClO CAEN V785

 

 

 

1

 

 

 

 

 

 

!

V

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L— Gate/ Delay * ADClO
Generator Gate
NIM-ECL 8183820
[Fan 31/03] Converter PH Sealer
NSCL Data
Acquisition Control

Figure 3.7: Schematic diagram of the trigger electronics for data acquisition of NSCL
experiment 07509.

the coincidence register. A schematic of the trigger electronics for 07509 is shown in
Fig. 3.7.

A critical requirement for fi-decay experiments with continuous implantation is
the ability to correlate implantations and their subsequent decays, and have a measure
of the time elapsed between the events. To this end, each event included a timestarnp
generated by a SIS3820 sealer module specially configured to act as a 50—MHz clock.
The 32-bit clock data word, which had a resolution of 20 ns per clock tick, was
scaled into a 24-bit parameter in software. This clock parameter, with a resolution of
5.12 [1.8 per scaled tick, was sufficient for the measurement of fi-decay half-lives in the

ms regime.

59

 

3.3.2 BCS calibrations

Each of the silicon detectors of the Beta Counting System was calibrated for energy
using a 228Th (1 source. An a spectrum was collected from the 228Th source for
each detector, containing sufficient statistics (~100 counts/peak) to allow position
determination of the four main (1 peaks below 8 MeV, in all strips including those at
the edge of the detector. Each strip was gain matched by adjusting a slope parameter
to place the lowest-energy (5.4 MeV) a peak at’channel 350 in a 9—bit histogram in
each strip of the detector. Calibrated spectra included, in addition to gain-matching,
adjustment by an offset determined by the pedestal of the ADC. A simple shift was
applied to each strip to align the first data channel for each strip at zero. Histograms of
the raw energy parameter for a representative strip (strip 20) on the front and back
of the DSSD are shown in Figures 3.8(a) and (b), respectively. Calibrated spectra
for the same detector strips following the gain-matching and offset adjustment, are
presented in Figures 3.8(c) and (d).

A 90Sr source was used to set energy thresholds for each silicon detector. The fi
decay of 90Sr has an end-point energy of 546 keV, but the daughter 90Y, which also
undergoes fi decay, has an end-point energy of 2.280 MeV [2]. The signal induced in
a 1 mm thick Si detector for such fi energies is a AE signal of order hundreds of keV.
Thus, the thresholds of detectors deep within the stack of the BCS detectors could
be checked even after other detectors were in place. Hardware thresholds were set for
each BCS detector (the DSSD and SSSDs) by comparing the analog output triggered
by the CFD output for the same detector channel on a digital oscilloscope. Spectra
were then collected for each strip using the 90Sr source, and software thresholds were
established based upon the position of the noise signal. The calibrated 90Sr spectra for
DSSD front strip 20 and back strip 20 are shown in Figures 3.8(c) and (f), respectively.
The arrow in the figures indicates the position of the software threshold, which was

applied when determining the signals contributing to sums, etc., in data analysis.

60

 

 

 

 

 

 

 

 

 

 

 

 

 

 
    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

431000.2(a)F2ront.20.hienergy £31000 (b) Back. 20. hienergy
8 800; 28Th 3 800 22 23Th
0 600; c) 600-
400% 400-
200;— W 200
G0“‘10072‘01'1‘7300‘400 500 00”‘100“200 300 400 500
Channel Channel
£1000:(C)Front.20.hiec @1000: (d) Back.20.hiecal
8 800: 228111 8 300: 228Th
c) 600; U 600:—
400; 400;—
200; J] J L 2002— [M
00‘ 100 200 300400 500 00400200300400 500
hannel Channel
«EZSOOE (e) Front.20.hiecal «'é’ 2500 (f) Back. 20. hiecal
: 905 :3 2000 .— 903r
O E O E
. 01500;
g 1000;—
i f software
0E 503E...- .thrsshsld .......
0 50 100 150 200 250 0 50 100 150 200 250
Channel Channel

Figure 3.8: Calibration spectra for a representative front and back DSSD strip from
NSCL experiment 07509. (a) and (b) are the raw ADC spectra for a 228Th source
on the front and back of the detector respectively, while (c) and (d) are the same
spectra following gain-matching and offset adjustment. (e) and (f) are calibrated 90Sr
spectra for the front and back strips of the DSSD respectively, from which software
thresholds were set.

61

 

3.4 Segmented Germanium Array

Detectors from SeGA [66] were used for monitoring prompt and fi-delayed ’y rays
during NSCL experiments 07509 and 05101. Each SeGA detector consists of a single
cylindrically symmetric, n-type high-purity Ge crystal, with a diameter of 7 cm, and
a length of 8 cm. The core electrode lies along the central axis of the detector. The
outside surface of each crystal is electrically segmented into 4 quadrants azimuthally,
and 8 x 10 mm thick slices longitudinally. The high segmentation of the SeGA de-
tectors is useful for in—beam '7-ray spectroscopy experiments with fast beams, where
a Doppler correction to the '7-ray detected energy is critical for achieving the best
possible resolution [66]. However for the case of fl-delayed 'y-ray spectroscopy, the
nuclei are stopped before ’y-ray emission. Therefore determination of the position of
interaction from the segmentation of SeGA is not required, and only the central con-
tact signal for each SeGA detector was read out during NSCL experiments 07509 and
05101.

A total of 16 SeGA detectors were mounted in a close-packed geometry surround-
ing the beam pipe containing the BCS detectors, as shown in Fig. 3.9. The detectors
were arranged in two concentric circles of eight detectors each, a configuration known
as ,B-SeGA or barrel-SeGA. The crystal of each detector was oriented with its long
axis parallel to the beam pipe, face to face with a detector in the opposite ring. The
array was positioned such that the implantation detector of the BCS defined the
plane between the two rings of detectors. The electronics for the SeGA detectors, and
details of the energy and efficiency calibrations for the array are described in the next

sections.

3.4.1 Electronics

A schematic of the SeGA electronics is presented in Figure 3.10. 'I\1vo identical output

signals are available from each SeGA detector from the internal preamplifier attached

62

 

Secondary Beam

Figure 3.9: Geometric arrangement of the 16 SeGA detectors surrounding the beam
pipe containing the BCS silicon detectors.

to the central contact signal. These two identical signals were distributed through
different pathways to provide both timing and energy signals. One signal was sent to
an Ortec 863 timing fraction analyzer (TFA) for fast shaping, and then into a Tennelec
TC455 constant fraction discriminator. One of the CFD outputs was delayed, and
used as the stop signal for a Philips CAMAC 7186H TDC that was started by the
MGLive signal. A second CFD output was sent to-a VME SIS3820 sealer module for
rate monitoring. The other central contact preamplifier signal was processed by an
Ortec 572 shaping amplifier and the unipolar output was digitized by a four—channel
Ortec AD413A CAMAC ADC. The ADC was gated by a signal derived from the
MGLive trigger. The width of this gate was set to 20 us to permit the detection
of isomers with half-lives in the ps range following implantation events. The time
between implantations and photon emission was measured by a time-to-amplitude
converter (TAC), which was started on the MGLive signal, and stopped by an OR of
all of the SeGA CFD outputs.

63

 

 

S 8G A Ortec
Ortec 572 _ AD413A Gated by
Central —~{ Preamp 1, M GLive

 

 

 

l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Amplifier Quad 8k
Contact v ADC
PhlllpS Start
Ortec 863 _ T311651? 1 7186H signal
Quad TFA f ' TDC from
_ SIS3820
' Sealer

 

 

 

Figure 3.10: Schematic diagram of the signal processing electronics for SeGA detec-
tors.

3.4.2 SeGA Calibrations

Energy calibrations were completed for the entire array of SeGA detectors before,
during, and after NSCL experiment 07509. TWO calibration sources were used to cali-
brate the full 4—MeV range of the y-ray histogram: a 56C0 source, for the high-energy
calibration, and a NIST-Standard Reference Material (SRM) source, containing the
radionuclides 154’155Eu and 125Sb, suitable from 40 keV to 1500 keV. Energy calibra—

tion data were collected by triggering the data acquisition system on a logical OR of

the CF D outputs for each of the 16 SeGA detectors. Calibration sources were placed

outside of the beampipe and moved during the run to ensure that each detector accu—
mulated sufficient statistics, ~50 counts in the 2.6 MeV peak of 56Co, to perform the
calibration. The calibration spectra were analyzed using the Oak Ridge Data Analysis
and Manipulation Module (DAMM) to determine the centroid and associated error
for the location of each ’y-ray transition, based on a Gaussian fit. Energy calibration
parameters were obtained from a third-order polynomial fit to the centroid for each
peak as a function of the known y-ray transition energy. A third-order polynomial was
required to account for both non-linearity of the detector response at low energies,
and a previously observed [67] non-linearity in the response of the Ortec AD413 ADCs

between low (<1.5 MeV) and high energies. Application of calibration parameters in

64

‘ 'th. ‘4-

software provided calibrated energy histograms for each SeGA detector. The energy
resolution of all detectors was 5 3.5 keV full-width at half-maximum (FWHM) for the
1.3 MeV transition in 60Co. During experiment 07509, one of the detectors of SeGA
exhibited poor gain stability, even shifting gain during a single hour-long run. Due to
the instability of this detector, it was omitted from all analysis, leaving a 15-detector
array for this experiment. All 16 detectors of the array were included in analysis for
the case of experiment 05101.

The residuals from the energy calibration applied to each SeGA detector are pre-
sented in Figure 3.11. The residual is defined as the difference between the known
7-ray transition energy and the value deduced from the calibrated spectrum. Vertical
error bars are the error in the centroid resulting from the fit of a Gaussian to a given
peak in the calibrated energy Spectrum. The residuals for the summed spectrum of all
15 SeGA detectors is given in Fig. 3.12. A conservative systematic error of :l:0.25 keV
was attributed to the energy calibration of the SeGA detectors. This error encom-
passes the complete distribution of the residuals, and corresponds to approximately
twice the root-mean square residual value. The errors quoted for 'y-ray energies in
the present work were determined by adding, in quadrature, this error from the en-
ergy calibration (i025 keV), and the error in the centroid of the peak locations as
determined using DAMM.

One of the SeGA detectors, SeGAll, had to be recalibrated due to a gain shift
during the course of experiment 07509. Well-known 'y-ray transitions from nuclides in
the cocktail beam made a recalibration possible. The 'y—ray transitions used to recal—
ibrate SeGAll during experiment 07509 are summarized in Table 3.1. The residuals
of the fit to these known transitions before the new energy calibration was imple-
mented is depicted in Fig. 3.13(a), while the residuals with the corrected calibration
are shown in (b). The recalibration did not alter the 21:0.25 keV systematic error for
the full array attributed to the energy calibration. The gains of all other detectors

were checked for gain shifts by monitoring the location of well-known transitions in

65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

S‘ 0.6 SeGAOI 2- SeGAOS .. SeGA09" SeGA13-
U _ . l l l T . i i ,: l 1 j
:3 n - ' - 1 l . ' V l , L , 1 ' , l ' - .v '
g V ' 1 1.. . 1 "HT 1.. 1
30.6 . . ‘ 1 , ‘ ‘ . ‘ E | . . ‘ E
'5‘ 0.6_ SeGAOZ ; SeGA06 » SeGAIOj SeGA14:
é 0;Omitted£rom_r . mi +_.1i'-. . ’ l . ‘u .. 17,. Q
- ' ’7‘? ' I " i
: analySIS l E , E E
0.6_ SeGA03 7: 1 SeGA07 _j SeGAll :: SeGAlSE
u ‘. + in '. t '7. .-. A , l7“ “hi. i l
U 1 1. ' 1 1 ' r ‘ .. ' T .
_ 1
0.6: SeGA04 _ } SeGA08‘ _: SeGAlZ; SeGA16E
ni' 'lnl l l -—».' .l L. 7". .'+ + A‘.* ..L1l A l,
u_. ’1 _ .,. q; |-. {11. 1,
41-6“Ass-niinnnl-n--n;nwwn.1;
0 1000 2000 J 1000 2000 3 1000 2000 ) 1000 2000

Energy (keV)

Figure 3.11: Residual plots for the 15 individual SeGA detectors included in the
analysis of data from experiment 07509. The residual is defined as Elfinm — E2”.

:l:0.25 keV

 

 

500 1000 1500 2000 2500
Energy (keV)

Figure 3.12: Residual plot for the sum of all 15 SeGA detectors used in experiment
07509. A systematic error of i025 keV (marked by the shaded bands) was attributed
to the SeGA energy calibration.

Table 3.1: Known 'y-ray transitions used to perform a re-calibration of SeGAll during

experiment 07509.

 

 

Source of Transition E7 (keV)
54Sc isomer decay 110:1:1.0 [68]
57T1 decay 174.8104 [69]
57v decay 267.8103 [70]
55T1 decay 3234104 [71]
56V decay 668.4:le.3 [70]
55Ti decay 672.5i0.4 [71]
57v decay 692.4104 [70]
58V decay 879.8104 [70]
5481: decay 10012105 [31]
56V decay 10061103 [70]
58v decay 10564104 [70]
“Se decay 14948108 [31]
57Ti decay 18615104 [69]
58V decay 22175104 [70]

 

the data, but no other corrections were necessary.

Absolute peak detection efficiencies were deduced for each SeGA detector by plac-
ing the SRM standard source at the position of the DSSD within the vacuum chamber.
Two calibration data sets were collected in parallel for each detector, one set using
the N SCL data acquisition system (DAQ) triggered on the output of the CF D for the
SeGA detector of interest, and the other using a PC—based multi-channel analyzer
(MCA). The PC-based MCA collected data independent of the DAQ trigger, and
recorded data for a dead-time adjusted total of 3600 3, thus assuring a true measure-
ment of the absolute detector efficiency. The DAQ system was known to have a trigger
rate dependence, but ambiguity in the ADC dead-time correction made absolute ef-
ficiency determination less certain. Thus, the two independent systems were used to
cross-check one another and ensure a good determination of the 7-ray efficiency of the
array. Peak efficiencies were deduced by comparison of the observed emission rates as
detected by SeGA with the known activity of the isotopes in the SRM source. A rel-
ative efficiency measurement for photon energies above 1.5 MeV was also completed

using a 56C0 'y-ray source. Data was taken using only the DAQ system, triggered by

67

 

(a) Original Calibration

g—e

fITTlllllllllllllllll lllllllll
an

 

Residual (keV)
O

[1

1111 llllLLlJlllllllllll llllllLLlllllleLlllAl

(b) Re- fit Calibration

[ l]
1[Hl[l[ [

400 800 i200 160011’2000‘l‘2‘400
Energy (keV)

 

0.6
0.4
0.2

 

Residual (keV)

-0.2
-0.4

-O.6

r—.—_—.

[[llllTTlllll llllllllllllllrglflllllTl—rl

 

 

 

on

Figure 3.13: Residuals for the energy calibration of SeGAll during gain-shifted runs
using (a) the original energy calibration, and (b) a re-fit energy calibration based
upon known 'y-ray transitions within the data.

68

 

 

 

 

log [Peak Efiic1ency]
b c':
\O \)

 

 

 

 

 

‘ O y = -0.14x5 + 1.31x4 - 3.82x3 X
+ 0.33x2 + 13.99x - 16.12
-1.5 ‘9
'1. i t g =
71.5 2.0 2.5 3.0 3.5
log [Energy (keV)]

Figure 3.14: Peak detection efficiency curve for N SCL experiment 07509. Data points
represent measured efficiences using the NSCL data acquisition system. Data were
fitted with a fifth-order polynomial, denoted by the solid line.

a. logical OR of the individual SeGA detector CFD outputs for the relative efficiency
measurement. Peak efficiencies were deduced from the 56Co data by assuming the
same absolute efficiency for the 873.2 keV transition in 154Eu from the SRM source
and the 846.7 keV transition in 56Co, and normalizing the other transitions in 56Co
to this value based on known relative intensities. The resulting efl'iciency curve for
SeGA for experiment 07509 is shown in Figure 3.14, and was fitted with a fifth-order
polynomial. The peak efficiency for the array corresponds to 6.6 % at 1 MeV and 3 ‘70
at 3 MeV. Similar peak efficiencies were obtained, and an analogous efficiency curve

produced for NSCL experiment 05101.

3.5 Data analysis: Correlations and data fitting

The previous sections of this chapter provided details of the physical experimental
set-up used in NSCL experiments 05101 and 07509, including the beam delivery,
detector systems, and electronics. This section describes the other critical component

of correlation experiments with continuously implanted beams: the logic and methods

69

used to build up correlations from the data and to extract the values of interest,

including half-lives and decay branching ratios, in a robust manner.

3.5.1 Implantation-decay correlations

The method of continuous implantation fi-decay spectroscopy relies on the ability to
correlate individual implantation events with their subsequent 6 decays. The method
makes use of both position and time information to perform the correlations.

Each event was evaluated in software to determine the nature of the event. Raw
signals from each detector were calibrated and compared to software-defined upper
and lower thresholds. Software flags were set to indicate valid data for those detectors
in which signals satisfied the threshold requirements. Additionally, for the segmented
detectors in which multiple strips may have had valid signals for a given event, the
energies observed in each strip were evaluated to localize the event to a single strip.
The spatial position, or pixel (56,31) of an event in the DSSD was defined to be the
front and back strip with the largest recorded energy signal.

Implantation events were identified as those with a valid signal in each of the
upstream PIN detectors (PINl, PIN2 and PIN3) as well in the low-gain histograms
of both a front and back strip of the DSSD. Implantation events additionally required
the absence of a valid signal in SSSDl. When these conditions were met for a given
event, the event was positively identified as an implantation and the AE, time—of-fiight
and time—stamp information was stored within a two-dimensional array in software,
in the array element corresponding to the (113,31) position of the pixel of the DSSD to
which the implantation had been localized.

Decay events were identified as those events which had no valid signal in any of
the upstream PIN detectors but had a valid signal in the high-gain histograms of
both a front and back strip of the DSSD. Once an event was assigned as a decay, a
series of checks were made based on time and position to correlate the decay event

with a previous implantation. The (11:, y) position of the decay event was checked to

70

 

see the last time that an implantation event occurred at the same geometric location
within the DSSD. Only identical (as,y) coordinates were considered in the case of
experiment 07509 (implantation rates of ~100 Hz). When rates were sufficiently low,
as in the case of the other experiment 05101 (average implantation rate ~30 Hz),
the correlation position was extended to also allow correlation of a decay with an
implantation in any of the eight nearest neighbor pixels (mil, yil). If an implantation
event had occurred, an additional check was made to ensure that there had not
been back-to-back implantations in that pixel within a short time frame, which could
cause ambiguity in assigning a decay to one implantation over the other. Once the
integrity of the implantation was verified, the time between the decay event and the
implantation was checked to ensure that the event had occurred within a pre—defined
correlation time window for each isotope, established as some multiple of the expected
decay half-life. With the geometric and temporal conditions met, the decay event was
considered to be positively correlated with a previous implantation.

Decay curves were constructed for all isotopes by histogramming the time differ—
ence between the implanted ion of interest and the correlated fl decay. Decay curves
were fitted as described in Section 3.5.2 and the half-lives deduced for each isotope.
Additionally, by integrating the decay curve for the parent isotope contribution, the
total number of detected 6 decays for the parent was deduced. Combined with the
total number of implanted ions from the particle identification spectrum, the aver-
age ,B-detection efficiency of the DSSD was calculated for each isotOpe. The average
,B-detection efficiency for all isotopes studied in NSCL experiment 07509 using a
single-pixel correlation was found to be 11.4i0.4%.

The basic requirements for correlation of an implantation and its subsequent decay
are well established. However, there are a number of variables which can be adjusted to
optimize the correlation efficiency based on the experimental conditions and expected
properties of the decay. The correlations are determined entirely by the constraints set

by the geometry and timing in analysis. The following section describes the adjustable

71

 

variables in the correlation procedure, and the choices made in the present analysis

based on implantation rates.

Implantation rates and correlation limits

As discussed in the previous section, the two time frames critical to the correlation
procedure are the minimum time between back-to—back implantations in a pixel, and
the correlation time window, corresponding to the maximum elapsed time over which
an implantation would be correlated with a decay. These time windows were adjusted
in the data analysis on an isotope-by-isotope basis to optimize the correlations, using
the expected half-life of the parent isotope. The correlation time windows were chosen
to be approximately ten half-lives of the parent nuclide, permitting a good determi-
nation of the parent, subsequent generations, and the background contributions to
a decay curve. The minimum time between back—to—back implantations was set to
match the correlation time.

To minimize random correlations certain conditions related to the rate of events
in the detector must be met. The implantation rate must be sufficiently low that, on
average, the time between back-to—back implantations in a pixel is greater than the
length of the correlation time window. The overall implantation rate for experiment
07509 was ~100 Hz. However, these implantation events were not distributed evenly
over the detector surface. The beam profile was such that pixels near the center of
the detector experienced a higher implantation rate than those at the edge of the
detector. An average of less than 5 s separated implantations in the most central
pixels of the implantation DSSD. The average time between implantations for each
pixel of the surface of the DSSD is shown in Fig. 3.15(a). However, for most nuclei
included in experiment 07509, even the highest implantation rate allows a sufficiently
long correlation time window. A more significant problem was posed by the build-
up of activity from subsequent generations in pixels with higher implantation rates.

With an average of four 6 decays to reach stability from each implanted fragment,

72

the accumulated activity in the detector creates a background of random correlations
in all spectra. In Figure 3.15(b) is shown the average number of observed fl-decay
events occuring in a one-second time interval in each pixel of the detector. Assuming
the average ,B-detection efficiency of 11.4:t0.4%, the average rate of ,6 decays is more
than 3 / s in the most central pixels. The higher background rates increase the chance
of random correlations, and both *y-ray spectra and half-life curves will have pixel-
dependent background contributions.

The non-uniformity of the beam profile was used to provide an alternate analysis
of decays which required a longer correlation time window. A cut was made in position
based upon the time between back-to—back implantations, and only a subset of pixels
corresponding to those with >100 s between back-to-back implantations was used
for the primary analysis of isotopes with longer half—lives. The pixels satisfying the
cut are shown in Fig. 3.15(c). The back-to-back implantation rate requirement was
used in software to limit analysis to the N800 pixels, or half of the detector surface
on the edge of the detector with lower rates. Imposing this restriction did not affect
the average fi-detection efficiency for a single-pixel correlation, but did result in a
reduction of statistics by a factor of ten.

The benefits of making a restriction on the back-to-back implantation rate are
best illustrated in an example. The 6 decay of 55Ti is reported to have a half-life
of 1.3:l:0.1 s, and 9 7—ray transitions have been previously reported [71]. 55Ti was
a component of the cocktail beam in NSCL experiment 07509, and its decay was
examined for both the subset of pixels of the DSSD shown in Fig. 3.15(c), and all
pixels, with a correlation time window of 5 s. The resulting fi-delayed 'y-ray spectra
are presented in Figs. 3.16(a) and (b) respectively. The known transitions in 55Ti
and its daughter 55V are marked by the filled circles. The background contribution
to the spectrum of Fig. 3.16(a) is reduced in the spectrum of Fig. 3.16(b), while the
known transitions are apparent in both spectra. The half—life curve is also affected by

background, as illustrated in Figs. 3.16(c) and (d) The decay curve generated from

73

v—tr—A
O
031D-

(a)

Time between
implantations (s)

 
 

<5.
Time between
implantatlons (s)

102

101

 

DSSD Back Strip

Figure 3.15: Rate profiles over the surface of the implantation DSSD. (a) shows the
average time, in seconds, between implantations for each pixel of the DSSD. (b) is the
average number of decay events in a given pixel within a 1 second time interval. (c)
illustrates the pixels of the DSSD in which the time between implantations is 2100 s.
This rate requirement, which encompasses 1/2 of the DSSD pixels, was applied in

analysis to select a subset of pixels.

74

 

 

    

 

 

 

    

 

 

 

 

 

 

 

 

 

 

E 2000:; (a) All pilJSCIS a F (C) T1/2([3) = 2.2:h0.l ms
N 1600:- x 8 .. All pixels
a 1200: $104.
‘5 ° ° :3 :
8 800?” g
U 403: 8 55TI
3, gogw)..Edge pixilf ‘ " ‘é’ (:d)T1/2(B)- — 1. 310. 2ms
N 605— 0 x 8 Edge pixels
\ . N
:2 g
t: 402- 4.:
8 7 ‘3 55Ti

20; 0100 bk d
U 0: U C' ............................ g..-

0 400 800 1200 1600 2000 0‘” i000 2000 3000,4000 5000

Energy (keV) Time (ms)

Figure 3.16: (a) and (b): fi-delayed 'y-ray spectra following the decay of 55Ti for data
taken from (a) all pixels of the DSSD, and (b) only pixels near the edge of the DSSD,
in which the time between implantations was 2100 s. (c) and (d): B-decay curves
derived from data using (c) all pixels of the DSSD, and (d) pixels near the edge of
the DSSD.

all data in Fig. 3.16(c) was fitted with an exponential decay for the parent, the growth
and decay of the daughter 55V, and a constant background. The resulting fit gave a
half-life a factor of two longer than the known value. The decay curve resulting from
data in the edge pixels only [see Fig. 3.16(d)] was fitted in the same manner and the
deduced half-life is in good agreement with literature [71].

Primary analysis for data from NSCL experiment 07509 was restricted to the
subset of pixels with low implantation rates as described above when the required
correlation time window was greater than 1 s. This includes the analysis of the ,6
decays of 53Ca and 5‘I'Sc, discussed in the next chapter. The restriction to a subset
of DSSD pixels allowed a clean analysis of the decay properties of these longer-lived
isotopes. However, it would be preferable in future experiments to further defocus
the beam over the detector surface to reduce the implantation rate in the central
detector pixels. The loss in statistics due to fragments missing the detector would

likely be less than that arising from limiting the analysis region. The implantation

75

 

rate was considerably lower for NSCL experiment 05101; the total implantation rate
was ~30 Hz. It was therefore not necessary to limit the analysis to any specific region

of the DSSD.

3.5.2 Decay curve fitting methods

One of the key values that can be extracted from fi-decay spectroscopy data is the
half-life of implanted nuclei. A critical step in extracting a half-life from continu-
ous implantation data is the correct correlation of implantation events with their
subsequent decays, which was described in the previous section. Equally important,
however, is the method used to fit the decay curve data with functions describing not
only the decay of the parent nucleus of interest, but also contributions from decay of
the daughter isotope(s) and randomly correlated background events, which must be
included due to the <100% fl-detection efficiency of the DSSD.

Typically, fitting techniques require the minimization of a “goodness of fit” pa-
rameter, which often takes the form of a X2 value. A commonly used parameter is the

Gaussian X2» defined as follows [72]:

 

N 2

2 (311 - 3011(3))

XGaussian = Z 02 a (3.1)
i z

where y,- represents the 1th data point, with associated variance 01-, and y f,t(a) is the
fit to the data point, which is a function of the set of fit parameters, a. The best fit
parameters are determined by minimizing the value of x2 iteratively, by considering
the numerical derivatives of x2 with respect to each of the fit parameters, a.

Data from low count-rate experiments follow Poisson statistics [4], and the use
of X2Gaussian is not appropriate. An alternative method for nuclear counting experi-

ments with low statistics is to use the maximum likelihood of the Poisson probability

76

distribution. The likelihood function (L) for Poisson statistics is given by [73]:

N

N [Jyze—u
£=Hamw=fl W, (M)
t Z

 

where Pp(y,-, p) is the probability of measuring a value of y,, when the true mean of
the distribution is given by p, for N events. Taking the natural logarithm of Eqn. 3.2,

the log-likelihood function is given by:

N
ln£ = Emmy-p—lnyil]. (3.3)

i=1
With some rearrangement of Eqn 3.3, a version of the X2 statistic derived from
maximizing the log-likelihood function for Poisson distributed data can be expressed

as:

N
2&1; = ZZlyfit — yi 1n(yfit) + [M31101 (3.4)

2
where llfit is the fit to the data point yi. Minimization of this xi L correctly determines
the fit parameters for Poisson distributed data, irrespective of the procedure used to
histogram the event data.

Results are discussed in the next chapter which include half-lives deduced using
two distinct methods: a curve fitting method based within the ROOT data analysis
framework [74], which optimized a fit to the binned decay curve data, and a maximum
likelihood approach, where each instance of a correlated decay event is evaluated and
associated with a specific member of a decay chain, or to background. Both of these
methods used the Poisson statistical approach and are outlined in more detail in the

following sections.

77

Functional curve fit with ROOT

The majority of cases under consideration in the present study had good statistics, and
the half-lives were deduced from the decay curve data using a traditional curve-fitting
approach. A ROOT-based fitting program was written that provided a graphical user
interface and the option to customize the fitting function based on the properties of
a given decay. Fit functions were based on the Bateman equations for nuclear decay
processes including parent, daughter, and grand-daughter decays as required, with
the option of including [B-delayed neutron branching and the associated fin daughter
decays. Two fitting algorithms were available with the ROOT package: minimization
of a Gaussian X2, defined as in Eqn. 3.1, and maximization of the Poisson likelihood
function by minimization of the xi L statistic as defined in the previous section. The

latter method was applied for all decay curve fits discussed in Chapter 4.

Maximum likelihood analysis

The Maximum Likelihood (MLH) fitting method was based upon the maximization
of a custom log-likelihood function defined for a given data set. As applied to the
analysis of nuclear decay half-lives, the MLH method provides a mathematically cor-
rect description of the probability of observing chains of decay events, and thus makes
use of all available information, on an event-by-event basis, to deduce the unknown
decay properties. The MLH method and its application to low-statistics fl-decay data
are described in detail elsewhere [65].

No B decays in the present work were analyzed using the MLH method to deduce
a half-life value. However, the method was adapted to treat low-statistics isomer 'y-ray
decay data for 50K, discussed in the next chapter. The nature of 'y-ray decay, with
discrete energy transitions, allowed simplification of the MLH method as compared
to the treatment of 6 decay. As it is possible to discriminate 'y-ray decays based on
energy, there are essentially only two options for the identity of a decay event — a real

parent 'y-ray decay, or a random background event. Contributions from the decays

78

 

of subsequent generations in the likelihood function can thus be excluded. Gating
on a specific 7-ray energy also significantly reduces the background rates associated
with any given isomer decay event. The elimination of contributions from subsequent
decays and background greatly simplifies the MLH method, reducing the Poisson

log-likelihood maximization technique to treatment of individual data points.

79

Chapter 4

Experimental Results

The previous chapters have outlined the techniques of B decay and fi-delayed and
prompt 'y-ray spectroscopy, as well as the details of the experimental set-up for NSCL
experiments 05101 and 07509. Results from these experiments are presented in this
chapter.

Prompt 'y-ray information provided information on as isomers for nuclei implanted
in both experiments. fi-decay half-lives and ,B-delayed y-ray spectra were also obtained
from implantation-decay correlations as described in the previous chapter. 77 matrices
were constructed for events with 'y multiplicities of two or higher, allowing analysis of
'7 coincidence information. These data were used to establish level schemes. Combined,
the data obtained permitted considerable expansion of the knowledge of the neutron-
rich f p shell nuclei.

Experiment 07509 included over 20 neutron—rich nuclei in the region surrounding
540a, and provided new information on the quantum structure of the neutron-rich
53’54’3?Sc isotopes, both through the decay of the parent 53’33Ca nuclides, as well as
via prompt ’y-ray emission from isomeric states in the even-A 54'56Sc isotopes them-
selves. Prompt 7 rays from §8K were also observed in experiment 07509, providing

information on the low—energy structure of this nuclide. New data for the low-energy

structure of neutron-rich géMn was obtained from experiment 05101, via 6 decay from

80

the parent giCr isotope. This chapter presents results, including fl-decay half-lives, fi-
delayed 'y-ray information and prompt ’y-ray information, for 50K, neutron-rich 21Sc

and 2008. isotopes from N =32 to N =35, and 61Cr.

4.1 Low-energy structure of neutron-rich 218C
isotopes

The presence of subshell gap at N :32, the result of a sizeable energy spacing between
the V2123 /2 single-particle orbital and the higher-lying V2p1/2 and u1f5/2 orbitals, has
been observed experimentally in the 20C&, 22Ti and 24Cr isotopes. Additional to this
subshell closure, the possibility exists in the 20Ca isotopes for a N :34 subshell closure,
resulting from the continued upward shift of the V1f5/2 orbital attributed to a reduced
monopole interaction. Confirmation of the presence or absence of a N =34 subshell
closure in the Ca isotopes has been the focus of a number of experimental efforts in
the f p shell. The primary goal of experiment 05101 was to investigate the 5 decay
of 54K to states in 54Ca, with the hopes of populating the first 2+ excited state in
54Ca. Observation of the ’y—ray de-exciting the 2] state in 54Ca would have provided
a direct measurement of the excitation energy of the state, and when considered in the
systematics of the 20Ca isotopes, potentially the first evidence for a N =34 subshell
closure. However, only 73 54K implantations were observed after one week of running
time. The production yields proved prohibitively low for a successful ,8—7 measurement
during the allotted time.

Experiment 07509 was also motivated by the possibility of observing the ’y-ray
decay of the 2] state in 54Ca and measuring E(2f). Within the data of experiment
05101, 3 counts were observed at 327 keV in the ’y-ray spectrum collected within
15 ,us following 54Ca implantations. Could an isomeric state be present in 54Ca?
The possibility for such an isomer arises when low-energy 4' and 5' negative parity

states, an outcome of the coupling of the ”2121/2 and 1x1 99 /2 orbitals, are considered.

81

 

 

_110 keV
(54Sc contamination)

 

 

 

00 1000 2000 3000 4000
Energy (keV)

Figure 4.1: 'y-ray spectrum collected within 20 [IS following a 54Ca implantation. No
evidence of an isomer decay is observed. The peak at 110 keV is due to random
correlations with the 'y ray in the isomer decay of 5430

The isomeric decay from a 5" state in 54Ca would be expected follow the sequence
5‘ —> 3] -—+ 2] —> 0]". Thus, the goal of experiment 07509 was to investigate the
possible isomeric decay of 54Ca, and measure the energies of the ’y—ray transitions
involved, in particular that of the 21L ——1 0:“ transition, expected to be 22 MeV. The
'y-ray spectrum collected within 20 us following a 54Ca implantation in experiment
07509 is shown in Fig. 4.1. No evidence of an isomer was observed.

While the structure of 54Ca has proven difficult to probe directly at present, the
possibility of an N =34 subshell closure at Z =20 can be investigated indirectly by
considering the level structures of neighboring isotopes, e.g. the 21Sc isotopes. The
low-energy structure of the Sc isotopes should be described by the coupling of the
single valence f7/2 proton to the valence neutrons. Thus, the low-energy levels in the
218C isotopes surrounding N :34 should be sensitive to the neutron single-particle
energy spacings, and may shed light on the possible N =34 subshell closure in the Ca
isotopes.

Four neutron-rich 21Sc isotopes from N =32 to N =35 were included in the cocktail
beam delivered to the NSCL 6 counting system in experiment 07509, as well as

three 20Ca isotopes from N :32 to N =34. The 20Ca isotopes provided access, via

82

their 6 decays and 6—delayed y-ray emissions, to the low-energy structure of their
daughter 2180 isotopes. Prompt 'y-ray emission in 54Sc complemented the decay data,
providing additional insight into the low-energy structure of this isotope. Prompt 7
rays provided the only access into the low-lying levels of 568C, for which the parent
56Ca was not produced with sufficient yield to permit 6—7 analysis. The results for
the low-energy structures of the Sc isotopes, determined both from decay of the Ca
isotopes and prompt 'y-ray emission from the Sc isotopes themselves, are presented

in the following sections.

4.1.1 6 decay of 53Ca to 53Sc

The 6—delayed ”y-ray spectrum for 53Ca in the range 0 to 3 MeV for decay events
within 5 3 following an implantation event is shown in Fig. 4.2. Due to the length
of the correlation time window used in the analysis of the 53Ca decay, this spectrum
includes only decays correlated with implantations isolated in pixels towards the edge
of the implantation detector, as discussed in Section 3.5.1. One transition is apparent
in this spectrum at 2109.0:l:0.3 keV, and has been assigned to the 6 decay of 53Ca.
This newly assigned transition has recently been confirmed in one-proton knockout
from 54Ti [75].

The decay curve constructed from 53Ca—correlated 6 decays with the additional
requirement of a coincident 2109—keV 7 ray is presented in Fig. 4.3(a). Extraction of
the half—life from the full data without a 7-ray coincidence requirement is complicated
by uncertain quantities, including daughter half-lives and neutron branching ratios,
which must be included in the fitting function. It is therefore desirable to additionally
gate the decay curve on a known *y ray, to remove contributions from both background
and subsequent decays in the decay chain. The newly observed 2109—keV "y ray could
be used in the case of 53Ca, and the full statistics of the DSSD could be used in this
case — the additional 2109-keV 7-ray coincidence requirement reduced background

events, allowing extraction of a clean decay curve. The 'y-gated decay curve was

83

 

 

VI

2109

(40

Counts {3 keV

N

II I IIII IIIT ITrr]

 

    

‘ l

[[1 1 . ~ [llllllll

00 500 1000 1500 2000 2500 3000
Energy (keV)

Figure 4.2: 6—delayed 'y-ray spectrum in the energy range 03 MeV following the decay
of 53Ca. The spectrum is limited to include ’y rays coincident only with 6 decays in
the subset of pixels near the edge of the DSSD. The transition assigned to the 6 decay
of 53Ca is marked by its energy in keV.

t—d

 

 

 

 

 

fitted with a single exponential decay and a constant background, yielding a half-life
value of 461i90 ms. This value is higher than the value of 230i60 ms previously
reported by Mantica et al. [76]. However, as noted in Ref. [76], the possibility of a
second 6—decaying state in 53Ca, which could account for the discrepancy between
the present result and previous measurements, cannot be excluded. A fit to the decay
curve without the additional 7 requirement is required to determine the total number
of observed 53Ca 6 decays. The fit to the un-gated decay curve, considering only
decay correlated with implantations towards the edge of the implantation detector,
and fixing the half-life at 461 ms, is presented in Fig. 4.3(b).

An absolute 'y intensity of 56:l:l2% was determined for the 2109—keV transition
from a Gaussian fit to the peak in Fig. 4.2, the absolute efficiency of the 15-detector
geometry of SeGA (4321:0270), and the number of 530a 6 decays (252) that were
correlated with fragment implantations, as determined from the fit to the decay curve
of Fig. 4.3(b). The absolute intensity of the 2109-keV transition suggests that the
majority of 6 intensity from the decay of 53Ca, excluding 6n contributions, proceeds
through an excited state depopulated by this transition. The 2109-keV transition is

thus proposed to directly feed the 53Sc ground state, and the associated 2109-keV

84

 

(a) T1/2([3-y) = 461190 ms

Counts/ 250 ms

 

All I”!

 

Counts/200 ms

 

 

 

 

10”” 1000 2000 3000 4000" 5000
Time (ms)

Figure 4.3: 6-decay curves for the decay of 53Ca. (a) Decay curve constructed consid-
ering 6-decay events correlated with 53 Ca implantations over the entire surface of the
DSSD, with the additional requirement of a coincident 2109-keV decay 'y ray. These
data were fitted with a single exponential decay and a constant background. (b) De-
cay curve constructed considering only data in the subset of pixels near the edge of
the DSSD, with a correlation time of 5 s. Data were fitted with an exponential decay
of the parent, with the half-life fixed at 461 ms, growth and decay of the 6 and 6n
daughters, assuming a 40% neutron-branching ratio [77] and a constant background.

85

(1/2)_ 0

 

    

 

53Ca T1/2 = 461 i' 90 ms
Q; = 9.2 i 0.3 MeV
Sn : 53 i 0.4 MCV £4. ‘5‘,“ ,__.,_.,§.‘._, '1': \\ 3(+) 0
9” 523C
1‘3 (%) 10g fi‘ Q0]

/2- \
56i12 4.5:0.2(3 ) "’ 2109'”

 

 

(7/2)- H 0
53Sc

 

Figure 4.4: Decay scheme for the decay of 53Ca to states in 5380. The number in
square brackets following the 'y-ray energy is the absolute 7—ray intensity. Apparent
log f t values were calculated based on the apparent fl-feeding values, the deduced half-
life and the excitation energy of the state [79]. The decay Q value, Q3, and neutron
separation energy, Sn, were deduced from data in Ref. [80].

state is tentatively assigned spin and parity (3 / 2)‘, on the basis of selection rules for
allowed [3 decay from the presumed (1 / 2)“ 530a ground state [76,78]. The proposed
level scheme for 5380 following the ,8 decay of 53Ca is shown in Fig. 4.4, including the

apparent fl-feeding branches and log f t values.

4.1.2 6 decay of 540a to 54Sc

The fl-delayed 7-ray spectrum following the decay of 54 Ca in the range 0 to 2 MeV is
shown in Fig. 4.5. With the short correlation time of 1 3, data from the entire surface of
the DSSD could be included in the analysis. One transition at 247.3i0.3 keV has been
assigned to the 6 decay of 540a. The absolute intensity of this single transition was
deduced to be (65i9)%. This transition corresponds to the 7 ray previously observed
by Mantica et al. [76] at 246.9i0.4 keV with an absolute intensity of (97:1:32)%.

The 247—keV transition is placed as a ground—state transition and the 247-keV state

86

 

360:— 247
N50:—
>, E
54°?
83°;— §Cr
20g-
10:—

 

  

 

 

0 500 1000 1500 2000
Energy (keV)

Figure 4.5: fi-delayed 'y-ray spectrum following the decay of 540a to states in 54Sc, in

the range of 0-2 MeV. Observed transitions assigned to the decay of 54Ca are marked
by their energy in keV, while transitions in the 6 decay of the daughter 54‘Sc are

marked by a filled circle.

assigned J 7r:(1)+ based on the apparent allowed 6 decay to this level from the 0+

540a ground state. As discussed by Mantica et al. [76], the 247-keV state populated in
the decay of 540a de-excites promptly (within a few us). A prompt 247-keV transition
from a 1“” state to the 54Sc ground state precludes a J "24+ assignment for the 54Sc
ground state, as Weisskopf estimates for a 247-keV M3 transition would suggest a
half-life of order days. The observed fl-feeding pattern to states in 54Ti from 54Sc
had previously limited the ground state spin and parity to (3,4)+ [31]. The present
result suggests a 3+ assignment for the ground state spin and parity of 543C — a 247-
keV E2 transition is expected to have a half-life in the ns range, consistent with the
observed prompt nature of the transition. The unobserved ,8 intensity of 35d:9% can
be attributed to a possible fin branch in the 540a decay, as direct feeding to the (3)+
ground state of 54Sc is unlikely from the 0'Jr ground state of 54Ca.

The decay curve derived from 54Ca-correlated fl decays within 1 s of an implan-
tation event is shown in Fig. 4.6(a). The decay curve of Fig. 4.6(a) was fitted with
a single exponential decay for the parent 540a, exponential growth and decay of the
[6 daughter isotope, 54Sc (T1 /2 = 526 :l: 15 ms, see Section 4.1.3), and a constant

background component. The deduced half-life for the decay of 540a was 101:l:9 ms,

87

 

 

: (a) T1/2(B) = 104m ms

Counts! 25 ms
53

 

\
\
[‘1‘ ll

/2([3'Y) = 107:]:14 ms

111A

L “nil.”
. (b) T1

 

Counts/25 ms
8
l Til—ILL

 

 

y—n
' I
LII
A
0
E
—/
"."

Q
llllllltlllll lLlLlll‘ l .111 I’LILJJ

0 200 * 400 600 so ‘iboo
Time (ms)

 

Figure 4.6: fi-decay curves for the decay of 54Ca. (a) Decay curve constructed from
54Ca—correlated B—decay events over the entire DSSD surface, using a correlation time
of 1 5. These data were fitted with an exponential decay of the parent, growth and
decay of the 6 daughter, and a constant background. (b) The decay curve for 540a,
with the additional requirement of a 247-keV decay 'y ray coincident with the 6 decay.
The curve was fitted with a single exponential decay and a constant background.
within 10 of the value of 86i7 ms reported by Mantica et al. [76]. The difference in
the deduced half-life value is a result of the new, longer half-life for the 54Sc daughter
nucleus (see Section 4.1.3). A fit to the present data using the previous 54Sc half-life
of 360i60 ms [31] used by Mantica et al. gave a half—life value of 88i13 ms. Shown in
Fig. 4.6(b) is the decay curve obtained by requiring a coincidence with the 247—keV
B-delayed 'y ray observed in the 540a decay. The 247-keV *y-gated decay curve yields
a half-life value of 107i14 ms, again consistent with both the un—gated decay curve
' and the previous value reported by Mantica et al. [76]. The proposed decay scheme

for levels in 548C populated following the 6 decay of 540a is shown in Fig. 4.7.

88

54 Tl/2= 107i14 ms
Ca \zf 10.3:03 MeV

 

 

 

 

 

E4444 ~- 444 44 Bu: (3549)%

Sn: 4,740.5 MeV *" 6:8 (7/2)-53 0
9‘03” Sc
1,, (%) logfl‘ «(4’
+ “lab,

65:9 45:02 (I) 2473

O)" o

54SC

Figure 4.7: Decay scheme for 54Ca. The energy of each state is given in keV, and the
number in square brackets following the 'y-ray energy is the absolute 7—ray intensity.
Qg and Sn were deduced from data in Ref. [80].

4.1.3 3 decay and isomeric structure of 54Sc

Analysis of the 6 decay of 54Se used a correlation time of 5 s, with primary analysis
restricted to the subset of pixels towards the edge of the implantation DSSD, as
discussed in Section 3.5.1. The fi-delayed ’y-ray spectrum for 54Sc in the range 0 to
3 MeV is presented in Fig. 4.8. Twelve transitions were identified in this spectrum.
The four lowest energy transitions were eliminated as candidates for transitions in
the decay of 54Sc on the basis of their apparent half—lives, and likely belong to the
decay of the daughter nucleus, 54Ti. 7*)! analysis indicates that these four transitions
are in coincidence with one another, and the lowest energy transition at 108 keV
corresponds to a known transition in 54V [68]. The remaining eight transitions are
assigned to the 6 decay of 54Sc, and are summarized in Table 4.1. The transitions
observed at 1002, 1021 and 1495 keV were observed previously in 3 decay [31] and

deep-inelastic studies [81].

The decay curve for 54Sc—correlated decay events including decay events over the

89

 

 

\l
C

rérlrlr
.

A
l 495

Counts/keV
O

Au:
O

[I 1111 IIITFII

 

    

NW
CO

 

p—u
O

 

 

 

 

O

o 500 1000 1500 2000 2500 3000
Energy (keV)

 

Figure 4.8: fl-delayed 7-ray spectrum following the decay of 54Sc, for 'y-ray transitions
in the energy range 0-3 MeV. Transitions in the decay of 54Sc are marked by their
energies in keV, while transitions belonging to the decay of the daughter are marked

by a filled circle. Transitions marked by shaded triangles were used to gate the fl-decay
curve of Fig. 4.9(a).

Table 4.1: Energies and absolute intensities of fi-delayed 'y rays assigned to the 6 decay

of 54Se. The half-life deduced from a 7—gated decay curve, considering data over the
entire surface of the DSSD, is also included for all transitions in which statistics were
sufficient to fit a curve.

E, (keV) Isbsolute (%) Initial State (keV) Final State (keV) Half-life (ms)

 

 

484.6 :l: 0.4 4 :l: 1 3000 2516 564i99
840.5 :l: 0.4 7 i 2 3338 2497 620i104
1002.4 :t 0.3 40 i 4 2497 1495.0 522:1:28
1020.8 :l: 0.4 9 :l: 2 2517 1495.0 556i53
1495.0 :l: 0.3 79 :l: 5 1495.0 0 525i19
1504.0 :l: 0.3 2 :l: 1 3000 1495 521i113
1965.7 :h 0.4 7 :l: 1 3460 1495 4582!:100

2517.5 :t 0.3 5 :l: l 2517 0 -

 

 

90

entire surface of the DSSD, with the additional requirement of a coincident 1002, 1021,
1495, 1504 or 1966-keV 7 transition, is presented in Fig. 4.9(a). A fit to these data
using a single exponential decay and constant background yielded a half-life for 54Sc
of 526:1:15 ms, longer than the value 360i60 ms determined by Liddick et al. [31].
One possible explanation for the discrepancy between the present half-life requiring
a coincident decay 7 ray, and the previous value would be the presence of a second
,B-decaying state in 54Sc. However, as noted by Liddick et al. [31], the ordering of low-
energy states predicted by the shell model is not supportive of a ,B-decaying isomer.
Additionally, decay curves gated on individual 7 transitions yielded half-life values
in good agreement with one another (see the last column of Table 4.1, which is not
indicative of an isomer.

Another possible explanation for the discrepancy between the half-lives is the
deconvolution of the previously observed fl-decay curve. A half-life of 2.1:l:1.0 s, used
in the present analysis, was determined in the 07509 data set for the daughter 54Ti and
is in agreement with, though slightly longer than the literature value [82]. Additionally,
the unobserved fl intensity in the present work is suggestive of a neutron-branching
contribution of ~20%. Inclusion of these factors, not considered by Liddick et al. [31],
would result in an underestimation of the parent half-life in the previous work.

The proposed levels in 54Ti populated by the 6 decay of 54Sc are shown in Fig.
4.10. Placement of the 1002-, 1021— and 1495-keV transitions follows the assignments
made in previous work [31,81], and is confirmed by both the absolute '7-ray intensities
of the transitions, and observed '77 coincidences. The new transitions with energies
484, 840, 1505 and 1965 keV were placed on the basis of the observed 77 coincidences,
as shown in Fig. 4.11. Energy-sum relationships were used to place both the 1505-keV
cross-over transition connecting the states with energies 3000 and 1495 keV, and the
2517-keV transition between the 2517-keV level and the ground state.

The apparent fl feeding and log ft values deduced from the absolute '7 intensities

are included in Fig. 4.10. J7r for the states with energies 1495, 2496 and 2517 keV are

91

 

 

(a) T1/2(B-y) = 5265:15 ms

H
I" I I T11

Counts/ 100 ms
ES
., . ....

 

fl
§.
. III! 1 VIII

Counts/100 ms

t—O
..§

 

 

 

 

0“" 1000 2000 3000 4000 5000
Time (ms)

Figure 4.9: Decay curves for the H decay of 543C to states in 54Ti using a correlation
time of 5 s. (a) Decay curve, considering data over the entire surface of the DSSD,
with the additional requirement of a coincident 1002, 1021, 1495, 1504, 1966 or 2518-
keV 7 ray (marked by the shaded triangles in Fig. 4.8). These data were fitted with a
single exponential decay and constant background. (b) 5480 fl-decay curve constructed
considering fl decays localized to the subset of pixels on the edge of the DSSD. The
decay curve was fitted with a function including a single exponential decay, growth and
decay of the daughter, ,Bn daughter and granddaughters, and constant background,
assuming a neutron branching ratio of 20%. The half-life of the parent 54Sc was fixed
at 526 ms, as determined from the 7-gated decay curve.

92

 

XS?‘
(4.5)+ 0” 110

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(3)+ l 0 Tl/Z = 526 i 15 ms
54SC QB: 11.4:0.4Mev
M44974
8,, = 6.8 : 0.2 MeV 9,031;
X/ ’

In (‘4') 1°31? gs“ XS -°‘\ «bx/‘10 3460
7:1 57:01 ‘9 193: 79\t.\"" x 3337
7:2 58:02 6,39 49°‘—\6x>\\x%\ x}

a
6:1 59:01 ‘* ‘6‘“ «6,901,901,; 3000
+ - Q- -
10:2 58:01 :+ v 15‘ (0’2 9°" /—-25‘7
33:4 53:01 fl w
0“”
a
66"“.
21:7 57:02 (2" ‘ " v ‘99 1495.0
0+ 11 ll 0

 

 

 

54Ti

Figure 4.10: Proposed decay scheme for 54Sc to states in 54Ti. The energy of each
state is given in keV. The number in brackets following the 7—ray transition energy is
the absolute 7—ray intensity. Apparent log f t values were deduced from the apparent 6
branches, the 54Sc half-life, decay Q value, and the excitation energy of the populated
states [79].

93

 

 

 
     
  

  

 

   
    

 

     

 

 

 

 

 

 

 

$2000 * (e) 1020-keV gate 1495[14]
516003
$1200
5 800
4
E 1002[48]
Q 5: \
£1 4; 1020[7] 315 1965[13]
5 33 g - 1020[12] \
8 2; 010 /
111 1111 “5
o | Ill L [11111111 0
E g: (C) 840-keV gate 1495[10] 2 33g) 1505-keV gat
Q 5: Q 2;
a 4: 1002[7] a» : 1495[4] ‘
: G » 1
E3, 8 »
U 2: i U 1
1
o, Mull“ JJ Illlllll.“ 9 lll
3205(6) 1002-keV gate 1495150] % 6:01) 1965-keV gate 1495113]
N16; :1 5:
\ ; \
i":12? :3 4,
g 3; 8 3“
U 4: 340m] U 2—
1
0 1.11.11 ‘1, lJLlrlllLJlJlflLhmHm
o 400 800 1200 1600 2000 400 800 1200 1600 2000
Energy (keV) Energy (keV)

Figure 4.11: (a) 'I‘wo-dimensional 'y'y coincidence matrix for 'y rays observed in co-
incidence with 54Sc~correlated decay events over the entire surface of the DSSD. 7
coincidence spectra gated on the (b) 485 keV, (c) 840 keV, (d) 1002 keV, (e) 1021
keV, (f) 1495 keV, (g) 1504 keV and (h) 1965-keV transitions in coincidence with a
54Sc-correlated fi—decay event. The number in square brackets following the energy is
the number of counts in the peak.

94

adopted from previous works [31,81]. Apparent allowed feeding to both the 2+ and
4+ states suggest a J 7' assignment of 3+ for the 54Sc ground state, in agreement with
the assignment made based on the fi decay of 540a into 54Sc, discussed in Section
4.1.2. No direct feeding is therefore expected to the 0+ 54Ti ground state. The missing
fl intensity can be accounted for by a fin branch of 16:1:9% in the decay. An allowed
,8 decay from the (3)+ 54Sc ground state limits the spin of the newly-placed states
with energies 3000, 3337 and 3460 keV to J 7' 2 2+, 3+ or 4+.

The '7-ray spectrum collected within a 20-ps window following a 54Sc implantation
event is shown in Fig. 4.12. Observation of a 110-keV isomeric transition in 54Sc was
first reported by Grzywacz et al. [68], where the 110-keV transition was assigned
E2 multipolarity, based on Weisskopf estimates. As shown in Fig. 4.12, the 110—keV
isomeric transition was observed with high statistics and an improved half-life for
this isomeric state was deduced. The prompt y-ray energy is shown as a function of
time after implantation of 54Sc fragments into the DSSD in Fig. 4.13(a). The 110—keV
transition is visible, with an intensity decaying with time. Fig. 4.13(b) is a projection
of the data in Fig. 4.13(a) onto the time axis, showing the time dependency of the
110—keV transition. This decay curve was fitted with a single exponential function with
a half-life for this isomeric state of 2.77:1:002 ,us. The present half-life value agrees
with measurement of Grzywacz et al. [68], but significantly improves the precision.

The improved precision of the half-life for the 110-keV isomeric transition in 54Sc
allowed confirmation, through comparison with Weisskopf estimates, of the E2 mu]-
tipolarity assignment for this transition. The (3)+ spin and parity assignment for the
54Sc ground state, and an E2 isomeric transition limits J7r of the 110-keV state to
J = 1, 5. A spin of J =1 is excluded by the non-observation of feeding to this state
by the fl decay of 54Ca. Thus, under the assumption of an E2 multipolarity for the
transition, the 110—keV isomeric state in 54’Sc is tentatively assigned a spin and parity
of J'”=(5)+, as was originally suggested by Grzywacz et al. [68]. However, this assign-

ment assumes a single-particle nature for the final and initial states. The situation

95

 

 

20000 1 10

16000

Counts/keV

1 2000

ll TllllllilTIlllllllIlll

8000

 

4000

 

llllhlllllllilll‘

 

C.)

mI I I I I I I . I I A . I 4 l—L—L—L—l—n
50 100 150 200 250 300
Energy (keV)
Figure 4.12: 7-ray spectrum in the range of 0—300 keV collected within the first 20 us

following a 54Sc implantation event. The 7—ray transition is marked by its energy in
keV.

 

         
 

 

200.82
$1805 100
a 16 ' 0
314
33 12 60
LS 100
>- 30 40
6
4 7 20
20
0 I I I I I I I I 0
a l (b) T172 (54Sc-110kev v)
:33 {- =2.77:0.0211s
g t
.. 1
“1000
E
U

 

WWW;
123456789
Time(us)

Figure 4.13: Time dependence of the 110-keV isomeric transition in 5480. (a) The
prompt 'y-ray energy plotted as a function of time following a 54Sc implantation. (b)
A projection of (a) onto the time axis. The data were fitted with a single exponential
decay to deduce a half-life for the isomeric state in 54Sc.

96

is less certain when more complicated wavefunctions involving configuration mixing
are considered. As will be discussed further in Section 5.1.2, a 4+ spin and parity

assignment for the 110—keV isomeric state may also be possible.

4.1.4 ,8 decay of 568C

The analysis of the 8 decay of 5680 only required a correlation time of 1 s, and the
full DSSD implantation detector could be used in the analysis. The 8—delayed 'y-ray
spectrum for 56Sc in the range 0 to 2 MeV is shown in Fig. 4.14. Nine transitions in this
spectrum have been assigned to the decay of 56Sc, and are summarized in Table 4.2.
Two additional transitions were assigned to the decay of the granddaughter nuclide,
56V (T1 )2 = 216 :l: 4 ms [70]) - no transitions are known in the decay of the daughter
56Ti (T1)2 = 200 : 5 ms [71]). The transitions with energies 592, 690, 751, 1129
and 1161 keV agree well with '7 rays previously observed in both ,8 decay [31] and
deep inelastic in-beam experiments [81]. In Ref. [31], it was noted that the transition
at 592.3:t0.5 keV was within the error of a known transition in 55Ti [83], and the
possibility of 8—delayed neutron emission was suggested. In addition to the 592—keV
transition, another known transition in 55Ti, at 1204 keV, is present in the 8-delayed
y—ray spectrum, confirming ,8-delayed neutron emission in the decay of 5680.

Liddick et al. [31] proposed two 8-decaying states in 56Sc: a low-spin state with
T1/2 = 35:1:5 ms, and a higher-spin state with slightly longer T1/2 = 60:1: 7. Given the
different spin values, the two ,8-decaying states were observed to populate different
levels in the 56Ti daughter. 'y-gated decay curves were generated for each ’y—ray tran-
sition identified in Fig. 4.14 and fitted with a single exponential decay plus constant _
background. The y-gated decay curves are presented in Figure 4.15, and the resultant
half-life values are summarized in Table 4.2. The values deduced from decay curves
gated on the 690 and 1161-keV transitions were 73d:10 ms and 78:1:9 ms respectively,
consistent within 10 of the previous half-life determination for the higher-spin isomer,

602t7 ms [31]. The transitions assigned to the 8n decay also have half-lives consistent

97

 

 

     

 

   
   
   
 

     

 

  

3602-

en:— 1129

840:: 690 1161

U E 59%: K
30: 751 _ 1467
20; 1/204]1495
10: (17'12

 

 

 

 

11.61611.1111..1.31‘.. ‘. .
800 1200 1600 2000
Energy (keV)

 

c?

 

Figure 4.14: 8-delayed 'y-ray spectrum in the range of 0-2 MeV following the decay of

56Sc to states in 56Ti. Transitions marked by their energies in keV are those assigned
to the decay of 56Sc. Transitions marked by a shaded square are attributed to the 8
decay of the grand-daughter nuclide, 56V.

Table 4.2: Energies and relative intensities of 8-delayed 'y rays observed following a

56Sc—correlated decay event and assigned to the decay of 56Sc. Observed half-lives for
'y-gated decay curves are also included.

 

 

 

E7 13””th Decay Initial State Final State T1/2
(keV) (%) Mode (keV) (keV) (ms)
591.7 i 0.3 14 i 2 8n 591.7 0 78 :1: 25
689.6 :1: 0.3 18 :1: 2 8 2979 2289 73 :1: 10
750.9 :1: 0.4 8 :1: 2 8 1880 1128.7 24 :1: 7
1128.7 i 0.3 48 :1: 4 8 1128.7 0 51 :t 6
1160.6 :1: 0.3 30 :1: 3 8 2289 1128.7 78 i 9
1203.5 :1: 0.3 8 :1: 1 8n 1795 591.7 68 :1: 19
1466.8 i 0.3 6 :1: 1 8 - - 60 :1: 13
1494.8 :1: 0.3 3 :1: 1 8 4474 2979 150 :t 44
1711.6 :1: 0.3 3 :1: 1 8 - - 29 :1: 10

 

 

98

with decay from the higher—spin state, as do the transitions with energies 1467 and
1495 keV.

The half-life of the lower—spin 8-decaying state in 56Sc was previously deduced
to be 35 :1: 5 ms from a two-component fit to the decay curve gated on the 1129-
keV 7 transition, which dep0pu1ates a state fed directly and /or indirectly by both
8—decaying states in 56Sc. 'I\1vo newly-identified 7—ray transitions with energies 751
and 1712 keV were found to have half—lives similar to that extracted previously for
the lower-spin isomer. These two 7 rays apparently depopulate states fed exclusively
by the lower-spin isomer. The weighted average of the half-lives for the 751- and
1712-keV transitions yields a half-life for the lower-spin isomer of 26 :1: 6 ms.

Levels in 56Ti and 55Ti populated in the decay of the two 8—decaying states in
5680 are shown in Fig. 4.16. The states in 55Ti are known from the 55Sc 8 decay
in NSCL experiment 07509 [84], previous 8-decay studies [31], and deep inelastic
work [83]. The three states at 1129, 2290 and 2980 keV in 56Sc were previously
identified and tentatively assigned spin and parities [31,81], which are shown in Fig.
4.16. 77 coincidences [see Fig. 4.17(a),(c),(d)] also confirm the placement of the 690-,
1129— and 1160—keV 7 transitions associated with these three levels. The observed 77
coincidences between the 1129— and 751-keV transitions [see Fig. 4.17(b),(c)] suggest
the placement of an additional state populated by the lower-spin 8—decaying state
at 1880 keV. 77 coincidences between the 1495— and 690-keV transitions [see Fig.
4.17(a),(e)] suggest that the higher-spin 8—decaying state populates a level at 4474
keV, in addition to populating the two states at 2290 and 2980 keV. Only the 1467-
and 1712-keV 7 transitions remain unplaced in the present level scheme for 56Ti.

Absolute 7-ray intensities were determined for the 8—delayed 7-ray transitions in
the 5680 decay by comparison of the number of observed 7 rays, adjusted for the abso-
lute efficiency of SeGA, with the number of observed 56Sc decay events. Typically, the
number of parent decays is obtained from the decay curve fit, as previously described

in Section 3.5.1. However, a precise value for 56Sc could not be obtained using this

99

 

 

 

  
   
 
  

       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
  
 

 

 

 

 

 

 

 

 

 

 

 

 

a — (a) T1/2(Bn-y)=78:25 ms £10 (1) Tl/2(Bn-y)=68:19 ms
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. U
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1: E a
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O O
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Q 10E 1160 keV
3 I
§ .
O
U 1:

c" 206‘ 400 606‘” 800 ”1000

 

 

Time (ms)

Figure 4.15: Decay curves for 56Se using a correlation time of 1 s, and data over the
entire surface of the DSSD, with the additional requirement of a coincident decay 7-
ray transition. Decay curves are gated on the (a) 592-keV, (b) 690—keV, (c) 751-keV,
(d) 1129-keV, (e) 1160-keV, (f) 1204—keV, (g) 1467-keV, (h) 1495-keV and (i) 1712-keV
7 rays in the decay. All curves were fitted with a single exponential decay (dotted
line) and a constant background component (dot-dashed line).

100

 

 

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101

 

DJ

§(a) 690-keV gal—“7 1160[7]
112915]
149512]

111111 11111.

(b) 751-keV gate

1-1111

690[5] (c) 1129-keV gate
7/51[2] fi60[3]

111111 1| 1. [1|

Counts/2 keV
YYTH'YITY YYITNITIT]

 

 

 

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Counts/ 2 keV
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Counts/2 keV
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E _. 690[9] (d)11601kev gate
”3i 112913]

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a 690[2]

a .- |

*a

:1

O

U

 

 

 

 

 

00 800““‘1‘2'00d‘i600d‘2000
Energy (keV)

b
.
J;

Figure 4.17: 77 coincidence spectra gated on the (a) 690-keV, (b) 751-keV, (c) 1129—

keV, (d) 1160-keV, and (e) 1495-keV transitions in coincidence with 56Sc-correlated
8-decay events. These coincident spectra include data within a 1 s correlation time,
for implants collected over the entire surface of the DSSD. The numbers in square
brackets following the energies are the number of counts in the peaks.

102

 

 

 

approach. The presence of the two 8-decaying states in this case results in a decay
curve fit with a large number of free parameters. Instead, the number of 5680 decays
was determined using the total number of implantations, taken from the particle iden-
tification, and the average 8-detection efficiency of 11.4:t0.4%. The absolute 7-ray
intensities are included in Table 4.2, and in the decay scheme of Fig. 4.16. Apparent
8 branches were deduced from the absolute 7—ray intensities. Decay from the higher-
spin isomer apparently p0pulates both the 4+ and 6+ states in 56Ti. This suggests
that the higher-spin isomer has J 7r25'", in contradiction to the previous assignment
of (6,7)+ by Liddick et al. [31]. However, the large Q5 value for the decay allows
the (4)+ state at 2289 keV to be populated by cascades from above, resulting in the
observed intensity difference between the 690- and 1161—keV transitions. Given this
possibility, the higher-spin 8—decaying state has been tentatively assigned as (5,6)+.
The state with an energy of 4474 keV, also populated by the higher-spin 8—decaying
state, has J7r limited to 4+, 5+, 6+ or 7+, depending on the spin and parity of the
higher-spin 8—decaying state in 56Sc.

Decay from the lower-spin 8—decaying state in 568C apparently directly feeds the
first excited 2+ state in 56Ti, which limits the spin and parity of this 8—decaying state
to 1+, 2+ or 3+. The J 7' for the 56Sc ground state can be further restricted if there is
direct 8 feeding to the 56Ti ground state. The absolute intensity of the 592-keV tran-
sition in the 8n daughter 55Ti suggests a lower-limit for the neutron branching ratio
of 14i2%. Even under the assumption that the two unplaced 7 transitions directly
populate the 56Ti ground state, there is 29i7% of the 8 intensity unaccounted for.
Two scenarios can account for the missing intensity: either direct feeding to the 56Ti
ground state or 8n decay populating the ground state of 55Ti directly. Each possibility
was investigated by reanalyzing the 8 decay of 5680 with the longer correlation time of
5 s. With a longer correlation time, it was possible to compare the intensities of 7—ray
transitions in the decay of the 8n daughter 55Ti (672.5 keV, Igbsome = 44:1:4%), and
the 88 granddaughter 56V (668.4 keV, 181’”th = 26 :1: 2%). Within a 5 s correlation

103

 

Table 4.3: Determination of the 8 and 8n contributions to the decay of 5680, based on
the observation of 7-ray transitions in subsequent decays within the 8 and 8n decay

 

 

 

chains.

5680 Decay Signature E7 Igbsomte Counts (5 8 Number of ‘70 of 56Sc
Decay Decay (keV) (%) Correlation Observed Decays
Mode Time Decays

5 56V4560. 6684:03 26:2 94:12 362:54 71:14
8n 55Ti—>55V 672.5:0.4 44:4 64:10 145:26 29:6

 

 

time, >90% of the 55Ti (T1 )2 = 1.3 :t 0.1 s [71]) populated in 8n decays would have
decayed, while 56Ti (T1 )2 = 200 :1: 5 ms [71]) populated in the 8 decay of 568C would
have decayed into 56V (T 1 )2 = 216:1:4 ms [70]), which would also have decayed. Thus,
the ratio of 8 to 8n decays in 568C can be determined by the ratio of the intensities of
the 668- and 673-keV transitions, which are detected with nearly the same efficiency
in SeGA.

The results of the 8n/ 88 analysis are summarized in Table 4.3. Approximately
70% of the decays of 568C populate states in 56Ti. Thus, the missing 8—intensity

cannot be fully accounted for by 8n decay to the ground state of 55Ti, and there is

apparent direct population of the 0+ 56Ti ground state. The higher-spin (5,6)+ 8-

decaying state cannot populate the 56Ti ground state directly, and so the lower-spin
isomer must decay directly to the 56Ti ground state. The apparent feeding of the 0+
56Ti ground state and the first 2+ excited state thus suggests a spin and parity for

the lower—spin 8-decaying state of J“=1+. Direct feeding from the (1)+ 8-decaying

state limits J7r of the state at 1880 keV to (0,1,2)+.

4.1.5 Isomerism in 568C
The 7-ray spectrum collected within a 20—118 time window following the implantation

of 56 Sc is presented in Fig. 4.18. Five transitions were observed, and are summarized
in Table 4.4. Those transitions with energies 140, 188, and 587 keV are in agreement

with the three transitions previously reported by Liddick et al. [31].

104

 

 

 

 

@140
\120—

Irlj

k

Counts

40
20

IIIIfiTIII III III III

 

 

48
140

 

188

 

11

 

587

727

 

”1'00 200300400 500 600 700 800
Energy (keV)

 

Figure 4.18: The prompt 7-ray spectrum collected within the first 20 [is following
a 5680 implantation. The 7 rays assigned to the isomer decay in 56Sc are marked
by their energies in keV. The additional peak visible in the spectrum at 110 keV is
contamination from the isomer decay of 54So.

Table 4.4: Energies and relative intensities of isomeric 7 rays observed in the 20 ,us
window following a 568C implantation event. Relative 7 intensities are corrected for
internal conversion [61], based on the transition multipolarity and energy. Transition
multipolarities were assigned based on Weisskopf half-life estimates.

 

 

 

E7 [relative Transition Total Internal Initial Final
(keV) (%) Multipolarity Conversion State State
Coefficient (atotal) (keV) (keV)
47.7 : 0.3 70 : 19 M1 (1.16:0.02)x10~7 775 727
140.5 : 0.3 61 : 7 M1 (66:01) x 10-3 727 587
187.8 : 0.3 61 : 8 E2 (2.63:0.04)x10'-2 775 587
587.2 : 0.3 100 : 12 M1 (2.34:0.04)x10-4 587 0
727.1 : 0.3 32 : 5 E2 (2.45:0.04)x10-4 727 0

 

 

105

 

keV)
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‘ 11.5‘L‘211i215‘”3.0
Time (118)
E (b) T1/2 (56Sc-isomeric y)
: +
3 10E 568C 290 _ 30 ns
23 Z
S : bkgd
O
U 1:— . i no” u on 0 00 «no
1;.'_ :.]“l—L‘- fl . I . I . . 1 .
I 2 3 4 5 . 6
Tlme (118)

Figure 4.19: Time evolution of the prompt 7-ray transitions in 56So. (a) Prompt 7-ray
energy plotted as a function of the time elapsed following a 563C implantation event.
(b) Projection of (a) onto the time axis, gated on the five prompt 7—ray transitions.
The data were fitted with a single exponential decay and a constant background.

The observed 7-ray energ is presented as a function of the time elapsed between
a 5630 implantation and prompt 7-ray emission in Fig. 4.19(a). The five transitions
with energies 48, 140, 188, 587 and 727 keV appear to decay with the same half-life.
Figure 4.19(b) contains a projection of the data of Fig. 4.19(a), gated on the five
isomeric transitions, onto the time axis. The resulting decay curve was fitted with a
single exponential decay and a constant background with a half-life for the isomeric
state in 568C of 290i30 us.

The low-energy structure of 56Sc populated by isomeric decay, presented in Fig. 4.16,

was established based on the observed 77 coincidences (see Fig. 4.20), and relative

106

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 8 (a) 48-keV gate %10§:(d)587-keV gate 140 22
i4 6 1401211 / <4 s;— 48[15] W20“ 1
+03 587[14] :3 6:
S4 5
o o 45—
U 72713]

2 \ U 2;—

O ‘ ' ‘ JM'HM'” O0 100 200 300 400
$10 48 [20] (b) 140-keV gate Energy (keV)
fi 3 587 [19] >
33 6 <1) f(e) 727-keV gate
G M .

:3 4 \ r 48121
o 59 :/
U 2 c: 1:
3E :3 ~
'I I .1 11.11.11. 0 ’—
g 2 (c)188-keV gate U E
M 587 [17] '. ......
E 4 C0 20 400 60 800
g Energy (keV)
0 2
U
0 111.1.
0 200 400 600 800

Energy (keV)

Figure 4.20: 77 coincidence spectra for the (a) 48-keV, (b) 140-keV, (c) 188-keV,
(d) 587-keV and (e) 727-keV transitions in the 20—113 time window following a 5680

implantation. The number of coincident counts are given by the numbers in square
brackets following the transition energies.

transition intensities corrected for internal conversion. Energy-sum relationships to
the cross-over transitions with energies 188 and 727 keV provided further support for
the proposed level scheme.

A novel approach was taken to determine which of the two 8—decaying states
in 56Sc is populated by the isomeric decay. A half-life curve was constructed in-
cluding only 8—decay events correlated with 56Sc implantations that were in turn
coincident with one of the five prompt 7 rays. The resulting decay curve is pre-
sented in Fig. 4.21. A fit to these data with a single exponential decay for the 56Sc

parent, growth and decay of the daughter (56Ti, T1/2 = 200 :1: 5 ms [71]) and grand-

107

 

«0100:-

E : T (isomer 56SC 1m lant-B)
8 1/2 3101’s

2 - 1 I 1

e 1

:1 10 .

8 1":‘l‘\ ] ] l ]

‘\
I».
1 ‘1
J
'1 X
I l, /
l ——11—
. .-
1 I
i—f—‘—‘.
. 1 .
I
I
II-I
I

H
I rrnilT—.L_111HH]

‘ n
U' "n

1 4
.. + e

_ 6..." 568cm 1 ”9%“ 56Ti1:\
.111111Hn1.l1.i.....l....l.:. l ....... L1...

200 400 600 800 1000

 

 

 

OS-

Figure 4.21: Decay curve for 56Sc-correlated 8 decays considering only 56Sc implan-
tations coincident with identified isomeric 7—ray transitions. The decay curve was
fitted with a single exponential decay, growth and decay of the 8-decay daughter and
granddaughter, and a constant background.

daughter(56V, T1/2 = 216 .1: 4 ms [70]), and constant background yielded a half-life
of 30:1:5 ms, consistent with decay of the lower-spin 8-decaying state, previously
assigned J“: (1)+ (see Section 4. 1. 4). Knowledge of the quantum numbers of the
lowest-energy state of the isomer ‘band’ permits tentative J 7' assignments for the
remaining low-lying levels populated in the isomeric decay of the isomeric state in
5680. The 188-keV transition, which directly depopulates the isomeric level, has E2
multipolarity, based on Weisskopf estimates (see Table 4.5). The 48—keV transition is
assigned multipolarity M 1, on the basis of the observed favourable competition with
the 188-keV transition, and comparison with Weisskopf estimates. It follows that the
140-keV transition must also have M1 multipolarity. The observed intensities of the
727-keV and 140-keV transitions depopulating the isomeric state then suggest the
former transition to be E2, which according to Weisskopf estimates, will proceed at a
comparable rate to the 140—keV M1 transition. Finally, the remaining 587-keV transi-
tion must have M1 multipolarity. These assignments lead to the tentatively assigned

7' = (2)+, (3)+ and (4)+ values for the states in 5680 at 587, 727 and 775 keV

excitation energy above the base state, assuming that the base state has J 7’ —.(1)+

108

Table 4.5: Weisskopf half-life estimates for the five prompt 7-ray transitions observed

 

 

 

 

 

 

in 5630.
E7 Weisskopf single particle half-lives
(keV E1 M1 E2 M2 E3 M3
47.7 4.7 ps 114 ps 209 ,us 5.9 ms 4.0 hours 1.5x106 years
140.5 184 is 4.5 ps 942 ns 27 118 7.6 s 92 years
187.8 77 fs 1.9 ps 221 ns 6.3 ,us 990 ms 6.7 years
587.2 2.5 fs 61 fs 738 ps 21 ns 339 118 2.1 hours
727.1 1.3 fs 32.2 fs 254 ps 7.2 ns 76 us 1084 s
4.2 Isomeric Structure of 5OK

The neutron-rich 19K isotopes with N Z 20 are situated on the border of two major
shells, with protons occupying the high-lying sd—shell single-particle orbitals, and
neutrons filling low-lying fp—shell orbitals. The low-energy levels in the K isotopes
are thus sensitive to the relative spacing of the proton single-particle orbitals below
the Z =20 shell closure. Recent evidence [85,86] suggests an evolution of the energies of
the 7rld3/2 and 71281/2 states for the K isotopes with N >28 outside of the predictions
of the most current sd- f p cross-shell effective interactions. The low-energy levels in
§8K31 are thus interesting to better understand the evolution of the proton single—
particle states below Z =20 with increasing neutron excess.

Isomerism in 50K was first reported by Lewitowicz et al. [87], with more details
included in the work of Daugas [88]. The prompt 7-ray spectrum for 50K implanta-
tions collected in this work is presented in Fig. 4.22(a). Three transitions are apparent
in this spectrum, at 43, 128 and 172 keV, and their details are summarized in Ta—
ble 4.6. The observed transitions are in agreement with those previously observed
by Daugas [88]. However, the additional two transitions with energies 70:1:1 keV and
101:1:1 keV also reported in Ref [88] are not apparent in the 7—ray spectrum depicted
in Fig. 4.22(a). Fragment-77 coincidences, shown in Fig. 4.23, indicate a coincidence
relationship between the 43— and 128-keV transitions, however, the ordering of these

transitions is not uniquely determined. The third transition at 172 keV in the spec-

109

Table 4.6: Energies, relative intensities and half-lives for the 7 rays observed within

the 20 us following a 50K implantation event. Relative intensities are corrected for
internal conversion [61], based on the transition multipolarity and energy. Transition
multipolarities were assigned based on comparison to Weisskopf half-life estimates
as discussed in the text. Half-lives for individual 7-ray transitions were determined
using the MLH method. A weighted average of the MLH values is also presented, as
well as the results of a fit to the data for all three transitions using the ROOT fitting
program.

 

 

 

 

E7 [felative Transition Total Internal Number of MLH
(keV) (‘70) Multipolarity Conversion Counts for Half-life
Coefficient (atom) T1/2 (ns)
42.8:0.3 84:22 M1 0107:0003 4 65733
128.4:03 75:15 M1 00059:00002 21 135%
172.2:03 100:19 E2 00287:00008 11 2293,35
MLH Weighted average: 154%: ns
ROOT fit: 158i27 ns

 

 

trum in Fig. 4.22(a) is placed as the cross-over transition, based on the energy-sum
relationship.

The time evolution of the 50K 7 rays is given in Figure 4.22(b). The three tran-
sitions observed in Fig. 4.22(a) are apparent, though statistics are low. The number
of counts are further reduced when considering only 7 rays with decay times greater
than 1 ps, after the background of prompt :1:—rays which occurs upon fragment im-
plantation into the DSSD. The 7-ray spectrum with this cut on the decay time is
shown in Fig. 422(0), and the low statistics are evident. The total number of counts
for each of the three transitions is summarized in Table 4.6.

An MLH analysis was used to extract the isomer half-life information due to the
low statistics for the observed 7 rays. The likelihood function (see Section 3.5) was
evaluated for each event, and maximized to yield a half-life value for each of the three
7 rays assigned to the decay of the 5OK isomeric state. The resultant half-lives are
listed in Table 4.6. The half-lives are consistent with one another, and a weighted
4+3

average yields a value of 15 _ ‘3 ns for the isomeric state with energy 172 keV in 50K.

110

 

> :
33100: (a) 172
N I 128
\
g 80_—
: 43
8 60—
U :

A
O
1

 

 

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

lllllLllllllllllllllllllilll1 1 1 1 1 1
0 50 100 150 200 250 300 350 400 450 500
Energy (keV)
9250-5 . . . - '
g; (b)
200:;
LII t...
1111-1 9.5.1.
10011-1135"
’ -
50 —" '
Hf '
1000
TAC Time (us)
> Z 128
$4) 105 (C)
E :
‘5 83' 172
O ..
C) 6:-
4}
2} 43 I

co
{)1
O

100 150 200 250
Energy (keV)

Figure 4.22: (a) 7-ray spectrum observed within the 20 ,us window following a 50K
implantation event, in the energy range of 0—500 keV. The transitions assigned to
the isomeric decay of 50K are marked by their energies in keV. (b) Time evolution
of the 7 rays observed following 50K implantations. The three observed transitions
are marked by arrows. (c) 7-ray energy spectrum of (a) with the requirement of a
TAC time greater than 1.0 ps, beyond the x—ray flash. The three counts with energy
199 keV in this spectrum are background.

111

 

 

    
   
   

 

:5 6» (a) 43-keV gate
5
E 4 .128 [14]
5 3
c
U 2 ]
1 7
> 0
3‘9 6 43 [12] (b) 128-keV gate
N 5
E 4
S 3
0
U 2
If

Not

(c) 172-keV gate ‘

 

 

 

>

U

#4

N

\

83

gl

0 .

U , 1i
‘ ‘1;

00 100200 300 400 500

Energy (keV)

Figure 4.23: 77 coincidence spectra gated on the (a) 43—keV, (b) 128-keV and (c) 172-

keV 7 rays observed within 20 us following a 50K implantation event. The numbers
in square brackets following the energy of a peak are the number of counts in that
peak.

112

Table 4.7: Weisskopf half-life estimates for the three prompt 7-ray transitions observed
- 50
in K.

 

 

 

 

E7 Weisskopf single particle half-lives
(keV E1 M1 E2 M2 E3 M3

42.8 6.5 ps 158 ps 359 as 10 ms 8.6 hours 4.1x106 years
128.4 241 fs 5.9 ps 1.5 11s 42 as 14.2 s 206 years
172.2 100 fs 2.4 ps 340 ns 9.6 as 1.8 s 14.7 years

 

 

The results of a decay curve fit, using the ROOT program with Poisson analysis,
to the summed data for all three transitions yields a value of 158:1:27 ns, consistent
with the average MLH result. Both half-life values agree with the value of 125:1:40 ns
reported by Daugas [88].

Comparison of the deduced lifetime with the Weisskopf estimates (see Table 4.7)
suggests an E2 multipolarity for the 172-keV transition. The competition of the 43-128
keV 7-ray cascade with the direct ground state transition from the isomeric 172-keV
state suggests that the multipolarities of the 43— and 128-keV transitions are M1. The
low-energy level scheme for 50K is presented in Fig. 4.24. Spins and parities for the
low-energy states populated in the prompt 7-ray decay of 50K are discussed in detail

in Chapter 5.

4.3 Structure of 61Mn from 8 decay of 61Cr

Below the Z :28 shell closure and approaching N :40, there is evidence in both the
24Cr and 26Fe isotopic chains of increasing collectivity, which develops below Z =28
with the approach of the 1g9/2 neutron orbital to the Fermi surface. While the onset
of collectivity has been investigated in the 24Cr and 26Fe isotopic chains, data in the
intermediate 25Mn isotopes is less abundant. The level structure of 61Mn will extend
the information in the Mn isotopic chain, and provide insight into the development
of collective behavior for Z =25.

Implanted 61Cr fragments were correlated with their subsequent 8 decays by re-

113

 

69’ x,
\‘ <11”
«999 (6,9679 x\s\
(3)- «f\‘ 611- 3’1 ’1718
tax/0'
(2)- 0“" 128 4

 

 

 

 

(D- 1 11 0

 

Figure 4.24: Proposed low-energy level scheme for 50K. The numbers in square brack-
ets following the 7-ray transition energies are the relative transition intensities. The
order of the two 7-ray cascade is not uniquely determined — the tentative 2‘ state
may alternately be located at an excitation energy of 42.8 keV.

quiring the presence of a high-energy implantation event in a single pixel of the DSSD,
followed by a low-energy 8 event in the same or any of the eight neighbouring pixels,
using a correlation time of 3 s. The decay curve for 61Cr-correlated 8 decays given
in Fig. 4.25 was fitted with a single exponential decay combined with an exponen-
tial growth and decay of the short-lived daughter, 61Mn, whose half-life was taken
to be 670i40 ms from Ref. [89]. A constant background was also included as a free
parameter in the fit. A half-life of 233:1:11 ms was deduced for the ground-state 8
decay of 61Cr. This new value compares favorably with the previous measurement
by Sorlin et al. [59] of 251i22 ms, but is more than 10 shorter than the 270:1:20 ms
value reported earlier by Ameil et al. [90].

The 8—delayed 7—ray spectrum from the decay of 61Cr is shown in Fig. 4.26. The
spectrum covers the energy range 0 to 2.5 MeV. The seven transitions assigned to the
decay of 61Cr are listed in Table 4.8. The peaks observed with energies of 207 and
629 keV in Fig. 4.26 are known transitions in the decay of the 61 Mn daughter [91]. The

1028- and 1205-keV transitions from the decay of the grand-daughter 61Fe [92] are

114

 

Counts/ 30 ms
8

 

10

...1... .I‘..1....1....1...‘.
0 500 1000 1500 2000 2500 3000
Time(ms)

 

 

 

Figure 4.25: Decay curve for the 8 decay of 61Or to 61Mn, constructed from decays
correlated with 61Cr implantations using a 3 s correlation time. The data were fitted

with a single exponential decay for the parent, growth and decay of the daughter, and
a constant background.
also seen in Fig. 4.26. The peaks at 355, 535, 1142 and 1861 keV correspond in energy
to the transitions previously reported by Sorlin et al. [59]. However, the transition
observed in that work at 1134 keV was not apparent in the present work, see Fig. 4.26.
The three additional 7-ray transitions at 157, 1497, and 2378 keV can be assigned
for the first time to the decay of 61Cr. It is worth noting that two transitions with
energies 155 and 355 keV had previously been assigned to the 8 decay of 62Cr [58].
Observation of these transitions in Fig. 4.26 suggests that they are associated with
levels in 61Mn, and their observation in Ref. [58] may be evidence for 8—delayed
neutron decay of the 62Cr ground state. The in-beam 7-ray spectra for 61Mn and
62Mn obtained by Valiente—Dobon et al. [57] include transitions with energies of 157
and 155 keV, respectively, supporting the present assignment of the 157-keV 7-ray
transition in Fig. 4.26 to the decay of 61Cr.

The proposed decay scheme for levels in 61M11 populated following the 8 decay
of 61Cr is presented in Fig. 4.27. The 8-decay Q value was taken from Ref. [80].
Absolute 7-ray intensities were deduced from the number of observed 61Cr 7 rays,
the 7-ray peak efficiency, and the number of 61Cr implants correlated with 8 decays,

as derived from the fit of the decay curve in Fig. 4.25. The two-7 cascade involving

115

 

8

_ [[IIIIIITIIIIIIIFF
\

Counts / keV

3

 
 
 
  
  

 

 

 

535

 

 

   

500

   

 

I“ l ,
If 1
. ‘. ] ‘
‘ ‘ Idllldl 1‘! I thin 11 l

1000

1142

1861

 

1497 2378
1500 , ['2000 2500
Energy (keV)

Figure 4.26: 8—delayed 7-ray spectrum for the 8 decay of 61Cr, in the emery range of
0-2.5 MeV. Transitions marked by their energies in keV are assigned to the decay of
61Cr. Transitions marked by a filled circle are known transitions in the daughter 61Mn,
while transitions marked by a square belong to the decay of the 61Fe granddaughter.

Table 4.8: Energies and absolute intensities of the 8-delayed 7 rays assigned to the
decay of 61Cr. The initial and final states for those transitions placed in the proposed

61Mn level scheme are also indicated.

 

 

E7 I absolute Einitial Efinal Coincident
(keV) (‘70) keV keV 7 rays (keV)

157.2:l:0.5 9i2 157 0
354.8:1:0.4 1621:? 1497 1142 535, 1142
534.6:1:0.5 5:121 2032 1497 355
1142.2:1:0.4 21:1:2 1142 0 355
l497.3:l:0.5 9:1:2 1497 0
1860.8:1:0.4 20i2 1861 0
2378.2:l:0.4 11:1:1 2378 0

 

 

116

the 1142- and 355-keV transitions was confirmed by 77 coincidence relationships (see
Fig. 4.28). However, the ordering of the two transitions is not uniquely determined.
The arrangement shown in Fig. 4.27 was based on the absolute intensities of the 1142-
and 355-keV transitions. No evidence was found for 7 rays in coincidence with the
157-keV ground-state transition within the statistical uncertainty of the measurement.
Two counts in the 355-keV coincidence spectrum of Fig. 4.28(b) suggested placement
of the 535-keV line in cascade from a higher—lying level at 2032 keV. This tentative
placement is represented in Fig. 4.27 by a dashed line.

The apparent 8-decay feeding to levels in 61Mn was deduced from the absolute
7-ray intensities. The deduced values, along with apparent log f t values, are also given
in Fig. 4.27. The observed 8 branches all have apparent log f t values between 4 and
6, consistent with allowed transitions. The 1142-keV level was found to have a small
8 branching with a large error, and might not be directly populated by the 8 decay
of 61Cr.

A ground-state spin and parity assignment of 5/2‘ was assigned to 61Mn by
Runte et al. [91], based on the systematic trends of ground-state J7r values for the
less neutron-rich, odd-A Mn isotopes. The first excited state at 157 keV has been
tentatively assigned J ”=7/ 2' from the in—beam 7-ray results. Allowed 8 feeding to
the lowest two states would then limit the J7r quantum numbers of the 61Cr ground
state to values of 5 / 2“ or 7/2‘. Gaudefroy et al. [58] tentatively assigned the ground
state of 61Cr to be J 7r=5/ 2“ on the basis of the observed 8-decay properties of the
progenitor, 61V, and such an assignment is adopted in Fig. 4.27. It is likely that the
1142—keV state has low spin, either J"=1/2‘ or J"=3/2'. The level at 1142 keV
is apparently weakly fed by 8 decay, was not identified in the yrast structure of
61Mn [57], and does not depopulate to the 7/2- level at 157 keV within the statistical
uncertainty of this measurement. The 1497-keV level is tentatively assigned a J7r of
3/2“ or 5/2- because of the apparent allowed 8-decay branch and the favorable

competition between the two depopulating 7 rays that suggests that both transitions

117

(5/2—) 0
T1/2=233i11 ms

 

 

 

 

 

 

 

 

 

 

 

 

 

61
Cl“ QB=9.4:04 MeV g
,3/
Q
‘7.”
$7
Ip(%) logft ge Q
«R? 43"
11:1 50:01 0?. \ 2378.2
.8 4'7
e’ 9
8° 3"
5+1 54+02 ————— —-.-—-°;7 —————— 2032
I . \ \
1 a? 4‘7 49'
20:2 48:01 ;‘ pvg 1860.8
1 0' .
: "9 3 4?
. 5 4°? «5'
(3/2'5/2‘) . 3: ‘9 4,?
20:5 49:02 ' ! $._1497
/
‘11
_ 3’
5:4 56:04 (1/2,3/2-) "' 1142.2
s
1L
Q,
S?
“)7
7/2') .5;
9:2 5.6:01 ( ~ 157.2
30:15 51:02 (5/2‘) ' 0
61Mn

Figure 4.27: Decay scheme for the 8 decay of 61Cr to states in 61Mn. The number
in brackets following the 7—ray energy is the absolute intensity. Qfi was determined
from data in Ref. [80].

118

 

Counts/ keV
w A
l T

OHM

 

w uh
I

535[2]

Counts/ keV

hot—N
l

b.)
I

355[4]

Counts/ keV

 

 

 

 

linumuluuln

 

(a) 157 keV

 

 

(b) 355 keV
1 142[3]

(c) 1142 keV

 

 

 

 

l
500

N
c°~1

 

1000 1500 2000
Energy (keV)

Figure 4.28: wry-coincidence spectra for the decay of 61Cr, gated on the (a) 157-keV,
(b) 355-keV and (c) 1142-keV 7-ray transitions. These coincident spectra include
data within a 3 s correlation time, for implants collected over the entire surface of the
DSSD. In square brackets following the energy for each peak is the number of counts

in that peak.

119

have M1 multipolarity. The proposed levels at excitation energies of 1861 and 2378 keV
are apparently fed by allowed fl decay as well, and can take J 7’ values in a range from

3/2— to 7/2".

120

Chapter 5

Discussion

5.1 Interpretation of the low-energy levels in
neutron-rich 218C

One of the more interesting questions with regard to nuclear structure in the f p shell
is that of the possible N :34 subshell closure in the 200a isotopes. The maximum
upward monopole shift of the V1f5/2 orbital with the completely empty 7r1 f7 /2 or-
bital in the Ca isotopes may result in a significant gap between the 1/1f5/2 orbital
and the lower-lying 112121 /2 orbital, creating a subshell gap at N =34 similar to that
previously observed at N :32. As discussed previously in Section 4.1, a number of
experiments have been performed to probe the structure of 54Ca directly, with the
hope of determining whether or not a subshell closure exists at N =34 for the Z =20
Ca isotopes. However, these experiments have proven difficult, and to date, no direct
measurement has been successful.

Having one proton in addition to the Ca isotopes, the low-energy structure of
the 218C isotopes may provide insight into the neutron single-particle energy spacing
near N =34, and thus into the possible N =34 subshell closure in Ca. The low-energy
structures of 53’54’568c have been determined in the present work, by considering

both the B decay of the parent nuclei 53154(3a, as well as the isomeric decay of 5415680.

121

The low—lying levels of these 2180 isotopes will be discussed in the context of the
extreme single-particle model, as a coupling of the odd 1 f7 /2 proton to the valence
neutron configurations in the 20Ca core isotopes. The success or failure of simple
coupling schemes to explain the observed low-energy structure of the Sc isotopes can
also provide indirect indications of the presence or absence of subshell closures in the
Ca core nuclei.

Below, the structures of the neutron-rich Sc isotopes are discussed in the frame-
work of the simple coupling of the valence proton and neutrons. The experimental

levels are then compared to the results of more realistic shell-model calculations.

5.1.1 Low-energy structure of odd-A 53Sc

The low-energy structure of 53Sc can be interpreted as a weak coupling of the valence
7r f7 /2 proton to states in 52Ca, which, assuming a robust N =32 subshell closure, can
be viewed as a doubly magic core [12]. Coupling of the valence proton to the first 2+
state in 52Ca should produce a quintet of states in 5380 with J 7‘ values ranging from
3/2- to 11/2‘, at energies centered around ~2.6 MeV. Studies of 53Sc produced in
deep inelastic reactions [93] have populated 9/2" and 11/2" states near this energy,
which are likely members of the 7r f7 /2®2+ multiplet (see Fig. 5.1). The fl decay of
53Ca was observed to populate only one state in 53Se. The population of a single
state in the decay of 53Ca decay is expected for allowed fl decay from the presumed
1/2" 530a ground state, since the decay should only populate the 3/2" state of the
7r f7 /2®2+ multiplet. Thus, the single new level at 2109 keV is a likely candidate for
the 3 / 2" member of the 7r f7 /2®2+ multiplet. The three known levels in 53Sc, shown
in Fig. 5.1, reside at above 2 MeV, as expected within the weak coupling framework.
While not all states of the expected quintet have been identified, this simple scheme
describes the three known levels well. The apparent success of the weak coupling
description for 5380 provides support for the robust nature of the N =32 subshell

closure in the 20Ca isotopes.

122

 

 

 

 

 

 

 

5/2 28 g
2 + (ll/22‘ 2617 1 / :___1
( ) 2562 (9/2)_ 2283 2% a;
“f7/2®52Ca(2+) (3/2)- 2109 E/ :
7%? lélgi
0+ 0 (7/2)- 0 7,2- 0
EXP EXP GXPFIA
52Ca 53sC 53SC

Figure 5.1: The comparison of the known levels in 53Sc [75,93] to states in 52Ca
suggests that 53Sc is accurately described by weak coupling of the odd 7rf7/2 proton

to the 5203. core. The experimental states are also in good agreement with predictions
of shell-model calculations using the GXPFlA effective interaction [94].

A more advanced approach to describe the low-energy structure of 53Sc comes
from considering more realistic wavefunctions, that allow configuration mixing. Shell-
model calculations using the GXPFlA effective interaction [34] were performed for
53Sc [94], and are presented in Fig. 5.1. The calculated levels are in good agreement
with the three known excited states, although there are significantly more calculated
levels. Additional experimental work is required to identify the remaining levels and

complete the expected 7r f7 /2®2+ multiplet in 53Sc.

5.1.2 Low-energy structure of even-A Sc isotopes

The structure of the even—A (odd-odd) 218C isotopes can be described by coupling the
valence 7rf7/2 proton particle with p3 /2, 191/2, f5/2, and at higher energies, 99/2, va-
lence neutron configurations. The success of such a description is shown most directly
by considering the cases of 508C and 52Sc, where this simple interpretation explains
many aspects of the known low-energy structures.

508C has one proton and one neutron outside of the doubly magic 48Ca core, and

the lowest energy levels can be described by coupling a valence 7r f7 /2 proton and 1423/2

123

neutron. The low-energy structure, known from fl decay [95], transfer reactions [96],
and charge exchange reactions [97] is summarized in Fig. 5.2(a). The four states
lowest in energy with J 7' = 2+ to 5+ arise from the configuration (71' f7 /2)1®(l/p3 /2)1.
The particle-particle coupling rules [21] predict the arrangement of the states of this
multiplet in a downward-opening parabola, which agrees with the experimental energy
level ordering. Promotion of the valence neutron in 5080 to the 1421/2 level gives the
configuration (7r f7 /2)1®(1/p1 /2)1, producing only two states with J 7r=3+, 47L. 'IWo 3Jr
states are identified in the level scheme of 508C above 2 MeV, and either is a candidate
for the 3+ member of this doublet. The energy spacing between multiplets arising
from configurations involving the V123 /2 and 1411/2 states depends on the up3/2-1/p1/2
single-particle spacing, and thus the Vp3/2-l/p1/2 spin-orbit splitting. The apparent
separation of these two multiplets in 5080 is on the order of 2 MeV, a gap sufficient
to account for an established N =32 subshell closure in 2180.

The structure of 52Sc can be similarly described by the coupling of a valence 7r f7 /2
proton particle and 1403/2 neutron hole, taking 520a as the inert core [93]. States in
this odd-odd nucleus have been identified in 5 decay studies [11], in—beam 7—ray spec-
troscopy following secondary fragmentation [98] and deep-inelastic work [93,99]. The
known levels are presented in Fig. 5.2(b). Shell model calculations for 5280 using the
GXPFI, GXPFlA and KB3G effective interactions are presented in Fig. 5.3(a). As
discussed in Refs. [93,99], the lowest-lying quartet of states in 528C can be associated
with the configuration (7r f7 /2)1®(Vp3 /2)—1. The four states with JW=2+-5+, should
form an upward-opening parabola, since the coupling involves a proton particle and
neutron hole. The lowest 3+ and 4+ states in this parabola are expected to be close
in energy. The energy separation between these states has not been established exper-
imentally, but is likely to be small [99]. The Pandya transform [100] can be applied
to relate the particle-particle (7r f7 /2)1®(I/p3 /2)1 states of 5080 to the particle-hole
(7r f7 /2)1®(up3 /2)_1 states in 5280. The Pandya relationship assumes the validity of

j j coupling and is based on the simple form of the coefficients of fractional parent-

124

(1)+ 2614 (1)+ 2746

 

 

 

 

(1) \-’2527
(3)+ 2331 (6)+ 2332+x
(3)+ /‘\2222
(1)+ 1848

 

(4)+ 1654+x
1 + 1

4 +

(2)+/—\587
(5)+ 212
(3)+ 328 (4)+ +X (1)+ 24 (5’6” x

g2)+ F, 252 x (4gp ——
(5)+ 0 (3)+ 0 ($43—ng Q)+ 0

503C29 523C31 54SC33 563C35

(a) (b) (C) (d)

 

 

 

 

 

 

 

 

 

 

V1f5/2

 

V2P1/2 —— —‘°—‘ —‘°_
v2p3/2—oooo— —ooo<>—- —-oooo—— —oooo-—

Figure 5.2: Experimentally known levels in the even-A (a) 50Sc29, (b) 528cm, (c)

54SC33, and (d) 563035 isotopes. Also included are the expected ground-state neutron
configurations in the f p—shell orbitals above the N =28 shell closure.

125

Table 5.1: Results of the application of the Pandya transform to the low-lying 7rf71/2 <8)
upfi/2 neutron-particle states in 50Sc to predict the 1r f.;/12 <8) "pl/2 neutron-hole states
- 52

1n Sc.

 

 

 

 

5030 (”f%/2VP§/2) 5280 (”[71/2Vpg/12)

J 7' Experimental J 7' Calculated Experimental A(Ecalc — Earp)
Energy (keV) Energy (keV) Energy (keV) (keV)

3+ 0 34 26 0 26

2+ 257 4+ 0 x -x

3+ 328 5+ 229 212+x l7-x

4+ 756 2+ 880 675 105

 

 

 

age (the probability of a given J state arising from a specific nucleon configuration)
relating one- and two-hole states [100]. The results of this transform applied to 508C
to the corresponding states in 5280 are presented in Table 5.1. For a small energy
separation between the 3+ and 4+ states (x) in 52Sc, the transform provides excellent
agreement, suggesting that the configurations of these low-lying levels in both nuclei
are fairly pure. Calculations using the GXPFl effective interaction [12] support the
relative purity of the four lowest-energy levels (see Fig. 5.3).

At higher excitation energies in 52SC, the coupling of the 7rf7/2 proton to an ex-
cited 1421/2 neutron to give a pair of states with J "2.3+, 4+ accounts for the observed
4+ state in 52Sc at ~1.7 MeV. The 6+ state at ~2.3 MeV in 528C has been shown in
shell-model calculations to also have parentage that includes this configuration, al—
though the extent of this contribution varies between shell-model interactions. Calcu-
lations using the GXPFIA interaction [99] suggest that the primary parentage of the
2.3—MeV 6+ state is (7rf7/2)1®(1/(p§/2p[/2)), while the (7rf7/2)1®(V(p§/2f51/2)) con-
figuration is predicted to dominate the first 8+ state in 52Se, experimentally observed
at ~3.6 MeV [99] [see Fig. 5.3(a)]. Experimentally, the energy separation between
states dominated by the (Wf7/2)1®(Vp3/2)_1 and (7r f7 /2)1<§§>(1/(p;23 /2p[ /2)) configura-
tions appears to be ~2 MeV, again corresponding to the spin-orbit splitting between

the 1423/2 and 1421/2 single-particle states, in agreement with the results for 508C. As

126

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127

noted by Fornal et al. [99], the apparent separation between the 1421/2 and V f5 /2
single-particle states, as inferred from the energy spacing between the 6+ and 8‘L
states in 528C, is slightly smaller than that assumed in the GXPFIA interaction.
The low-energy structure of 54Sc, with two additional neutrons, should be sig-
nificantly different. The 1423 /2 orbital is now fully occupied, and the 54Sc structure
at low energy should reflect coupling of the valence f7/2 proton particle to either a
121/2 or f5/2 neutron, again taking 52Ca as an inert core. The 1421/2 single-particle
level is expected to lie below the V f5 /2 state in the 218C isotopes, based on the ob-
servations in 52Se. Assuming this ordering, the (7rf7/2)1®(Vp1/2)1 coupling yields a
doublet of states with J 7r23+, 4+, which is expected to be lowest in energy in 54Sc.
Shell model results [31,94] predict the 3+ and 4+ states of this configuration to be
close in energy, and thus the spin and parity of the 54Sc ground state is not clear from
a theory perspective. The ground state of 54Sc has been tentatively assigned J 7r23+
in the present work (see Sections 4.1.2 and 4.1.3). Considering the situation purely in
terms of the proton-neutron coupling, it may be natural to assume that the isomeric
110-keV level corresponds to the 4+ state arising from the (7r f7 /2)1®(up1 /2)1 config—
uration. However, within the simple coupling framework it is difficult to understand
why the in-multiplet M1 transition is hindered strongly enough to yield the experi-
mental isomer half-life of 2.8 us. In this case, the two other states identified in 54Sc,
the isomeric (5)+ level and higher-lying (1)+ state, may arise from the configuration
(7rf7/2)1®(1/f5/2)1. This coupling results in a sextet of states ranging from J"=1+
to 6+, and the particle-particle coupling would produce a downward-facing parabola.
There are however, inconsistencies in the level ordering compared with the spin and
parity assignments made in 54Se. The 1+ state lies above the possible 5+ state in
energy in the level scheme as presented in Fig. 5.2(c), a result which is inconsistent
with the expectations of the particle-particle parabola, and calculations using the
GXPFI, GXPF 1A and KB3G effective interaction [see Fig. 5.3(b)]. An alternative

J 7' assignment for the states in 54Sc with a 4+ ground state and 6+ llO—keV isomeric

128

 

level is a possibility, but the placement of the 6+ level below the 1+ level is also unex—
pected would also contradict the shell-model predictions. The apparent experimental
level ordering could be better explained if the (7r f7/2)1®(1/p3 /2)_1 configuration was
the origin of the 3+ and 5+ states. However, as demonstrated for the lighter Sc iso-
topes, the Vp3/2-l/p1/2 spin-orbit splitting is a fairly constant N2 MeV, so that the
V f7 /2-up3 /2 multiplet should reside at ~2 MeV in 543C.

An alternative to the 5+ assignment for the 110-keV isomeric state is a 4+ assign-
ment. While not expected based on comparison of the deduced isomer lifetime with
Weisskopf single-particle estimates, which favor an E2 multipolarity for the 110—keV
transition, a 4+ spin and parity cannot be excluded for the 110—keV state. Calculations
using the GXPFl [33], GXPFIA [34] and KB3G [35] interactions all predict a doublet
of states near the 54 Sc ground state with J 7r23+ and 4+. The transition probabilities,
B(M 1 : 3+ —> 4+) and B(E2 : 3+ —> 4+) calculated with these three interactions
are shown in Table 5.2, along with the calculated partial half-lives. In all cases, the
M1 component would dominate the transition. However, the B(Ml : 3+ —> 4+) val-
ues are small, giving rise to half-lives of order nanoseconds or longer — much slower
than the picoseconds expectation from the single-particle Weisskopf estimate. The
B(Ml : 3+ —+ 4+) value is very sensitive to the degree of mixing in the wavefunc-
tions for the 3+ and 4+ states [94]. With increased configuration mixing, there is
increased suppression of the B (M 1 : 3+ -—> 4+) value, hindering the transition. A 4+
spin and parity assignment is in better agreement with the expectation for the level
ordering in 54Sc. However, more work is required to make a firm spin assignment for
the llO—keV isomeric state in 54Sc.

The 1+ state at energy 247 keV in 54Sc can only be explained by the (7r f7 /2)1®(u f5 /2)1
configuration. Even if this is the only member of the multiplet identified, the energy
separatiOn between the ground state with (7r f7 /2)1®(up1 /2)1, and the excited state
with (7r f7 /2)1®(V f5 /2)1, appears to be small. Shell model results using the GXPFI

and GXPFlA effective interactions [31,94] predict a upl/g-I/f5/2 separation of more

129

 

Table 5.2: Calculated transition probabilities and half—lives for the transition between
the 3+ and 4+ states in 54Sc, using the GXPFl, GXPFIA and KBBG shell-model
effective interactions. The Weisskopf single-particle estimates for the half-life of a
110—keV transition are also included.

 

 

GXPFI GXPF 1A KB3G Single-Particle

 

B(Ml : 3+ —+ 4+) (11%,) 0.02611 0.00369 0.00080

T1/2(M1)(s) 8.10x10“10 1.56x10-8 8.94x10‘7 9.30x10-12
B(E2 : 3+ —» 4+) (e2fm4) 5.07 6.24 6.96
T1/2(E2)(s) 4.05x10-6 1.72x10-5 1.03><10-3 2.89x10—6

 

 

than 1 MeV, which manifests itself in 54Sc as an expanded low-energy level structure,
seen in Fig. 5.3(b). The compression in the experimentally established structure of
54Se suggests a Vp1/2-Vf5/2 single-particle energy separation smaller than that as-
sumed in the GXPFI and GXPFIA effective interactions, and is inconsistent with a
robust N :34 subshell closure.

Another rapid structure change should be evident in the heavier 56Sc nucleus,
since the addition of two neutrons to 54Sc will fill the 1411/2 single-particle orbital.
The unpaired valence neutron will then occupy the V f5 /2 state. Under this assump-
tion, the lowest energy states in 568C would have a (7r f7 /2)1®(V f5 /2)1 configuration.
The resulting sextet of states with J"=1+ to 6+ should be arranged in a downward
facing parabola, with the 4Jr state at the vertex. The challenge in comparing these ex-
pectations in 568C to the new data is that the absolute energies of the two fi-decaying
states are not known. The states expected at low energy in 568C with J”:1+, 2+
and (5,6)+ are likely attributed to the (7r f7/2)1®(1/ f5 /2)1 configuration. The 3+ and
4+ states cannot be trivially assigned the same configuration, as they may also arise
from the (7r f7 /2)1®(Vp1 /2)1 coupling, depending on the relative position of the 1421/2
and uf5/2 single-particle orbitals. In fact, significant mixing would be expected be-
tween the 3+/4+ states in the 7r f7 /2-u f5 /2 and 7r f7 /2-Vp1 /2 multiplets if there is only
a small energy gap between the uf5/2 and 1491/2 effective single-particle energies, as

suggested in 54Se. This mixing can also be seen in the calculated levels [94], even with

130

a large Up1/2-l/f5/2 gap.

5.2 Re-ordering of proton single-particle states in
neutron-rich K isotopes

The neutron—rich 19K isotopes with N 2 20 sit on the border of two major shells,
with protons occupying the nearly full sd shell below Z =20, and neutrons occupying
the next major shell, the f p shell. As such, shell-model descriptions of the neutron-
rich K isotopes remain challenging, as cross-shell interactions are required to describe
the interaction of valence sd—shell protons and f p—shell valence neutrons. Interactions
which account for excitations of nucleons across the shell gaps are even more chal—
lenging than those within a given shell. However, new interactions do exist which
attempt to accurately reproduce the cross-shell interactions between the sd and fp
shells [101—103]. The results of shell-model calculations using such interactions will
be discussed for the region surrounding 50K in the following sections. However, the
structure of the neutron-rich K isotopes will first be described in terms of coupling
of the valence nucleons, and the expected shifts in nucleon single-particle energies
resulting from the monopole interaction. The systematics of the neutron-rich 19K iso-
topes surrounding the N =28 shell closure are examined within this framework in the

next section.

5.2.1 Systematics of the 19K isotopes around N :28

As discussed in Chapter 1, the tensor monopole interaction between protons and
neutrons is attractive between j< (l — 1 / 2) and 3') (l + 1 / 2) orbital pairs and repul-
sive for j<-j< or j>-j> orbital pairs. The strength of the interaction is maximized
between single-particle orbitals with similar I values [17]. Considering the effect of

1f7/2 (1+1 / 2) neutrons on the proton sd—shell orbitals, it is apparent that the tensor

131

 

min-La!"

monopole interaction with the 1d3/2 (l-1/2) proton orbital will be attractive, while
the interaction will be repulsive for the 1d5/2 (1+1 / 2) proton orbital. The 2.31/2 pro-
ton orbital should exhibit no tensor monopole shift, since there are no partner orbitals
for [20. Thus, based solely on the energy shifts expected due to the tensor monopole
interaction, the 1d3/2 proton orbital is expected to decrease in energy relative to the
231/2 orbital with increasing neutron 1f7/2 occupancy. This expectation appears to
be borne out in the experimental data for the even-N K isotopes between N =20

and N =28. The first 3/2+ state in the odd-A K isotopes can be associated with the

--1

1d; /12 proton-hole configuration, while the first 1/2+ state is associated with the 231/2

proton-hole (equivalently, the 23b2 proton-particle) configuration. This relationship
has been confirmed in the case of 39K in the analysis of proton pick-up reactions with
40Ca [104]. Thus, the relative energy of the 3/21” and 1/2] experimental levels is
directly related to the separation between the proton 1d3/2 and 281/2 single—particle
orbitals. A change in the energy separation of the 1d3/2 and 2.91/2 proton-hole states
in the odd-A K isotopes with increasing 1/1f7/2 occupancy is apparent in Fig. 5.4.
The 71281712 state, which is. initially well—separated from the 7r1d; /12 ground state in
39K, rapidly drops in energy relative to the «1d; /12 state as the neutron 1f7/2 or-
bital is filled. In fact, in 47K28, with a full 111 f7 /2 orbital, the proton 1d3/2 orbital has
dropped below the 7r2sl/2 orbital, and 47K has been experimentally confirmed to have
a ground state J 7' of 1/2+ [105], corresponding to a 231712 proton hole configuration.

Moving past the N =28 shell closure, neutrons begin to occupy the 2123/2 orbital.
The tensor monopole interaction between the 2123/2 neutron orbital and the 1d3/2
proton orbital, while attractive, is weaker than the V1f7/2-7I'1d3/2 tensor interaction.
Again, the «231/2 orbital should exhibit no tensor monopole shift. However, a second
component to the monopole interaction, known as the central force [106], plays a
significant role in the evolution of the relative spacing of the 231/2 and 1d3/2 proton
orbitals in this region [107]. The central force is an attractive interaction between pro-

tons and neutrons, which does not have the spin dependence of the tensor monopole

132

 

 

— N
r—IUINUI

.3
QUI

 

 

 

 

 

I

9

{J1
I

l

20 22 24 26 218 30 32
Neutron Number

 

B(I/zt) - E(3/2‘{) (MeV)

Figure 5.4: Systematic behavior of the separation between the 3/2+ and 1/2+ states
in the odd-A potassium isotopes between N :20 and N =30. The observed energy
separation is directly related to the separation between the 1613/2 and 231/2 proton
orbitals in the K isotopes. Experimental data points are indicated by filled circles,
while predictions using the SDPF-U effective interaction [101] are represented by the
open squares.
force. The central force does have an I dependence, and like the tensor force it is max-
imized for similar 1. Below N =28, the central force between the u1f7/2 and 1r1d3/2
orbitals is stronger than that between the u1f7/2 and 7r2sl/2. The central force con-
tribution, in that case, reinforced the tensor monopole interaction and lowered the
7r1d3/2 state relative to the 7r2sl/2 state. However, above N =28, the central force
between the u2p3/2 and W281/2 orbitals is expected to be stronger than the combined
tensor monopole and central forces between the u2p3/2 and 7T1d3 /2 orbitals. Thus,
with the addition of neutrons to the 2193/2 orbital, the W281/2 orbital is expected to
drop in energy relative to the 7r1d3/2 orbital, and the inversion of the proton orbitals,
which was observed between 45K26 and 47K28, reverses. The open question is how
quickly this reversal occurs, which is related to the strength of the monopole inter-
action between the neutron and proton orbitals in the fp and 3d shells respectively.
An examination of the experimentally known low-energy structures of the K isotopes
beyond N =28 can provide first insight into this question.

States in the nucleus 48K, which has one neutron beyond N =28, are known from

deep-inelastic work [108] and recent multinucleon transfer reactions [85] and are shown

in Fig. 5.5. The ground state of this nucleus was initially assigned a spin and parity

133

 

of 2‘ on the basis of the expectations from the shell model and observed fl feeding to
states in 48Ca [109]. However, Broda et al. [85] reassigned the ground state of 48K as
J ”:1- following analysis of multi-nucleon transfer and deep-inelastic reaction data.
Such an assignment is still consistent with 48K fi-decay results since direct fl decay
to 3' states in 48Ca is not observed. Taking the J7r re—assignments from Ref. [85],
the ground state and first excited state at energy 143 keV in 48K can be interpreted
as arising from the coupling of the 2123/2 neutron with the 231/2 proton hole, which
gives rise to a 1‘ state (the ground state) and a 2‘ state (the 143-keV state). The
higher-energy states in 48K at 279 keV and 728 keV should correspond to the 2‘ and
3" states of the (V2p3 /2)1®(7r1d3 /2)"1 multiplet. The 0' and 1" members of this
multiplet are unknown at this time. The expectation of an upward-opening parabola
for the particle-hole coupling would place the O“ and 1‘ levels above the 2‘ state
at 279 keV. The separation between the 1613/2 and 231/2 proton hole states in 48K
appears to be of order a few hundred keV, consistent with a narrowing of the 7r1d3 /2-
«231/2 gap with the addition of a single 2123/2 neutron. This interpretation suggests '
that the «131/2 level remains above the 1d3/2 level in 48K29.

The addition of two neutrons in the K isotopes beyond N =28 corresponds to the
odd-A nucleus 49K. Recent data [86] for 49K from multinucleon transfer suggest that
the proton 251/2 orbital still remains above the 1d3/2 orbital, as indicated in the
systematics shown in Fig. 5.4. In this nucleus, the 7r1d3/2-7r2sl/2 energy separation
has narrowed further to only 92 keV.

Moving further to 50K, one can explore the relative position of the 7r1d3/2 and
«231/2 orbitals with three neutrons now in the 2123/2 orbital. The low-energy levels
in 50K from the present work are presented in Fig. 5.6. Assuming that the proton
231/2 orbital has dropped further in energy and is again below the 7r1d3/2 orbital,
the ground state configuration in 50K would arise from the (V2193 /2)-1®(7r1d3 /2)—1
configuration. This configuration would account for the 0" ground state as previously

assigned based on the 18 decay of 50K to states in 50Ca [110]. However, it is difficult

134

(7*) 3586

 

 

 

 

 

 

(5+) 2177
_ - (712d )'1®(v2p )1
(3 ) 728 3/2 0_ 3/2
_. 3- 1_

(23 279_ 2-

143' _1 1
(1') 0_*—' (“151/2) ®("Zips/2)

48K

Figure 5.5: Known states in 48K [85,108], and the possible origin of the low-lying
states in the simple framework of the independent particle model.

135

 

to understand the presence of the observed isomer in 50K if the low-lying states all
arise from the (V2p3/2)“1®(7T1d3/2)—1 configuration. As discussed in Section 4.2, the
deduced half-life of 15473?3 ns for the 50K isomeric state at 172 keV is consistent with
an E2 multipolarity for the 172-keV transition. The observed high level of competi-
tion between the direct 172-keV ground state transition and the two ’7—ray cascade
suggests that the first M1 transition of the cascade must be hindered. Such hindrance
is unexpected for an in-multiplet M1 transition.

An alternative is that the ground state in 50K has the (V2123 /2)'1®(7r2sl /2)_1
configuration. The ground state would be expected then to have a spin and parity of
1‘, with the first excited state being the J "=2” state of the 281/2 proton—hole con-
figuration. The isomeric state could then be explained as the (112])3 /2)_1®(7r1d3 /2)—1
configuration. The isomeric state would most likely correspond to the 3‘ state of this
multiplet. The M1 transition connecting the 3‘ isomeric state and the lower-lying
2‘ state would be hindered as a result of the forbidden nature of a 7r1d3/2-7r2sl/2
transition. Such a hindrance would explain the observed competition between the di-
rect 172-keV E2 ground-state transition, and the two 'y-ray cascade. Thus, a J ":1—
ground state in 50K, arising from a 231/2 proton hole configuration, seems to provide
a-more satisfactory understanding for the observed isomerism in 50K than any state
arising from a (1d3/2)—l configuration. Such a result would suggest that, even with
three 2123/2 neutrons, the 2231/2 orbital remains above the 7r1d3/2 orbital. The rela-
tive energy of states arising from the two proton-hole configurations would suggest a
7r1d3/2-7r231/2 gap comparable to that in 48K, of order a few hundred keV. However,
to resolve the uncertainty in this situation, a direct measurement of the ground state

spin and parity is necessary.

136

 

 

 

 

 

 

 

37— 671
3:—— 335
l 312
\ \
_ .38; ‘ ,,
(fl2d3/2)—1®(V2p3/2)_1 ._ (3) N, 53’ “$8 171.8
’ (2)‘ ~33" 128.4
(fl251/2)—1®(V2p3/2)—1 .4 2——— 89
_ (I). 0 0-___0
EXP SDPF-U
50K

Figure 5.6: Proposed low-energy level scheme for 50K, and the possible origin of
the low-lying states in the simple framework of the independent particle model. The
energy of the suggested 2‘ state is not uniquely determined, and may alternately
be located at energy 42.8 keV. The states below 1 MeV, calculated using the SDPF-

U [101] effective interaction are also shown.

137

 

5.2.2 Comparison to shell-model calculations using sd— f p

cross-shell interactions

There has been significant work in recent years on the deveIOpment of shell-model
effective interactions for calculations in the sd— f p valence space, due primarily to the
experimental observation of a weakening N =28 shell closure [111,112]. These new ef-
fective interactions consist of three basic components: (a) a proton-proton interaction
in the sd shell, (b) a neutron-neutron interaction in the f p shell, and (c) a cross-shell
proton-neutron interaction. Generally, standard interactions are used for the intra-
shell parts, such as the USD interaction for the sd shell [113], and the KB [114] or
GXPFIA [34] interactions in the f p shell. The most uncertain part of the 361- f p shell
model calculations is the cross-shell component.

Utsuno et al. [102] have recently developed a new sd— f p shell interaction that
makes use of the USD interaction in the sd shell, and the GXPFIB interaction (a
slight modification of the GXPFIA interaction with a better 1p3/2-1p1/2 energy gap
around the Ca isotopes [102]) in the f p shell. The cross-shell part of the interaction
is built up from three components: a central force, a spin-orbit force and a tensor
force. Results for the K isotopes using this effective interaction have been found to
be consistent with experiment through 47K [102], correctly predicting the inversion
of the «231/2 and 7rld3/2 single-particle orbitals.

Another recent sd— f p shell effective interaction has been developed by Nowacki
and Poves [101]. Their SDPF-U interaction is a refinement of the previous SDPF-NR
effective interaction [115], which makes use of the USD interaction in the 3d shell,
the KB interaction in the f p shell, and the G matrix calculations of Kahana, Lee and
Scott for the cross-shell interaction. The monopole part of the cross-shell interaction
was empirically modified to produce the correct evolution of effective single-particle
states by fitting to a number of reference states across the region of interest. Results

from this interaction for the 19K isotopes are in good agreement with experiment up

138

to and including N =28, correctly predicting the inversion of the 7r2sl/2 and 7r1d3/2
single particle orbitals in 47K [101]. However, immediately beyond N =28, the SDPF-
U effective interaction predicts a 3/2+ ground state in 49K30, in contradiction with
recent experimental results [86]. The separation between the 71'281/2 and 7r1d3/2 sin-
gle particle orbitals predicted by the SDPF-U interaction for N > 30 continues to
increase [101] and is inconsistent with the suggested (V2p3 /2)‘1®(7r2s3 /2)"1 ground
state configuration in 50K. Shell-model calculations for 50K were performed using
the SDPF-U effective interaction [94] and are presented in Fig. 5.6. The apparent
discrepancy between theory and experiment may be related to the 2p3/2-1d3/2 and
2123/2-131/2 monopole strengths. These monopole interactions largely determine the
evolution of the «231/2-7r1d3/2 single-particle energy spacing with the filling of the
V2193 /2 orbital beyond N =28. Additionally, the 2p3/2-1d3/2 and 2123 /2-281 /2 monopole
strengths were changed between the SDPF-U interaction and the previous SDPF-NR
interaction, which had correctly reproduced the 1/2+ 49K ground state [101]. Addi-
tional data will be required to better constrain the cross-shell effective interactions,

and improve the predictive power of sd—fp shell interactions.

5.3 Onset of collectivity in the 25Mn isotopes

Approaching N =40 below the Z228 shell closure, an increase in collectivity has
been inferred at low energy for the neutron-rich 24Cr and 25Fe nuclei. The apparent
onset of deformation in these isotopes has been associated with the presence of the
neutron 199/2 single-particle orbital near the Fermi surface as N =40 is approached.
The observed structural changes in this region are again attributed in part to the
tensor monopole interaction. The repulsive interaction between 1 f7 /2 (l+ 1 / 2) protons
and 199/2 (1+ 1 / 2) neutrons is reduced with the removal of 1f7/2 protons below Z 228,
and the 199/2 orbital drops in energy towards the Fermi surface. The role of the

V1 99 /2 orbital in driving deformation, as a function of nuclear charge, will be critical

139

to assessing the persistence of the N =50 shell gap in 7BM and other neutron—rich
nuclei in this region of the nuclear chart.

As noted in Chapter 1, the systematic variation in E(2'1f) values [F ig. 1.9(b)] sug-
gest that collectivity sets in already at N = 36 for the Cr isotopes, while first evidence
for such effects in the Fe isotopes occurs at 64Fe, which has N = 38. Therefore, the
low-energy structure of 61Mn, with N = 36, might exhibit features at low energy sug-
gestive of a change in collectivity when compared to other odd-A Mn isotopes nearer
to stability. The 6 decay of 61Cr to states in géMn36 was studied in the present work.
The newly identified states extend the systematics of the odd-A Mn isotopes through

N :36, and can be investigated for signs of developing collectivity.

5.3.1 Systematics in odd-A Mn

The systematic variation of the known energy levels of the odd-A Mn isotopes with
A = 57 — 63 is shown in Fig. 5.7. The levels below 2 MeV for 57Mn were taken from
H decay of 57Cr [116], in-beam y-ray spectrOSCOpy [117], and the (d,3He) transfer
reaction [118]. [3 decay populates seven excited states below 2 MeV, as well as the
57Mn ground state. The states directly fed by 16 decay are all assumed to have negative
parity, since the 57Cr parent has ground state J 7' = 3/2‘. The negative parity yrast
states observed in 57Mn were populated by a heavy-ion induced fusion-evaporation
reaction, that provided tentative spin assignments of the levels up to J = 25 / 2. The
(d,3He) transfer reaction provided unambiguous J 7’ assignments to the negative parity
states below 2 MeV at 84, 851, and 1837 keV, based on angular distribution data.
Positive parity was deduced for the excited states with energies 1753 and 1965 keV.
Based on the spectroscopic strengths for proton pickup [118], the first 7/2“, 1/2+,
and 3/2+ levels in 57Mn were deduced to carry ~ 40% of the summed single—particle
strength from shell model expectations.

Valiente—Dobon et al. [57] studied neutron-rich Mn isotopes by in-beam *y-ray

spectroscopy following deep inelastic collisions of a 70Zn beam on a 238U target.

140

Negative-parity yrast states were identified up to J = 15/ 2 in 59Mn34 and J = 11/2
in 61Mn36. Only a single transition, with an energy of 248 keV, was assigned to the
structure of 63Mn38. The non-yrast levels in 59’6an shown in Fig. 5.7 were identified
in fl-decay work. The B decay of 59Or to levels in 59Mn was most recently reported by
Liddick et al. [69]. The ground state spin and parity of the parent 59Cr, tentatively
assigned to be J 7‘ = 1/2“, restricts the range of states in 59Mn accessible by allowed
[3 decay to those with J7r = 1/2-,3/2_. The ground state of 59Mn is known to
have J7r = 5/2— [119]. The non-yrast J7r values for 59Mn were inferred‘from the
fl- and *y—decay patterns. The present work has expanded the knowledge of states in
61Mn, identifying three new states, in addition to the three previously known yrast
states [57].

The negative parity yrast structures below 2 MeV in odd-A 57’59’61Mn exhibit
little variation as a function of neutron number. These levels are consistent with
shell model calculations reported in Ref. [57] employing the GXPFIA, KBBG and
f pg effective interactions. The authors of Ref. [57] do note, however, that the proper
ordering of the 9 / 2“ and 11/2" levels at N 1 MeV is reproduced for all three isotopes
only by the f pg interaction. The experimental energy gap between the ground state,
with J7r = 5/2", and the 7/2" first excited state exhibits a regular increase from
57Mn (83 keV) to 65Mn (272 keV) [58]. Both the GXPFIA and fpg shell model
interactions reproduce the observed trends well.

The shell model calculations in Ref. [57] were extended to include non-yrast states
below 2 MeV. The calculations were performed with the code ANTOINE [120] using
the GXPFlA [34] and fpg [46] effective interactions. The full fp model space was
utilized for the calculations with the GXPFIA interaction. The valence space for the
calculations with the cross shell interaction f pg was limited to 2 neutron excitations
from the fp shell to the 1g9/2 orbital. As compared to Ref. [57], truncation of the
basis states was necessary to reach convergence for the higher density of states at

lower spin for the most neutron-rich Mn isotopes considered here. However, in those

141

 

A
v

%2— 3 ..........
5 §-—-/3 3 —' 3"“

.......... l
66 7-~-- 7
33 ..__—- — 5-—-— _5
I: _ 5"“‘/ w..-

 

 

7.-...-,._/ 7—-—*"‘—'/

5 —‘ 5 —
Expt GXPFIA fpg Expt GXPFIA fpg

57Mn32 59M1134

 

 

 

 

L
7

Energy (MeV)
N

 

   

__ 7—-——\

7 4- —— _\___

 

 

 

 

5 5
Expt GXPFIA fpg Expt GXPFIA fpg

61Mn36 63Mn38

Figure 5.7: Systematic variation of the low-energy levels of the neutron-rich, odd-A
25Mn isotopes, along with the results of shell model calculations with the GXPFIA
and f pg interactions. Only levels below 2 MeV are presented. In addition, the shell
model results shown are limited to the three lowest energy levels calculated for J 7' =
1/2" — 7/2‘, and the yrast levels for J7r = 9/2" and 11/2". Levels with assumed
negative parity are shown as solid lines, and those with positive parity are presented
as dotted lines. Spins are given as 21 and, in nearly all cases, are tentative as discussed
in the text.

142

cases where the calculations were completed with both 2 and 6 neutron excitations
allowed from the f p shell, similar results were obtained.

The low density of levels below 1 MeV is persistent in 57’59’61Mn, and agrees well
with the shell model results with the GXPF 1A effective interaction. The only excited
state in this energy range is the 7/2‘ level, which is expected to carry a reduced
1f7/2 single-particle component with the addition of neutrons [118]. The low-spin
level density below 1 MeV is shown to increase at 61Mn in the shell model results
with the fpg interaction. Here, the influence of the 199/2 neutron orbital becomes
apparent at N = 36. However, this is not borne out in the observed level structure.
The regular behavior of the low-energy levels of the odd-A 25Mn isotopes through
N = 36 follows the similar trend observed in the even-even 26Fe isotopes, where the

possible onset of collectivity at low energy is not evident until N = 38 is reached.

5.3.2 Even-A Mn isotopes

Although no new data for the even-A Mn isotopes are reported in this work, the
systematic variation of these states provides additional support for the delayed onset
of collectivity in the Mn isotopes. Only a few excited states in the odd-odd 60’62Mn
were established based on fl-decay studies [58,121]. The low-energy levels in these
isotopes are shown in Figure 5.8. Two ,B-decaying states are known in both isotopes,
but the location and ordering of the proposed 1+ and 4+ states has not been estab-
lished in 62Mn37 [58]. Good agreement was noted between shell model results with
the GXPFI interaction and both the low-energy structure and fi-decay properties
of 60Mn35 [121]. The low-energy structure of 62Mn built on the 1+ fi-decaying state
shows marked similarity to that in 60Mn, albeit the excited 2+ and 1+ states are
both shifted ~ 100 keV lower in energy with the addition of two neutrons. Although
Valiente-Dobon et al. reported a number of in-beam 'y rays associated with the de-
population of yrast levels in both 60Mn and 62Mn, no level structures were proposed

due to the lack of coincidence data [57]. Again, the systematic variation of the (few)

143

 

 

 

 

 

 

 

 

 

 

 

E 2 ’-
,gs __
CI
LT-l
1 _
1+
1+
2+..—
4+ (04'2“) if
2“—
._ + 1+ +
0 1 mm 1
60MI135 64Mn39

Figure 5.8: Experimentally known low—energy level structures for the even—A Mn
isotopes from N235 through N239. The location and ordering of the proposed 1+
and (3+, 4+) states in 52Mn is unknown — for the purposes of the figure, the 1+ states
were aligned for all isotopes.
excited levels established in the odd-odd Mn isotopes through N 2 37 does not sug-
gest a sudden onset of collectivity, in line with the trend established for the yrast
states of even-even 26Fe isotopes.

Beyond N237, low-energy levels in 64Mn are known from the 6 decay of 64Or [122].
A low-lying 2‘ state has been identified at 40 keV in 64Mn, as shown in Fig. 5.8.
Identification of such an unnatural parity state is an indication for the approach of
the 11ng /2 level close to the Fermi surface in this isotope. This structural signature
provides the first indication of the approaching deformation-inducing 1g9/2 orbital

in the Mn chain. Additional spectroscopic measurements in this isotopic chain are

required to more fully characterize the onset of deformation in the Mn isotopes.

144

 

 

 

 

 

30 32 34 36 38 40 42 44 46
Neutron Number

 

Figure 5.9: Two neutron separation energies in the N 240 region. Hollow symbols
indicate masses taken from the 2003 Atomic Mass Evaluation [80], while filled symbols
are masses measured recently using the time—of-flight method at NSCL [123]. Figure
was adapted from Ref. [123].

5.3.3 Deformation in comparison to neighboring 24Cr

and 26Fe isotopic chains

The low density of states in 61Mn has been shown to agree with the results of shell
model calculations in the f p model space without the need to invoke neutron ex-
citations into the 199/2 orbital. There is no compelling evidence for the onset of
collectivity in the 25Mn isotopes through N237. However, at N239, there is evi-
dence of the influence of the 1g9/2 neutron orbital, in the form of a 2‘ unnatural
parity state at low energy in 64Mn. These observations are consistent with the be-
havior of the neutron-rich Z +1 26Fe isotopes, where no indication of collectivity was
observed until N 238. While spectroscopic information is not available beyond N239
in the Mn isotopes, nuclear mass systematics in the region surrounding N 240 have
recently been extended in the Cr, Mn and Fe isotopes [123]. The systematics of the
mass observables, such as the two—neutron separation energies (82"), are sensitive to
deformation effects, as discussed in Chapter 1. Two-neutron separation energies are

shown in Figure 5.9 for the isotopes surrounding N 240 and Z225.

145

 

As discussed by Estradé [123], a reduction in the slope of the Sgn values as a func-
tion of neutron number has been observed to coincide with the onset of deformation
in the Fe isotopes. The reduced slope corresponds to extra neutron binding as defor-
mation sets in. The reduction in the slope begins in the 25Mn isotopes at N237, in
agreement with the spectroscopic observations to date. A change in the slope of the
two neutron separation energies for the Fe isotopes is observed at N 240, coinciding
with the onset of deformation in the Z226 isotopic chain. The Cr isotopes present a
less clear case. A subtle change in the slope begins at N 236, in agreement with the
earlier onset of deformation in the even-even 24Cr isotopes evident in the systematic
variation of the 2? states. Thus, mass systematics appear to agree with spectroscopic
observations for the onset of deformation in the Cr, Mn and Fe isotopes. Collectivity,
resulting from the lowering of the [1199/2 orbital closer to the Fermi surface, occurs
earliest in the 24Cr isotopes, while the onset of deformation in the 25Mn isotopic
chain occurs later, more like the situation in the 26Fe isotopes. With the removal
of additional 1f7/2 protons below 24Cr, in the 22Ti and 20Ca isotopes, the V199 /2
orbital is expected to be lowered further, and collectivity may develop even sooner.
The lowering of the V1 99 /2 may also lead to a new “island of inversion” surrounding
3%Ti40, as first suggested by Brown [124], and discussed by Tarasov et al. in light of

enhanced production cross sections in the region near 62Ti [125].

146

Chapter 6

Conclusions and Outlook

6. 1 Conclusions

The low—energy level structures of nuclei within and near the fp shell have been
investigated using fi-delayed and prompt 7-ray spectroscopy, to find evidence for
changing nuclear shell structure.

The low-energy levels of neutron—rich 535436180 were investigated through the
fi decay of the parent nuclides 53'54Ca, as well as through prompt isomeric 7-ray
emission from 541568c. These nuclei reside in the vicinity of the known N 232 subshell
closure, a result of the large gap between the u2p3/2 orbital and the higher-lying
V2121 /2 and V1f5/2 orbitals. The low-energy structures of the Sc isotopes were analyzed
in the extreme single-particle model framework, as a coupling of the valence 1f7/2
proton to states in the corresponding 20Ca core. Such a description worked well for
53Se, where the valence proton weakly couples to states in doubly-magic 33Ca32. The
success of this description provided further confirmation for the validity of the N 232
subshell closure in the Ca isotopes. Interpretation of the low-energy levels in the even-
A Sc isotopes as resulting from the coupling of a 1f7/2 proton and valence neutrons

to a Ca core provided information on the separation between the V2p1/2 and u1f5/2

orbitals. The energy separation between these orbitals is proposed by some shell-

147

model interactions to be sufficient to produce a new subshell closure at N 234 in the
Ca isotopes. While more work is required to complete the relevant multiplets of states
in 541568c, early indications suggest that the low-energy levels in the Sc isotopes are
compressed relative to shell-model predictions and that a significant N 234 subshell
gap does not exist between the 121/2 and f5/2 neutron levels in the 218C isotopes.
More information is required for the 20Ca isotopes, specifically at 54Ca to determine
conclusively whether the removal of the final f7/2 proton is sufficient to create a
substantial subshell closure at N 234.

The low-energy isomeric structure in §8K, with protons in the sd shell and neu-
tron occupying the f p shell, was investigated using prompt 'y-ray spectroscopy. The
observed isomeric structure of 50K was suggestive of a re—ordering of the proton sin-
gle particle states below the Z 220 shell closure. The isomeric structure was best
explained with a V2123 /2 <8) 71231/2 configuration for the ground state in 50K, which
gives rise to a 1‘ ground state spin and parity. This is inconsistent with previous
assignment of 0‘ for the ground state of 50K, based on fl-decay measurements [110].
The predictions of the most recent sd- f p cross-shell effective interactions, the SDPF—
U interaction from Nowacki and Poves [101], and the newest interaction from Utsuno
et al. [102], are also inconsistent with the suggested 1‘ ground state in 50K. Theo-
retical work is required to reconcile the predictions of these cross-shell interactions
with the recent experimental results in the K isotopes. Additional spectroscopic in-
formation is also required for the K isotopes beyond N 228 to provide the constraints
necessary to more fully understand the monopole interactions involved at work, and
the evolution of the proton single-particle energies below Z 220 in the region.

The 6 decay of 61Cr was studied to extract details on non-yrast excited states
in the daughter nucleus ggMn36. This nucleus is situated near N 240, in a region
where evidence of collectivity has been observed in the neutron-rich 24Cr and 25Fe
isotopes, with an apparent onset at N 236 and N 238 respectively. The structure of

the neutron-rich Mn isotopes is important to determine the onset of deformation in

148

 

the Z225 isotopic chain, and improve the understanding of the role of the V199 /2
orbital in enhancing deformation. The dependence of single-particle energy shifts on
the proton number Z in this region can also be probed through study of the low-
energy levels in the Mn isotopes. The low—energy level scheme for 61Mn, deduced
following 6 decay of 61Cr, features five new excited states above a l-MeV excitation
energy. However, the low-energy structure below 1 MeV did not resemble that from
the shell model results that consider the 199/2 orbital. The low density of states below
1 MeV is a consistent feature observed in the odd—A Mn isotopes with A 2 57, 59, 61,
and follows the results of shell model calculations restricted to the f p model space.
There is also little variation in the yrast structures of these odd-A Mn isotopes up to
J 2 15 / 2, as reported by Valiente—Dobon et al. [57]. No compelling evidence was found
for the onset of collectivity in the low-energy structures of the Mn isotopes through
N 2 37. The only evidence for the onset of collectivity in the Mn isotopes comes at
N 239, where a unnatural parity states suggests the approach of the V1 99 /2 orbital
close to the Fermi surface. These observations are consistent with the behavior of the
even-even, Z +1 26Fe isotopes, but not with that of the even-even Z —1 24Cr isotopes,
where possible onset of collectivity at low energy has been suggested from the E(2f)
energy at N 2 36. Little data are available for both yrast and non-yrast levels in
the 25Mn isotopes beyond N 2 36. Such data will be critical to evaluate the role of
the neutron 199/2 orbital in defining the structural properties of the neutron-rich Mn

isotopes.

6.2 Outlook

6.2.1 Open questions in the fp shell

While the results presented here have provided information on the nuclear structure
in and around the f p shell, a number of questions remain. Further experiments are

necessary in these regions may serve to provide the information critical to clarify the

149

situation.

The present work has provided information on the low-energy level structures of
the neutron rich 53:54:568c isotopes in the region surrounding N 234. However, the
actual parentage of the low-energy states in 54 Sc and 56Sc needs to be confirmed. Firm
assignments for the spin and parity of these low-energy states, and determination of
the purity of the single-particle configurations would serve to more fully characterize
these nuclei. A measurement of the angular distribution, or internal conversion of the
isomeric 110-keV transition in 54Sc would provide the required information to confirm
the multipolarity of the transition, and establish the spin and parity of the 110—keV
state. Neutron knock-out reactions into both 54Sc and 568C would access the neutron
spectroscopic factors for the low-energy states in these nuclei. Spectroscopic factors
will be critical in providing the final confirmation for the parentage of the low-energy
states in 541568c, and providing the most robust check for shell-model calculations.
However, due to the close energy spacing in the low-lying levels of 54,5630, these
experiments may benefit from the improved resolution expected using next—generation
'y-ray detector arrays, with sub—segment position resolution. The direct study of the
low energy states of neutron-rich 54’56Ca isotopes is also critical, but will likely have to
wait for next generation accelerator facilities due to the low production cross-sections
for these isotopes.

Evidence for the inversion of the 2d3/2 and 1.51/2 proton orbitals in the potas-
sium isotopes beyond N 228 is based on indirect measurements. The present data
in 50K is suggestive of a 1‘ ground state, arising from a configuration involving a
231/2 proton hole. The tentative assignment suggests that the 71’231/2 orbital remains
above the 7rd3/2 past N 228. However, absolute confirmation of the ground state spin
could be obtained through a measurement of the ground state hyperfine splitting in
4950K. Measurement of the ground-state g-factors in the K isotopes beyond N 228
would also provide valuable information. Such a measurement using fi-N MR and laser

spectroscopy has been proposed at ISOLDE, and will provide information regarding

150

the ground-state configurations in the K isotopes from N 229 to N 232 [126]. Proton
transfer reactions would provide the spectroscopic factors necessary to disentangle
the proton single-particle contributions to excited states in 49’50K. Knowledge of the
parentage of these states would further clarify the relative spacing of the 7r1d3/2 and
«231/2 orbitals, and the appropriate strength of the cross-shell proton-neutron tensor
interactions.

There is evidence of a new region of deformation developing in the 24 Cr, 25Mn and
26Fe isotopes near N 240, as the neutron 199/2 orbital drops in energy with increased
occupation of the proton 197/2 orbital. The present results extended the knowledge in
the Mn isotopic chain at N 236. Within this region, further fl-decay studies of the Cr
isotopes beyond N 236 into the Mn daughters would provide an important extension
of the knowledge in this isotopic chain. It appears that collectivity in the Mn isotopes
does not occur until N 238, as was the case in the Fe isotopic chain. Determination of
the level densities in the odd-A 63’65Mn, which is achievable through 6 decay, could
provide the experimental signature for developing collectivity in the Mn isotopes.
thure facilities will also prove critical in this region, in pushing spectroscopy of

isotopes in the Cr, Mn and Fe chains to larger neutron excess.

6.2.2 The NSCL 6 Counting System with Digital Data
Acquisition

The NSCL 6 Counting System provides a means for determining critical fl-decay
properties needed to test nuclear structure models far from the valley of stability.
The work presented in this dissertation is an example of the value both isomeric
and fl-delayed 7-ray spectroscopy with the combination of the BCS + SeGA can
play in characterizing the evolution of nuclear shell structure as a function of isospin.
However, planned improvements to the BCS will serve to expand its capabilities.

A digital data acquisition system (DDAS) has been developed at NSCL based

151

on the Pixie-16 Digital Gamma Finder (DGF) modules by XIA LLC [127]. When
used with segmented germanium detectors such as SeGA, one of the greatest assets
of digital data acquisition is the opportunity for pulse-shape analysis of digitized
signals. Pulse shape analysis permits the localization of 'y-ray interaction points to
sub-segment resolution, which in turn permits more accurate Doppler corrections,
critical for in-beam 7 spectroscopy.

DDAS is being adapted for use with the BCS. Preliminary testing of the BCS dual-
gain preamplifiers with DDAS has shown that the system is compatible with the fast
(~300 ns rise time) output signals of these preamplifiers. With correct settings of the
DDAS energy filter parameters, the resolution achieved with DDAS was comparable
to, or slightly better than that achieved with the standard BCS analog electronics.
Figure 6.1 illustrates the 228Th spectra obtained for a single strip in a 1 mm SSSD
using both DDAS and the standard BCS analog electronics. The main advantage in
using digital data acquisition for the BCS is the improved detection efficiency. The
application of DDAS with the BCS silicon detectors is expected to reduce noise levels.
This noise reduction will increase the detection efficiency of the BCS, since more of
the low-energy 6 particles will produce true triggers. A gain in efficiency will also
be realized due to the zero dead-time option of DDAS — data storage buffers permit
readout of the modules with no dead—time losses. In addition to the gains in efficiency,
the ability to capture and record waveforms will expand the possibilities for the use of
the BCS in charged-particle decay studies, where short-lived (~ as) charged particle

decays may be characterized via detailed waveform analysis [128].

152

 

3
o

 

 

 

 

 

 

 

 

 

 

 

 

 

’83 : a")
“a 35 - Analog — 2500 4:
it: — DDAS : a
712/ 30 L 2000 m
E 25 3 §
0 8.78 MeV I 0
U _. U
200 I] I i 1500
150 —§ 1000
~ A FWHM _
100 ~ 95 keV :
—_ 500
50 J _
o 1 1 1 1 I . ._ - —J1 1 I 1 14 1 l 14_1 1 0

Figure 6.1: 228Th a spectrum collected in a single strip of a 1 mm thick SSSD using
DDAS (red line) and the standard analog BCS electronics. The resolution achieved
in DDAS is comparable to that obtained with the analog electronics.

153

 

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