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.. i1 LIBRARIES
” . MICHIGAN STATE UNIVERSITY
EAST LANSING, MICH 48824—1048

This is to certify that the
dissertation entitled

Beta Decay Studies of Neutron-rich Nuclides and the
Possibility of an N = 34 Subshell closure

presented by
Sean Nicholas Liddick

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Chemical Physics

,4 ,
(”2

Major Professor’s Signature
lL {1] Z8 0+

Date

 

 

MSU is an Affinnative ActiorVEquaI Opportunity Institution

 

PLACE IN RETURN BOX to remove this checkout from your record.
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_—_————- - ——.———-

BETA-DECAY STUDIES OF NEUTRON-RICH NUCLIDES
AND THE POSSIBILITY OF AN N = 34 SUBSHELL CLOSURE

By
Sean Nicholas Liddick

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Chemistry
2004

ABSTRACT

BETA-DECAY STUDIES OF NEUTRON-RICH NUCLIDES
AND THE POSSIBILITY OF AN N = 34 SUBSHELL CLOSURE

By
Sean Nicholas Liddick

An inspection of periodic trends in ionization energies is one manifestation of
electronic Shells in atoms. Analogously, trends observed in nuclear masses led to the
development of the nuclear shell model. Areas of increased stability at the traditional
magic nucleon numbers 2, 8, 20, 28, 50, 82, and 126 have been associated with large
energy gaps encountered in the filling of shell-model orbitals. The reordering of levels
within the Shell model is an important question in nuclear structure studies as it may
lead to the development of new magic numbers far from stability.

The experimental characterization of the N = 32 subshell closure in Cr, Ti, and
Ca isotOpes stimulated shell model calculations, using a new effective interaction
labeled GXPFI [1], that also indicated the possibility of an N = 34 subshell closure
in the 22Ti and 20Ca isotopes. The N = 32 and suspected N = 34 subshell closures
were attributed to a strong proton-neutron monopole migration of the V f5/2 state as
protons are removed from the 7r f7/2 level. One indication for the subshell closure at
N = 34, predicted by GXPFl calculations, is an energy of ~1500 keV for the the first
excited 2? state in 56Ti, Similar to the energy of the 2? state in 54Ti at the N = 32
subshell closure.

fl decay studies have been performed at the National Superconducting Cyclotron
Laboratory on neutron-rich pf-shell nuclides to investigate the possibility of a subshell
closure at N = 34. The nuclides that were studied included 563C, 57Ti, 58"59V, and 60Cr
and were produced through the fragmentation of a 140 MeV/ nucleon 86Kr beam on
a 9Be target. The nuclides were implanted into a Double—Sided Si Strip Detector
which was used to detect both implanted ions and decays. Decays were correlated

with implanted ions on an event-by-event basis and 7 rays were monitored with 12

detectors from the Segmented Germanium Array. For all nuclides studied, half-lives
and level schemes were deduced.

The experimental study focused on the fi decay of 56Sc, to determine the energy
of the 2;“ state in 33Ti34. A value of 1129 keV was determined for the energy of the
2+ -—+ 0+ transition in 56Ti, 400 keV lower than predicted, suggesting the absence
of a shell closure in the 22Ti isotopes. The ground state J’r assignments for 5680 and
57Ti along with other nuclides around the N = 32 subshell closure were used to infer
the migration of the neutron f5/2 state with the removal of protons from the f7/2
level using an extreme single-particle model. While the migration of the f5/2 agrees
qualitatively with calculations, the increase in energy of the uf5/2 with the removal
of protons from the f7/2 seems to be overestimated in GXPFl. However, there still
exists the possibility that with the removal of the last two protons from the f7/2 state,

the N = 34 subshell closure develops.

ACKNOWLEDGMENTS

First, I would like to thank my advisor Paul. Without his assistance this disser-
tation would not have been possible.

I would also like to thank all the members of the beta group for their willingness
to help run the beta decay experiment that this dissertation is based on and for the
numerous discussions on data analysis that followed.

My fellow graduate students at the lab were also invaluable during my time at
the lab. I would be remiss if I did not Specifically mention both Bryan and Jeremey.
Both of them listened to the numerous problems that were encountered along the way
to graduation and both have helped put things into perspective when things seemed
overwhelming. Jeremey, I’m sorry to say that there is no personal anecdote anywhere
in this dissertation. Thank you Bryan for always giving me an audience practice talks.
I’m sure that after listening to my Sc—56 talk more than a dozen times you might be
able to write about the beta decay of 80-56.

Finally I wouldn’t have been able to make it had it not been for the constant sup-
port from my wife (who is extremely excited about being mentioned in this document
and is now jumping up and down) and family. They always had encouraging words,

especially when it seemed that the dissertation was always just a few days from being

finished.

iv

Contents

1 Introduction

1.1 Description of Shell Closures .......................
1.2 Reordering of Single Particle States ...................
1.3 Observation of Shell Closures ......................

1.3.1 E(2f) ...............................
1.4 Proposed Measurement ..........................

2 Technique

2.1 fl decay ..................................
2.1.1 fi-delayed neutron decay .....................
2.2 7 decay ..................................
2.2.1 Internal Conversion ........................
2.3 Application ................................

3 Experimental Setup
3.1 Isotope Production and Delivery for Experiment NSCL—02004

3.2 Detector Setup for Experiment NSCL—02004 ..............
3.3 Beta Calorimeter .............................
3.3.1 Electronics .............................
3.3.2 Calibration ............................
3.3.3 Correlation ............................
3.4 'y-ray Detection ..............................
3.4.1 Calibration ............................
4 Experimental Results
4.1 5680 ....................................
4.2 58V .....................................
4.3 57Ti ....................................
4.3.1 57V .................................
4.4 59V .....................................
4 4.1 59Cr ................................
4.5 60Cr ....................................

5 Discussion
5.1 Comparison with Shell Model Results ..................

CDNICJTCHHH

14
14
19
19
21
22

24
24
26
28
30
32
38
42
43

50
51
57
63
70
71
82
87

93
97

5.2 Monopole Migration of Vf5/2 Based on Ground-State Spin and Parity

Assignments ................................ 103

5.3 Summary ................................. 105

6 Conclusions and Outlook 107
Bibliography 109

vi

List of Figures

1.1
1.2
1.3
1.4
1.5
1.6
1.7

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9

Atomic and Nuclear Shell Closures ...................
Nuclear shell structure ..........................
Migration of the 7/2+ state .......................
E(2+) in Ca isotopes ...........................
Chart of the nuclides ...........................
Low-energy level structure of N = 29 isotones. .............
E(2+) for the 24CI‘, 22Ti, and 20Ca lSOtOpBS ................

Layout of the N SCL ...........................
Experiment 02004 particle ID spectrum .................
Schematic of the 6 counting system ...................
Experiment 02004 DSSD electronics ...................
Experiment 02004 PIN electronics ....................
DSSD 228Th calibration ..........................
DSSD 90Sr calibration ..........................
Distribution of implanted ions across DSSD ..............
Implantation multiplicity in the DSSD .................
Decay condition in software .......................
6 detection efficiency ...........................
Correlation in strip number between DSSD and SSSDl and SSSD2

Experiment 02004 SeGA electronics ...................
Schematic arrangement of Ge detectors .................
Residual plot for first Ge calibration ..................
Residual plots for the individual SeGA detectors ............
Residual plot for the second Ge calibration ...............
Ge calibration between 900-1100 keV ..................
Detection efficiency for Ge detector array ................

Sample 58V 77 and time-7 matrices ...................
56Sc fl-delayed 7-ray spectrum ......................
56Sc half-lives ...............................
56Sc isomeric 7-ray spectrum .......................
5680 level scheme .............................
56Sc 77 coincidence spectra .......................
58V fi-delayed 7-ray spectrum ......................
58V 67 spectra with cuts on the correlation time ............
58V half-lives ...............................

vii

31
33
35
36
37
38
38
40
42
43
44
45
47
48
48
49

51
51
53
54
55

59
60

4.10 58V 77 coincidence spectra ........................ 61

4.11 58V level scheme .............................. 62
4.12 57Ti fi-delayed 7-ray spectrum ...................... 63
4.13 57T i [37 spectra with cuts on the correlation time ........... 64
4.14 57Ti half-lives ............................... 66
4.15 57Ti half-lives ............................... 67
4.16 57Ti 77 coincidence spectra ....................... 68
4.17 57V level scheme .............................. 69
4.18 57V 77 coincidence spectra ........................ 71
4.19 59V fl-delayed 7-ray spectrum ...................... 72
4.20 59V ,67 spectra with cuts on the correlation time ............ 74
4.21 59V 7-gated half-lives ........................... 75
4.22 59V 7-gated half-lives ........................... 76
4.23 59V 7-gated half-lives ........................... 77
4.24 59V 7-gated half-lives ........................... 78
4.25 59Cr half-life ................................ 80
4.26 59V half-life ................................ 80
4.27 59V 77 coincidence spectra ........................ 83
4.28 59V 77 coincidence spectra ......................... 84
4.29 59V 77 coincidence spectra ........................ 85
4.30 59Cr level scheme ............................. 85
4.31 59Cr 77 coincidence spectra ....................... 86
4.32 59Mn level scheme ............................. 86
4.33 60Cr fi-delayed 7-ray spectrum ...................... 87
4.34 60Cr 67 spectra with gates on correlation time ............. 88
4.35 59Cr decay curves ............................. 90
4.36 60Cr 77 coincidences ........................... 91
4.37 60Cr level scheme ............................. 91
4.38 60Fe level scheme ............................. 92
5.1 Spin-orbit splitting ............................ 94
5.2 Proton-neutron monopole interaction .................. 95
5.3 E(2+) for the 24Cr, 22Ti, and 20Ca isotopes ................ 97
5.4 E(2+) for the N = 32 isotones ...................... 98
5.5 Low—energy level structure of 54568C from shell model calculations using

the GXPFl interaction. ......................... 99
5.6 Experimental and Theoretical decay scheme for 57Ti .......... 102
5.7 J7r of nuclear ground states near N=32,34 ................ 103

viii

List of Tables

2.1
2.2

3.1

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

fl decay selection rules .......................... 18
7 transition rates and Weisskopf estimates ............... 21
List of 7—ray energies in keV for the two Ge energy calibrations. . . . 45
5680 fl-delayed 7 rays. .......................... 52
58V ,6 delayed 7 rays ........................... 57
57Ti fl-delayed 7-rays. .......................... 65
Ratio of 113- and 175- to the 1579-keV transition area ........ 70
Calculated 57Ti internal conversion coefficients from Ref. [2]. ..... 70
59V fi-delayed 7—rays ............................ 73
Increase in intensity of 59V daughter and grand-daughter 7 rays . . . 79
60Cr ,B-delayed 7-rays ........................... 87

ix

Chapter 1

Introduction

1.1 Description of Shell Closures

Discontinuities observed in the ionization energies of atomic electrons as a function
of Z, shown in Figure 1.1, have been linked to the filling of electronic shells. After the
filling of an electronic shell, the next valence electron is placed into a higher energy
orbital decreasing the energy needed to remove the last electron from the atom. Thus,
discontinuities in the ionization energies of atoms were correlated with the underlying
“shell structure”. In studies of the bulk properties of nuclei near the valley of stability,
discontinuities in a number of different physical observables involving nuclear masses
also suggested an extra stability of the nuclear system at ’magic’ nucleon numbers of
2,8,20,28,50,82, and 126. For example, consider the one-neutron separation energies
defined by

Sn(A,Z) = BE(A,Z) — BE(A — 1, Z) (1.1)

where BB is the binding energy of a nucleus, A is the mass number and Z is the atomic
number of the nuclide. From equation 1.1 we associate S7, with the energy necessary
to remove a neutron from the nucleus. Similar to the atomic case, just after a magic
number for an isotopic chain, a sudden drop in Sn is observed. The effect of the magic

numbers on the neutron separation energy can be emphasized by taking differences

between one-neutron separation energies between neighboring isotopes, defined as

A5,, = BE(A, Z) — BE(A — 1, Z) — [BE(A + 1, Z) — BE(A, 2)] (1.2)

where again BE is the binding energy, A and Z represent the mass number and atomic
number of the nuclide, respectively. A3,, is shown in Figure 1.1 for all even-even
nuclides up to 94Pu.

Theoretical attempts to reproduce the observed magic numbers gradually led to
the development of the nuclear shell model. In contrast to the atomic case, where the
electronic shell structure arises from the well known Coulomb potential created by the
protons, the potential for the description of nucleons inside the nucleus was poorly
understood and various models were tested in an attempt to explain the behavior.
A few simple potentials were tried for the nuclear shell model, such as the harmonic
oscillator and the square well, but these potentials were not realistic descriptions of
the expected nuclear potential especially since both require the potential go to infinity
at large radii. In spite of the infinite energy of the harmonic oscillator and square well
potentials, both were able to reproduce the shell closures up to 20 and showed that
the closures are associated with a large energy spacing between two different single-
particle orbits. A more realistic potential approaches zero far from the nucleus, a
condition fulfilled by a Woods-Saxon potential of the form:

-Vo

V”) = 1+ e(T—Ro)/G

 

(1.3)

where a is the diffuseness of the nuclear surface, R0 is the mean nuclear radius, r
is the distance from the center of the nucleus, and V0 is the depth of the potential.
While the Woods-Saxon potential is more realistic (V—>0 at large r) it was still unable
to reproduce the magic numbers observed above 20. The problem was finally solved
with the introduction of a spin-orbit force that breaks the degeneracy between the

pairs of states with l > 0 [3,4]. The spin-orbit force results in the reduction in the

 

 

 

 

 

 

 

 

 

 

 

 

30
9
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G)
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D
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.5
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0 25 50 75 100
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9 i i i 126
g ‘ 1. I
v 4 ’ v .A‘ El...

C ' "LT“ V

g I F !" “c? f A

2 _ first " x

0 1 I

0 50 100 150
N

Figure 1.1: In the top of the figure, the ionization energy is plotted as a function of the
atomic number. Large drops in the ionization energy occur. following the filling of an
atomic shell. The bottom part of the figure shows the differential neutron separation
energies as a function of neutron number. Lines connect series of isotopes. The peaks
located at the magic numbers suggest additional stability that can be associated with
the filling of nuclear shells.

6

99/2 p1/2
f5/2 p3/2
f7/2
s d3/2
1/2 d

5/2
p1/2
p3/2

@
51/2

Figure 1.2: Nuclear shell structure up to nucleon number 50 for a Woods-Saxon po-
tential with a spin-orbit interaction. Energies are not to scale and states are labeled
by l and j.

energy of the l + 1 / 2 state and reproduces the known shell closures. The shell structure
described by the Woods-Saxon model with a spin-orbit force is shown in Figure 1.2
up to the nucleon number 50 shell closure [5]. For example, from Figure 1.2 the magic
numbers at 28 and 50 are a result of the spin-orbit splitting between the f7/2 — f5/2
and 99/2 — 97/2, respectively.

Using the known shell closures, shell model calculations can be performed by di-
viding the nucleus into an inert core, containing most of the nucleons coupled to 0+,
and a small number of valence particles outside the core. An effective shell model
interaction is developed for the valence nucleons to describe the nuclei in a specific
region. In this manner, the nuclear shell model, schematically displayed in Figure
1.2, has proven to be very successful in the reproduction and prediction of nuclear
properties close to the valley of H stability. It should not be assumed, however, that
the relative energies between levels shown in Figure 1.2 are static. The possible re-
arrangement of single-particle levels is of great interest in shell structure studies and

can result in the development of new magic numbers.

1.2 Reordering of Single Particle States

A significant reordering of single-particle states has been observed in nuclei close
to stability in the N = 50-82 shell. The reordering involves the migration of the
proton 97/2 orbit in the Sb isotopes inferred from the shift in energy of the 7/2+
state as neutrons are added to fill the neutron 1111/2, see Figure 1.3 [6]. Notice that
when neutrons are added to the h11/2 state (beginning around N = 66) the energy
of the 97/2 state decreases and is reflected in the energy of the 7/2+ of Sb, which
eventually becomes the ground state in é¥3Sb72. The reduction in the energy of the
97/2 single particle level has been attributed to an attractive proton-neutron monopole
interaction, between the 7ng/2 - Vh11/2 states, reducing the energy of the 97/2 level
by approximately 2 MeV across the Sb isotopes. This is an additional interaction
on top of the spin-orbit interaction discussed above. While the monopole interaction
is significant between the 7ng/2 — Vh11/2 levels, as evidenced in the Sb isotopes, it
is strongest when proton and neutron orbitals have similar values of orbital angular

momentum, [(proton) ~ l(neutron) [7].

1.3 Observation of Shell Closures

In the single-particle picture shown in Figure 1.2, shell closures occur where there is
a large energy difference between consecutive single-particle states. At a shell closure,
a nucleus may be considered a spherical system with limited collective features at
low excitation energies. The low-energy level structure of nuclei at shell closures can
usually be described using single-particle excitations. However, as nuclei progress
away from a shell closure, collective interactions (involving many nucleons at the
same time) become more likely. Collective behavior in the proximity of shell closures,
is associated with the vibration of the nuclear shape. At midshell, the highly collective
system displays features that can be described as the rotation of a statically deformed

nucleus. The increase in collectivity leads to the evolution of the nuclear shape from

r- 1558
“’2 _1501 1419 1427 —1484 h
_ 11/2
_ 1348 .1159 “11 2
“11/2 — 1300 fig h “1 /
11 2 11/2
/ “up 1112

83222 315
769 _
_g 97/2 97/2 97/2 724
7/2 972
’ 527

97/2
270

9 9
7/2 7]:7 95/2
0 O 0 0 0 0 0 0 O _. 0 0 0 0 0 0

d5/2 d5/2 d512 d5/2 d5/2 d5/2 d5/2 d5/2 d5/2 d5/2 d5/2 -150 d5/2 d5/2 dS/Z d512 d5/2

 

97/2 -332

97/2 -491
97/2 24.5

9
7’2 -798

97/2 -963
97/2

50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82
Neutron Number

Figure 1.3: Migration of the 7/2+ state in Sb isotopes as a function of neutron number.
Energies of the different states relative to the d5/2 level were taken from experimental
data. The migration is attributed to the proton-neutron monopole interaction between
1rg7/2 and uhn/g. As neutrons are added to the flu/2, beginning around N = 66, there
is a steady drop in the energy of the proton 97/2 state.

spherical to a static deformation, resulting in either oblate (discus-like) or prolate
(football-like) shapes. The static deformation can be characterized by the quadrupole
deformation parameter, ,3). The sign of ,82 describes the shape of the nucleus with
positive values associated with prolate shapes and negative values associated with
oblate shapes. There exist a variety of different probes to measure the quadrupole
deformation of the nucleus. For the current study the energy of the first excited 2+
state, E(2f), in even-even nuclei will be used and, qualitatively, a higher E(2f) values

for more rigid spherical nuclei is expected.

1.3.1 E(2f')

The experimental signature for the possible presence of a shell closure used herein
will be the energy of the first excited 2+ state in even-even nuclei, E(21+). Globally,
the E(2f) is a good indication of shell structure when compared systematically across
a range of isotOpes. The behavior of an E(2f) value can be related to the degree of
collectivity in the nuclear system in a relatively simple way . At shell closures, the
nucleons completely fill the single-particle levels below a large energy gap. To create
a 2+ state, a pair of nucleons must be broken and one nucleon promoted to a higher
single-particle state across the energy gap due to the Pauli principle. This costs a
considerable amount of energy, resulting in a high E(2f) value. Further from a shell
closure, the configuration of the nucleons is more complicated with unfilled orbitals
and the energy of the 2+ state is lowered as a result of collective interactions among
many nucleons and can be describes in terms of a vibration or, if a static deformation
exists, a rotation of the nucleus.

Grodzins [8] developed the following empirical relation between the quadrupole

deformation parameter, ,82, and E(2+)

1225MeV

E9” = W

(1.4)

 

 

 

 

4000 ——1
9 3000 — "
g . . .9
E, 2000 — ‘3... °
9:: t .......... . .......... o" "o.
“J 1000 -— '-
0 L l L l I l l
20 24 28 32

Neutron Number

Figure 1.4: E(2+) values in the 20Ca isotopes as a function of neutron number. The N
= 28 shell closure and N = 32 subshell closure are revealed from a peak in the E(2+)
values.

where A is the mass number of the nuclide. As a shell closure is approached the
nuclear shape becomes more spherical, 32 decreases, and the E(2f) increases. As a
progression is made to the nuclei in the middle of a major shell collectivity increases
and leads to a reduction in the E(2f).

The E(2f) values for even-even 20Ca isotopes are shown in Figure 1.4 as a spe-
cific example. Indications of the shell closures at N = 20,28 are observed in Figure
1.4 as peaks in the E(2f) value. Also, in the neutron-rich Ca isotopes, there might
be a smaller peak located at N = 32 [9]. The reduced height of the peak at N =
32 can be attributed to a subshell closure in which the energy separation between
two consecutive single—particle orbits is significant but not as large as a shell closure.
The existence of the N = 32 subshell closure, and the possibility of additional sub-
shell closures in neighboring neutron-rich nuclei, is an interesting question since the

development of a subshell closure would inhibit the onset of collectivity.

1.4 Proposed Measurement

The present study concentrated on the region of the chart of the nuclides shown in

Figure 1.5. The region is centered above the Z = 20 proton closed shell and the N =

 

 

F---
“A

”0156 Cr57 Cr58 Crs9j Cr60 Cr61 Cr62 cuss Cr64 Cr65 42

5V55 V56 V57 V58 V59 V60 V61 V62 V63

E
1.

£71154, T155 Ti56 T157 Ti58 Ti59 Ti60 THE] 40

N
A

 

 

 

 

 

 

 

I
Sc53 Sc54 Sc55 [Sc56 Sc57 Sc58 Sc59
' _

 

Proton Number
nfiU2____.

N

N

N
O

Ca52 C853 C1154 0155 C856 C857 38

32 34 36
vpf

 

 

 

 

 

 

 

 

 

 

V

Neutron Number

Decay Q-value Range
Q(B-)>0
D Q(B-)-S N>0
I Naturally Abundant

Figure 1.5: Chart of the nuclides focusing on the region around Z = 20 and N = 32.
Nuclides available for study in this experiment are colored white and outlined with
the dashed gray line. The five nuclides have a decay Q value that is greater than the
neutron separation energy. Limited spectroscopic information was available for the
nuclides in this region before the study presented here.

32 neutron closed subshell. The B decay of 5680 to levels in 56Ti was investigated to
determine E(21+) in 56Ti at N = 34 and the possibility of a neutron subshell closure.
In addition, new data on the ,8 decays of 5"'Ti, 58"59V, and 6OCr were obtained.

As mentioned in Section 1.2, the migration of the 7rg7/2 state in the Sb isotopes
was due to the monopole interaction between the 1rg7/2 and Vh11/2 states, which have
similar 1 values. The strongest proton-neutron monopole interaction occurs between
nucleons in orbitals that are spin-orbit partners and may lead to a significant reorder-
ing of single-particle states far from stability. Due to the large spin-orbit splitting,

this overlap is strongest in neutron-rich nuclei between the 1r(l + 1 / 2) and V(l - 1 / 2)

single-particle states that lowers the energy of the V(l — 1/2) level, possibly leading

 

 

4 1 J
9 , ——; N=29 isotones
Q) I
>~ I _
g '1 I: #2
.5 ——m‘ : -'
c 2‘ —-,: 5
8 :'-' :
.13 , l' I
E 1 - 2!: . ' 1 -
‘. "—#.JJ_2-_w
.- ._ :
’—
o - J— _ _ £24-
SM Exp 2211 240 26I=e Exp SM
zoca 28Ni

Figure 1.6: Low-energy level structure of N = 29 isotones. The energy of the 5/2+
state drops dramatically with the filling of the 7r f7/2 level and is attributed to the
proton-neutron monopole interaction between the 1r f7 /2 and Vf5/2 states.

to a dramatic reordering of single-particle states [10]. In the pf shell, the spin-orbit
parnters 7r f7 /2 — V f5 /2 are ideal candidates for the development of novel shell structure
far from stability. The low-energy structure of neutron-rich nuclei with nucleons occu-
pying the proton f7 /2 state and neutron f7/2, p3/2, f5/2, 101/2 orbitals, shown in Figure
1.6, is dramatically affected by the strong and attractive proton-neutron monopole
interaction between the spin-orbit partners 1r f7 /2 and uf5/2. As protons are added to
the 7r f7 /2 orbital, going from 2008. to 23Ni, the effective single-particle energy of the
uf5/2 orbital decreases significantly relative to the Vp3/2 state. The lowering in energy
of the V f5/2 orbital, in combination with the large spin—orbit splitting between the
1433/2 and ”191/2 levels, is suggestive of a subshell gap at N = 32 for nuclides in which
the 7r f7 /2 orbital is occupied by four or fewer protons.

In addition to the E(2+) value for SgCa, discussed in the previous section, the
masses [11] of the Ca isotopes suggested added stability and provided early evidence

for a subshell closure at N = 32. However, systematic data for isotopes beyond

10

 

52Ca are unavailable, and it was believed that the appearance of a subshell gap at
N = 32 was reinforced by the proton shell closure at Z = 20. Experimental evidence
for a potential subshell closure at N = 32 for the 24Cr isotopes was reported in
Ref. [12], based on the systematic variation of E(21+) in the even-even Cr isotopes.
The value E(2f) = 1007 keV of 5601‘32 is more than 100 keV above that observed in
the neighboring 54’5'8Cr nuclei.

The systematic variation of E (21*) along the N = 32 isotonic chain was recently
completed for the 7rf7/2 nuclides with the determination of E(2‘f) = 1495 keV for
54Ti [13]. The increase in E(2f) from 24Cr to 2008. with removal of protons from
the f7/2 orbital, parallels the expected growth of the single-particle energy gap at
N = 32 due to the monopole migration of the Vf5/2 orbital (see Figure 1.6). The data
available for the higher-spin states in even-even 50’5’2’54Ti isotopes provide additional
evidence for the N = 32 gap [13]. In 54Ti, the significant spacing between the 61* state
at 2936 keV and the cluster of levels 8?, 91*, and 10fL at ~ 5800 keV suggests that a
substantial energy gap must be overcome when promoting one of the coupled 1493 /2
neutrons to either the Vp1/2 or the uf5/2 level.

It was predicted [14] that the continued monopole shift of the V f5 /2 orbital may
also lead to the development of a shell closure at N = 34, and that the low-energy
structure of 54Ca may be similar to that of 480a, which is doubly-magic. The shell
model calculations by Honma et al. employed a new effective shell model interaction,
designated GXPFI. The GXPFl calculations have been successful in reproducing the
experimental E(2'f) values in the neutron-rich 2003, 22Ti and 24Cr isotopes, as shown
in Figure 1.7, including the systematic increase in E(2f) at N = 32. The onset of an
N = 34 shell closure was first expected to be evident in the Ti isotopes, where E (21*)
for 56Ti34 was predicted to lie at approximately 1500 keV, similar in energy to its
neighbor 54TI32, see Figure 1.7.

The current experimental study focused on the measurement of E(2f) in 56Ti3,4,

populated following the B decay of 56Sc to test for evidence of a new subshell at

11

 

512:) (MeV)
S
13 l
j

 

N
1

 

N U #0

11111111

d

 

 

 

26 2'8 3b :32 54 ab 3'8 40

Neutron Number
Figure 1.7: E(2+) as a function of neutron number for the 24Cr, 22Ti, and 200a isotopes.
The circles connected by lines represent GXPFl calculations and the black bars are

experimental points. GXPFl predicts a shell closure at N = 34 in the Ti and Ca
isotopes evidenced by the systematic behavior of the calculated E(2f) values.

12

N = 34 for neutron-rich nuclides. Details regarding the study are provided in this
dissertation, and are organized in the following manner. A review of the different
decay paths for a neutron-rich parent nuclide are given in Chapter 2. A description
of the experimental endstation for the detection of implanted ions, [3 and 7 decays is
given in Chapter 3. Also included in Chapter 3 is a description of the calibration of
the both 3 and 7 detectors, the correlation between implanted ions and decays and
the electronic system used during the experiment. The results from the analysis of
the £3 decay of 56Sc, along with the 6 decays of 5"'Ti, 5859V, and 60Or, are given in
Chapter 4. A comparison between experimental results and calculated level structures
is given for 56Sc and 57Ti in Chapter 5. The tentative ground state spins and parities
of nuclides around the N = 32 subshell closure are analyzed in an attempt to describe
the monopole migration of the uf5/2 state as a function of proton number in the f7/2

in Chapter 5. The conclusions and outlook are given in Chapter 6.

13

 

Chapter 2

Technique

The primary purpose of this study was to measure the E(2f) of 56Ti to determine the
possible presence of an N = 34 subshell closure as discussed in the previous chapter.
The E(2f) values for even-even nuclei can be measured using a variety of different
methods including Coulomb excitation [15], direct reactions [16], and deep-inelastic
reactions [13]. For the present study, 6 decay was used to selectively populate the
low-spin states in an even-even daughter nuclide. A parent nuclide was produced
and its 6 decay was monitored. The 6 decay may populate excited nuclear states
in the daughter and these daughter states can then decay through 7-ray emission,
internal conversion, or if energetically allowed, through the emission of a neutron.
The observation of the secondary radiation is used to construct a decay scheme for
the parent nuclide into the different daughter states using absolute 7-ray intensities

and 77 coincidence information.

2.1 fl decay

fl decay involves the weak-decay process of converting a neutron (proton) into a proton
(neutron) keeping the mass number constant. Concomitantly, an energetic electron ()8

particle) and a low mass electrically neutral particle, called a neutrino, are emitted.

14

 

,6 decay collectively refers to three distinct decay processes listed below:

)8_ Z QXN 42+1YN_1 +33- +7+Q3 (2.1)
[8+ 1 gXN 49—1 YN+1 + ,B+ + l/ + Q3 9 (2.2)
Electron Capture : QXN + e“ a?“ YN_1 + V + Q5 (2.3)

where e‘ is an atomic electron, 6* is a beta particle, 11 is a neutrino, and V is an
anti-neutrino. 62;; is the characteristic amount of energy released in a specific 6 decay
process and represents the difference in mass-energy between the initial and final
states. If Q3 is positive the decay is energetically possible. To the neutron-deficient
side of the valley of stability both [3+ and electron capture processes occur, though
for a specific nucleus both may not be energetically possible because the emission of
a ,6“ has a threshold of 1.022 MeV.

During an electron capture process, a proton captures one of the atomic electrons
converting a proton into a neutron. Along with the conversion, 8 mono-energetic
neutrino is emitted. The capture of an atomic electron leaves a vacancy in one of
the lower electronic shells, typically the K shell. The hole in the atomic shell left by
the capture process is unstable and the electrons quickly reconfigure. The reconfig-
uration leads to detectable X-rays and Auger electrons. Though it is probable that
neutrinos have some mass, it is very small [17,18] and even so the neutrino escapes
undetected from most experimental apparati due to the low weak interaction cross
section; therefore, the identification of electron capture decay must be followed by
tracking the secondary emission of X—rays or Auger electrons.

Whenever, the mass difference between initial and final states exceeds twice the
mass of an electron (1.022 MeV) [3+ decay becomes possible. During [3+ decay, a
proton is converted to a neutron, similar to the electron capture process, with the
emission of a neutrino and 6+ particle. The 0+ will interact electromagnetically with

the medium after emission gradually losing energy and slowing down. Once the 6+

15

particle has reached thermal energies it will quickly combine with an electron and
annihilate, producing two 511-keV 7 rays propagating in opposite directions. The 6+
decay can be followed both through detecting the energy deposited in a detector by
the 6+ itself or by detecting the annihilation 7 rays.

For the current work, [3‘ decay was the decay mode of interest. 6‘ decay occurs
on the neutron-rich side of stability in which the weak interaction converts a neutron
into a proton with the emission of a 6‘ particle and an anti-neutrino. The decay is
observed by detecting the emission of the 6‘, as it will interact electromagnetically
with the electrons of the detection material. Since B emission is a three body process,
the total Q3 value for the reaction is equally shared between the daughter nucleus, 3‘
particle, and neutrino. This results in a 6 particle energy spectrum that extends from
zero to the Q3 value (minus a small amount of energy for the mass of the neutrino and
the nuclear recoil). For the decays in the present study, the Q3 values are typically
around 10 MeV. With such a large Q3 value, it is difficult to stop the electron in
the detection system, and the possibility of undergoing B delayed neutron emission
appears.

Important information obtained by monitoring the 6 activity is the rate constant,
A, of the decaying nuclides from which the half-life can be determined. An expression

for the half-life as a function of /\ can be derived using the first order rate law.

dINl _
(ll—1i, _ —NA (2.4)
'17,, = e_’\*t (2.5)

where t is time, No is the number of nuclei at time zero, and /\ is the rate constant.

At a value of N / N0 = 1/2 the half-life is

In 2
t1/2 = T.

16

,8 decay is useful as a spectroscopic tool owing to the selectivity of the decay
process. Angular momentum must be conserved during the transition between the
initial and final states in the 6 decay process leading to a restrictive set of selection
rules. Note that both of the created particles have an intrinsic spin, S=1 / 2. If the 6
particle and neutrino are emitted with zero orbital angular momentum, l = 0 (the
so-called allowed approximation), then only the intrinsic spins of the 6 particle and
neutrino need to be considered in the transition between initial and final states. If
the spins of the [3 particle and neutrino are anti-parallel (S=0), the total change
in nuclear spin, AJ, between initial and final states must be 0 and the fi decay is
termed Fermi decay. If the electron and neutrino are emitted with their spins aligned
(S=l), called Gamow—Teller decay, then AJ = 0,1. In both Fermi and Gamow-Teller
decays, the condition I = 0 means that the parities of the initial and final states
must be the same, following the condition Arr = (—l)’, where 7r is the parity of the
system. If the 6 particle and neutrino are emitted with l aé 0, the decay is classified
as “forbidden”. Unlike the name suggests, “forbidden” decays can occur, just with
a much smaller probability than allowed decays. Each value of l results in a higher
order of forbiddenness. The first, second, third,. .. forbidden decays result from the
5 particle and neutrino emitted with l = 1,2,3, . .. respectively. For each forbidden
decay, both Fermi and Gamow-Teller types can occur, and the parity change between
initial and final states may not be the same. For example, the first forbidden decay
involves l = 1. If the [3 particle and neutrino are emitted with spins anti—aligned (Fermi
type) then AJ=0,1. If the spins of the two emitted particles are aligned (Gamow-Teller
type) then AJ=0,1,2. In both cases the parity must change between initial and final
states because I = 1 in both cases. The probability of undergoing each successive level
of forbidden decay decreases by a factor of about 10“. The selection rules for ,6 decay
are summarized in Table. 2.1

If the 3 decay branching ratio to a particular daughter state is known then the

17

Table 2.1: fl decay selection rules for allowed and forbidden transitions from Ref. [19].
Logft ranges taken from Ref. [5].

Type AJ A7r logft
Allowed 0,1 no 3.5-7.5
First Forbidden 0,1,2 yes 5-19
Second Forbidden 1,2,3 no 1018
Third Forbidden 2,3,4 yes 17-22
Fifth Forbidden 3,4,5 no 22-24

 

 

 

 

 

 

 

 

partial rate constant of the B decay transition to that state can be determined from
A,- = BR, :1: A, (2.6)

where A,- is the partial rate constant to state i, BR,- is the branching ratio to state i,
and At is the total decay rate. The sum over all partial rate constants, A,, equals the

total rate constant. The partial half-life to state i can be calculated from

1' £0. 1n 2
T5721 1: A. . (2.7)

 

From the partial half-life a comparative half-life, ft, where t is in seconds, can be
calculated, where f is the “Fermi” function related to the shape of the [3 spectrum
that arises from the differing atomic numbers of the daughter and the endpoint energy,
allowing a comparison of different ,8 decay transitions. The comparative half-life can
be used to gauge the level of forbiddenness in a given 6 transition, but should not
be considered absolute. While compilations exist for finding logf values, a purely

empirical equation for the calculation of logf is [20]:

logf3— = 4.010gEo + 0.78 + 0.02Z — 0.005(Z - 1)logE0 (2.8)

where E0 is the ,B-decay energy and Z is the atomic number of the daughter nuclide.
As the value of the comparative half-life can extend over many orders of magni-

tude, the number frequently reported is logft. The logft value associated with different

18

types of decays are shown in Table. 2.1.

2.1.1 fl-delayed neutron decay

Neutron decay is the emission of a neutron from the nucleus under study. The equation
for such a decay is:

QXN H§_l XN_1 + II + Qn (2.9)

The Q, value for the reaction is again the mass-energy difference between the initial
and final products. The neutron separation energy is defined as the negative of the
Q, value when the product is left in its ground state. The neutron separation energy
is a positive number for all bound nuclei so that neutron decay from the ground
state is not possible. As neutrons are added to the nucleus the neutron separation
energy decreases. When the separation energy reaches zero it is not possible to bind
an additional neutron to the nucleus, and if a neutron is added, the nucleus will
undergo spontaneous neutron emission. However, in a fi‘ decay with a large Q3 value
it may be possible to populate excited states in the daughter nucleus that are above
the neutron separation energy. Such states could then decay by neutron emission
and this process is called fi-delayed neutron emission. Neutron emission occurs via
the strong, or nuclear, interaction and competes very favorably with electromagnetic
decay. The neutron decay can populate states in the A‘IX daughter which may then

undergo electromagnetic decay typical of that nucleus.

2.2 7 decay

Following a H decay, the daughter nucleus may be left in an excited state. The excited
state will generally decay to the ground state through the emission of one or more
7 rays. The emission of 7 rays results from a change in either the charge or current

distribution of the nucleus giving rise to an electric or a magnetic moment, respec-

19

tively. Thus, 7 ray emission can be classified as electric or magnetic in character. 7
rays, like 6 particles, carry off angular momentum from the excited nuclear state and
must satisfy the relation

|J,- — J,| _<_ ,\ g J,- + J, (2.10)

where A is the multipolarity of the transition and J,- and J I are the spins of the initial
and final states, respectively.

The change in parity, Avr, between initial and final states depends on the electric
(E) or magnetic (M) character of the transition and the angular momentum involved

as:

A71(EA) = (—1)" (2.11)

A71(MA) = (—1)"+1 (2.12)

The transition rates, W, of an electric or magnetic 7-ray transition are summarized

in the following pair of equations [19]:

87r(A+1) 1 E,
,\[(2,\ +1)!!]2E E

W(MA) = ahc( 218:6,»2 £3133], El—c(—bhj—;)2"+IB(MA) (2.14)

 

W(EA) = ahc )2"+1B(EA) (2.13)

 

 

where B(EA) and B(MA) are the reduced electric and magnetic transition probabilities
that contain information on the initial and final nuclear wavefunction, c is the speed
of light, a is the fine structure constant, Mp is the mass of a proton, and h is Plank’s
constant divided by 27r. .

It is useful to obtain some simple estimates for the values of the reduced transition
probabilities, B(EA) and B(MA), but this requires a model of the nucleus. Adopting
an extreme independent particle model, and assuming that the 7 radiation involves

the transition of one nucleon from an initial to a final single-particle state, the reduced

20

Table 2.2: 7 transition rates and Weisskopf single particle estimates for the reduced
transition probabilities from Ref. [19].

A wan) W(MA)
1.02x 1071/12/38? 3.15x1013Eg
7.28x107A4/3E9, 2.24x 107A2/3Ei’,

1.02x 10A2EZ; 1.04x 10A4/3E3
1.02x10-5A8/3Eg 3.27x10‘6A2E,y

1.02 x 10-"11’A10/3E},1 7.36x 10-13A8/3E33

 

 

 

 

 

 

CfirD-OONJH

 

transition probabilities can be calculated as:

1 3
Bw(EA) = Z; m)2(1.2)2’\A2A/382fm2” (2.15)
B MA _ 1'2 3 2 1 2 2A—2A(2A-2)/3 2 2A-2 2 16
w< )—,,<-—-—-,+3)<.> 11me (. >

where 113; is the nuclear magneton, A is the multipolarity, and A is the mass number.
Equations 2.15 and 2.16 are called the Weisskopf single-particle estimates for the re-
duced transition probabilities. Table. 2.2 lists the transition rates for different electric
and magnetic multipoles using the Weisskopf single-particle estimate for the reduced
transition probability.

For a given 7 transition, it is possible that several multipole radiations may be
emitted. From the estimated transition rates shown in Table 2.2 it can be seen that
the lowest multipole 7 transition will dominate the decay. Secondly, it is possible for
transitions to be of mixed type with magnetic and electric transitions, but the only

prominent case is when a mixed M1 / E2 transition is possible.

2.2.1 Internal Conversion

A competing process to 7-ray emission that may be significant for low energy transi-
tions or transitions involving a high value of A is internal conversion. Internal conver-
sion occurs when the electromagnetic fields responsible for the emission of a photon

interact with one of the atomic electrons resulting in its emission from the atom with-

21

out creation of a photon. In contrast to ,6 decay, the electron is not created during the
decay process, but is a preexisting atomic electron. The energy of the emitted electron
will equal the decay energy minus the binding energy of the electron. It is possible to
emit electrons from different atomic shells, and a measurement of the relative prob-
abilities of emitting conversion electrons from different atomic shells is one way to
determine the multipolarity of the transition involved. The probability of internal
conversion will increase if: Z is increased, the energy of the decay is decreased, or the
multipolarity of the transition is increased. The probability of internal conversion for

a particular decay is defined by the internal conversion coefficient, a.
a = — (2.17)

where A is the rate of decay of each radiation type, defined as 0.693/ 6173‘“. The inter-
nal conversion coefficient can vary between 0 and 00. An important case of internal
conversion occurs in transitions between 0+ states. Since A = 0 and Avr = (--1)0 = +1,
these are E0 transitions. In such transitions, 7 emission can not occur and the decay

must proceed through internal conversion or pair production.

2.3 Application

,6-delayed 7-ray spectroscopy was utilized to investigate evolution of shell structure
around the N = 32 and the suspected N = 34 subshell closure. Parent nuclides were
produced and the 6 decay into daughter states was observed. From the selectivity of
the ,6 transition, daughter states were populated if they satisfy the relation AJ = 0,1
with the same parity. Detection of the delayed 7 rays enabled the determination of the
excited nuclear states in the daughter, in particular, the energy of the first excited 21+
state was determined giving an indication on the possible existence of shell closures in

the region of study. 6-delayed neutron emission was detected through the observation

22

of 7 rays in the A-l mass chain with respect to the nuclide being examined. Internal
conversion was not directly observable but needed to be considered, especially for low-
energy transitions as the process will reduce the observed 7—ray intensity. The 6 decay
to, and the energies of, excited nuclear states in the daughter provided information on
the underlying nuclear shell structure in this region of exotic nuclei. The next chapter
will focus on the method of production for the parent nuclides and the instrumentation

used for the 67 measurements.

23

 

Chapter 3

Experimental Setup

3.1 Isotope Production and Delivery for Experi-

ment NSCL-02004

Except for the few long-lived natural radioactive elements, such as U and its radioac-
tive daughters, radioactive isotopes must be artificially produced on earth. At the
National Superconducting Cyclotron Laboratory (NSCL), radioactive isotopes are
produced using the projectile fragmentation method. In this method, a very fast pro-
jectile is impinged onto a target and a fraction is converted into one of a myriad of
reaction products. The reaction products, both stable and radioactive, emerge from
the target with large forward momenta and are analyzed to select only the nuclides
of interest.

The primary purpose of the current experiment was to study the 6 decay of
56Sc. 5630 was produced using the projectile fragmentation of a primary 86Kr beam.
The 86Kr beam was extracted from the K1200 at an energy of 140 MeV/nucleon
and was impinged on a 376 mg/cm2 9Be fragmentation target. The A1900 fragment
separator [21] was used to isolate the interesting reaction products from the resulting
assortment of nuclei produced in the 86Kr on 9B8 fragmentation reaction. A schematic

layout of the K500 and K1200 superconducting cyclotrons and the A1900 fragment

24

R’T-ECR

Q!) and, a a. K500
(3?“.% final
SOECR 90° '3 focus
6 \
998 A1900 ‘ 8-“
a
_ : ls dispersive g

plane /
h 53%?

production %9@ BBBLBBBQ

target

 

Figure 3.1: Layout of the K500, K1200 and A1900 components of the NSCL.

separator is shown in Figure 3.1.

A key feature of the present study was the production, separation, and identifica-
tion of each isotope prior to its decay. For this study, the A1900 had to be tuned to
optimize the production of 56Sc. The magnetic rigidity of the first half of the A1900
was set to Bpl = 4.239 Tm. At the second intermediate image the beam achieved
its maximum dispersion in the horizontal direction and was passed through a 330
mg/cm2 Al energy-loss wedge and 1% momentum slits allowing for a physical separa-
tion of the transmitted beam at the focal plane (labeled “dispersive plane” in Figure
3.1). A small momentum slit was chosen due to the unavailability of the scintillator
at the dispersive plane, which is necessary for time of flight correction to the particle
identification when a larger momentum acceptance is used. The magnetic rigidity of
the second half of the A1900 was set to Bp2 = 3.944 Tm. The transmitted particles
were brought back into focus at the final image and then delivered to the experimen-
tal endstation in the N3 vault. The rate of 5680 at the endstation was measured to be
0.0045 particles/s pnA. With an average primary beam current between 10 and 15
pnA the rate of 568C was ~3/min. Along with 563C, 57Ti, 58"59V, and 60Cr fragments
were also transmitted to the experimental endstation.

The fragments were implanted directly into a Double-Sided Silicon Strip Detector

(DSSD) to be described later in this chapter. Particle identification was achieved

25

 

through a combination of energy loss signals in silicon detectors at the endstation and
a measurement of fragment time of flight (TOF). The cyclotron rf signal was used as
the TOF stop throughout the experiment. Two different timing arrangements served
to create the start signal for the TOF measurement. The first start signal came from a
thin scintillator in the experimental vault approximately 2 meters upstream from the
DSSD. One third of the way through the experiment a beamline vacuum pump failed,
resulting in the loss of the scintillator and necessitating its removal from the beam
line. A replacement signal, used for the remainder of the experiment, was created from
a silicon PIN detector (PIN 1) located only 1m upstream of the DSSD. While using
the timing signal from the PIN detector resulted in a poorer TOF resolution, due
to poorer intrinsic resolution, the particle identification plot was still clean enough
to clearly identify all transmitted products and 568C was well separated from other
implanted isotopes. The energy-loss signal used in particle identification was derived
from the same silicon PIN detector. Plotting the energy loss as a function of TOF
results in the particle identification plot shown in Figure 3.2 (using the first timing
arrangement). The five different isotopes implanted at the experimental endstation
again were: 568C (12300), 57Ti (192100), 58V (153400), 59V (539800) and 60Cr (275100),
where the number in parentheses was the total number of implanted ions for that
nuclide used in the analysis presented in the next section. Notice that 568C was <1%

of the secondary beam delivered to the experimental endstation.

3.2 Detector Setup for Experiment NSCL-02004

During experiment number NSCL-02004 two different detector systems were used in
coincidence to monitor implanted ions, 6 decays and 7-ray transitions. The radioactive
beam was implanted into the DSSD of the 6 calorimeter setup to be discussed below.
The 6 calorimeter was also used for 6 decay detection. The correlation of implanted

nuclei with their subsequent decays was performed in software. 6-delayed 7 rays were

26

 

 

AE (arb. units)

flIfgfIlTIITllllllllI

100

    

 

    

Time 0 Flight (arb. units)

 

 

   
    

  

' - - -- - I .
0 -\-'qg'.'.'.‘.-..-.-.l.l..‘.~.
--

   

\c-----

me ofF

   

Figure 3.2: Particle identification using Time of Flight (start from scintillator 2 m
upstream of the DSSD and stop from the cyclotron rf signal) and energy loss in
the first PIN detector. 56Sc is well separated from the other implanted isotopes even
though it constitutes <1% of the total beam.

27

monitored with 12 HPGe detectors from the Segmented Germanium Array (SeGA)
[22].

3.3 Beta Calorimeter

The low rates for the production of very neutron—rich radioactive beams makes bulk
activity measurements in which the beam is cycled on and off to study 6 decay
properties intractable [23]. A device for 6 decay studies using a continuously implanted
beam into an active detector is preferable, eliminating the need for cycling the beam
on and off. Implanting ions into an active detector would also enable the identification
of implanted ions and subsequent decays on an event-by-event basis allowing for the
study of species which constitute a small percentage of the total number of implanted
nuclei. To this end, the NSCL Beta Counting System [24] was developed. A schematic
diagram of the 6 counting system is shown in Figure 3.3 The center piece of the 6
counting system is a 4cm x 4cm x 1482/1m Micron Semiconductor Double-Sided
Silicon Strip Detector (DSSD) segmented into 40 1-mm strips on both the front and
back faces that results in a total of 1600 pixels, each of which is an individual detector!
The detector was oriented so that the p—type Si was the front and the n-type Si was
the back of the detector. The DSSD was biased with +215 V on the back of the
detector.

Following downstream from the DSSD were six 5cm x 5cm Single-sided Silicon
Strip Detectors (SSSD) which constitute the 6 calorimeter. The thicknesses of SSSDl
through SSSD6 were; 9906m, 977nm, 981,11m, 975nm, 9896m, and 988,um thick, re-
spectively. Each of the six SSSDs are segmented into sixteen strips on one face and
were mounted behind the DSSD so that the strip orientation alternated between the
x and y directions, see Figure 3.3. The SSSDs were placed with ~2 mm between the
center of each detector (~1mm between faces). The DSSD and the first SSSD were

separated by 7mm. Following the six SSSD detectors are two 5cm x 50m PIN de-

28

Drawing not to scale Beta Calorimeter

 

 

 

  

PIN1a PIN2a [SSSDI SSSD3 SSSDS PIN3 ]
1061-16 2007-8 2194-1 2186-5 2194-14 2103-14
PIN2 SSSD2 SSSD4 SSSD6 PIN4
2095-23 2194-12 2186-10 2194-4 2103-12
V 1 DSSD "
\ 2035-3 \\\\\
1
‘N
l // Rummwmm / K ”3"“? K
9mm9mm 1mm 1mm

   
     
   

PIN 1

1404.3 Al degrader Scintillator

 

 

 

 

I6mm1

Figure 3.3: Schematic of the 6 counting system and its position relative to other
detectors used during the experiment. Drawing is not to scale and inter-detector
distances are given. Silicon detector serial numbers are given below the name of the
detector that will be used throughout this document.

29

tectors that are 993;1m and 998,um thick, respectively, for a total of approximately 8
mm of silicon behind the DSSD, sufficient to stop 6 particles up to about 4 MeV [25].
The decays in the present experiment have 6-decay Q values in the range of 10 MeV.
To stop the high-energy 6 particles that escape the Si stack an additional 2 inches of
plastic scintillator were placed after PIN4.

Upstream of the DSSD were four PIN detectors designated PIN 1, PIN 1a, PIN2,
and PIN2a which were 474nm, 488nm, 992nm, and 96611m thick respectively. PIN 1
provided both energy loss and TOF signals used in the particle identification discussed
above. The signal from PIN2a was split and input into high- and low-gain amplifiers
to observe 6 decays and implanted ions, respectively.

The thickness of the upstream Al degrader (435 mg/cmz) located between PIN 1
and PIN la was optimized to allow for the implantation of 56Sc at a depth of ~600um
in the DSSD in the direction parallel to the beam axis. With 56Sc implanted at
~600/1m in the DSSD there was an increased probability of recording a 6 particle AE

signal above noise when the 6 particle was emitted in the direction of the SSSDs.

3.3. 1 Electronics

A schematic diagram of the signal processing system is shown in Figure 3.4. The
signals generated in each strip of the DSSD were first sent to a grounding board.
The grounding board paired each signal with a ground line and grouped the signals
into blocks for further processing in commercial 16-channel electronic modules. The
, “segmentation” process grouped the channels 1-16, 17-32, and 33-40 together for both
the front or back of the detector. These blocks of channels for the front or back were
then sent into preamplifiers. The challenge of detecting 6 decays and implantation
events in the DSSD is the large difference in the total energy deposited for the two
events; high energy implantation events deposit x 1’8 GeV while low energy decay
events deposit z 100’s keV. To overcome the disparate energy scales, Multi Channel

System (MOS) preamplifiers with both low- and high-gain outputs were used with

30

 

Low-gain CAEN 785

   
 

 

Grounding
Board

 

 

 

A OR of 16 strips

  

 

Figure 3.4: Electronics setup for the DSSD during experiment 02004 along with trigger
conditions. The diagram shown on top represents one block of channels for the DSSD
readout.

the DSSD. The MCS preamplifiers were also used with the SSSDs, where only the
high-gain side of the preamplifier was used. High-energy implantation and low-energy
decay signals were obtained from the low-gain (0.03 V/pC) and high—gain (2 V/pC)
outputs of the preamplifier, respectively. The low-gain signals were then sent directly
to a VME ADC. The high-gain signals were further processed through Pico Systems
shaper/ discriminators. Following shaping, the energy signals (high-gain) were sent to
VME ADCs. The complete diagram of the electronics setup for the DSSD, including
the trigger logic, is shown in Figure 3.4. The timing signals of the 40 front channels,

from the Pico Systems module, are OR’ed together, as are the 40 back channels. The

31

OR’ed front and back signals are AN D’ed to provide the master gate signal in the
experiment. The master gate signal AN D’ed with a computer not—busy signal define
the master live signal. The master live signal triggered computer acquisition to read
the detectors. The 12 Ge detectors were read on every event but could not trigger
the acquisition independent of the DSSD. The DSSD was read in blocks of 16 low-
and high— energy channels. For example, if front strip 10 registered a decay event,
front strips 1 through 16 were read into the analysis from both the high and low gain
signals. The SSSDs were read out two detectors at a time. For example, if strip 1 in
SSSDl registered an event then strips 1 through 16 were read into the analysis for
both SSSDl and SSSD2.

A schematic diagram of the PIN electronics are shown in Figure 3.5. A mentioned
before, PINl was used as the TOF start signal and the cyclotron rf signal was used
as the TOF stop for particle identification. PIN2a was used as both a fragment and
a 6 detector.

Implanted ions and decays were “time stamped” on an event-by-event basis for use
in the software correlation. The time signal was derived from two 16—bit EG&G RCO 14
Real Time Clock (86Hz) modules Operated in parallel. The 86Hz internal pulser from
Clockl was downscaled by a factor of eight and counted by Clockl. At the reduced
frequency, Clockl filled its 16 bit field in 2 s, a resolution of 30.5 us. When Clockl
reached the end of its range an overflow signal was sent to Clock2, which counted
the number of resets. The two clocks were read out on every event (both implanted
ions and decays) to determine the time stamp. The time stamp was derived from the
equation:

timestamp = Clockl + 65536 :1: clock2

3.3.2 Calibration

Each Si detector was calibrated with both a 90Sr 6 and 228Th alpha source. A 228Th

alpha spectrum was accumulated for each strip for gain-matching purposes. The strips

32

    
 

PIN Tc178
1a,2,3,4 preamp

PIN Tc178 1
2a preamp
/ Hih Gain CAEN 785
3 ADC
.9
U)
Low Gain CAEN 785
ADC

Figure 3.5: Electronics setup for PIN detectors during experiment 02004.

 

 

 

33

were gain-matched in software based on the centroid of the lowest energy alpha peak
at 5.4 MeV. The total 228Th spectra created by summing all 40 strips on front and
back of the DSSD are shown in Figure 3.6(a-d). Two different methods were used to
determine the energy of the alpha particle for the spectra, shown in Figure 3.6, and are
labeled as either Esum or Em. Esum was determined by summing the energy collected
in the DSSD (above threshold) for all 40 strips, shown in Figure 3.6(a,c) for either
the front or back of the DSSD, respectively. Ema; was determined by comparing the
energies deposited in the individual 40 strips of the DSSD (above threshold), for either
the front or back of the detector, and only reporting the maximum energy, shown in
Figure 3.6(b,d). Two important observations were made concerning the alpha spectra.
First, the resolution of the front is much better than the back of the DSSD. As a
result, the energy signals from the front of the DSSD were used whenever a DSSD
energy signal was needed. Secondly, in calibration spectra reporting the maximum
energy deposited into one channel, Figure 3.6(b,d), there is significant low-energy
tailing on the individual alpha peaks, especially for the back of the detector. Low
energy tailing in the maximum-energy spectra can result from either the incomplete
collection of charge in the DSSD, or the division of charge between two adjacent
strips. Comparing the two spectra from the back of the DSSD (sum versus maximum
energy) it is seen that most of the low-energy tailing is removed when the energy sum
is used, suggesting charge division between adjacent strips on the back of the detector
is important. The small low-energy tailing is not improved significantly between the
sum and maximum-energy spectra for the front of the DSSD suggesting that its origin
might be incomplete charge collection.

Threshold calibrations using a 90Sr source were also performed. First, hardware
thresholds were set for each strip individually by observing the shaped output of the
DSSD on an oscilloscope triggered with a CFD signal. A 90Sr spectrum was then
collected for each strip and used to determine the software threshold. Representative

9°Sr spectra for the front and back of the DSSD are shown in Figure 3.7. Strips near

34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DSSD Front (sum) DSSD Front (max)

 

 

 

 

 

 

 

 

 

 

 

DSSD Back (sum) DSSD Back (max)

Figure 3.6: DSSD 228Th calibration for the front and back of the DSSD. Arrows mark
the 5.4 MeV 228Th alpha peak that was used for gain-matching. Panels a,c report the
total energy collected in the DSSD determined from the sum of the energy deposited
in each strip. Panels b,d report the maximum energy collected in one channel.

35

 

 

 

30 30

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) [L (b)
19 20 £1 20 .
it)
o 10 o 10 —l]‘ . ,1]
0 HI" I 0 — lmlll 1 A
DSSD Front Strip 17 DSSD Front Strip 27
30 30
_ (c) - (d)
= a
8 10 a o 10 — [W
t . “ [an
0 111.11.: A o in 11
DSSD Back Strip 17 DSSD Back Strip 27

Figure 3.7: Representative DSSD 90Sr calibration for the front and back of the DSSD.
Arrows mark the location of representative software thresholds.

the edge of a readout cable, such as strip 17, were inherently noisier and required an
increased hardware threshold. Additionally, the back of the DSSD was noisier than
the front, supporting the choice of the front strips for DSSD energy information. The
average threshold for the DSSD strips was ~120 keV.

To take advantage of the high number of pixels in the DSSD, the secondary frag—
ment beam was defocused to illuminate as much of the detector as possible. The
defocusing resulted in the illumination of approximately 2/3 of the DSSD. The im-
plantation distribution in the x and y dimensions of the DSSD for all implantation
events is displayed in Figure 3.8(a). The distribution for 56Sc events is shown in Figure
3.8(b). The problem encountered early by Prisciandaro [23] using single output pream-
plifiers, where the average implantation multiplicity was six, making the localization
of an implant event difficult, was remedied by using the dual-output preamplifiers
discussed in Section 3.3.1. Using the dual-output preamplifiers the location of an im-
plantation event could be well defined, for example Figure 3.9 shows the implantation

multiplicity for the front and back of the DSSD.

36

 

 
    

,..0n1y‘5_§sc.1mpiahts~

        

.\

-_'— 1'

' —'i'-

 
 

Figure 3.8: The radioactive beam is defocused to illuminate approximately 2/ 3 of the
DSSD and the distribution of implanted ions in the x and y dimension across the face
of the DSSD is shown in (a) The implantation profile is still distributed across the
face of the DSSD when (b) only 56Sc events are displayed.

37

1000000

 

 

 

 

 

 

 

800000 20001
is 600000 » 1000_
S
63

400000 —

013:.
5 6 7 8 9
200000 —
r3

 

 

 

Implant Multiplicity

Figure 3.9: Implantation multiplicity of the DSSD. The inset shows implantation
multiplicities, five through nine, with a higher resolution on the y axis.

front
back

I!

PIN2a
SSSDl

 

Figure 3.10: Software condition between the front and back of the DSSD, PIN2a,
SSSDl which was defined as a decay.

3.3.3 Correlation

Correlations between implanted ions and decays were performed in software on an
event-by-event basis. An implanted ion was defined as a signal above threshold in
PINl and a front and back (low-gain) strip of the DSSD, combined with no signal in
the first SSSD. A decay was defined as a signal above threshold in a front and back
strip (high-gain) of the DSSD, combined with either a signal in PINZa or SSSDl or,
alternatively, a signal in neither PIN2a nor SSSDl, see Figure 3.10. An event which

fired both PIN 2a and SSSDl was identified as a penetrating light particle which leaves

38

an energy signal in every detector of the 6 counting system. After defining the condi-
tions necessary for identification of implanted ions and decays the two distinct events
must be correlated. Correlations between implanted ions and decays were performed
in software on an even-by-event basis based on pixel location and timing informa-
tion. Previous analyses of data from the beta counting system had restricted the
decay-implant correlation to events that occur within the same pixel (see for example
Ref. [26]). The average implantation rate in the current experiment over the entire
detector was lower than 10Hz. The low implantation rate allowed for the expansion
of the fragment-6 correlation field to the surrounding 8 pixels.

The two parameters defining the decay-implant correlation function are the maxi-
mum correlation time and the minimum time between implanted ions. The maximum
correlation time is defined as the longest time window in which a 6 decay can be cor-
related with an implanted ion. The longer the maximum correlation time, the greater
the chance of correlating the implanted ion of interest with a background event. In
addition, the maximum correlation time needs to be long enough to encompass a few
half-lives of the nuclide under study in order to extract a reasonable decay curve. The
minimum implantation time is defined as the minimum amount of time between two
successive implantation events before the second implanted ion will be considered in
the correlation. The shorter the minimum implantation time, the greater is the chance
of incorrectly correlating a decay with an implantation.

In the present analysis the maximum correlation time and the minimum time
between implanted ions were both set to one second for the analysis of 56Se, 5"'Ti,
58V, and 59V. Due to the longer half-life of 60Cr, its analysis was conducted with
the maximum correlation time and minimum time between implanted ions set to
five seconds. A decay curve for each isotope was constructed by histogramming the
time difference between the implanted ion of interest and the correlated 6 decay. An
example is shown in Figure 3.11(a) for the decay of 58V. By integrating the decay

curve for the parent isotope the total number of detected 6 decays from 58V can be

39

 

fragment-B (a)

   

    

Counts/50ms
AE (arb. units)
TWIIT Y—T TY’TT] T I fl 1“! 1*

58Cr

 

Time-of Flight (arb'.~ units)
Figure 3.11: The decay curve in (a) is produced by histogramming the time difference
between 58V implanted ions and the correlated 6 decays. By fitting the decay curve,
the contribution due to 58V 6 decays (shaded region) can be determined. Using the
total number of 58V decays and the total number of implanted ions, from the parti-
cle ID spectrum shown in (b), the 6 detection efficiency for the calorimeter can be
determined. The 6 detection efficiency for all isotopes was ~30%.

determined. Combined with the total number of implanted ions, from the particle ID
shown in Figure 3.11(b), the 6—detection efficiency of the DSSD was calculated. For
all the isotopes studied the 6—detection efficiency was ~30%.

During the course of the present analysis, two methods were used for handling
the correlation of multiple decays within the maximum correlation time, following a
specific implantation event. In the first method, once a decay was correlated with an
implanted ion, the implantation information was deleted (back-to—back decay rejec-
tion). If another decay is detected that would have been within the correlation time
of the deleted implanted ion the decay is ignored. Back-to-back decay rejection led
to the suppression of correlations at longer times in the decay curve that were asso—
ciated with daughter and grand—daughter activities. The effect is not very significant
for those decay chains with daughter half—lives in the second range (such as the decay
chain associated with 58V). However, the reduction at longer correlation times signif—
icantly affected the decay curve of 563c, where the half-lives of all three generations
are fairly short (40 ms, 200 ms, and 216 ms for 56Sc, 56Ti, and 56V, respectively) and
should reasonably be expected to occur within the one second correlation time. Using
back-to-back decay rejection resulted in an inability to fit the 56Sc decay curve with

multiple generations over the one second correlation window, making it difficult to

40

extract the 56Sc half-life. The second method of correlating multiple decays within a
given correlation time ensured that all decays that occurred after an implanted ion,
up to the maximum correlation time are correlated. Since the implanted ion infor—
mation was never erased, multiple decays can be correlated with the same implanted
ion. The removal of back-to—back decay rejection increased the events at longer cor-
relation times, associated with daughter and grand-daughter decays, and enabled the
fitting of the 5680 decay curve through all three generations. The back-to—back decay
rejection condition was removed for all analyses presented here.

Using the high segmentation of the DSSD combined with the segmentation of the
SSSDs, particles can be tracked through the 6 calorimeter by making multiple mea-
surements of their x and y positions as energy is deposited in the different Si detectors.
With this capability, different events in the SSSDs can be identified. Light particles
transmitted to the endstation along with the primary beam follow straight line paths
through the stack. Since there is little deviation in their path as they traverse the
stack, such events will show a high correlation between y positions (or x positions)
measured with different detectors. For example, the strips on the front of the DSSD
were oriented in the y direction as were the strips of SSSDl. A plot of the measured
y position from the DSSD versus the measured y position from SSSDl is shown in
Figure 3.12(a). Two distinct distributions can be seen. The first distribution is a
highly correlated pattern running across the diagonal which can be associated with
light particles following straight-line trajectories. The second distribution observed in
Figure 3.12(a) originates from 6 particles. This distribution can be isolated by ap-
plying the aforementioned software condition for identifying 6 decays, PIN2a, DSSD,
and SSSDl can not all fire in coincidence, and results in Figure 3.12(b), which is free
from light particles. There is a small correlation between the two different y-position
measurements but due to the isotropic emission of 6 particles, it is much weaker than
the correlation observed with light particles. Lastly, when the y dimension, from the

front of the DSSD, is plotted against a measurement of the x position, a plot similar

41

 

 

40
3o _‘
20 ‘J

   

10

 

   

4 '8
Front DSSD strips versus Front DSSD strips versus
SSSDl strips SSSD1 strips

 

 

 

 

‘ A i 8
Front DSSD strips versus Front DSSD strips versus
SSSD2 strips SSSD2 ships

Figure 3.12: Correlation, in strip number, between the front of the DSSD (y direction)
and (a) SSSD1 (y direction) (b) SSSD1 (y direction) with a restriction to only decay
events, (c) SSSD2 (x direction), and (d) SSSD2 (x direction) with a. restriction to
only decay events. In (a) the two distinct distributions arise from light particles and
decay events which can be isolated, and are shown in (b). Plotting the x versus y
coordinate in (c,d) recovers a plot similar to the implantation profile.

to the implantation profile should result. Shown in Figure 3.12(c,d) are the plots of
the DSSD front (y position) versus SSSD2 (x position) for all nuclides, and gated on

decays, respectively. As can be seen, there is no correlation observable in the xy plot.

3.4 7-ray Detection

7 rays were monitored using twelve HPGe detectors from the MSU Segmented Ger-

manium Array (SeGA) [22]. Each Ge crystal has a diameter of 70 mm, a length of

42

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

amp 8k ADC
LeCroy 2551
Scaler
Ge preamp L Ofifip‘afl —— T222655 Bit Register
Phillips 7186H
TDC

 

 

 

Figure 3.13: Electronics setup for SeGA during experiment NSCL—02004.

80 mm and is divided into eight segments along its length and four segments along
the cylindrical axis for a total of 32 segments. As the 6-decay studies are conducted
with a stopped beam, the high segmentation typically used for the Doppler correction
of 7-ray energies is not needed and only the central contact which provides a total
energy signal of each detector was used in the present study. A schematic diagram of

the Ge electronics are shown in Figure 3.13.

3.4. 1 Calibration

The twelve 7-ray detectors were arranged in two separate rings of six detectors each,
with each cylindrical axis parallel to the beam axis, as shown in Figure 3.14. In this
relatively close-packed configuration the energy and efficiency calibration data were
measured with a Standard Reference Material (SRM) source, containing 125Sb, 154Eu,
and 155Eu, along with a separate 56Co source.

The SRM and 56Co sources were placed at the DSSD location and the raw Ge
energy spectra were accumulated for all 12 Ge detectors simultaneously. The peak
locations were fitted using the Oak Ridge Display, Analysis and Manipulation Module
(DAMM) [27]. Energy calibrations were obtained from a second order polynomial fit

to the true peak energy versus the channel position in each of the twelve detectors.

43

 

Secondary
Beam

Figure 3.14: Schematic arrangement of the twelve HPGe detectors from SeGA around
the beam line containing the 6 calorimeter. Serial numbers for individual Ge detectors
are given as well.

Two different Ge energy calibrations have been used to analyze the data.

In the first analysis a number of different energies from the standard sources were
used to calibrate the array from 123.1 to 2598.4 keV, shown in Table 3.1. The resid-
uals of the first calibration, defined as the difference between the true energy and
the calibrated energy and shown in Figure 3.15, displayed a pronounced curvature
and deviated from actual values by more than 0.5 keV at an energy of 1 MeV. This
calibration was used in Ref. [28] and resulted in a small mismatch between the fitted
energy of two 56V 7-ray transitions and the results of previous measurements. The
energies for 56Sc 7—ray transitions were also consistently low compared to a comple-
mentary Gammasphere experiment performed on 56Ti [29]. As a result, a new energy
calibration was constructed.

The second Ge energy calibration used two energy ranges. The first energy range
(low) extended from 123.1 keV through 1596.5 keV and the second energy range
(high) started at an energy of 1274.4 and extended through 3253.4 keV. The 7 ray

44

Table 3.1: List of 7-ray energies in keV for the two Ge energy calibrations.

 

 

 

 

 

 

 

 

 

 

Source First Calibration Second Calibration
SRM 123.071 123.071 low
SRM 247.93 247.93 low
SRM 591.763 591.763 low
SRM 723.305 723.305 low
56Co 846.771 —

SRM 873.19 873.19 low
56Co 1037.84 —
5600 1238.282 -
SRM 1274.436 1274.436 low and high
SRM 1596.495 1596.495 low and high
5600 1771.351 1771.351 high
56Co 2015.181 —
56Co 2034.755 2034.755 high
5600 2598.459 2598.459 high
SRM 2614.533 —
5600 3201.962 —
56Co 3253.416 3253.416 high
56Co 3272.99 -
1
9 0.5 . l [ ii [
a l i ]
to
° 1
‘3‘ -0.5 i
-1 . 1 a
0 1000 2000 3000
Energy (keV)

 

Figure 3.15: Residual plot for the 12 detector Ge array using the first energy cali-
bration. Similar curvature is also observed in each of the twelve individual detector
residual plots. There is significant deviation from true values, especially at 1 and 2.5
MeV.

45

transitions used in the low and high energy calibrations are listed in Table 3.1. To
evenly weight the fit over the entire energy range considered, an attempt was made to
use evenly distributed energy values, and in the case of a cluster of energies, at 3200
keV for example, only one of the energies was used. The transition between the low-
and high-energy calibrations was arbitrarily chosen to occur at an energy of 1460 keV
and it was checked that the position of the transition did not affect the calibrated
energies. The low— and high-energy calibrations greatly reduced the magnitude of
the residuals. The individual residuals for all 12 detectors are shown in Figure 3.16.
The residuals of the Ge array, composed of all twelve individual detectors, is shown
in Figure 3.17. Using the low- and high-energy calibrations, the residuals have been
reduced dramatically to :l:0.15 keV, and the curvature has been minimized. The error
on reported 7 ray energies provided in the results section were obtained by adding in
quadrature the error from the fit (0.15 keV), the error from the peak position given
by DAMM, and the error from the random number generator (0.3 keV). The random
number generator was used to correct for the ADC real-to-integer number conversion.
The error from the random number generator was estimated by observing the shift
in peak energy with a different value used as the start seed. An enlarged region of
the calibration spectrum for all twelve detectors is shown in Figure 3.18 from 900-
1100 keV. The two peaks located at 996.3 and 1004.7 are separated almost to the
baseline and the full width at half maximum is 3.6 keV. Both peaks in Figure 3.18,
not included in the energy calibration, are symmetric suggesting that the detectors
are gain-matched correctly.

7-ray peak efficiency measurements were completed with the SRM source using
7-ray transitions with known emission rates extending from an energy of 27.4 keV
to 1596.4 keV. The absolute emission rates of transitions in 56Co source used for
efficiency calibration were not known, but by matching the efficiency between the
846.8 keV 56Co transition and the 873.2 keV SRM 7 ray, the 56Co source was used

to provide relative efficiencies up to 3273 keV. The logarithm of the efficiencies as a

46

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ge 01 Ge 09
05 - 05- i
0'" "ii-inf ] l 0"; i" Ii! 3
-0.5 - -05- I l
0'1 Ge 02 ] '1 Ge 10 h
.5 _ 0.5-
O-'! ”*9in i h 0a.!” 1;}; ]
-0.5 - -05-
_1 1 1 1 1 1 1 _1 1 1 1 1 L 1_
05 Ge03 05 Ge 11
1 ' h l
A On. !|' ‘I{Il i f 9 O-I! I"i.li } i J
30.5 - ] g -0.5—
To _1 1 1 1 1 1 1 E _1 1 1 L 1 1 1 I
g Ge04 ,3 Ge 12
" 0.5L "' 0.5-
g '1}. f g 5
031' '1 i l 0" i"! ”l l
-0.5 — [ -0.5- ] ]
_1 1 1 1, 1 1 1 _1 1 1 1 1 1 1
Ge 05 Ge 13
0.5 - 0.5- in
-0.5 - -0.5- ;
_1 1 1 1 1 1 1 I _1 1 1 1 1 1 1 ‘
Ge06 Ge 14
0.5 - 0.5-
i I.
0". '.0 iiig i H 011! {Iii‘ilii I I
-0.5 - -0.5r- ]
_1 1 1 1 1 1 1 _ 1 1 1 1 1 m7
0 1000 2000 3000 10 1000 2000 3000
Energy (keV) Energy (keV)

Figure 3.16: Residual plots for the individual SeGA detectors. The switch between
low- and high-energy calibrations occurred at 1460 keV.

47

 

0.15

 

Residual (keV)
O

 

 

 

-0.15

 

0 ‘ E00 A 2000 ‘ 3000
Energy (keV)

Figure 3.17: Residual plot for the sum of all twelve detectors in the second Ge cali-
bration. See text for details.

 

 

 

 

 

 

10000
1004.7
8000 r-
13 6000 — 996.3
:3
8 4000 —
2000 - fl
0 1 1 T;— —'
900 950 1000 1050 1100
Energy (keV)

Figure 3.18: Sum Ge spectrum for all twelve individual Ge detectors between 900-
1100 keV. The two peaks around 1 MeV are cleanly separated and the full width at
half maximum is 3.6 keV.

48

 

y = 0.3095x5 - 4.8369x4 + 29.823x3
- 90.777x2 + 135.91x - 80.651

 

log efficiency
3

 

 

 

-1.4 ~
-1.6 -
-1.8 . . . .

1.8 2.2 2.6 3 3.4 3.8

log Energy (keV)
Figure 3.19: Efficiency of the array of 12 HPGe detectors as a function of energy. The

diamonds represent calculations with the MCN P code using a point source geometry
at the DSSD location. The squares represent experimentally determined efficiencies.
A fifth order polynomial relating the energy with efficiency is shown by the solid line.
function of the logarithm of the energy were then fitted with a fifth order polynomial.
The results are shown in Figure 3.19. The array efficiency was also simulated using
the MCNP code and accurately reproduced the experimental data down to 105 keV,

sufficient for the 7 rays observed in the present study. The efficiency of the array at

1 MeV was determined to be 5.3% .

49

Chapter 4

Experimental Results

The nuclides implanted into the DSSD during experiment NSCL-02004 included:
SfSc, SgTi, SS’SQV, and gflCr. Of these nuclides, 568C has not previously been studied,
and the other nuclides have been isolated only in small quantities. Thus, the present
results represent huge improvements in basic knowledge of the 6-decay properties of
these nuclides. Additionally, the experiment was configured to detect isomeric 7 rays
emitted from the implanted nuclides if present. Altogether, a wealth of information
was obtained for each nuclide. For all implanted nuclides a decay curve and 6-delayed
7-ray spectrum were obtained by making a cut on implantation-correlated 6 decays.
For multiplicity-two 7-ray events (m, = 2), a 77 matrix was constructed by plotting
the energy of the second detected 7 ray against the energy of the first 7 ray. An
example of the 77 matrix for 58V is shown in Figure 4.1(a). Gated slices of the 77
matrix provided a coincidence spectrum for each 7-ray transition. For multiplicity-one
7 rays (m, = 1), a plot of the the decay curve versus the 7 spectrum was created,
from which a 7-gated decay curve for each 7-ray transition was extracted through a
slice perpendicular to the time axis. An example of such a plot is shown in Figure
4.1(b). The only exception to the 7 gated decay curve procedure described above was
in the analysis of 56Sc. To avoid the loss of statistics associated with the restriction of

the 7-ray multiplicity to a value of one, each individual Ge spectrum (m, 2 1) was

50

 

 

  
   

 

 

 

 

 

4000 (a) 1000 -
33200—1 €800
v2400— , v600 ,-
>~ . GE, . .1 ~
$1500 -: , 1: 400 f
L” 800 T 200 :7 ._

0 68.140 ' 1 ' 1 l l 0 .21: .....'l’:- il’ ,1. iii . , . .
0 800 1600 2400 3200 4000 0 800 1600 2400 3200 4000
Energy (keV) Energy (keV)

Figure 4.1: For 53V, two dimensional plots of (a) the energy of the the second detected
7 ray versus the energy of the first detected 7 ray in a multiplicity-two 7—ray event
and (b) the time versus the 7—ray energy for 7 multiplicity-one events. Projections of
(a) produced 77 coincidence spectra while projections of (b) onto the y axis produced
7-gated decay curves.

 

Counts/1 keV

 

 

0 500 1000 1500 2000
Energy (keV)

Figure 4.2: 56Sc 6-delayed 7-ray spectrum from 0—2 MeV for events occurring within
one second after a 56Sc implanted ion.

gated on the 5680 transition of interest. The twelve individual gates were summed

together to extract the 56Sc decay curve.

4.1 5680

The 6-delayed 7—ray spectrum obtained for 56Sc from 0—2 MeV, shown in Figure 4.2,
contains 67 events that occurred within the first second following a 56Sc implanted
ion. A total of seven new transitions have been identified in this spectrum. As the

56Ti daughter has no known 7—ray transitions [30] the five remaining transitions have

51

Table 4.1: 568C 6-delayed 7 rays along with adopted values, absolute intensities and
the initial and final states for those transitions placed in the 56Ti level scheme.

stud

 

 

 

 

E,,6—decay E,,Adopted 1:53 Initial State Final State
(keV) (keV) (%) (keV) (keV)

592.3 :1: 0.5 592.3 :1: 0.5 7 i 2

690.2 :l: 0.4 690.1 :l: 0.4 19 :l: 4 2980 2290

751.5 :1: 0.5 751.5 :1: 0.5 9 :t 3

1128.2 :l: 0.4 1128.5 :h 0.4 48 :l: 11 1129 0

1160.0 :1: 0.5 1160.5 :l: 0.5 21 :t 5 2290 1129

 

 

 

 

 

 

been assigned to the 6 decay of 56Se, and are listed in Table 4.1.

The transitions located at 690.2i0.4, 1128.2:t0.4, and 1160.0:l:0.5 keV compared
favorably with the energies of 690.0 :E 0.5, 1128.8 :1: 0.5, and 1161.0 :1: 0.5 keV found
in deep inelastic work reported in Ref. [29]. The weighted averages of the 6-decay
and in-beam results, 690.1 :l: 0.4, 1128.5 :1: 0.4, and 1160.5 :t 0.5 keV, were adopted
as the energies for these three 7-ray transitions in 56Ti. The most intense transition
in the 67 spectrum is located at 1129 keV and has been tentatively identified as the
2;” —> 0f transition [28]. The 7-ray transition with energy 592.3 i 0.5 keV falls within
the error of the single 7—ray transition previously observed in 55Ti [31] and could be
due to a 6—delayed neutron branch from 56Sc to levels in 55Ti. Such a branch is feasible
considering that the 13.7:t0.8 MeV Q-value for the 56Sc 6 decay is considerably larger
than the 5.3 :l: 0.3 MeV neutron separation energy in 56Ti.

The decay curve derived from 56Sc—correlated 6 decays is shown in Figure 4.3(a).
The decay curves obtained by requiring an additional coincidence with the 1129-, 690-
, or 1161-keV 6-delayed 7 rays are shown in Figures 4.3(b-d). The half-life deduced
from the 1129-keV 7-gated decay curve is statistically different from those deduced
from the 690— and 1161-keV 7-gated decay curves, suggesting that two 6-decaying
parent states were populated in the production of 568C. A weighted average of the
half-lives extracted from the 690— and 1161-keV 7-gated decay curves results in a
value of 60 :l: 7 ms, which was postulated as the half-life of a high-spin 6-decaying

state in the 5680 parent. Since the 1129-keV 7 ray has been tentatively assigned to the

52

 

  

 

    
 
 

 

 

 

 

 

 

 

 

a _ (ii-690)
a, 1000 ( ) 555c(1+)T1{52(1+m(B)S g 12 '11,, = 58 :1: 9 ms
E 65C (5 7+) o
S N 56
\ o. \ 8 SC
‘9 100 ‘9
5 56V 5
8 8 4
--.\f'_‘9d.--._--.:"€’fi .1,”ka

g 56.5c T1/2 = 35 i 5 ms g 3 T1,2 = 64 :h 11 ms
Q 20 Q 6
19 15 19 -
S g 4 -

10 [
8 5 8 2

bkgd l 0. likes! n.
0 500 1000 0 500 1000
Time (ms) Time (ms)

Figure 4.3: Decay curves for 563C showing (a) fragment-6 correlations where the data
were fit with an exponential parent decay, an exponential growth and decay for both
daughter and grand-daughter and a linear background, (b) fragment-6 correlation
with an additional requirement of a coincident 1129-keV 7 ray, (c) fragment-6 corre-
lation with an additional requirement of a coincident 690-keV 7 ray, (c) fragment-6
correlation with an additional requirement of a coincident 1161-keV 7 ray. Decay
curves shown in (b—c) were fitted with an exponential decay and linear background.
2? —+ 0]” transition, it appears that a lower-spin 5630 state has a shorter half-life, and
that the 1129-keV 7-gated decay curve is then a mixture reflecting both the low- and
high—spin state half-lives. The percentages of 6 decays due to the low- and high-spin
state are (83 :l: 11)% and (20 :l: 4)%, respectively, based on absolute 7-ray intensities
and the deduced 6-feeding to the 56Ti ground state.

The E"‘Sc-correlated 6-decay curve, Figure 4.3(a), was first fitted using a single
exponential decay component for 5680 with daughter and grand-daughter generations.
The resulting half-life is consistent with the previous determination [28]. However,
evidence for two 6-decaying states in 5680 resulted in a re—examination of the overall
fragment-6 decay curve. Since the half-life of the high-spin 6-decaying state was
extracted from the decay curves gated on the 690- and 1161-keV 7-ray transitions,

the value for the low-spin half-life can be deduced from the total 6-decay half-life

53

 

Counts/2 keV

 

 

 

Energy (keV)

Figure 4.4: Isomeric 7-ray spectrum collected within a 2011s time window following a
56Sc implanted ion.

curve. The decay curve in Figure 4.3(a) was fitted to a function that included the
high-spin state half-life, along with the percentage of 6 decays attributed to the high-
and low-spin states, the exponential growth and decay of the daughter and grand-
daughter isotopes, 56Ti [30] and 56V [26], and a linear background component. In this
way, a half-life of 35 :l: 5 ms was deduced for the lower-spin state in 56Se. The isotopes
58"59V, 57Ti, and 60Cr, which have previously measured half-lives, were implanted
along with 56Sc. The decay curves for these four isotopes were also fitted and used to
verify the linear background.

The experiment as configured also permitted the detection of isomeric 7 rays that
decay following the implantation of a nucleus into the DSSD. The isomeric 7-ray
spectrum collected within a 20-ps time window following a 56Sc implanted ion is
shown in Figure 4.4. Three transitions were observed at 140 :l: 2, 188 :t 2, and 587:l: 2
keV with absolute 7-ray intensities of (1.4 :l: 0.1)%, (1.8 :l: 0.3)%, and (2.2 :l: 0.6)%,
respectively. It is possible that the 587—keV transition is a doublet. Unfortunately,
the errors on the absolute intensities and the lack of coincidence data do not permit
placement of any of the three isomeric transitions in the low-energy structure of 56Sc
at the present time.

The proposed decay scheme for levels in 56Ti populated following the 6 decay of

56Sc is shown in Figure 4.5. The 6-decay Q value was derived from the mass excess

54

 

56$c
T1,2 = 354:5 ms T1,2 = 60:1:7 ms

(1+) 0+x (547+) 0+y

\ 3.

Q‘3 = 13.7108 MeV

 

 

 

 

 

 

+ + +
(t )) (6 (,7 )) 615$
I % I %
B B + q°°
_ 100 (6 )6 2980
Q9
696
- o (4*) «2" 2290
8
\°‘
.gp

35:1:11 '

1;»
+ l
65:13 - 0 0

Figure 4.5: Proposed 56Ti level scheme populated following the decay of 56Sc. The
number in brackets following the 7-ray decay energy is the absolute 7—ray intensity.
The Q value was deduced from data in Ref. [32]. Absolute 6-decay intensities are not
shown due to the presence of a possible 6-delayed neutron branch to states in 55Ti
(see text).

55

 

 

2 L690-kev gate 1129 (a)

u 1i l1l ill

2 - (c) 590 1129-keV gate

1’ Ill. lllll .l

- 752-keV gate (b) (d) 1161-keV gate

3,] H J - ,lll l .l -

0 500 1000 1500 2000 0 500 1000 1500 2000
Energy (keV) Energy (keV)

11-

 

 

 

 

 

 

 

 

NO
NO

 

 

 

Counts/2 keV Counts/2 keV

 

Counts/2 keV Counts/2 keV

 

 

 

Figure 4.6: 7—7 coincidence data for the 690-, 752-, 1129-, and 1161-keV transitions
following a 56Sc 6 decay.

of both parent and daughter as compiled in Ref. [33]. Absolute 7-ray intensities were
deduced from the number of observed 56Ti 7 rays, the simulated 7-ray efficiency
curve, and the number of 5630 implanted ions correlated with 6 decays. The last term
was derived from a fit of the decay curve in Figure 4.3(a) as described in section
3.3. Details of the 7 ray placements and spin and parity assignments were aided by a
complementary experiment carried out at the ATLAS accelerator at Argonne National
Laboratory with the Gammasphere multi-detector array to study the yrast structure
of neutron-rich Ti isotopes as described in Ref. [29]. Note that the placement of the
690-keV 7 ray feeding the 1129-keV state in 56Se was also confirmed by fragment-677
coincidences (see Figure 4.6).

6 feedings to levels in 56Ti from both 6 -decaying states were deduced from the
absolute 7-ray intensities, and are summarized in Figure 4.5. The apparent 6 feedings
should be considered upper limits, based on the sizeable 6-decay Q—value and the
possible existence of unobserved 7 decays below our detection limit of a: 6% absolute
intensity and the possibility of a 6-delayed neutron branch to 55Ti. From the intensity

of the 7 ray at 592 keV, a lower limit for the 6-delayed neutron branch is 7%. This

56

Table 4.2: 58V 6 delayed 7 rays with absolute 7-ray intensities, initial and final states.
E, (keV) If” (%) Initial State (keV) Final State (keV)

 

 

879.8 :1: 0.4 56 :l: 3 880 0
1042.4 :l: 0.7 2.2 :l: 0.9
1056.4 :1: 0.4 23 i 2 1936 880

1381.4 :1: 0.4 2.3 :l: 0.4
1500.0 i 0.5 2.1 :l: 0.5
1678.7 :1: 0.6 1.7 :l: 0.7
2217.5 i 0.4 8.2 :t 0.6 3097 1936
3123.4 :1: 0.6 3.1 :l: 0.8

 

 

 

 

 

 

value compares reasonably well with the predicted R, value of 12% from Ref. [34].
Apparent logft values for the observed 6-decay branches are not quoted due to the
uncertainties in the ordering of and energy differences between the low- and high-spin
6-decaying states in 5630. 6—decay branching to the 56Ti ground and first excited 2+
state of 56Ti led to the tentative assignment of 1+ to the spin and parity of the parent
5680 low-spin 6—decaying state. Apparent direct feeding to the 6*, 2980-keV level in
56Ti from the high-spin 56Sc 6-decaying state limits the spin of the high-spin isomeric
state to values of 5, 6, or 7. Absence of direct 6 feeding to the 4:“ state (the absolute
intensities of the 690- and 1161-keV transitions are equivalent within experimental

errors) further restricts the spin of the 56Sc high-spin 6-decaying state to J = (6, 7).

4.2 58V

The 6-delayed 7-ray spectrum for 58V in the range 0—3.6 MeV is shown in Figure
4.7(a,b). There are a total of eight 7 rays observed in the spectrum, and they are
listed along with their absolute 7-ray intensities in Table 4.2. Of these eight 7 rays,
those with energies of 880, 1042, 1056, 1500, and 2218 kev have been previously
observed [26]. The 7 ray reported at 1571 keV in Ref. [26] was unobserved in the
current experiment and a revised energy of 1500 keV is assigned to the 1501 keV 7
ray from Ref. [26]. Three new 7 rays at 1381, 1679, and 3123 keV all have absolute

57

 

500

 

 

 

 

 

 

 

 

 

E 400- 380 (a)
q 300 —
‘3 200- 1056
8 100— 10:2]

01 ' 200

Energy (keV)

40 _ 2218 (b)
>
g" 30 Z 1381 1500
a 205 1.45579
c —
8 10 3123
U

01200 2000 2800 3600

Energy (keV)

Figure 4.7: 58V 6-delayed 7-ray spectrum from (a) 0-1.2 and (b) 1.2-3.6 MeV for
events occurring within one second after a 58V implanted ion. The 7 ray marked with
an asterisk is from the decay of 59Cr.

58

 

250

 

 

 

 

    
    

 

 

0-lsec a
a 200— (l
x
Q 150—
*2
3 100-
u ]
M ..._.._-.11 -.
0 -Ssec
>
5‘2
2
19
C
D
8
0
> 4.5—9v 9-10sec (c)
g r/880
1; 4 1056
O
U .1 , p
0 11'

 

0 875 1750 2125 3500
Energy (keV)

Figure 4.8: 58V 6—delayed 7 spectra. The maximum correlation time and minimum
time between implantation were both set to 10 s. Gates on subsets of the correlation
time were created and applied to the 67 spectrum. 6-delayed 7-ray spectra are shown
with an additional cut on the correlation time extending between (a) 0—1 s, (b) 4-5 s,
and (0) 9-10 8.

intensities at or below 3%, which is lower than the detection limit in Ref. [26]. To
determine whether any of these 7-ray transitions can be attributed to longer lived
species, the correlation time and maximum time between implantation were both
changed to ten seconds, and three different cuts on correlation time were applied
to the 67 spectrum. Time cuts between 0—1 s, 4-5 s, and 9-10 s resulted in the
spectra shown in Figures 4.8(a,b,c). Prominent peaks located in Figures 4.8(b,c) can
be identified with daughter and grand-daughter decays in the A=58 decay chain or

with contamination from 59V, due to an overlap in the particle ID gates.

The measured decay curves for 58V 6 decays, along with 7—gated decay curves over

59

 

  
 

  

 

 

 

  
  

10000 13 (a) 60 31056 (c)
E T1/2= 191:1:3ms g T1/2=177:l:4ms
8 34
@1000 g
3 bk d 3
8 x 58Cr 9 82
100 . .\ 1 4 m __. L..
i— T ‘31-ng 3 (b) 12 r 1313;18166)
= :1: ms = :1: ms
g 120 1/2 E 1/2
3 Q 8
c 60 a
3 3
u 40 8 4

1000

 

 

 

‘2000

Time (ms)

3000 0

 

0

  
  

 

 

n n . fl
2000
Time (ms)

3000

 

Figure 4.9: Decay curves for 58V showing (a) fragment-6 correlations where the data
were fit with an exponential parent decay, an exponential growth and decay for the
daughter 58Cr and a linear background, (b) fragment-6 correlation with an additional
requirement of a coincident 880-keV 7 ray, (c) fragment-6 correlation with an addi-
tional requirement of a coincident 1056-keV 7 ray, (c) fragment-6 correlation with an
additional requirement of a coincident 2218-keV 7 ray. Decay curves shown in (b—c)
were fitted with an exponential decay and linear background.

a three second correlation time were extracted, fit, and are shown in Figures 4.9(a—d).
The 58V decay curve shown in Figure 4.9(a) was fit with an exponential decay along
with the exponential growth and decay of the daughter nuclide 58Cr (131/2: 7s). The
grand-daughter, 58Mn (131/2: 38), decay was found not to contribute to the half-life fit.
A linear background was also included in the fit. A value of 191 :l: 3 ms was extracted
for the half-life of 58V in agreement with previous values of 185 :t 10 ms [26], 205 :l: 20
ms [35], and 200 :t 20 ms [36]. 7-gated decay curves for the 880-, 1056-, and 2218-
keV 7-ray transitions are shown in Figure 4.9(b—d) and are all in agreement with each
other, suggesting the absence of multiple isomeric 6-decaying states in the 58V parent.

The 880—keV transition has previously been assigned as the 2+ —> 0+ transition

in 5’3Cr [26]. 7-7 coincidences were determined for the 880-, 1056-, and 2218-keV

60

 

12
(a) 1056 880-keV gate

 

 

 

8—
4 2218
‘ /

0 (b) 1056kV t
E, 12" 880 'e 939
q.
\ 8—
:2,
8 4

Omm 1111141 11111111

3 _(c) 880 2218-keV gate

2.—

 

 

 

 

;llllll l. I

0 1000 2000 3000 4000
Energy (keV)

Figure 4.10: 7-7 coincidence data for the (a)880-, (b)1056—, and (c)2218-keV transi-
tions following a 58V ,8 decay.

transitions and are shown in Figure 4.10. From the coincidence data it can be seen
that both the 1056- and 2218—keV transitions feed the 880-keV 2+ state. The ratio
of intensities between the 1056- and 221&keV transitions observed in the 880-keV
coincidence spectrum agrees with the ratio between the 1056- and 2218-keV intensities
observed in the fi7 spectrum suggesting the transitions are in parallel. Furthermore,
based on the intensity of the 880—keV transition observed in the 1056-keV 7-gated
coincidence spectrum (see Figure 4.10(b)), if the 2218-keV 7 ray were in coincidence
with the 1056-keV transition, a peak with an area of approximately seven counts
would be present and is clearly absent in Figure 4.10(b). The coincidence spectra
lead to the level scheme shown in Figure 4.11. From the number of 58V B decays

detected, the 7-ray intensity and the SeGA efficiency curve, the absolute intensity

61

(1+) 0 T1,2 = 19113 ms

Q =11.6:1:0.4 \
58V N B $2»

 

 

 

 

 

 

 

O /\.
IBM) logft W 3097
8.2:l:0.6 5.43:0.1
e3
95
b.
59" 1936
231:2 5.191009
<15le
2+ l‘q.
25:13 5.37i0.08 Lin—Lb 88°
+
4433 5.28i0.08 0 0
58cr

Figure 4.11: Proposed 58Cr level scheme populated following the decay of 58V. The
number in brackets following the 7—ray decay energy is the absolute 7 ray intensity.
The Q value was deduced from data in Ref. [32]. Observed coincidences are represented
as filled circles. Absolute B—decay intensity and logft values for the fi decay to each
state in 58Cr is shown on the left of the figure.

62

 

 

1200
175 57V (3)

80° _ 113

400— R
_ 5
0 . I 9V 571d

0 10 200 300 400
Energy (keV)

 

Counts/1 keV

 

 

 

 

57V 1579 (b)

 

 

Counts/1 keV

 

 

500 1000 1500 2000 2500
Energy (keV)

Figure 4.12: 57Ti B—delayed 7—ray spectrum for events occurring within one second
after a 57Ti implanted ion from (a) 0-0.4 and (b) 0.4-2.5 MeV.

of a 7-ray transition can be determined. From the absolute intensity and the level
scheme the apparent fl-decay intensity to each state can be calculated along with an
apparent logft value, using a fi-decay Q value of 11.6 :1: 0.4 MeV [32]. Supposing that
the 58V 6 decay proceeds through an allowed transition to both the 2+ and 0+ states

of 58Cr as indicated by the logft values, the parent 58V ground state is most likely a

1+ state.

4.3 57Ti

The fi-delayed 7-ray spectrum for 57Ti in the region of 02.5 MeV is shown in Figures
4.12(a,b). The spectrum includes all 7 rays detected within one second after the
implantation of a 57Ti ion. Six 7 rays, including two prominent ones located at 268

and 692 keV, have been assigned to the daughter decay of 57V in a previous work [26].

63

250

 

 

 

 

 

       
    

 

 

O-lsec a

E 200L H
H
g 150*-
g 100-

sor .l 1 .l. J

0 J A LA... 1.. --A.,
> (b)
3 15
:1
{1.} 10
8
u 5

0
> 12
(D
in: 59M”
:3 8 Sjvn. 58V
8 4 : \ Cr

..| ‘
0 I11“ ‘1‘ ‘ I 1
0

625 1250 1875 2500
Energy (keV)

Figure 4.13: 5""I‘i fi-delayed 7 spectra. The maximum correlation time and minimum
time between implantation were set to 10 8. Gates were created on subsets of the
maximum time and applied to the 67 spectrum. fl-delayed 7-ray spectra are shown
with a cut on the correlation time extending between (a) 0—1 s, (b) 4-5 s, and (c) 9-10
3.

To observe decays with longer half-lives, cuts on the correlation time between 0-1 s,
4-5 s, and 9-10 s were again applied to the B7 spectrum and the results are shown in
Figure 4.13. The presence of 7 rays belonging to the decay of 5859V can be explained
by an overlap in the particle ID gates with 57Ti. As there are no 7 rays present in
the 4-5 s and 9—10 8 cuts that cannot be assigned to known transitions, the remaining
7 rays in the ,87 spectrum were attributed to the decay of 57Ti and are listed along
with absolute intensities in Table 4.3. It should be noted that there are no 7 rays in
Table 4.3 that can be associated with 56V. Therefore, it does not appear that there

exists a delayed neutron branch which passes through the 2+ state in 56V.

64

Table 4.3: 5"'Ti ,B-delayed 7-rays with absolute 7-ray intensities, along with initial and
final states for those transitions placed in the level scheme.

 

 

E, (keV) 1‘be3 (%) Initial State Final State
(keV) (keV)
113.1:l:0.4 14i1 113 0
174.8 :1: 0.4 31 i 2 175 0
744.0 :t 0.4 2.3 :l: 0.4 2475 1732
1557.3 :1: 0.5 2.2 :l: 0.5 1732 175
1579.4 3: 0.4 16 :1: 2 1754 175
1861.5 :t 0.4 14 i 2 2036 175
1922.9 :1: 0.5 2.6 :l: 0.5 2036 113
2003.7 :1: 0.6 1.8 i 0.5
2114.6 i 0.5 0.7 d: 0.3
2300.4 :1: 0.4 5.0 :t 0.5 2475 113

 

 

 

 

 

 

The half-life of 57Ti deduced from a fit of the decay curve shown in Figure 4.14(a) is
98i5 ms. Previous measurements of the 57Ti half-life include 67$ 25 ms [37], 180:1:30
ms [36], and 56 i 20 ms [38]. However all three of these measurements isolated 5"'Ti
in only very small quantities. The half-life fit includes the exponential decay of the
parent, exponential growth and decay of the daughter, 57V, and a linear background
term. The half-life of the daughter, 57V, was taken to be 350 ms as reported in
Ref. [26]. The 7-gated half-lives from the decay of 57Ti are shown in Figures 4.14(b—
h) and Figures 4.15(a-b). All 7-gated half-lives were fit with an exponential decay
and linear background component and are consistent, within errors, with the half-
life determined without any 7-ray coincidence, further aiding their assignment to the
decay of 57Ti. Furthermore, based on the consistency of 7-gated half-lives there is no
reason to suspect multiple fi-decaying states I

A 77 matrix was created to identify coincidences between the observed 7 rays.
Coincidence spectra for various 57Ti 7 rays were extracted and are shown in Figure
4.16. Based on the efficiency-corrected intensity ratios between the 113- and 175-keV
peaks in 1579- and 1861-keV 7-gated coincidence spectra, approximately 50% in both
cases, the 113- and 175-keV transitions were placed in parallel. From an inspection of

the 1923—keV coincidence spectrum, the 1923-keV transition has been placed directly

65

 

 

    
    
  
  

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

I; (a) 20_ 0—1557 (e)
m T =9 iSms 10155 T =102i25ms
$10000 :- 1’2 E, 1’2
Q I 571-! Q 12
:3 : 23 E
g . g 8 :
8 1 57V 8
1000 bkgd 4 F
400 4‘ AU ' " 0: l
B-113 (b) . 0-1579 (0
g 300 Tm: 114i5ms 380; T1/2=97:l:7ms
O Q ~ 571'
Q 5711 Q 60 2'
13 200 :
8 g 40 _-
U 100 U 20 E.
bkgd 0 bkgd
0-175 (c) 16 B-1732 (9)
m 600 T =1o3i4ms 1n T =81:I:40ms
g 1/2 E 12 1/2
51 400 ‘2
:2 12 8
D 3
8 200 571”: 8 4
bkgd
0 . 1 0 1 1 1 l 1
0-744 ((0 [3-1861 (h)
u, ; T =97:1:18ms m T =89¢10ms
. 1 2
§ 20 _ / ”DE, 50 1/2
\ ;, \
fig 5 7T1 12 40
= 10 :- g
8 =_ 20
:bkgd
0 1 1 1 1 0 7
0 500 1000 0 500 1000
Time (ms) Time (ms)

Figure 4.14: Decay curves for 57Ti showing (a) fragment-fl correlations where the
data were fit with an exponential parent decay, an exponential growth and decay
for the daughter 57V and a linear background and (b—j) fragment-fl correlations with
an additional requirement of a coincident gamma ray with an energy of (b) 113 keV,
(c)175 keV, (d) 744 keV, (e) 1557 keV, (f) 1579 keV, (g) 1732 keV, (h) 1861 keV. Decay
curves shown in (b—h) were fitted with an exponential decay and linear background.

66

 

 

 

 

 

 

 

0-1923 (a) _ 57 B-2300 (b)
32 g TI T1/2=113:1:22ms
s 0 s 20"
3 9 —
C C
3 10 8 10-
U U

0 bkgd
(l) 500 1000 0 500 1000
Time (ms) Time (ms)

Figure 4.15: Decay curves for 57Ti showing fragment-fl correlations with an additional
requirement of a coincident gamma ray with an energy of (a) 1923 keV and (b) 2300
keV. Decay curves shown in (a) and (b) were fitted with an exponential decay and
linear background.
feeding the 113-keV state due to the absence of a 175-keV coincidence peak, which
would be expected to be twice as strong as the 113—keV transition, based on intensity
ratios observed in the 1579— and 1861-keV coincidence spectra. The absence of either
the 113- or 175-keV transition in the 1732-keV gated coincidence spectrum, which
does display a coincidence with 744, establishes the 1732-keV level. The level scheme
constructed from the coincidence data is shown in Figure 4.17. Since the 113- and
175-keV transitions are in parallel there should be a transition of 62 keV between the
175- and 113-keV states in order for both energies to appear in the 1579 and 1861
coincidence spectra. Such a transition would have been below the hardware thresholds
of the SeGA array and, therefore, not observed. Additionally, such a low energy 7 ray
would probably be highly converted. The spin and parity assignments of 57Ti and 57V
will be discussed in the next chapter in after comparison to theoretical calculations.
The only concern is with the 113- and 175-keV coincidence spectra. The coinci-
dence spectrum for the 175-keV transition displays a peak located at 113 keV and
vice versa. A determination of whether these two 7 rays are truly in coincidence was
made by inspecting intensity ratios between different transitions in the two separate
spectra . Supposing the 113- and 175-keV transitions are in series, a gate placed on

175 keV should reveal a one-to-one ratio between the efficiency corrected areas of the

67

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E, 6 _ 175 1 13_kev (a) E, 175 1579-keV (e)
Q Q10-
5 4 - 1579 1861 19
g 2 g 5... 113
u
0 0 1111 l 11 l 11 114 4
> 175-keV 1579 (b) > 3— 744 1732-keV (f)
:32 9"113 3
Q 6— Q 2—
.9 1861 4‘3
c C
3 3- 8 1
8, volllllllllll. .e
5 - 175 744-keV (c) 5 175 1861-kev (9)
a: - 1732 #10—
.19 _ \
g _ 1557 l g 51 113
o _ I 8
U ll [\1l 0 1] 111 l 111 L 1
a 2— 175 1557-keV (d) % 3L 113 1923-keV (h)
x x
Q Q 2-
£3 1.. E!
C C
a Ill] 1 H 51111 1
U 0 ,, l l 0__] 1 1 1
0 1000 2000 a 175 2300-keV 0)
Energy (keV) #9 4- 113
\
£3
5 2—
O
U l
0 L 1 1
0 1000 2000
Energy (keV)

Figure 4.16: 7-7 coincidence data for the (a)113-, (b)175-, (c)744-, (d)1557-, (e)1579—,
(f)1732-, (g)1861-, (h)1923—, and (f)2300—keV transitions following a 57Ti [3 decay.

68

H 9 T =98:1:5 ms
5711 QB”: 10.6:1:0.6

IB(%) log 0:

7.3107 5.0102 —"——°;~,.€$'

 

 

 

 

 

 

 

 

 

 

 

 

 

1612 4.8102 98338? 2035
’\ ”v '\~
1612 4.9102 __,.__¢’_§\°i°3’ 1754
1.1i0.7 6.0i0.2 - 1732
'\ 99'
03’ ’\\"»\'
563 5.7102 LL 1% <0V§5°_/H5
5413 4.7102 1-
57v

Figure 4.17: Proposed 57V level scheme populated following the decay of 57Ti. The
number in brackets following the 7-ray decay energy is the absolute 7-ray intensity.
The Q value was deduced from data in Ref. [32]. Observed coincidences are represented
as filled circles. Absolute fl decay intensity and apparent logft values for the 6 decay
to each state in 57V is shown on the left of the figure.

69

Table 4.4: Ratio between the efficiency corrected areas of the 113- and 175-keV tran-
sitions to the 1579-keV transition. If 113- and 175-keV transitions are in series the
ratio should be 1. Areas are efficiency corrected.

113-keV spectrum

 

175-keV spectrum

 

 

E, (keV) Area E, Area
113 104 :l: 59 175 87 :l: 20
1579 490 i 74 1579 172 :l: 25

 

 

 

Ratio = 0.21 :l: 0.12 Ratio = 0.5 d: 0.2

 

 

 

 

Table 4.5: Calculated 57Ti internal conversion coefficients from Ref. [2].

 

 

Energy (keV) E1 E2 E3 E4 M1 M2 M3 M4
113 0.022 0.24 2.2 19 0.016 0.16 1.4 13
175 0.0058 0.044 0.28 1.8 0.0054 0.036 0.22 1.5

 

 

 

 

 

 

 

 

 

 

 

1579- and 113keV peaks. What is found is that the 113 keV area is approximately
20% of the expected 1:1 ratio, see Table 4.4. It is unlikely that internal conversion
could make up for the difference in intensities (see Table 4.5). Similarly, if a gate
is placed on the 113 keV transition the 175—keV peak is not in a 1:1 intensity ratio
with the 1579 keV peak. Therefore, the 113 and 175 keV transitions are most likely
in parallel and they appear in coincidence only due to random coincidence.

4.3.1 57V

Through the decay of 57Ti it was also possible to study the decay of the daughter
nuclide 57V. The delayed 7 rays of 57V appear in Figure 4.12 as a daughter activity.
This nuclide has been previously studied [26], and a level scheme was constructed
based on sum energy relationships and the fact that none of the three most intense
transitions were in coincidence. With the greater statistics in the present experiment,
a coincidence spectrum was extracted by gating on the 268-keV transition and is pre-
sented in Figure 4.18. The coincidences between the 268-keV transition and the 424-
and 1314-keV transitions can be seen, confirming the placement of these 7 transitions

in the level scheme reported in [26].

70

 

 

 

 

 

6

5 268-keV

‘q‘ 4" 424 1314

3 1111111111

c 2-

:1

8 0 111.1] 11111
0 1000 2000

Energy (keV)

Figure 4.18: 7-7 coincidence data for the 268-keV transition following a 57V 6 decay.
4.4 59V

The 6-delayed 7-ray spectrum for those events observed within one second after a
59V implanted ion is shown, in the energy range of 0-3 MeV, in Figures 4.19(a,b,c).
Numerous 7-ray transitions are observed in this spectrum and are listed in Table 4.6.
Of the 7 rays listed in Table 4.6, the ones at 102 and 208 keV have been observed in
previous studies of the 6 and isomeric decay of 59V and 59"'Cr, respectively [37, 39].
To determine if any of the transitions originate from longer lived species three
different gates on the correlation time were applied to the 67 spectrum between 0-1
s, 4—5 s and 9—10 3, and are shown in Figure 4.20. From the time-gated 67 spec-
trum there are multiple 7—ray transitions that can be assigned to daughter activities.
The 112-, 662-, 1126-, 1238- and 1899-keV transitions were assigned to the decay
of 59Or. The 7 rays at 112- and 1238-keV have been previously observed [40,41].
The transitions located at 472, 570, 590, and 726 keV can be assigned to the decay of
59Mn. Further confirmation of the assignments to daughter and grand-daughter decays
were obtained from a comparison between the Ge spectrum taken with, and without,
back-to—back decay rejection. In such a comparison, 7-ray transitions belonging to
the daughter and grand-daughter nuclei in the A = 59 decay chain were identified by
changes in intensity. The changes in intensity with, and without, back-to—back decays

as compared to the 606-keV transition are shown in Table 4.7 for the 472, 662, 1126,

71

4000

 

 

 

 

 

 

- 208 (a)
a 3000 —
E — 102
§ 1000 — 590
u _

0 l l 1 L——-¢-—M_

0 100 200 300

Energy (keV)
400 278 6065914" 59Cr 0?)
267

>
52’ 300 _ 317 59M"

Q 463592 590 1031 59Cr
£200 372 4261491[70:\(§28fsl) \1056 1222
3 100 ~- . . ‘ 1 96°97

 

 

 

 

 

 

 

 

1158
K
0, , __...1--......._....
250 500 1000 1500
Energy (keV)
60
1593
5 "' 1530 590 (C)
fi 40 681
E
2090
g 20 2199 2375 601
8 '.
0 HLuLJLL 1.1-
1500 2000 2500 3000

Energy (keV)

Figure 4.19: 59V 6-delayed 7 rays in the range (a) 0-0.3, (b) 0.25-1.5, and (c) 1.5-3.0
MeV for events occurring within one second after a 59V implanted ion. Numerous
transitions from daughter and grand-daughter generations can be observed.

72

Table 4.6: 59V 6-delayed 7—rays with absolute 7 ray intensities, and initial and final

states for those transitions that were placed into the 59C‘r level scheme.

 

 

 

 

 

 

Energy (keV) lg“ (%) Initial State (keV) Final State (keV)
102.0 :1: 0.4 21 :l: 2 310 208
207.8 :t 0.4 41 :l: 3 208 0
317.3 21: 0.4 3.0 d: 0.4 525 208
371.7 i 0.5 1.6 :l: 0.3
425.5 :1: 0.4 1.7 :1: 0.3 1341 915
490.8 :1: 0.5 2.3 :l: 0.4 800 310
592.4 :t 0.4 4.2 :t 0.3 800 208
606.0 :t 0.4 6.4 :t 0.4 915 310
707.6 :1: 0.5 1.1 :t 0.3 915 208
784.1 :1: 0.4 1.8 :L' 0.3
799.9 :1: 0.5 1.1 :t 0.3 800 0
823.2 :1: 0.6 1.1 i 0.3
841.4 :1: 0.4 2.7 :l: 0.3 1366 525
879.9 :1: 0.5 ' 3.0 :1: 0.4
959.9 :1: 0.4 2.2 :t 0.3
977.2 :1: 0.5 1.4 :1: 0.2 2509 1532
1030.8 :1: 0.4 2.4 :l: 0.3 1341 310
1056.0 :1: 0.4 2.5 :l: 0.3 1366 310
1157.8 :1: 0.5 0.8 :t 0.2 1366 208
1206.5 :1: 0.6 0.6 :l: 0.2
1222.1 :1: 0.4 2.5 :t 0.3 1532 310
1529.6 :1: 0.5 1.0 :t 0.3
1593.4 :1: 0.5 2.2 :t 0.4 2509 915
1680.9 :1: 0.5 1.9 :t 0.3
2089.6 :1: 0.5 0.9 :1: 0.2
2198.7 i 0.5 0.5 :1: 0.2 2509 310
2375.0 :1: 0.6 0.8 :l: 0.2
2601.3 :1: 0.6 1.2 :1: 0.2
2812.5 :1: 0.5 0.2 :l: 0.1

 

 

1238,and 1899-keV transitions. The statistics in the Ge spectrum using back-to-back
decay rejection were too low to identify the peaks at 570, 590, 726 and 112 keV.

Since 59V was produced in copious amounts, it was possible to deduce 7—gated half-
lives for most of the observed 7-ray transitions. These 7-gated half-lives are shown in
Figures 421,422, and 4.23. The 59V half-life deduced from the 7-gated decay curves
is 97 i 2 ms.

The 7—gated decay curves shown in Figure 4.24 are those associated with 59Cr and

73

 

0-1sec (a)

 

 

 

Counts/lkev

 

Counts] 1keV

 

 

 

0 500 1000 1500 2000
Energy (keV)

Figure 4.20: 59V 6—delayed 7 spectra The maximum correlation time and minimum
time between implantation were set to 10 s. Gates were created on subsets of the
maximum time and applied to the 67 spectrum. 6-delayed 7—ray spectra are shown
with a cut on the correlation time extending between (a) 0—1 s, (b) 4-5 s, and (0) 9—10
s. The asterisks in (b) are due to 59Cr decay.
5"Mn decays. With the exception of the 1238-keV transition, all of the 7 rays were
fairly weak and it is unknown why the decay curves in Figure 4.24(a—e,g) do not show
the expected growth of a daughter or grand-daughter at small correlation times.
The 7-gated half-life spectra for the 880- and 1056-keV lines are both slightly
longer than the other 7-gated half-lives. Transitions at 800- and 1056-keV are also
observed following the 6 decay of 58V. The difference in the half-lives of the 880- and
1056-keV transitions, compared to the other 7 gated half-lives, may be due to 58V

contamination in the particle ID. In an attempt to eliminate possible contamination

from 58V, a restricted particle ID was placed on the central portion of the 59V particle

74

 

 

 

 

‘é’ T1,2 = 97 :1: 2 ms 3
o o 60
Q Q
‘2 ‘2 40
8 3
0
[3-208 (b)
g T1/2=97:!:2ms £82
0 0 -
] 0
V’ T B1347 7 (c) ”100
= :l: ms
g 160 t. 1/2 {E 80
E 120159)] E 50
C C
3 80 1 :3 40
U 40 l V 8 20
bkgd
0 ‘ ‘ ‘ ‘ T 0
m B-372 (d) m
T = 112 :1: 11 ms
g 1/2 §120
\ \
9 9 80
D 3
8 3 40
1000 0

Time (ms)

 

 

 

 

 

  

 

 

 

   

 

 

 

 

0-426 (e)
:: T1,2 = 95 :i: 9 ms
59v
:bkgd
B453 (0
B-491 (9)
59V T1)2 = 116 :l: 11 ms
bkgd
[1592 (h)
_ T1,2 = 96 :1: 7 ms
59v
E-bkgd
. I J 500 1000
Time (ms)

Figure 4.21: Decay curves for 59V showing (a—h) fragment-6 correlations with an
additional requirement of a coincident gamma ray with an energy of (a) 102 keV, (b)
208 keV, (c) 317 keV, (d) 372 keV, (e) 426 keV, (f) 463 keV, (g) 491 keV, and (h) 592
keV. Decay curves shown in (a—h) were fitted with an exponential decay and linear

background.

75

 

  
 
 

 

B-823 (e)
59V T1/2 = 101 :l: 14 ms

[+606 (a) 50“
T1,2 = 98 :l: 6 ms E

     

 

 

  
  
  
  

0 i 7 r 7 r i g 7% i _ I
5-703 (b) 108-

T1,2 = 72 :l: 10 ms 3 80;

   
 

B-841 (f)
59v T1/2 = 101 :h 9 ms

Counts/50ms

 

 

 

 

m 1 I - I c
:l [3'734 (C)

 

B-880 (9)
T1]2 = 124 :l: 15 ms

(”V + 59V)

 
    
 

Counts/SOmS
3
nts/
as
O

 

   

 

B-960 (h)

50: B'800 (d) 60.
”’ ' T1/2=102:I:11 ms

40:? 59v T1/2 = 95 :i: 14 ms m .
3o:- \ 40E"
20i- a
10 ibkgd 10:“ l
0o ' 500 1000 o 500 l ‘1000
Time (ms) Time (ms)

Counts/50ms

 

 

 

 

 

 

 

 

Figure 4.22: Decay curves for 59V showing (a—h) fragment-fl correlations with an
additional requirement of a coincident gamma ray with an energy of (a) 606 keV, (b)
708 keV, (c) 784 keV, (d) 800 keV, (e) 823 keV, (f) 841 keV, (g) 880 keV, and (h) 960
keV. Decay curves shown in (a-h) were fitted with an exponential decay and linear
background.

76

 

  
 
  

B-977 (a)
T1/2 = 110 :l: 19 ms

 

 

Counts/SOms

20_

  
   

 

3-1031 (b)
T1,2 = 97 i: 12 ms

  

 

 

 

 

 

 

   

 

 

 

 

50 B-1056 (C)
m T = 118 :l: 15 ms
E 40 59V 1/2
3 30 (58V + 59V)
‘2
a 20
8 10
bkgd
53 [3—1222 (d)
m T = 108 :l: 14 ms
E 1/2
c 40
Q 30
2. ”v
8 10
bkgd
06 L ‘ l ' 500 1000
Time (ms)

Counts/SOmS Counts/50ms

Counts/SOmS

 

   
 
   
       

(e)

  

5-1530

 

   

 

p-1593 (f)

  

  

- -

 

 

58 [3-1681 (9)
40 T1/2=87:tlSms
3
2

 

Time (ms)

Figure 4.23: Decay curves for 59V showing (a-f) fragment-fl correlations with an ad-
ditional requirement of a coincident gamma ray with an energy of (a)977, (b) 1031
keV, (c) 1056 keV, (d) 1222 keV, (e) 1530 keV, (f) 1593 keV, and (g) 1681 keV. Decay
curves shown in (a-g) were fitted with an exponential decay and linear background.

77

 

 

[3-1126 (e)

Counts/SOms
°3

 

Counts/SOmS

 

 

 

(b) 805 B-1238 (f)

 

Counts/50ms
Counts/50ms

k l L l L 1

B-1899 (lg)

 

 

Counts/SOms
S

 

Counts/50ms

 

 

ll1fillllLll

 

1 1 1 I I l L P—

'1000 0o l 500 1 o

 

0 [_1 14L: 1 l

o 500 ‘
Time (ms) Time (ms)

Figure 4.24: Decay curves showing (a—g) fragment—fl correlations with an additional
requirement of a coincident gamma ray with an energy of (a) 472 keV, (b) 663 keV,
(c) 726 keV, (d) 1126 keV, (e) 1238 keV, and (f) 1899 keV.

78

Table 4.7: Ratio of peak intensities between Ge spectra without and with back-to-
back decay rejection relative to the increase observed for the 606-keV transition. 'y
rays that can be assigned to daughter or grand-daughter transitions show a dramatic
increase in peak intensity.

Energy (keV) Ratio Source
102.0 i 0.4 1.01 :l: 0.08 59V
207.8 2!: 0.4 1.00 :i: 0.06 59V
592.4 d: 0.4 0.99 :i: 0.09 59V
472.9 :J: 0.5 1.6 :t 0.6 59Mn
662.6 :1: 0.4 1.4 :l: 0.4 59Cr
1126.5 :1: 0.5 1.6 :i: 1.8 59Cr
1238.0 :1: 0.4 1.6 :i: 0.2 59Cr
1899.5 :1: 0.5 1.5 :t 0.3 59Cr

 

 

 

 

 

 

 

 

ID gate. The 880— and 1056-keV transitions are still observed following the decay of
59V. Additionally, the intensity of the 1056-keV transition is higher than that of the
880—keV transition. The 1056-keV transition was also observed in coincidence with
59V '7 rays and thus can conclusively be placed as following the decay of 59V. The
880—keV transition, not in coincidence with any 59V 7 ray, may result from a possible
fi-delayed neutron branch into the 2;" state of 58V. If such a branch exists, the Pn
value for 59V would be ~3%. This value is a lower limit as it is determined based on
the observed ’y-ray intensity of the 2+ —» 0+ transition in 58V.

A fit of the fragment-fl decay curve was complicated by the relatively poor knowl—
edge of the daughter, 59Cr, half—life. The first measurement of the 59Cr half-life,
740 :l: 240 [40,41], was obtained from an average of the negated half-lives of 1.0 :l: 0.4
s and 0.6 :l: 0.3 s, for the 1238- and 112-keV 7-rays, respectively, weighted by rel-
ative intensities. The second measurement conducted on 59Cr resulted in a half-life
of 460 :l: 46 ms [42]. The inconsistency of these two results made it difficult to fit
the half-life of the 59V parent. In an attempt to determined the half-life of 59Cr the
1238-keV y-gated decay curve from 0-5 s was fit and the results are shown in Figures
4.25(a—b). When the decay curve in 4.25(a) was fit with no restriction on the half-life
of the 59V parent, the deduced half—life for 59Cr is 1100 :i: 200 ms and the fitted half—

79

 

 

  
  

      

 

 

 

 

 

 

 

(a) in ,2: 84:1:19 ms 03) :3” ,2: 97 ms
g 100 Cr 1,2 = 1117i140 ms 5 100 Cr 1,2 = 1050190 ms
8 8
Q Q
19 19
C E
g 8

U
10 bkgd 1°.
0 2500 5000 0 2500 5000

Time (ms) Time (ms)

Figure 4.25: Decay curve showing fragment-fl correlations with an additional require-
ment of a coincident gamma ray with an energy of 1238 keV. Fit includes the expo-
nential growth and decay of the daughter 5S’Cr with a linear background. In (a) the
59V half-life was a variable in the fit, in (b) it was constrained to 97 ms.

 

 

 

 

 

Counts/20ms

 

 

 

500
Time (ms)

Figure 4.26: Decay curve showing fragment-B correlations for events occurring within
one second after a 59V implanted ion. The decay curve is fit with an exponential
decay of the parent, growth and decay of the daughter and grand-daughter and a
linear background term. The half-life of the daughter was set to 1100 ms deduced
from the '7 gated decay curve fit of the 1238-keV transition.

life for 59V (84 :i: 19 ms) agrees, within error, with most of the 59V 7-gated half-lives.
The decay curve in 4.25(b) was fit, restricting the parent half-life to 97 ms, taken
from a weighted average of all '7 gated half—lives; a 59Cr half-life of 1050 :i: 90 ms was
deduced. From a weighted average of the two 1238-keV 'y ray fits, the half-life of 59Cr
was adopted to be 1100 :i: 100 ms. The adopted 59Cr half-life was then used to fit the
59V fragment—fl decay curve, shown in Figure 4.26, leading to a half-life of 95 :i: 3 ms

for 59V. Taking a weighted average of the 95 :l: 3 half-life with the 'y-gated half-lives

80

resulted in a value of 97 :t 2 ms, adopted for the the 59V half-life. Previous values of
the half-life include 130i 20 ms [36] and 75 :l: 7 ms [37] but both studies suffered from
a lack of statistics and used an imprecise value for the 59Cr half-life.

77 coincidence spectra for transitions in 59V are shown in Figures 4.27, 4.28, and
4.29. The 7 rays with energies of 102 and 208 keV had been identified and placed
into a level scheme previously [37] with the 102— and 208-keV transitions in series.
The series placement of these two 7 rays, with the lowest excited state at an energy
of 208 keV, was confirmed using the 77 coincidence spectra for 59V. In particular, the
7 rays at 317, 592, and 707 are present only in the 208-keV 7-gated spectrum, and
the coincidence spectra gated on the 317-, 592-, and 707-keV transitions only show a
coincidence with the 208~keV transition not with the 102-keV transition, placing the
208-keV state at the bottom of the level scheme. The ordering is in contrast to the
recent findings of Ref. [43] where the 102— and 208-keV transitions are reversed in the
level scheme.

The proposed level scheme for 59Cr populated through the 6 decay of 59V is shown
in Figure 4.30. The logft values and [3 decay branching ratios are not shown due to the
large number of decays that have not been placed into the level scheme. However, it
should be noted that based on the number of 6 decays observed and the low intensity
of the 7-ray transitions that have been placed directly feeding the ground state there
is a significant 3 branch to the ground state of 59Cr. The previous work performed on
the isomeric 59Cr decay established a tentative 9/2+ excited state at 503 keV which
deexcites through an M2 7 emission [39] of 193 keV, then cascades through two 7-
rays with energies of 102 and 208 keV, respectively [37]. The M2 transition from the
9 / 2+ 503-keV state suggests a J1r assignment for the 310—keV level of 5 / 2“. From the
77 coincidence spectra obtained by gating on transitions feeding the 310 keV state
the efficiency corrected intensity ratio between the 102- and 208-keV transitions is
approximately 60%. The discrepancy from the expected 100% can be resolved if the

102-transition is an E2 transition (E2 internal conversion coefficient = 0.39). This

81

leads to a 1/2‘ assignment to the 208-keV level and a ground state of 3/2'. The
previous suggestion of a 5 / 2" ground state for 59V [37] would lead to a large ground

state branch in the 59V —> 59Cr decay which is observed.

4.4.1 59Cr

The intensity of 59V ions also allowed a study of the 59Cr 76 decay. As mentioned
above, the half-life for the 59Cr B decay has been adopted as 1100 :t 100 ms following
the analysis of the 1238-keV 7-gated decay curve shown in Figure 4.25. 7-coincidence
spectra have also been extracted for transitions suspected to be in the daughter, 59Cr,
and are shown in Figure 4.31. The 662- and 1238-keV transitions were found to be in
coincidence. Additionally, if the 112-keV and 1238-keV transitions were in coincidence
there would be a significant peak at 112 keV in the 1238-keV 77-coincidence spectrum,
which was unobserved. The statistics were too low to identify possible coincidences
between the 662-keV and either the 112- or 1126-keV transitions. The level scheme

for 59Mn derived from the 6 decay of 59Cr is given in Figure 4.32.

82

 

 

 
 
   
  

 

 

     
    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

> 208 (a) > 102 (9)
g 200 " 102-keV gate % 8 _ 208 426-keV gate
\ ” \
g 100 - g 4+ 606
8 .. 8 1530
a 0 (b) a 0 208 (h)
g 20 606 102-keV gate sq: 4_ 102 463-keV gate
19 1031 4‘3
S 10 977 0561530 g 2
8 3. U
0 0 .
> _ (C) > 20 (I)
g 200 102 208-keV gate g 15 - 8 491-keV gate
\ _ \ _ /102
i? 100 .. *3 1° ‘
§ 8 5-[
U
> > 0 l 1 11 11 116) ll 1
3 3 20 - 208 592-keV gate
Q Q -
10 fl _
c 1: 10
3 3 I102
o 8 ~‘
U OFM‘Hnul 11 1 1111 1 11%.
> 30— (k)
3: _eg _ 208 606-keV gate
Q Q 20 _
a g; “(.102
g 5 10-
8 8 _ 426
0 208 (I)
E if 8 ' 708-kev gate
Q Q '
1‘3 15 4..
C C
8 8 -] Ii
U 0 U 0 .11111111111 H. l
0 1000 2000 0 1000 2000
Energy (keV) Energy (keV)

Figure 4.27: 7 — 7 coincidence data following a 59V H decay for the (a)102-, (b)102—,
(c)208-, (d)208-, (e)317-, (0372-, (g)426—, (h)463-, (0491-, (j)592—, (k)606-, and (1)708-
keV transitions.

83

 

 

  

 

 

 

 

       

 
     
  

 

 

 

 

 

 

 

 

> M208 (a) > 6— 208 (g)
a) 2- _ 0’ -
sq: 102 784 keV gate i 4 .\102 977 keV gate
0 0
U 0 liliiii iii“ i U 0 11111111011 .1
5 3- (b) a 12— 208 0‘)
fl 800-keV gate fi — 1031-keV gate
E 2' E 63/102
C C
8 1 3 -
U U —
0 208 (c) i > 0 208 (i)
> 6—
% 4 463 823-keV gate g _ 10556g5eg£gte
\ - \ 4— 102
:3 2 1222 *‘g _ 880 ( +
8 k 3 2—
o 8 —
0 0 _
5 208 (d) a 5— 208 0)
fi 12- 841-keV gate fl — 102 1222-keV gate
\ 8* \ 4—
8 4_ 317 3 2_
U U -
0 (e) 0 ()
> 3- ——> > 3
3 1056 880-keV gate 3 662 1238-keV gate
Q 2- (58v) % 2
‘2 1— 5 1
3 [H i l | l l 8
U 0 207 ' 0
> 3— (f) g 2102 (I)
3 959-keV gate a: 208 1530-keV gate
q 2- Q
B B 1
C C
° 1' ” [Hill] I] H
O O
u 0 ill [I Hill]. 9 0 . , .

0 1000 2000 0 1000 2000
Energy (keV) Energy (keV)

Figure 4.28: 7 -7 coincidence data for following a 59V 6 decay for the (a)784~, (b)800-
, (c)823-, (d)841-, (e)880-, (0959-, (g)977—, (h)1031-, (i)1056—, (j)1222—, (k)1238-,
(1)1530keV transitions. Panel (e) and (i) contain contamination from 58V due to
a particle ID overlap.

84

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

> 2__ 1593-keV gate (a) 5 1_ 1681-kev gate (b)
£2 x

Q Q

fl 1m 3

C C

3 :1

U 0 1 7 m I U o 1 l 1

0 1000 2000 0 1000 2000
Energy (keV) Energy (keV)

Figure 4.29: 7—7 coincidence data following a 59V ,8 decay for the (a) 1593-, (b)1681—
keV transitions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

52' 0 T1/2=97:I:2 ms
QB = 10.8:h0.4 MeV
59V
\ x
e‘" e‘” x?“
«9 69 4‘
w .5 o, 2509
m5)
' '\ ‘\
w”\ Q?) Q?) 19x VB lb
’1' Q: Q \ \ -
0 '\- b' ‘5 ‘3: \
___‘l__ _Q‘o_qg.\_ 6,9 (0‘? 1532
~~ at »e_- ia
a? e as
w «5‘ «9‘6 9\m9‘\§’\ 3° 915
u—l—l-i‘qoL‘?) '09 7"b\v \ 800
(5/2:)‘\ v v ‘ ¥ * 5&0 310
(1/2-)-’ W 208
(3/2) , 0

Figure 4.30: Proposed 59Cr level scheme populated following the decay of 59V. The
number in brackets following the 'y—ray decay energy is the absolute 'y-ray intensity.

The Q value was deduced from data in Ref. [32]. Observed coincidences are represented
as filled circles.

85

 

 

  

 

 

 

 

 

 

E, 2- 662-keV (a) E 3 — 6621238-kev (b)
E 3: 1238 g 2 '
53 3 1mm” Ill 5 f,— ||||.|lllllll. |

0 Enelrggfl keV) 2000 O EnelrggcikeV) 2000

Figure 4.31: ’77 coincidence spectra for two of the transitions suspected of belonging to
the decay of ”Or. The 1238- and 662-keV transition are in coincidence. A coincidence
between the 1238 and 112 keV transitions, if present, should be observable in the 1238-
keV gated spectrum based on the intensity of the 662 keV peak. Intensities were too
weak to determine coincidences between 662- and either 112- or 1126- keV transitions.

(3/2‘) 0 T1,2 = 1100i100 ms
= . :t .
Sgcr \QB 76 03MeV

\
'9'
8‘ 5»

$9 (06". 1900

 

 

 

 

 

i N 112
W%

59Mn

Figure 4.32: Proposed 59Mn level scheme populated following the decay of 59Cr. The
number in brackets following the v-ray decay energy is the relative 7—ray intensity. The
Q value was deduced from data in Ref. [32]. Observed coincidences are represented
as filled circles.

86

 

58v

 

 

 

_. 348
13 57 59 75 "
8 800 — I/Idn '
U 58V 60
400 — F659
‘ l L / N C’ 1532
0 500 1000 1500 2000
Energy (keV)

Figure 4.33: fl-delayed 'y-ray spectrum for those decays observed within 5 s of the
implantation of a 60Cr ion.

Table 4.8: 60Cr fi-delayed 'y-rays with absolute 'y—ray intensities and initial and final
states for those transitions placed into the 60Cr level scheme.

 

 

 

 

 

 

 

 

E(keV) Iff”(%) Initial State (keV) Final State (keV)
348.6 :l: 0.4 6.4 :i: 0.5 349 0
410.1 :l: 0.4 5.2 :l: 0.4 759 349
746.0 :l: 0.6 0.9 :l: 0.4
758.2 :E 0.4 5.0 :i: 0.5 759 0
4.5 60Cr

The ,B-delayed ’y-ray spectrum for events that occurred within 5 s after 3. 6"Cr im-
plantation event are shown in Figure 4.33. The correlation time was extended due to
the longer half-life of 6"Cr. Observable in Figure 4.33 are numerous lines that belong
to the decay of longer lived species, as seen from the fly spectra with different cuts
on correlation time shown in Figure 4.34. The remaining 'y rays, attributed to 6"Or,
are listed, along with their absolute ’y-ray intensities, in Table 4.8.

The decay curve for those events that occurred within 5 s of a 60Cr implantation
is shown in Figure 4.35(a). From the shape of the decay curve below 1000 ms, it is
apparent that the daughter, 60Mn, has a shorter half-life than 60Cr. Fitting the decay
curve in Figure 4.35 with a parent exponential decay, an exponential growth and
decay of the daughter, and a linear background, a half-life of 490 :l: 10 ms for 6"Cr is
deduced. The 60Cr half-life agrees favorably with previous values of 510 :l: 150 ms [42]

87

 

 

Counts/1keV

 

’E9v w 60R,   (b)

 

Counts/ 1keV

 

 

Counts/1keV

 

 

0 500 1000 1500 2000
Energy (keV)

Figure 4.34: 6"Cr fi-delayed 7 spectra. 8 delayed 'y ray spectrum for those decays
observed within (a)0—1 s, (b) 4-5 s, and (c) 9—10 5 following a 60Cr implanted ion.

88

and 570i60 ms [41]. The 'y-gated decay curves are shown in Figures 4.35(b-d) and are
consistent with the 490 :l: 10ms half-life extracted from Figure 4.35(a). In the fit, the
half-life of the daughter was considered a parameter, resulting in a value of 280 :i: 20
ms for the 60Mn half-life, in contrast to previous measurements in Refs. [41,44,45].

A half-life of 1.8 :l: 0.1 s was deduced for a 3+ isomeric state in 60Mn at an energy
of 272 keV [44,45]. The half-life of the 0+ 60Mn ground state was first determined to
be 51 :i: 6 s [41] and it was suggested that the 60Mn ground state 5 decay proceeded
directly to the 60Fe ground state. Later studies of 60Mn suggest that 0+ is the correct
J1r assignment for the 60Mn ground state but, due to contaminations from higher
masses, the 51 i 6 s half-life of 60Mn is probably incorrect [46].

'77 coincidences following 60Cr decay are shown in Figure 4.36. The level scheme
determined from the 77 coincidence data is shown in Figure 4.37. From the absolute
intensities there appears to be a large ground state branch to 60Mn.

The ground state of 60Cr should be 0*. Therefore, the decay into 60Mn should
only populate low spin states and a significant fraction would be expected to proceed
to the 0+ 60Mn ground state, which is observed. Similarly, fl decay from the 60Mn 0+
ground state would be expected to populate low-spin states in 60Fe. 7—ray transitions
at 823 and 1150 keV match known transitions in 60Fe. The 1532-keV transition could
also be a transition between the second excited O+ at 2358 :i: 3 keV and the 823 keV
2+ state in 60Fe, but such a transition has not been observed in previous 3 decay
work. The [3 decay into levels of 60Fe from 60Mn is shown in Figure 4.38 The 7-gated
decay curves for the 823-, 1150-, and 1532-keV transitions are shown in Figures 4.35(e-
g). The decay curves in Figures 4.35(e,f) were fitted with an exponential daughter
growth and decay, fixing the half-life of 60Mn at 280ms. The resulting 60Cr half-life
was 450 :l: 40 and 320 :l: 30 for the 823- and 1150—keV transitions, respectively. It was

not possible to fit the 1532-keV decay curve.

89

 

 

 

  

 

 

  
   
    
 

  

 

 

 

 

 

 

 

 

 

10000 g (a) 1%?) ’ B-823 (e)
E 0 Trl/z = 4901:“) ms {'5’ = 450i40 ms
C M” 1/2 = 280i20 mS 8 = 280 ms
Q Q 403
E1000 jg
. :J F
8 z \ : ,3 2°
. l 1 1 L I l 10—____——.'_.
m 100‘ B-349 (b) m 60 3-1150 (f)
E T = 500 :1: 40 ms E Cr T1: 320:1:30 ms
0 3° 1’2 o 20 M5001 280
o o n11,2 = ms
% 60 §
g 40 g, 10
8 20 u
.—-0—————-—; - - 0
341° (C) :' -1532 (9)
E 60 I T1/2=590:!:60 ms 3 8'] B
O O
a 40 1‘ a 6;
g 20 g h
8 r 8 [Mr
m 52;] A A AB-758 (d) 0o 1000 2000 3000 4000 5000
= :l:
g 40 ‘ T1]2 430 50 ms Time (ms)
8
g 305 l‘
g 202' .
U 102- \ .
\:.‘h __ __:

 

 

 

9;

1000 2000 3000 4000 5000

Time (ms)

Figure 4.35: Decay curves for 60Cr showing (a) fragment-fl correlations where the
data were fitted with an exponential parent decay, an exponential growth and decay
for the daughter 60Mn and a linear background, (b—d) fragment-B correlations with
an additional requirement of a coincident gamma ray with an energy of (b) 349 keV,
(c)410 keV and (d) 758 keV, (e-g) fragment-fl correlations of transitions following the
6 decay of 6"Fe with an additional requirement of a coincident 7 ray at an energy of
(e) 823 keV, (f) 1150 keV, and (g) 1532 keV. Decay curves shown in (b—d) were fitted
with an exponential decay and linear background. Decay curves shown in (e-f) were
fitted with an exponential growth and decay and linear background.

90

 

 

 

 

 

 

 

 

 

 

 

5 16 e 410 (a) % 758-kev gate (c)
§ 12 C 349-keV gate fi 1 _
\ \
e a - e l [
5 4 - 5

_ O
8 OMJLLIIII 111. 111 11.11 11 1 U 0 1 1 7
5 _ 349 (b) 0 1000 2000
fig: 3 _ 410-keV gate Energy (keV)
I? .—
5 4 *
U 1—

0 L 1mm 11 1.1
0 1000 2000
Energy (keV)

Figure 4.36: ’77 coincidences for the (a)349—, (b)410—, and (c)758-keV transitions fol-
lowing the [3 decay of 60Cr.

4.
(O) 0 2=490i10ms
60Cr\ QB=6..7:1:03MeV

 

 

 

113(0/0) log ft {)9 {04>

639' $5 at
5.0105 4,310.1 '\ “ (53$. 759
1.22:1:0.6 4410.1 “’9 349
88.6i0.6 4510.2 (0+) 1 0

 

60Mn

Figure 4.37: Level scheme deduced following the 3 decay of 60Cr into excited levels

in 60Mn. fi-decay branching ratios along with logft values calculated using Q3 from
Ref. [33].

91

(0+) 0

T1,2 = 280 :1: 20 ms
60Mn\ QB = 8.2 :l: 0.1 MeV

 

 

 

1%
I»
a? x
'5 s
0+ '3’ 6‘? 2356
<0.
9* ’4" 1 74
®
Q?
..,?~
2+ , v ‘9’ 823

 

 

 

 

0+ 0

 

Figure 4.38: Levels in 60Fe populated following the fi decay of 60Mn. Relative 'y-

ray intensities given in brackets following the 'y decay energy. Q5 determined from
Ref. [33].

92

Chapter 5

Discussion

At present, complete ab initio calculation of nuclei are only possible for the lightest
nuclei, A S 17. Beyond that the number of shell model orbitals and the amount of
calculations are prohibitively large. One of the bases of shell model calculations is
the presence of shell closures, allowing the computational problem to be divided into
two parts; an inert core containing most of the nucleons coupled to 0+ and a small
number of valence nucleons outside the core constrained to a certain range of orbitals
called the model space. The properties of the nucleus are then determined by the
valence nucleons. Knowledge of the location of shell closures becomes important for
the study of exotic regions of nuclei. As the locations of the traditional shell closures
at 2,8,20,28,50,82, and 126 are based primarily on experiments performed with stable
nuclei their extrapolation to exotic regions can be questioned. With the development
of radioactive nuclear beams it has become possible to search for the appearance or
disappearance of shell closures far from stability and numerous recent results suggest
that shell closures, particularly in the neutron-rich region, may be dynamic [12,47—50].
A variety of different effects may result in so—called shell quenching. The proton-
neutron monopole interaction discussed in the Introduction is such an effect and was
already demonstrated in near-stable nuclei using the proton single-particle states in

Sb (see Figure 1.3). While the monopole interaction is strong between orbits of similar

93

(a) (b)

485C 565C
f5/2 —— f5/2 —— f5/2 —— f5/2 —'—
p1/2 ——- p1/2 —— ID1/2 —- p1/2 +
p3/2 —— p3/2 —— p3/2 —— p3/2 —0”0—
f7/2 —.-——- f7/2 W f7/2 —.—— f7/2 W
proton neutron proton neutron

Figure 5.1: The large spin-orbit splitting prevents spin-orbit partners from being oc-
cupied simultaneously as in (a) for 488C. Far from stability the spin-orbit partners will
both be occupied, shown in (b) for 56Sc, leading to strong proton-neutron monopole
interactions.

1 the most dramatic reordering of single-particle states should occur when the orbital
angular momentum, l, is the same for both protons and neutrons [7]. Due to the
large spin-orbit splitting, this condition will be satisfied in neutron-rich nuclei far
from stability (see Figure 5.1). Dramatic changes in effective single-particle energies
due to strongly attractive interactions between spin-orbit coupling partners has been
discussed by Otsuka et al. [10] in the context of the disappearing N = 8,20 magic
numbers for neutron-rich exotic nuclei.

The migration of the neutron effective single-particle energy due to the monopole
interaction as a result of the filling of proton single-particle levels can be calculated

using the equation below [51]:

é... = 5,, + Zealvmljumuj. (5.1)

in
where 115,-” is the effective neutron single-particle energy, 81-” is the ’bare’ single-particle
energy, and (jujfllVMljujfl) is the two body interaction between protons in state j7r
and neutrons in state j”, and 11,-, is the occupancy of the proton orbit. The potential,
VM, in equation 5.1 is attractive in nature serving to lower the energy of the neutron
single-particle state and is linearly dependent on the occupancies of the proton orbits.

Evidence of a significant reordering in single-particle states can be seen in Figure 5.2

94

 

 

 

(b)

4 _

3 ._
9
a
Z
V
>- 2 _
E’
o
C
III
a
.5 1 —-
1:
.5
to
o
> + - .
1?, 0 g 5 2 5 2, 3p 3/2_
70'
a:

49 57 -
_1 _ 7 2 ”Ca” 28NI29
91 131
_ 40er1 50$“ 81

 

Figure 5.2: The proton-neutron monopole interaction between (a) the ug7/2-7rgg/g and
(b) V f5/2-1r f7/2. In both cases the reduction in energy of the neutron level resulting
from the filling of the proton single-particle state is ~3 MeV.

where a large drop in the energy of the 7/2+ state is observed as protons are added to
the gg/g single—particle level from Zr to Sn. Information on the spectrosc0pic factor (S
factor) provides the link between the single-particle state, 1297/2, and the observed J"
of the low-energy level. The S factor describes the fraction of a particular state that is
derived from a specific nuclear configuration and can vary between 0 and 1. The drOp

of the 7/2+ level observed in Figure 5.2 is attributed to the monOpole interaction

between the ngg/g-Vg7/g levels. Although the single-particle level density is high in

95

this mass region the drastic change in single—particle energies results in the formation
of a shell gap at N = 56, evidenced by the high 2? energy in 96Zr [52] compared to
other Zr isotopes, that subsequently is washed out as the 1rgg/g state is filled, lowering
the 1197/2 level.

In regions of lower single-particle level density, such as the pf shells, the substantial
reordering of single-particle states due to the proton-neutron monopole interaction
make neutron-rich nuclei near N = 28 ideal candidates for the emergence of new shell
structure. Between the Ca and Ni isotopes, as protons are added to the f7/2 single-
particle state the monopole interaction between 7r f7/2 and Vf5/2 results in a decrease
in the energy of the f5/2 single-particle state, resulting in a reduced energy of the
5/2' state, see Figure 5.2(b). As protons are removed from the f7/2 single-particle
level the neutron f5/2 state increases in energy and could result in the formation of N
= 32 and N = 34 subshell closures in the Ca and Ti isotopes due to the large energy
separation between the p3/2,p1/2, and few neutron single—particle states.

The low energy structure of the even-even neutron-rich isotopes beyond the N =
28 shell closure have been investigated to follow the evolutiOn of possible new subshell
closures at N = 32,34. As previously mentioned, the systematic variation of the E(2+)
in even-even nuclei gives an indication of shell closures. Along with the E(2T) energies,
the branching ratios of the 6 decay of the odd-odd parent into the even-even daughter
allows the inference of a tentative spin and parity assignment to the parent ground
state. The ground state J1r assignments can be used to track the monopole migration
of the V f5 /2 level as a function of protons in the f7/2 state which can be compared to
with shell model predictions to infer single-particle level ordering. With the current
experimental data, the E(2+) values for the N = 34 ggTi and 24Cr isotopes can be
compared with theoretical predictions to gauge the possible presence of an N = 34

subshell closure.

96

 

 

1.51

E(ZI) (MeV)

O

0

0|
1

 

”0&0

Lllllll

 

d

 

 

 

26 2'8 3'0 3'2 3'4 3'8 3'8 40
Neutron Number

Figure 5.3: E(2+) as a function of neutron number for the g4Cr, 22Tl, and 2003 isotopes
The circles connected by lines represent the GXPFl interaction. Crosses connected
by lines correspond to KB3G interaction and the black bars are experimental points.
GXPFl does well at reproducing the N = 32 subshell closure in the Cr, Ti, and Ca
isotopes while KB3G does not predict an N = 32 subshell closure in the Cr isotopes.
GXPFI predicts a shell closure at N = 34 in the Ti and Ca isotopes evidenced by the
peak in E(2+) values.

5.1 Comparison with Shell Model Results

Shell model calculations employing the GXPFl [1,14] and KB3G [53] interactions are
compared to the experimental energies of the first excited 2+ state of the even-even
24Cr, 22Ti and ggCa isotopes beyond the N = 28 shell closure in Figure 5.3, and were
presented in Ref. [28]. The evolution of the N = 32 subshell gap, as described by
the GXPF 1 interaction, arises from the gradual migration of the V f5/2 orbital, due to
the proton-neutron monopole interaction, with the removal of protons from the fig

leading to a increasing energy gap between the Vf5/2 and Vp3/2 orbitals. The widening

97

 

3200 —

0 o o E(4+)
:3 \ \o—o/ O‘~o
a 1600 T . .
«‘13 \
ch _ .\ / \._.

800 0 E(2+)
N = 32
0

 

 

 

i) 212 214 26 28 310 312
Proton Number (Z)
Figure 5.4: E(2+) for the N = 32 isotones showing the rise in energy that is expected
to parallel the increasing energy separation between the neutron f5/2 and 193/2 single—

particle states.
energy gap between the uf5/2 and Vp3/2 can be seen as well in the increasing energy
of the E(2+) in the N = 32 isotones as protons are removed from the nucleus, see
Figure 5.4. The GXPFl calculations also do well in reproducing the high-spin states
observed in various neutron-rich Ti isotopes [13]. The GXPFl and KB3G calculations
diverge concerning the possible subshell closure at N = 34 in the Ti and Ca isotopes.
The GXPFl interaction predicts that as the last few protons are removed from the
f7/2 state the V f5 /2 single-particle state continues to increase in energy resulting in a
significant energy gap between the upl/g and u f5 /2 orbitals, and a new magic number
at N = 34 for the 22TI and 2003 isotOpes. A first indication of the subshell closure at
N = 34 would be found in the systematic variation in E (2?) in Ti and Ca isotopes.
Unfortunately, the energy of the 2" state in 56Ti, only 1129 keV, does not bear out
this possibility; falling midway between the GXPFl and KB3G predictions [28].
Shell model calculations using the GXPFl interaction were carried out and are
compared to the fi-decay properties of 56Sc, along the lines of similar investigations
for the neutron-rich V [26] and Ti [30] nuclides, and were presented in Ref. [31].
The calculations were performed using the codes OXBASH [54] and CMICHSM [55].
Both high- and low-spin fi-decaying states have been observed in 56Sc. The low-spin
state decays primarily to the ground state of 56Ti, with a measured branching ratio

of (65 :t 13)%. The results of shell model calculations using the GXPF] interaction

98

 

 

 

 

 

 

 

 

 

1821 3+
1745 5+
1681 +
1676 6+
9 .— 1522__;+
150 1505 5+ 3+
1444 4+
1275 4+
1020__1+
543 6+
490 2+
123 3+
0 4+ 0 1+
54Sc 565C

Figure 5.5: Low-energy level structure of 54"r"5Sc from shell model calculations using
the GXPFl interaction.

99

predict a 42% B—branch for the 568C 1+ decay to the ground state of 56Ti. Based
on direct feeding to the first 6+ state in the daughter 56Ti, the spin and parity of
the high-spin fi-decaying state in 568C has been tentatively assigned as (6+, 7+). The
shell model calculations performed predicted a 68% fl-decay branching for the 56Sc
6+ decay to the first excited 6+ state in 56Ti, and this was the only direct feeding to
excited states in 56Ti below 4 MeV.

The calculated fl—decay half-lives for the 1+ and 6+ states were 16 ms (35 :l: 5 ms)
and 110 ms (60 :l: 7 ms), respectively, where the corresponding experimental numbers
are given in parenthesis. For both calculations, a QB value of 13.7 MeV [32] was used,
as the energy separation between and order of the high- and low-spin fi-decaying states
is unknown. The calculated half-lives were corrected by a factor of two to account for
the reduction in calculated Gamow-Teller strength for neutron-rich nuclides in this
region. The experimental half—lives for the two fl-decaying states in 568C fall within a
factor of two of the shell model results.

The presence of two fi-decaying states in 56Sc can be described by studying the
change in level structure between 54'563c. The calculated low-energy level structures
for odd-odd parents 54’56Sc are shown in Figure 5.5. The ground state of 548C is
predicted to have spin and parity 4+, and is separated by only 123 keV from the
first excited state, which is calculated to have J1r 2 3*”. A very different low-energy
structure is expected for 5680. The ground state of 568C is predicted to have spin and
parity 1*, and a doublet of states with J1r = 2",6+ is calculated at an energy of
~ 500 keV above the ground state. The following discussion focuses on the significant
changes to the low-energy structure and the fl-decay prOperties of these nuclides that
result from the addition of two neutrons in going from 54Sc to 568C.

The presence of an E2 isomeric transition with energy 110 keV in “SC [31] provides
an insight into the low-energy structure of the 54Sc parent. The calculated. position of
the first 1+ level in 54Sc, which has composition (7r f7/g)1(up3/2)4(u f5/2)1, compared to

the ground state doublet, which is most likely (7r f7/g)1(up3 /g)4(up1 /2)1, furthers the

100

understanding of the relative position and energy separation of the Vf5/2 and upl/g
single-particle orbitals. If the monopole migration of the Vf5/2 is overestimated in the
GXPFl as suggested in Ref. [28], the 1+ state may reside much closer to the ground
state, and could give rise to the observed E2 isomeric transition.

56Sc differs from 5480 by two neutrons, and the unpaired neutron is expected to
occupy the l/f5/2 orbital. A 1+ ground state is predicted for 56Sc from the shell model
calculations employing the GXPFI interaction. Similar to the situation in 54Sc, the
separation between the V f5 /2 and upl/g single-particle states is expected to be smaller
than that reflected in the GXPFI results shown in Figure 5.5. A condensed low-energy
spectrum for 56Sc may produce several isomers, which are observed experimentally.
The three isomeric 'y rays observed in 5680 have not been placed. The low statistics
in the current experiment did not permit the analysis of coincidence relationships
between the three '7 rays. Additional data on the time evolution of each of the isomeric
7 rays would also help to place these transitions in the level structure of the 5680
parent.

Calculations of the 6 decay of 57Ti to low energy levels in 57V have also been
carried out using the GXPFl interaction and compared with the 5"'Ti —+ 57V decay.
GXPFI calculations predicted a ground state J1r of 5/2‘ for 57Ti with a first excited
state, at 422 keV, assigned as a 1/2‘ level. The low energy level structure of 57V
was also calculated, resulting in a ground state of 7/2‘ with a 5/2‘ excited state
at an excitation energy of 95 keV. The calculated 6 decay of 57Ti, using a 5/2‘
ground state, to levels in 57V, presented in Figure 5.6, shows a large ground state
branch of 44% which compares favorably with the measured value of 54:1:3%. The 3
decay calculations also predict a significant amount of feeding to four states above
1500 keV which was also observed in the experimental level scheme. Considering that
the lower detection limit for absolute intensities in the 57Ti 6 decay was ~0.7%, the
experimental and calculated level scheme agree quite well and suggest that the ground

state spin and parities of 57Ti and 57V are 5/2‘ and 7/2‘, respectively.

101

 

 

 

 

 

 

 

(5/23 0 T1,2 =9815 ms 5 2'
57Ti ¥ QB = 10610.6 MeV 5711
13(96) 15(96)
2.5 7/2‘
2475 11.3 572N-
_ 0.6 3 2'
7.31:0.7 0.2 7fi_\_
2036 4.9 5 '
1512 J— 0 3/2':
1&2 1754 8.2 7/2'
1.1107 1-7-33 4.7 5/2'
oar 5/2'
0 3/2'
5:63 5 5/2'
5413 (7/2)‘ 44 7/2'
57V
experimental

0 _
T1/2 -47 ms
QB = 10.6 MeV

 

 

 

 

 

 

 

 

 

 

 

57v

theoretical

2494
_1/2272
2251

2061

_/
_/1934

1871
1749

1665

529

Figure 5.6: The experimental decay scheme for levels in 57V populated following the 6
decay of 57Ti are shown on the left hand side of the figure. The theoretical calculations
are shown on the right hand side of the figure and assume a 57Ti ground state of 5 / 2’.
There is overall very good agreement between the calculated and observed branching
ratios, especially for the ground state branch

102

 

 

 

 

 

 

 

 

 

 

 

 

 

55 1+ 57 58 1+
V :91]: 3'91]:
“('7’ 1), '0—32 SI! ”32 512
M 000—41911;
55 (512-) 55 57 (5/2-)
11 VP”: V9112
““7192 32 V7512 32 V's/2

“VB/2 MVP
54 (3,4)+ 55 55 (1M
Sc stn -.—st/2
1!0qu I 32 :1] 32 Wm
“00-" «_u-_vvu

33 34 35

Figure 5.7: Spin and parities of odd-odd and odd-A nuclear ground states near
N=32,34

A tentative 3 / 2‘ ground state assignment has been previously put forward for 57V
based on the characteristics of the B decay into levels of 57Cr [35], most importantly,
a large ground state 6 branch of 55%. Later, the 57V —> 57Cr ground state branch
was remeasured and resulted in a value of 21% [26]. A comparison of the 57V 6 decay
characteristics with GXPFI shell model calculations assuming a 3/2’, 5/2‘, and
7/2“ ground state for 57V found the 3/2‘ 57V ground state assignment was unable
to reproduce the large ground state branch to 57Cr. Calculations instead favored a
5/2’ or 7/2’ assignment to the ground state of 57V, in agreement with the present

tentative 7/2“ 57V ground state.

5.2 Mon0pole Migration of Vf5/2 Based on Ground-
State Spin and Parity Assignments

Using the tentative spin and parity assignments for the 54'568c, 55“Ti, and 56'58V
isotopes, the monopole migration of the uf5/2 state with removal of protons from the
7r f7 /2 level can be qualitatively described. The spins and parities for the ground states
of Sc, Ti, and V nuclei around the N = 32 subshell closure, together with schematic

neutron single-particle levels, are shown in Figure 5.7. Working from the N = 32

103

subshell closure, the extreme single-particle model was used to infer the proton and
neutron orbitals that couple to produce the observed ground state spins and parities.

Starting in the 21Sc isotopes, the odd proton is located in the 7r f7/2 state, as
evidenced by the ground state spins and parities of odd-A Sc isotopes [31]. Coupling
this proton to an odd neutron in the Vf5/2 orbital results in a range of spin and parity
of (1-6)+, while coupling an f7/2 proton to an odd neutron in the Vp1/2 state would
lead to spin and parity of 3+ or 4". The ground state spin and parity of 54Sc has been
tentatively identified as (3,4)+. N ordheim rules [56,57] argue against the coupling of
a proton in the 7r f7 )2 to a neutron in the V f5 /2 level resulting in a. (3,4)+ ground state,
suggesting that the 33rd neutron occupies the UPI/2 orbital in agreement with shell
model calculations. The tentative spin and parity of 1+ in 56Sc in a single-particle
picture is only possible with the placement of the 35th neutron in the 1/ f5 /2 level. From
the schematic neutron levels, it is seen that the Vf5/2 level is located above the UPI/2
state in the 2180 isotopes.

In the 23V isotopes, the odd proton is still located in the 71'f7/2 orbit. Both 5653V
have been assigned 1+ ground states, placing the both the 33’" and 35th neutrons in
the Vf5/2 state and suggesting that the Vf5/2 orbital is lower than the upl/g level in
23V nuclei.

The 6 decay of the odd-even nucleus 55Ti has also been studied [30] and, while
the spin and parity have not been firmly established, the complex feeding observed in
the B decay of 55’Ti is not indicative of a dominant up1/2 single-particle configuration
for the 55Ti ground state. The results reported on the 6 decay of 55Sc into the low-
energy levels of 55Ti suggest a significant fl-decay feeding the ground state of 55Ti [31].
Assuming J = 7/ 2 for the 55Sc parent state, a ,B-decay branch directly to the daughter
ground state also suggests that the ground-state spin of 55Ti is greater than 1 / 2,
limiting the J7r to (9/ 2, 7/2, 5/2)‘. In an extreme single-particle model, only a 5/2‘
assignment is possible by filling the odd neutron into the f5/2 state.

The inclusion of the B decay of 57Ti completes the picture. A tentative spin and

104

parity assignment of 5 / 2‘ to the ground state is based on favorable comparisons
to theoretical shell model calculations in the previous section, most importantly the
large branch to the ground state of 57V. In a single-particle picture, to obtain a 5 / 2‘
spin and parity the odd neutron should be placed in the f5/2 single-particle level.
Thus 55'57Ti suggest that the V f5/2 state is lower in energy than the UPI/2 state in
agreement with observations in 5E’Ti.

While the l/f5/2 and Vp1/2 single-particle level orderings, inferred from the spin
and parity assignments to the ground states of odd-odd 541563c and 5658V isotopes,
agree with shell model calculations, the present data on the low-energy levels of the
neutron-rich Sc and Ti isotopes do not support a large energy separation between
the V f5 /2 and Vp1/2 orbitals predicted using the GXPFl interaction. As noted in
Ref. [28], a reduction of a: 0.8 MeV in the single-particle energy of the Vf5/2 state
would account for the absence of an N = 34 shell closure. To preserve calculated
levels in other nuclei, a weaker monopole interaction should be considered to account
for the slower rise in energy of the Vf5/2 state with the removal of protons from the
1rf7/2 orbit [1] and a location of the first 2+ state in 54Ca around 4 MeV. However,
the monopole migration of the Vf5/2 state is expected to continue with the removal of
the last two protons from the 7r f7 /2 orbital in the ggCa isotopes. Further investigation
of the low-energy level structure of neutron-rich Ca nuclei is warranted to determine

if a 11 f5 /g-z/p1 /2 energy gap dominates at N = 34, resulting in a shell closure.

5.3 Summary

The 6 decay of (a large number) of neutron-rich nuclides was studied. The half-
lives, branching ratios, and 'y feeding patterns were determined for these nuclides.
Among the most interesting, the low—energy levels of neutron-rich 56Ti was studied
through the 6 decay of the parent nuclide 56Sc, respectively. The systematic variation

in E(2f) for the even-even ggTi isotopes reveal a peak at N = 32 indicative of a

105

subshell closure, similar to the increase in E(2f) at N = 32 observed for the ggCa
and 24Cr isotopes. Evidence for a shell closure at N = 34, predicted for the Ti
isotopes by shell model calculations carried out using the new p f-shell interaction
GXPFl, were not substantiated. Based on fl-decay branching ratios, tentative spin
and parity assignments were made for the odd-odd parent nuclei. A survey of the
spin-parity assignments of the ground states of the odd-A and odd-odd nuclides in
this region was used to analyze, in a schematic way, the monopole migration of the
V f5/2 orbital. While there is evidence that the Vf5/2 — Vp1/2 level ordering changes
between 23V and 21Sc, there is no substantial proof that a large energy gap between
the uf5/2 and Vp1/2 develops for the 22TI isotopes. Support for this conclusion is
found in the systematic variation of E (2?) for the even-even Ti isotopes and the
presence of isomeric transitions in 54'568c, which suggest a more compressed low-
energy spectrum than predicted for these nuclides by the shell model results reported
here using the GXPFl interaction. It is important to continue to track the progression
of the monopole migration to the ggCa isotopes, which have no f7/2 protons. The “full”
monopole shift of the V f5 /2 orbital may lead to a large gap in the V f5 )2 —Vp1/2 effective

single particle energies, producing a shell closure at N = 34 for the Ca isotopes.

106

Chapter 6

Conclusions and Outlook

The shell structure of neutron-rich nuclei above 48Ca has been investigated through
the H decay of odd-odd and odd-A nuclides. Fast fragments from the NSCL facility
were implanted in the DSSD and correlated with subsequent B decays on an event-by-
event basis. Delayed 'y rays, observed using twelve detectors from SeGA, have been
observed. Half-lives and level structures were determined for 56Sc, 57Ti, 58'59V and
60Cr, representing a significant improvement in the knowledge of nuclear properties
in this neutron-rich region. Tentative spin and parity assignments have been given,
at a minimum, for the ground states of the studied nuclides. The possibility of an
N = 34 shell closure was investigated. Shell model calculations, using the GXPFl
effective interaction, predicted that the strong proton-neutron monopole interaction
between the spin-orbit partners 1r f7/2-u f5/2 would result in a gradual increase in the
single-particle energy of the uf5/2 level as protons were removed from the 7r f7/2.
Moreover, the rise in energy of the neutron f5/2 would lead to the development of an
N = 32 subshell closure and an N = 34 subshell closure in the Ti and Ca isotopes.
While the N = 32 subshell closure has been identified experimentally, the E(2T) value
for 33Ti34 was ~400 keV lower than theoretical predictions, suggesting the absence
of a subshell closure at N = 34 in the Ti isotopes. The spins and parities of the

neighboring odd-odd nuclei were analyzed in an extreme single-particle framework

107

assuming N = 32 is a good subshell closure. The results suggest that the f5/2 has risen
in energy above the p1/2 level as expected but there is not a large energy separation
between the two orbitals to bring about a neutron subshell closure at N = 34. Further
experiments on the neutron-rich Ca isotopes, in particular 54’56Ca are warranted to
determine if the subshell closure is present with the complete removal of protons from
the f7/2 state. However, the study of these very-neutron rich nuclides through 6 decay
may have to wait for the next generation accelerator facility due to the extremely
low production cross section. It may be possible to investigate these nuclei through
Coulomb excitation or possibly deep-inelastic reactions. The monopole interaction
might have a role in the evolution of shell structure in heavier neutron-rich nuclei. For
example, the filling of the 1199/2 level following the N = 40 subshell closure may alter
the single-particle energy of the 7r f5 /2 and 7rgg/g states possibly affecting shell structure
in the vicinity of 78N i [58]. Additionally, the proton-neutron monopole interaction
between the spin-orbit partners 7rgg/2 — 1197/2 and 7rh11 /2 — Vh9/2 may affect the energy
of the 1197/2 and Vh9/2 single-particle states, disturbing the energies of the N = 82,126

shell closures [10].

108

Bibliography

[1] M. Honma, T. Otsuka, B.A. Brown, and T. Mizusaki. Phys. Rev. C, 69:034335,
2004.

[2] http://www.nndc.bnl.gov/. .
[3] MC. Mayers. Phys. Rev., 75:75, 1949.
[4] O. Haxel, J. Hans, D. Jensen, and HS. Suess. Phys. Rev., 7511776, 1949.

[5] K. S. Krane. Introductory Nuclear Physics. John Wiley & Sons, Inc., New York,
1988.

[6] RA. Meyer, I. Morrison, and W.B. Walters. Proton-neutron interactions in the
a = 100 nuclides. In Exotic Nuclear Spectroscopy. DNCT, American Chemical
Society, 1990.

[7] P. Federman and S. Pittel. Phys. Lett. B, 692385, 1977.
[8] L. Grodzins. Phys. Lett., 2:88, 1962.

[9] A. Huck, G. Klotz, A. Knipper, C. Miehe, C. Richard-Serre, G. Walter, A. Poves,
H.L. Ravn, and G. Marguier. Phys. Rev. C, 31:2226, 1985.

[10] T. Otsuka, R. Fujimoto, Y. Utsono, B.A. Brown, M. Honma, and T. Mizusaki.
Phys. Rev. Lett., 87:082502, 2001.

[11] XL. Tu, X.G. Zhou, D.J. Vieira, J.M. Wouters, Z.Y. Zhou, H.L. Seifert, and
V.G. Lind. Z. Phys. A, 337:361, 1990.

[12] J.I. Prisciandaro, P.F. Mantica, B.A. Brown, D.W. Anthony, M.W.Cooper,
A. Garcia, D.E. Groh, A. Komives, P.A. Lofy, A.M. Oros—Peusquens, S.L. Tabor,
and M.Wiedeking. Phys. Lett. B, 510:17, 2001. .

[13] R.V.F. Janssens, B. Fornal, P.F. Mantica, B.A. Brown, R. Broda, P. Bhat-
tacharyya, M.P. Carpenter, M. Cinausero, P.J. Daly, A.D. Davies, T. Glas-
macher, Z.W. Grabowski, D.E. Groh, M. Honma, F.G. Kondev, W. Krolas,
T. Lauritsen, S.N. Liddick, S. Lunardi, N. Marginean, T. Mizusaki, D. Sew-
eryniak, H. Schatz, A. Stolz, S.L. Tabor, C.A.Ur, G. Viesti, I. Wiedenhover, and
J. Wrzesinski. Phys. Lett. B, 546:55, 2002.

109

[14] M. Honma, T. Otsuka, B.A. Brown, and T. Mizusaki. Phys. Rev. C, 65:061301R,
2002.

[15] T. Glasmacher. Annu. Rev. Nucl. Part. Sci., 48:1, 1998.
[16] PG. Hansen and J.A. Tostevin. Annu. Rev. Nucl. Part. Sci., 53:219, 2003.
[17] OR. Ahmad and SNO Collaboration. Phys. Rev. Lett., 89:011301, 2002.

[18] Y. Fukuda and Super Kamiokande Collaboration. Phys. Rev. Lett., 81:1562,
1998.

[19] S. S. M. Wong. Introductory Nuclear Physics. John Wiley & Sons, Inc., New
York, 1998.

[20] G. Friedlander, J. W. Kennedy, E. S. Macias, and J. M. Miller. Nuclear and
Radiochemistry, 3’“ ed. John Wiley & Sons, Inc., New York, 1981.

[21] D. J. Morrissey, B.M. Sherrill, M. Steiner, A. Stolz, and I. Wiedenhoever. 204:90,
2003.

[22] W. F. Mueller, J.A. Church, T. Glasmacher, D. Gutknecht, G. Hackman, P.G.
Hansen, Z. Hu, K.L. Miller, and P. Quirin. Nucl. Instr. and Meth. A, 466:492,
2001.

[23] J .I. Prisciandaro. Beta Decay Studies of 69Ni and 58 V: Development of subshell
gaps within the N = 28 - 50 shell. PhD thesis, Michigan State University, 2001.

[24] J.I. Prisciandaro, A.C. Morton, , and RF. Mantica. Nucl. Instr. and Meth. A,
505:140, 2003.

[25] G. F. Knoll. Radiation Detection and Measurement. John Wiley & Sons, Inc.,
New York, 2000.

[26] PF. Mantica, A.C. Morton, B.A. Brown, A.D. Davies, T. Glasmacher, D.E.
Groh, S.N. Liddick, D.J. Morrissey, W.F. Mueller, H. Schatz, A. Stolz, S.L. Ta-
bor, M. Honma, M. Horoi, and T. Otsuka. Phys. Rev. C, 67 :014311, 2003.

[27] W.T. Milner. Oak Ridge National Laboratory, unpublished.

[28] S. N. Liddick, P.F. Mantica, R.V.F Janssens, R. Broda, B.A. Brown, M.P. Car-
penter, B. Fornal, M. Honma, T. Mizusaki, A.C. Morton, W.F. Mueller, T. Ot-
suka, J. Pavan, A. Stolz, S.L.Tabor, B.E. Tomlin, and M. Wiedeking. Phys. Rev.
Lett., 92:072502, 2004.

[29] B. Fornal, S. Zhu, R.V.F. Janssnes, M. Honma, R. Broda, P.F. Mantica, B.A.
Brown, M.P. Carpenter, P.J. Daly, S.J. Freeman, Z.W. Grabowski, N. Hammond,
F.G. Kondev, W. Krolas, T. Lauritsen, S.N. Liddick, C.J. Lister, E.F. Moore,
T. Otsuka, T.Pawlat, D. Seweryniak, B.E. Tomlin, and J. Wrzesiriski. Phys. Rev.
C, (in press).

110

[30] P. F. Mantica, B.A. Brown, A.D. Davies, T. Glasmacher, D.E. Groh M. Horoi,

S.N. Liddick, D.J. Morrissey, A.C. Morton, W.F. Mueller, H. Schatz, A. Stolz,
and S.L.Tabor. Phys. Rev. C, 68:044311, 2003.

[31] S. N. Liddick, P.F. Mantica, R. Broda, B.A. Brown, M.P. Carpenter, A.D. Davies,

[32]
[33]
[34]

[35]

[35]

[37]

[38]

[39]

[40]

B. Fornal, T. Glasmacher, D.E. Groh M. Honma, M. Horoi, R.V.F. Janssens,

T. Mizusaki, D.J. Morrissey, A.C. Morton, W.F. Mueller, T. Otsuka, J. Pavan,
H. Schatz, A. Stolz, S.L.Tabor, B.E. Tomlin, and M. Wiedeking. Phys. Rev. C,

(in press).
G. Audi and A. H. Wapstra. Nucl. Phys. A, 5952409, 1995.
G. Audi, A. H. Wapstra, and C. Thibault. Nucl. Phys. A, 729:337, 2003.

P. Méller, J.R. Mix, and K.-L. Kratz. At. Data and Nucl. Data Tables, 66:131,
1997.

O. Sorlin, V. Borrel, S. Grévy, D. Guilemaud-Mueller, A.C. Mueller,
F. Pougheon, W. B6hmer, K.-L. Kratz, T. Mehren, P. Méiller, B. Pfeiffer,
T. Rauscher, M.G. Saint-Laurent, R. Anne, M. Lewitowicz, A. Ostrowski,
T. Dérfler, and W.-D. Schmidt-Ott. Nucl. Phys. A, 632:205, 1998.

F. Ameil, M. Bernas, P. Armbruster, S.Czajkowski, Ph. Dessangne, H. Geissel,
E. Hanelt, C. Kozhuharov, C. Mieha, C. Donzaud, A. Grewe, A. Heinz, Z. Janas,
M. de Jong, W. Schwab, and S. Steinhauser. Eur. Phys. J. A, 1:275, 1998.

O. Sorlin, C. Donzaud, L. Axelsson, M. Belleguic, R. Béraud, C. Borcea, G. Can-
chel, E. Chabanat, J .M. Daugas, A. Emsallem, M. Girod, D. Guilemaud-Mueller,
K.-L. Kratz, S. Leenhardt, M. Lewitowicz, C. Longour, M.J. Lopez, F. de Oliv-
eria Santos, L. Peitzon, B. Pfeiffer, F. Pougheon, M.G. Saint-Laurent, and J.E.
Sauvestre. Nucl. Phys. A, 669:351, 2000.

T. D6rfler, W.-D. Schmidt-Ott, T. Hild, T. Mehren, W. Béhmer, P. Méiller,
P. Pfeiffer, T. Rauscher, K.-L. Kratz, O. Sorlin, V. Borrel, S.Grévy,
D. Guillemand-Mueller, A.C. Mueller, F. Pougheon, R. Anne, M. Lewitowicz,
A. Ostrowsky, M. Robinson, and MG. Saint-Laurent. Phys. Rev. C, 54:2894,
1996.

R. Grzywacz, R. Beraud, C. Borcea, A.Emsallem, M. Glogowski, H. Grawe,
D. Guillemaud-Mueller, M. Hjorth—Jensen, M.Houry, M. Lewitowicz, A.C.
Mueller, A. Nowak, A. Plochocki, M. Pfuztzner, K. Rykaczewski, M.G. Saint-
Laurent, J.E. Sauvestre, M. Schaefer, O. Sorlin, J. Szerypo, W. Trinder, S. Vi-
teritti, and J. Winfield. Phys. Rev. Lett., 81:766, 1998.

U. Bosch, W.-D. Schmidt-Ott, P. Tidemand-Petersson, E. Runte, W. Hille-
brandt, M. Lechle, F.-K. Thielemann, R. Kirchner, O. Klepper, E. Roeckl,
K. Rykaczewski, D. Schardt, N. Kaffrell, M. Bernas, Ph. Dessagne, and
W.Kurcewicz. Nucl. Phys. A, 164:22, 1985.

111

[41] U. Bosch, W.-D. Schmidt-Ott, E. Runte, P. Tidemand-Petersson, P. Koschel,

[42]
[43]

[44]

[45]

[46]

[4 7l

[48]

[49]

[50]

[51]

[52]
[53]

F. Meissner, R. Kirchner, O. Klepper, E. Roeckl, K. Rykaczewski, and
D. Schardt. Nucl. Phys. A, 477 :89, 1988.

T. Dérfler. Phys. Rev, 120:927, 1996.

SJ. Freeman, R.V.F. Janssens, B.A. Brown, M.P. Carpenter, S.M. Fisher, N.J.
Hammond, M. Honma, T. Lauritsen, C.J. Lister, T.L. Khoo, G. Mukherjee,
D. Seweryniak, J.F. Smith, B.J. Varley, M. Whitehead, and S. Zhu. Phys. Rev.
C, 692064301, 2004.

EB. Norman, C.N. Davids, M.J. Murphy, and RC. Pardo. Phys. Rev. C,
17:2176, 1978.

E. Runte, K.-L. Gippert, W.D. Schmidt-Ott, P. TidemandPertersson, L. Ziegeler,
R. Kirchner, O. Klepper, P.O. Larsson, E. Roeckl, D. Schardt, N. Kaffrell,
P.Peuser, M. Bernas, P. Dessagne, M. Langevin, and K. Rykaczewski. Nucl.
Phys. A, 441:237, 1985.

W.-D. Schmidt-Ott, K.Becker, U. Bosh-Wicke, T. Hild, F. Meissner, R.Kirchner,
E.Roeckl, and K. Rykaczewski. Inst. Phys. Conf. Sen, 132:627, 1992.

H. Simon, D. Aleksandrov, T. Aumann, L. Axelsson, T. Baumann, M.J.G.
Borge, L.V. Chulkov, R. Collatz, J. Cub, W. Dostal, B. Eberlein, Th.W. Elze,
H. Emling, H. Geissel, A. Grunschloss, M. Hellstriim, J. Holeczek, R. Holzmann,
B. Jonson, J .V. Kratz, G. Kraus, R. Kulessa, Y. Leifels, A. Leistenchneider,
T. Leth, I. Mukha, G. Muznzenburg, F. Nickel, T. Nilsson, G. Nyman, B. Pe-
tersen, M. Pfiitzner, A. Richter, K. Riisager, C. Scheidenberger, G. Schrieder,
W. Schawb, M.H.Smedberg, J. Stroth, A. Surowiec, O. Tengblab, and M.V.
Zhukov. Phys. Rev. Lett., 832496, 1999.

T. Motobayashi, Y. Ikeda, Y. Ando, K. Ieki, M. Inoue, N. Iwasa, T. Kikuchi,
M. Kurokawa, S. Moriya, S. Ogawa, H. Murakami, S. Shimoura, Y. Yanagisawa,
T. Nakamura, Y. Watanabe, M. Ishihara, T. Teranishi, H. Okuno, and RF.
Casten. Phys. Lett. B, 346:9, 1995.

D. Guillemaud-Mueller, C. Detraz, M. Langevin, F. Naulin, M. De Saint-Simon,
C. Thibault, F .Touchard, and M. Epherre. Nucl. Phys. A, 426237, 1984.

A. Ozawa, T. Kobayashi, T. Suzuki, K. Yoshida, and I. Tanihata. Phys. Rev.
Lett., 84:5493, 2000.

K. Heyde, J. Jolie, J. Moreau, J. Ryckebusch, and M. Waroquier. Nucl. Phys.
A, 466:189, 1987.

Table of Isotopes. edited by RB. Firestone. Wiley, New York, 1996.

A. Poves, J. Sanchex—Solano, E. Caurier, and F. Nowacki. Nucl. Phys. A, 694:157,
2001.

112

[54] BA. Brown, A. Etchegoyen, and W.D.M. Rae. The computer code oxbash.
MSU-NSCL Report 524, MSU-NSCL, 1998.

[55] M. Horoi, B.A. Brown, and V. Zelevinsky. Phys. Rev. C, 67:034303, 2003.
[56] L. Nordeim. Rev. Mod. Phys, 23:322, 1951.

[57] M.H. Brennan and A.M. Bernstein. Phys. Rev., 120:927, 1960.

[58] A.M. Oros—Peusquens and RF. Mantica. Nucl. Phys. A, 669281, 2000.

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