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This is to certify that the
dissertation entitled

THE STUDY OF BETA-DELAYED NEUTRON DECAY
NEAR THE NEUTRON DRIP LINE

presented by

CHANDANA SUJEEWA SUMITHRARACHCHI

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Chemistry

 

 

 

 

 

 

MSU is an affinnative-action, equal-opportunity employer

 

A_-—.-.—-—.—.-..—-—.-—-—---

—.—u—-—.-—-—-—---—c-.-o-o—u-a-n—o-o-n—o—n—n—o—n-—--—-----. —

THE STUDY OF BETA—DELAYED NEUTRON DECAY
NEAR THE NEUTRON DRIP LINE

By

Chandana Sujeewa Sumithrarachchi

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

2007

ABSTRACT
The Study of Beta—delayed Neutron Decay Near The Neutron Drip Line
By

Chandana Sujeewa SuInithraracl'ichi

The study of neutron-rich oxygen and fluorine isotopes can provide important
information on the evolution of nuclear shell structure close to the neutron drip line.

The structural changes in this region are reflected with observations of the rapid

change in the location of the drip line at fluorine and appearance of a new shell

closure at N = 14. The recent experiments along with the shell model calculations
provide evidence for the doubly magic nature of 220. The negative parity states in
22O rooted in the neutron pf orbitals are not experimentally known. The knowledge
of nuclear structure in 23P, which has the structure of a single proton outside the
doubly magic 220, is also important as it. should be sensitive to the proton s and d
orbital splitting. The present work focused on the beta-delayed neutron and gamma-
ray spectroscopes from 22N and 230 beta decay.

The measurements of 22N and 230 were carried out at. the NSCL using fragments
from the reaction of 48Ca beam in a Be target. The desired isotopes were stopped in
the implantation detector and then monitored for beta-delayed neutrons and gamma-
rays using a neutron spectroscopic array and eight detectors from SeGA, respectively.
The half-lives and the total neutron emission probabilities were determined to be
20(2) and 97(8) ms, and 57(5)% and 7(2)%? respectively, for 22N and 230. Single and
two beta—delayed neutron decay of 22N was observed and five new negative parity
states identified in 220. The II’lt‘flSllI‘GIllOlIt also revealed three garmna-ray transitions
in 22O and a single gamma—ray for each in 210 and 200 associated with the beta-
delayed neutron decay of 22N. Ten gamma-ray decays in 23F and a single gt-llllllla—I‘ay

- ' 1. ' ° or.) Y
in 22F were observed from 2"0 beta. drmay. The tentative decay schemes of “N and

s . no: In

 

II:

230 were established and cm’npared with shell model calculations. The beta decays
of the major contaminants in the beam from the fragment separator 25F, 2'40 and
26Ne have been investigated to establish decay schemes as well.

The observation of a relatively high energy for the first 2+ state in 220 supports
the shell closure at N = 14. The observation of large beta decay strength at high
excitation energies in 220 indicates the indirect evidence for the halo structure of
22N. The experimental results of the 22N beta decay are in poor agreement with the
shell model calculations suggesting the evolution of single particle structure in this
region. However, the overall beta decay results of 230 are in reasonable agreement
with shell model calculations. The excitation energies of the first 1/2+ and 3/ 2+
states in 23F have been determined at 2243 and 3866 keV and show a widening of
the 5/ 2+ - 1/2”“ state gap indicating the appearance of the N=14 shell closure in the

fluorine isotopes.

 

To
my mother, my wife Indikanz’, my daughter Alrmckya
all my teachers

and friends

iv

 

Pr. -.

ACKNOWLEDGMENTS

It is impossible in words to really express the gratitude that I have to the people
who I have worked with and met. along this road. Without the support, patience and
guidance of the following people. this study would not have been completed. First I
owe my deepest gratitude to my advisor. Professor Dave J. Morrissey, for his guidance.
supervision, and encouragement during this work. His patience, sense of humor, and
understanding has been greatly appreciated and are acknowledged. I must especially
thank him for his efforts during my experiment, for the experience I gained from
working alongside him and allowing me to work independently, while always being
available to help. I thank Professor Paul Mantica for being my second reader and giv-
ing additional guidance. His support during experiment and suggestions to complete
this work have been especially acknowledged. The contributions of my committee to
my education will always be remen’ibered. I would like to thank Professors Michael
Thoennessen and Hendrik Schatz for working as members of my dissertation corn-
mittee and for giving advice through this work. The NSCL technical staff is totally
outstanding and helped make the project real. I really need to thank Mr. Len Morris
for his design work. the NSCL Machine Shop for prmlucing parts for our setup and
all cyclotron operators. I whish to thank Dr. Mauricio Portillo for support through
A1900 work and Professor Thomas Glasmacher and the gamma group for providing
the support in use of ScGA. I am grateful to Professor Alex Brown for providing shell
model calculations for this work.

There are multiple people I would like to acknmvlcdge for their contril‘nitions
during the experiment. I would like. to thank Andrew. Debbie. Elaine, Josh. V’Veerasiri,
Dr. Fancina and Dr. Shimbara. giving support thorough the experiment. I especially
want to thank Elain Kwan for all her help. Our long discussions were. inspiring to
me. I have appreciated your friendship and willingness to help along the way. I wish

to thank the Morrisscy group members. Dr. Foldcn and Greg Pang for discussions

 

about various projects. My fellow graduate students at the lab were also invaluable
during my time at the lab. I offer Special thanks to my oflicemates W'es, Greg, Josh
and Philip, to great friends from the accelerator group, Susan and from the theory
group, Jeremy and former graduate students Bryan, Sean and Tao for the interesting
conversations to make time in graduate school enjoyable. I wish to thank Jeremy for
reading this.

I am grateful to the Department of Chemistry, Michigan State University and the
National Science Foundation for their financial support during this work. I wish to
thank especially the Chemistry Graduate Oflice, Lisa and Debbie for their kind help
throughout my studies.

The people that heard me grip the most over the past three years have been my
family. I cannot imagine being where I am today without them, and I am blessed
to have had their unconditional love and support throughout my academic career
and my life. Ariyawathei Sumithrarachchi, my mother, who has always supported,
encouraged and believed in me, in all my endeavors. Inikani, my wife, without whom
this effort would have been worth nothing. Your love, support and constant patience
have taught me so much about sacrifice, discipline and compromise. I want to mention
here about my loving daughter, h-Ianekya. She is everything for me. Her love is always

a gripe to my life.

Ir-.'

 

Contents

1 Introduction 1
1.1 Location of The Neutron Drip Line ...................... 5
1.2 Disappearance of Traditional Magic Numbers ................ 6
1.3 Shell closure at N = 14 and N = 16 ...................... 7
1.4 Halo structures near neutron drip line .................... 9
1.5 ;\/Iotivation ..................................... 11

1.5.1 Knowledge of the Structure of 220 and 223' ............ 11
1.5.2 Knowledge on the Structure of 23F and 230 ............ 14
1.0 Present \Vork .................................... 16

2 Overview of Beta Decay 17

2.1 Theory of Beta Decay .............................. 18

2.1.1 Selection Rules .............................. 21
2.2 Beta—delayed Neutron Decay .......................... 23
a. Gamma—ray decay ................................. 23
2.4 Gamow-Telli-ér Transition strength ...................... 24
2.5 Applicz’ttion ..................................... 26

3 Experimental Setup 28
3.1 Fragment. Production ............................... 28
3.2 Implantation Detector System ......................... 31

3.2.1 Data Acquisition System ........................ 33
3.3 \eutron Spectroscopic Array .......................... 36
3.3.1 Detail of the Neutron Spectroscol)ic Array ............. 36
3.3.2 Neutron Energy Calibration ...................... 38
3.3.3 Neutron Peak Shape and The Background ............. 44
3.3.1 Time Walk Correction .......................... 46
3.3.5 Neutron Efficiency Calibration .................... 48
3.4 Segmented Gernu—inium Detector Array .................... 51
3.4.1 SeGA ("letectors .............................. 51
3.4.2 SeGA Energy (J'a‘libration ........................ 52
3.4.3 ScGA Efficiency Calibration ...................... 54

4 Data Analysis and Results 59

4.1 Anaysis of The 22N Beta Decay Experiment .................. 59
4.1.1 Total Number of Beta. Decay Events ................. 61

i _ 4 . .‘ 7 . - . - ‘ ‘ 'I) v
4.1.2 The analysls of the neutron tnne-of—flight spectrum from 2-N

cocktail beam ............................... 64
4.1.3 Camilla—ray Identification ........................ 66
4.1.4 Beta Decay Scheme of 22X ....................... 71
4.2 Beta Decay of 22F ................................. 76
4.3 Beta Decay of 2’10 ................................ 83
4.4 Analysis of 230 Deta Decay Experiment. ................... 89
4.4.1 Total Number of Beta. Decay Events ................. 92
4.4.2 Beta-delayed neutron time-of-flight measurement ......... 94
4.4.3 Beta-delayed gamma—ray measurement ............... 97
4.4.4 Beta Decay Scheme of 230 ....................... 99
4.5 Beta Decay of Q‘lNe ................................ 102
5 Discussion 108
5.1 Beta Decay of 22X ................................. 108
5.2 Beta Decay of 230 and Energy States in 23F ................ 112
5.3 The 1Jr Excited States in 26Na ........................ 117
5.4 The Half—lives and Total Neutron Emission Probabilities of Neutron-
rich Light Nuclei .................................. 119
5.5 Conclusion and Sumnmry ............................ 120
A Beta Decay Fitting Model 122
Gamma-ray Spectrum Analysis 128
Bibliography ........................................ 135

viii

List of Figures

1.10

The differential single. neutron separation energy . . . . . . . .......

Schematic diagram of the single-particle states
Part of the chart of nuclides .
Single neutron separation energies for nuclides of different isospin

The excitation energy of the lowest 2+ states of even—even oxygen iso-
topes .....

Beta decay of the halo nuclei 11Li and 11Be . .
5 i) .
Level scheme of 2‘0. . . .
. 1):) 7
Beta decay chain of “N
. .).
Beta decay chain of "‘0
Experimentally km;>wn energy levels in 23F
Sclnnentic ('liagram of Beta—delayed Neutron Decay

Schematic (‘liagram of the NSCL C‘ouplcd Cyclotron Facility and the
A1900 fragment: separator

Ex1_)erimental setup with the neutron and SeGA array
Implantation detector system . .

Electronic setup for the implantation detector
Schematic electronic diagram for the neutron bar array .
The time calibration spectrum for the neutron ('lctector .
Total neutron time-of-flight s}.)ectra of MC and ”N
Energy caliln‘atitm of the neutron array .

Peak shape calibrz—ition

GURU)

10
12
13
14

23

3.10 Study of neutron background shape . ..... . . . . . . ......... . 46

3.11 A scatter-plot. oftime.vs.(__‘ncrgy from a P.\IT . . . . . . . . . . . ..... 47
3.12 Beta decay curves of 1“C and ”N . . . . . . . . . . . . .......... . 49
3.13 Neutron efficiency :alibration . . . . . . . . . . . . . . . . .......... 50

3.14 Schematic diagram of the implantation detector and SeGA array . . . . 52

3.15 Schematic electronic diagram for SeGA array . . . . . . . . . . ...... 53
3.16 Residuals of the energy calilaation for seGA detectors . . . . ...... 54
3.17 Coincidence efficiency caliln‘ation for SeGAzggN experiment ....... 57
3.18 Coincidence efficiency calibration for SeGA2230 experiment ..... . . 57
4.1 Identification of mrclides produced in 23): experiment .......... . 59
4.2 Growth and decay curves for the 22N decay series . . . . . . ...... . 62
4.3 Ungated beta decay curve of the 22X? experiment ............... 63
4.4 Neutron time-of—flight spectrum from the 22N experiment . . ..... . 65
4.5 Neutron gated decay curves from the 22N exlgreriment ..... . . ..... 67
4.6 Total beta-garmna coincidence spectrum from the 22N exI')erin'1ent:
Partl.... ..... .......... 68
4.7 Total beta-gamma coincidence spectrum from the. 22N experiment:
Paitll ............ 69

4.8 Two gamma gated half—lives from the ”N beta decay . . . . . . . . . . . 71
4.9 Beta. decay scheme of 22X . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.10 The 25F beta decay chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.11 Growth and decay curves for the 22F decay series . . . . . . . . . . . . . 79
4.12 Gamma gated half-lives for the 22F beta decay . . . . . . . . . . . . . . . 80
4.13 Beta decay scheme of 2‘31" . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.14 2'10 beta decay chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.15 Growth and decay curves for the 3'0 decay series . . . . . . . . . . . . . So
4.16 Gamma gated decay curyes of the 3'0 beta decay . . . . . . . . . . . . . 86

4.17 Beta decay schemeof 2‘10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

g1
C)

5.10

Al

The identilication Ofimplantcd nm’lidcs . . . ...... . . . . . . . . . . 89
Growth and decay curves for the 23() decay series . . . . . . . . . . . . . 91
Ungated beta (ilecay curve for the 230 . . . . . . . . . . . . . . . . . . . . 92
Nmitron time—of—tlight spectrum: the 33() ex1_)erin’1e1’1t . . . . . . . . . . . 94
Beta-gannna coincidence spectrum for 230 experiment: Part I ..... 95
Beta—gannna coincidence s1.)ectrum for 230 experin'ient: Part II . . . . . 96
Gamma gated beta decay curve 0123(4) . . . . . ..... . . . . . . . . . . 98

Betadecayschemeof230 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Known level scheme of 26Na . . . . . . . . . . . . . . . . . . . . . ..... 102
26Ne beta de ray chain . . . . . ..... . . . ....... . . . . . . . . . . 103
Gamma gated half-lives of QUNe beta decay . ............ . . . . 104
Beta decay scheme of QGNe . . . . . . . . . . . . . . . . . . . . . . ..... 106

Comparison of half-life. and neutrmi emission probal‘nlity of 22X . . . . 109
Theoretical beta decay scheme of 22X . . . . . . . . . . . . . . . ..... 110
Comparison of the su22O energy levels . . . . . . . . . . . . ....... . 111
Comparison of Gamow-Teller strengths BtGT) for the bet a decay of 22N113
Theoretical decay scheme 01‘230 . . . . . . . . . . ..... . . . . . . . . . 114
Comparison of 23F levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Com )arison of beta decay l‘n'anchinw and Gammow—Teller stren rths for
‘ . h i-
the beta decay of 23O. . . . . . . . . . . . . . . . . . . . . . . . . . ..... 116

The location of experimental energy states in odd-mass fluorine ist)to}_)es117
. . .‘)‘ -
Theoretlcz’il beta decay scheme of -“.\e . . . . . . . . . . . . . . . . . . . . 118

Variation of half-lives and neutron emission probabilities with neutron
number...... ..... ..... 119

The 0'rowth and decay of'the ')ttl'(‘lll nucleus. . . . . . . . . . . . . . . . . 123

xi

List of Tables

2.1 Classification ofbeta decay . . . . . . . . . . . . ..... . . . . . ..... 22
3.1 A1900 magnet settings and beam purity at the Al900 . . . . ...... 30

3.2 Calculated and actual degrader thickness . . . . . . . . . . . . . . . . . . 32
3.3 Beam—on/otl period. half-life and production rates . . . . . . . . ..... 33
3.4 Time calibration results for neutron detectors . . . . . . . . . . ...... 39
3..) Energy calibration results for neutron detectors. . . . . . . . . . . . . . . 41

3.6 Fitting data from mC and l7.\' neutron time-of—lliglrt. spectra . . . . . . 42

3.7 Energy calibration ofneutrtm array . . . . . . . . . . . . . . . . ...... 43
3.8 Neutron peak shape calibration . . . . . . . . . . . . . . . . . . . ..... 44
3.9 Time walk ("'oi'r‘e(_-ti(m functions . . . . . . . . . . . . . . . . . . . . ..... 48

3.10 Efficiency calibration of neutron array . . . . . . . . . . . . . . . . . . . . 01
3.11 Off—line. coincidence efficiency calibration data for SeGA ........ . 05
3.12 Orr-line coincidence etliciency calibration data for SeGAsz experiment 56
3.13 On-line coincidence efficiency calibration data for SeGA:23() experiment .38

4.1 Beam composition ()1'22N experiment after the .41900 and at. the im-

plantationdetector . . . . . . . . . . . . . . . . . . . . . . ...... . . . . 61
.' 5) , _
4.2 Detected beta decay events from the -)~.\ experiment . . ......... 64

- {)t) , . v . o . .
4.3 “-3 neutron tnne—ol-llrght fittlne‘ data. neutron energn‘s and gated hall-

liyes ..... 66

. . , . (y)

4.4 Assignments of gamma—ray and neutron energies for beta decay of “-N 75
. . f)‘ T

4.5 Prtmertles oi the “2.\ beta decay. . . . . . . . . . . . . . . . . . ...... 76

1 - . . . 0- 4
4.6 Gamma-ray and neutron energies assignments lor the -31. beta decay . 81

4.7 Properties oftlre 25F beta decay . . . . . . . . . . . . . . . . . . . . . . . . 83

xii

4.8

4.9

4.10 Beam purity of the 230 experiment from the Alt)00 and the implanta-

4.1 1

B3
B4

13.6

B.7

Gamma-ray and neutron enere‘ies ass1 rnments tor the beta decay of “10 87
. r”? .

Properties of the L”(3) beta ('lecay .

tion detector

Detected beta. decay events from the 230 experiment

o . ()-
Gauuna—ray assignment for the beta decay of ~50

l’rrmerties of the 23('1) beta decay .

Gamma—ray assignment for the beta decay of ”We . .

. 0" ,
Properties of the ~(’e.\e liieta decay
Decay curve fitting parameters
Cauuna—ray measitrements and litert-rture
(.lz’umna—ray measurements and literature
Gamma-ray measurements and literature
Gannna—ray measurements and literature
., . .
Gamma—ray measurements and literature

Gamma-ray measurements and literature

(ilannm—r-ray measurements and literature. data. for 2'30 (II) .

xiii

data for
data for
data for
data. for
data for

data for

221;“)

29x (n).

92x (111)
22X (IV)

22x (V) .

‘~’3o (I)

89

90
93

Chapter 1

Introduction

Quantum mechanical shell structure is a very important aspect of nuclear structure.
The most simple study of bulk properties of nuclei close to the valley of stability
shows evidence for the existence of shell structure in the nucleus. As an example.
Fig. 1.1 shows the difference between single neutron separation energies of neighboring
isotopes as a function of neutron number(N). The peaks suggest that nuclear systems
with certain nucleon numbers called magic numbers have extra stability. The known

magic nucleon numbers are 2. 8. 20. 28. 50 82, and 126, which are seen from the

 

 

 

 

8
20 82

A6 L l 2f 510 1
fig . , 126
24 _ ‘3 A1 , l

2 _ 33-17 ._..,. ' '2‘: _

O 1 a

0 50 100 150

Neutron number

Figure 1.1: The difference between single neutron separation energies of neighboring
isotopes as a function of neutron number [I]. The magic nucleon numbers are shown.
Series of isotopes are connected by lines.

properties of nuclei close. to the valley of stability [2]. Over time several descriptions
have been used in the shell model to represent a nuclear system in terms of neutrons
and protons, and their underlying interactions in order to explain nuclear properties
including magic numbers. In the simple shell model, the motion of each nucleon
is governed by the attractive force of all other nucleons resulting in the formation
of a average potential well and individual orbitals. Several types of potentials were
introduced to the shell model to represent. the attrz-rctive force and to reproduce
the experin'lental observations. The most realistic approximation is a VVoods-Saxon
potential as compared to other potentials such as the harmonic oscillator and the

square well. The VVoodsSaxon potential form is written as:

 

. _ V0
W” _ 1+ E.1‘p[(r— mm} (1'1)

where R is the nuclear radius defined liiy roAl/3 (r0 = 1.27 fin and A 2 mass). V0 is
the well depth the nuclear potential, and a. is the nuclear skin thickness or diffuseness.
However, the model with this potential was unable to reproduce the magic numbers
above 20. The spin-orbital potential (VS-0(1)), given in Equation 1.2. was introduced

in the model to improve the prediction for heavy nuclei.

_ 0.4411) (1 '1

v. — —
we 3 at] . qu — W]

 

(1.2)

The higher magic numbers were reproduced with this modification. Therefore. the
Spin—orbit. force is thought. to be responsible for the major shell closures that occur near
the valley of stability. The shell structure generated by the \Voods-Saxon potential
with a spin—orbit force. up to nucleon number 50 is shown in Fig. 1.2. The magic
numbers are those that (’torrespond to filling groups of orbitals that lie below large
gaps in energy. The ordering of the sin gle—particle states generated by the Wood-Saxon
potential (left) and spin orbit forces (right) is shown in the figure. The maximum

number of nucleons in each single-particle state (2j+l) is given on the right side of

 

CD

ld :-- 099/2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

09 "”“u’ ld5/2 é
50
"a. 099/2 10
“F Of5/2 6
1p ”3:253:32: ] [31/2 2
Of 4:5,“ ‘ 28 lps/z 4
..—""‘ Ofwz 8
20
IS ____ 0d3/2 4
0d =::EE:=":"' 131/2 2
""" 0d5/2 6
8
Op -::::: ------- Cpl/2 2
"""" Ops/2 4
2
OS ............. 051/2 2
nl nlj 2j+l

Figure 1.2: Schematic diagram of the single-particle states with two potential models,
shown up to the 1d5/2 state. On the left is shown the single particle spectrum produced
by the VVoods—Saxon potential. On the right is the single particle spectrum obtained
by the Woods-Saxon potential with a spin orbit force. n is the principle quantum
number. The angular momentum l is represented by the labels 5, p, d, f, g and h
corresponding to l = 0.1,2,3,4.5. respectively. The projection of the total spin of the
shell is j. The magic numbers are indicated between each major shell gap [1].

the figure.

At. present. the model space is so large that. shell model calculations start with
the assumption that the low-lyii‘ig nucleons make an inert core and the higher lying
nucleons (valence nucleons) can be treated separately from the core. 111 general. the
experimental single—particle encrérgies and liiinding (mergies are used in the calculations7
if they are available. For example, U SD (Universal 3(1) calculations are availal')le for
light. nuclei based on a least. square fit of 447 binding energies in the mass region
A216—40 and under the constraints coming from the excited states in 15—200 [5%].

This version of the shell model is very successful in reproducing and predicting the

 

 

    
 

 

 

 

 

 

 

 

 

 

 

 

Experimentally l
; Known Neutron!
7 10 n 12 14 . ‘ drip line i
Be. ‘ Be Be Bel . . ;
8 n w . : 1
LI Ll Ll . : :
6 8 . ' .
He' He 2 - - .
3H . L A LT :bOds/Qai 18“? :' 0d3/2 ":
h V—b N

Figure 1.3: Part of the chart of nuclides. the experimentally known neutron drip line
up to fluorine isotopes is shown. The solid black squares represent beta stable nuclei.
The last proton and neutron arrangements in the shell orbitals are shown for oxygen
and fluorine isotopes. The isotopes (320 and 23F) that present study focused on are
highlighted.

nuclear properties close to the valley of stability [3]. The nuclei near to the drip lines
have been described reasonably well using the USD shell model but the extrapolation
of the single particle energies using mean field models are generally not good. It is
important to observe the trends of single—particle energies from the experimentally
known nuclei and in particular to study nuclei near to the drip line. One of the
primary objectives of the exotic beam facilities is to study the. structure of nuclei close
to the neutron-rich drip line. Recent experiments with exotic nuclei near and at the
drip line have indicated changes of the nuclear structure. for example. the significant
change in the neutron drip line location at the region of O and F isotopes [l]. the
disappearance of traditional magic numbers and appearance of new magic numbers
when approaching to the drip line [1H]. and halo structures near the neutron drip
line [7]. These features will be discussed in the following sections as an outline of the

motivation for the present work.

1.1 Location of The Neutron Drip Line

The existence of a given nucleus is one of the interesting phenomena to be explored in
nuclear physics. The recent. development of rare isotope beams (RIB) allows searching
for the existence of a nucleus when increasing proton or neutron number and access
to the more exotic drip line isotopes. A number of experiments have shown that
the neutron drip line has been reached for all isotopes up to oxygen as shown in
Fig. 1.3. The last oxygen nucleus is 240, which was first observed by Artukh et
a1. [>4]. Several theoretical groups had 1.)redicted that the next particle stable oxygen
isotopes would be 260 and 280. and the latter would be a doubly magic nucleus [0].
However, the. particle instability of 25260, has been clearly shown by two experiments
[lllg ii] and more recent. attempt to observe 260 by Schiller et. a]. [J 3] also failed.
Although the stability of 280 as a closed shell nucleus has been predicted by sweral
mass models, Sakurai et a]. [lit] have shown the particle instability of 280 from an
extrapolation of the experin'iental yields of nuclei in this region. The heaviest known
fluorine isotope. 31F, was observed for the first time by the same group. Thus. it has
been confirmed that the heaviest nitrogen and oxygen isotopes are 23N and 2"10 with
the same neutron nurnl‘wr N = 16, while the heaviest isotope of fluorine has been
extended up to 31F with N = ‘22. It. is interesting to note that. at least six additional
neutrons can be bound by adding one proton and moving from oxygen to fluorine.
There are theoretical attempts to explain the drip line locations for O and F isotopes
by Iricxlification to the mean field in this region [l H]. The theory predicts that. the
empty d3/2 orbit in 21O is unbound to neutron decay and neutrons in the nuclei
beyond 2'10 would have to occupy this unbound orbit. This makes isotopes beyond
240 unstable and leads to the drip line location at. 2’10. A very recent expm'iment at
NSCL measured the neutron-unlx‘iund first. excited state at 4.2 i\leV in 2'10 supporting
the predictions [1?]. The theoretical exl'flanation for the large range of fluorine isotopes

is that. the monopole interaction between the occupied (1.3/2 proton and d.; 1,.) [it‘llil‘Ol'l
._ . I ,_

 

 

1 5000 12000

  

 

 

  

 

 

 

 

 

 

 

’(a) (bl
12000 -
A
E ’>" 8000
x 9000 - a:
v x
C L v
(I) 6000 ~ (0:
4000
3000 ~
0 g l A L L L A l A l A l A I L A I 4 l A I A l A l A I
0 4 8 12 16 20 24 28 6 20 24 28 32 36 4o

Neutron number Neutron number

Figure 1.4: Single neutron separation energies for nuclides of different isospin. a) Sn.
for odd-odd nuclides. b) Sn for even-odd nuclides. Isospin values are given at the
right side of each graph. The traditional magic numbers are shown by boxes and the
appearance of a new magic number at N = 16 is highlighted by ovals.

orbitals lowers the d3/2 single-particle energy, allowing extra binding energy for heavy
fluorine isotopes [10']. Thus, the extension of the drip line location to 31F indicates
that one of the pf -shell orbits must be bound. Measurements that determine the pf -

shell orbits are specially important to understand the large number of the fluorine

isotopes.

1.2 Disappearance of Traditional Magic Numbers

It has been predicted that an increasing thickness of the nuclear skin will reduce the
strength of the spin-orbit force when approaching the drip line [17]. The attenuation
of the spin-orbit force may result in the modification or collapse of the shell closures in
the region near to the drip line since the positions of the single-particle levels depends
on the spin-orbit force.

One of the best ways to identify a magic number is the presence of a discontinuity
in the single and two nucleon separation energies as a function of mass number [ti].

Fig/1.4 shows the neutron number dependence of the experimental S”, values for nuclei

with odd neutron number (N) and even proton number (Z). and odd N and odd Z
at. constant isospin 1;)1‘ojection values. The isospin values are shown at the sides of
graphs. Note that the isospin value for a set of nuclei increases toward the neutron
drip line. The signature of a magic number in the neutron separation energies is a
sudden decrease of Sn with the increase of neutron nui‘nber by one at constant isospin
value. These drops at the traditional magic numbers are highlighted with boxes in
the figure. At low isospin values, such as T = O, 1/2 and 1. it. is clearly seen that
there are discontinuities at N = 8 and ‘20 en‘iphasizing the existence of traditional
magic numbers near to the valley of beta stability. When approacl'iing the. drip line
with high isospin values (T3) of 23/2. 2. 5/‘2. 3 and 7/2, the signature of the magic
number N =20 still survives while the magic number at N = 8 appears to vanish for
those nuclei with 23/2 and 5/2 isospin values. The nuclei with isospin values at T g =
4, 9/2 and 5 show the disappearance of the signature of the magic number N = 20. In
addition. a discontinuity becomes significant. at N = 16 with nuclei having T g = 53/2.
3. 7/2 and 4, and may signal new magic number at N = 16. Shell model calculations
also provide supporting evidence about changing shell structure closer to the neutron
drip line [it]. However, the umlerstanding of the nuclear structure evolution near the

neutron drip line is poor due to the limited access to those nuclei.

1.3 Shell closure at N = 14 and N z: 16

Another experimental signature of magic. numbers is the presence of a relatively high
energy for the first 2+ excited state of an even-even nucleus [‘30]. Fig. 1.5 shows both
the experimental and calculated excitation energies of the lowest 2+ states of the
neutron-rich even-even oxygen isotopes. The first. 2+ state of 220 has an energy of
3199 keV [2]]. which is 1562 keV higher than that of 200. The shell model results
suggest that the N = 14 shell closure results from the filling of the (15/2 neutron shell in

220. In addition. the presenrc of a small electromagnet.ic matrix element. [13032) value

\I

 

 

—-— Wildenthal et at.
' :1: --*--Experiment

 

 

 

N (O -b 01 O) ‘1 oo
‘fir—‘T fij“ Y

Y

 

2* state energy (MeV)

A
I—r

 

 

 

8 10 12 14 16 18
Neutron number

Figure 1.5: The excitation energy of the 2+ states of even—e\v'cn oxygen isotopes. The
calculated and experimental 2+ state energies are taken from Refs. [h] and [11)],
respectively.
of 21(8) 02fm4] for the 2+ state in 220 from an inelastic scattering experiment. [22
supports the N = 14 shell closure argument. The same trend in B(E2) values is also
seen with the sd-shell model calculations with USD interactions [2tl](see Fig. 1.5).
The recent observation of the 2‘L state in 22C) using elastic and inelastic scattering
found that the ratio of neutron to proton contributions to the transition in this state
was 2.5(10), which is similar to N/Z value. of 1.75. indicating that the excitation is
carried by both protons and 1.1eutrons in the valance shells [251.21]. In contrast, the
excitation of the 2+ state in 200 was found to be carried mostly by neutrons [‘35]. The
indication that both particle types contribute to the transition in 220 demonstrate the
shell closure at. N =14 is just as good as the Z =8 shell closure. With this experimental
and theoretical evidence. 220 ap11)ears to be a doubly magic nucleus.

240 has been predicted by shell model calculations to be another doubly magic
nucleus with a high 2+ state energy as sl’mwn in Fig. 1.5. The absence of any gamma-
ray decay from the excited states in 24 (i) in a recent GANIL experiment [21] indicates

that the first excited state may be neutron unbound. A lower limit. of 3.6(3) MeV

(neutron separation energy) was set for the 2* state. Fig. 1.5 shows the lower limit
for the first excited state in 2‘10. A recent experiment carried at NSCL has found
positive evidence for a 42(3) MeV excitation energy of the first. excited state in 2‘10.
which is neutron unbound [l3]. These results with theoretical predictions stronglv

L.

support. the idea of a shell closure at N = 16 for the neutron-rich nuclei.

1.4 Halo structures near neutron drip line

When approaching the neutron drip line the neutron separation energy decreases
gradually and the bound states come close to the continuum region of the nuclear
potential. The comliiination of the short. range of the nuclear force and the low neu—
tron separation energy allows in some cases the special structure called a. nuclear
halo, where valence nucleons liiehave very differently from the core nucleons. The
very weakly bound nucleons can tunnel into the classically forbidden region outside
the range of the nuclear force and form a “halo" [7]. The halo nuclei have a large
radius compared to the stable nuclei (the root-n1ean-square(RhIS) radius does not
follow the RzRUAl/3 law). One and two-neutron halo nuclei have been found in the
neutron—rich light nuclei. namely, 11Be. “Li, HBe and 19C [T]. In addition to the
characteristic prormrties of the halo structure. one. and two beta-delayed neutron de-
cays were observed for two of these nuclei. For example. one and two neutron modes
of the l‘lBe beta decay are known to be 81(~l)% and 5(2)%. T(—‘S})(‘('ll\'t~‘l}' [20]. Cluster—
core model [‘37] calculations predict many halo nuclei in the light region including
22N and 230 [2‘1]. In particular, 230 has been suggested as a likely candidate for a.
one—nwtrcm halo nucleus with the experiim‘ntal observation of a. narrow momentum
distrilmtion for the 220 fragments produced from the one-neutron removal reaction
from 23O and the large reaction cross-section of 230 [3‘1].

The halo structure may have a direct. influence on the beta decay in several ways.

One, way is that the overlap between parent ground state and hay-lying states in the

9

 

 

 

 

 

 

  
     

2 0 r
( 11LI 11Be r
1 5 I. 0.04 " 0.59
F: C
Q1 .0 . g
a: m 0.02 -
0.5 ~
I
' 0'00 0 2 4 6 8 10
0 5 10 15 20
Level energy (MeV) Energy Level (MeV)

Figure 1.6: Beta decay of the halo nuclei 11Li and 11Be. The experimental Garnow-
Teller strength distribution of 11Li (left) and 11Be (right) as a function of excitation
energy of the daughter [19,330, 7].

daughter may be reduced to due the large spatial extension of halo states resulting
a general reduction of beta decay strength to such states [17]. Another possibility
is the valence neutron may decay separately from the core neutrons producing an
unusual pattern for the beta decay. The characteristic: feature that has been observed
in beta decay of a halo nucleus is the transitions with large Garnow—Teller strength
[B(GT)] go to states at high excitation energy in the daughter nucleus. Figure 1.6
shows the experimental B(GT) distribution as a function of the excitation energy
for beta decay of 11Li and 11Be that. are known as two and one neutron halo nuclei,
respectively. In both cases. the relatively high B(GT) values are associated with high
excitation energies. Therefore, beta. decay provides a signature of halo structure. The
determination of beta decay to the high excitation energies in a nucleus near the drip
line is much harder, since branching ratios would be. lower and more decay channels
are open due to high Q—value. Thus. one can expect the complicated beta decay with

nuclei near to neutron drip line.

10

1 .5 Motivation

Very little spe(i‘t.1‘osc(')pic informaticm on neutron-rich light nuclei is available at present
to investigate nuclear structure in the. region. Systematic studies using beta-delayed
neutron spectroscopy on nuclei. especially in the region of oxygen isotopes. have been
carried out during the past. [31, 3;}, 351. 31]. The present. study is focused mainly on
the nuclear structure of the isotOpes 220 and 23F, produced via beta decay of 22N
and 230. The isotopes are located in the chart of nuclides between the N = 8 and
N = ‘20 closed neutron shells. The position in the chart of nuclides including the
surrounding isotopes can be seen in Fig. 1.3. The last two protons in oxygen fill the
p1/2 orbit. forming the Z = 8 shell closure. In 220, the last six neutrons fill the d5/2
orbital reaching the maximum occupancy of the orbital. In the case of 23F. the 14
neutrons occupy the same orbitals as 220 and the last single proton goes into a (15/2
orbital. The current knowledge of the nuclear structure of 220 and 23F are presented

in following sections.

1.5.1 Knowledge of the Structure of 22O and 221V

The study of the single particle structure of 22O particularly has been important for
the understanding of nuclear structure near to the neutron drip line. The gamma
decay for 220 was reported by F . Azaiez. [330] and Belleguic et al. [37] from an in-
beam fragmentation experiment at GANIL. They reported gamma-ray transitions at.
1370 and 3200 keV and assigned the 3200 keV gamma-ray to the Qf—Jlffi. transition
in 220. and the other to the decay from a 4510 keV excited state to the ‘2+ state.
The excitation energy for the first 2+ state was confirmed by a radioactive beam
coulomb excitation ex1;)erin'1ent at. the NSCL, where a 2? state was measured to be
3.17 MeV [:32]. The gamma-ray at 1370 keV was not. ol')ser\-'ed in this latter work. The
energy level scheme for 220 with positive parity states has been extemled by Stanoiu

et al. recently using single and double step fragment reactions at GAN IL ['31]. This

11

6936

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

,. 6509
1: 5 fo‘ _ _
.V. 2% 5' ‘0 " l
O :1) "I: 5.8
A c7) 8 or) 1.3
C: r ‘0 A 4909
El “3 4582 3+ i
K. (5,; 2.6 4'5
r- : 00
2+. ‘ _ 3199 2+ 3.2
a
2 3.2
a:
O
0* . °° 0 0+ ,
(I) 220 (ii) 220

Figure 1.7: Level scheme of 220. (left) The level scheme was deduced from an in-
beam gamma-ray spectrosc0pic experiment [21.]. The transition energies are in keV
with their relative intensities in parentheses. The 3199 keV energy level is assigned to
be 2+. (right) The level scheme was produced using a knockout reaction by Cortina—

Gil et al. [3.3]
work reported five excited states with their gamma-ray decays and relative intensities,
as given in Fig. 1.7. The spins and parities of states were not assigned except for the
first excited state. A one-neutron knockout experiment carried at GSI to measure
the longitudinal momentum distribution for neutron—rich oxygen isotopes reported a
spectrum with three gamma-rays at. 1.3. 2.6 and 3.2 MeV from the deexcitation of
220 [3.3] (see Fig. 1.7). The first two gamma-ray energies were assigned to the negative
parity state (0‘, 1‘) at 5.8 MeV. which deexcited into 2"L and 3+ states at 3.2 and
4.5 MeV, respectively. This negative parity assignment. was based on arguments by
Brown et al. from calculations of the spectroscopic factors in the l2C(230,220)X
reaction [1 l]. The first excited and ground states of 220 have also been studied using
the 22()(p. p’) reaction and reconfirmed the N : 14 magicity in 220 by probing the
proton and neutron contribution to the 2‘L excitation [23] mentioned above.

The negative parity stz-rtes in 220 are not. experimentally known except for the

. 99 g . . .
only tentative state at 5.8 l\-IeV. The beta decay of "N should provrde information

12

predominately on the negative parity states in 220. which are favored by the beta
decay ()f the negative Iiiarity ground state of 22N. The ground state of 22N is experi-
mentally unknown at. present but simple shell model calculations predict the ground
state as 0". The beta decay of 221V leads mainly to the mass(A) = 22 decay chain
with the subsequent. decays of 220 and 22F. The A = 21 decay chain with decays of
210 and 21F is expected to be observed as a result of beta-delayed neutron decay.
The 22N beta decay series is shown in Fig. 1.8, where black squares represent beta

stable isotopes.

 

 

 

 

 

 

 

 

 

 

 

n B—
22N

 

 

 

 

Figure 1.8: Beta decay chain of 330. Beta decay chains produced from the beta decay
to the bound states and from the beta-delayed neutron decay are shown with the
stable isotopes in black squares.

Mueller et al. [38.] reported the beta decay half-life of 22N to be 243’; ms and
Reederis group reported a shorter half-life of 141(6) ms [30]. that is just. within the
error bars. The total neutron emission probability (P1,) was found to be. 35(5)% for
22N beta decay [ $8.31)]. A more recent beta decay study done by Yoneda et. al. reported
the beta—delayed neutron multiplicities for 22N to be P1,, = 41(+12—10)% and P2,, <
13%. with a half-life of 16.5(+8.5—4.8) ins [ 10]. Although the half-lives and (Pn) vahies
agree. within errors. the uncertainties are. large. There is no spectrt)scopic information

for the beta decay of 23N.

13

1.5.2 Knowledge on the Structure of 23F and 230

 

 

 

 

 

 

 

 

23
O

 

 

 

Figure 1.9: Beta decay chain of 230. Beta decay chains produced from the beta decay
to the bound states and from the beta-delayed neutron decay are shown with the
stable isotopes in black squares.

23F should have the structure of a single proton outside the proposed doubly magic
220. The ground state of 230 is known to be 1/2Jr [35, 11] so that one can expect
beta feeding predominately to excited states in 23F as direct feeding to the ground
state of 23F, which was continued to be 5/2+ by Sauvan et al. and Cortina-Gil et
al. [11,35], would be a. first forbidden decay. The beta decay chain of 230, shown in
Fig. 1.9, includes the decays of 23F and 23Ne from beta decay to the bound states,
and decay of 22F from bet a—delayed neutron decay. All beta decay paths shown in the
figure are expected to be observed with the 230 beta decay experiment.

Mueller et al. reported a. total neutron emission probability (Pu) 0f 31(7)% for
beta decay of 230 with a l'ralf—life of 82(37) ms, which is the only mez’isurement for
the half—life [38]. An upper limit for the P" value was published later by Reeder et
al. as < 29% [:19]. There are several theoretical estimations for the half-life of 230,
which range from 12.8 to 196 ms [fix-"11.174. The predicted Pu values for 230 beta
decay were close to 30% and agreed with the e;*x1‘)erinienta.l values except for the
value of 2% predicted by \K’ildentha] et al. [Is]. The energy levels in 23F. the beta

decay daughter of 230. have been measured using the l'iea.\-'y—ion transfer reaction

14

6250

 

 

 

 

 

 

 

 

 

 

5000
+
9/2 4050 90+ 3”
—— 3810
‘2
72+ (1
/ 2930 7/2 W 2900
2310 02+
8
8 3
(\l
N
0 Ago 5/2+
“th 0” 23F (iii) 23F

Figure 1.10: Experiment.ally known energy levels in 23F. (left) The level scheme was
produced using a heavy-ion transfer reaction by Orr et a1 [.12]. The gannna-ray decay
schemes produced using a fragmentation reaction by Belleguic et al. [37](middle) and
using a proton transfer reactions by Michimasa et al. [13] (right) are shown. The
energies are given in keV .
r - w '7 r). .. I ‘_ _ .
22Ne(1i~o. 1‘F)-'3F by Orr at. al. [-13]. six levels at 2.31, 2.93. 4.05. 5.00. 0.2.5, and
8.18 MeV were observed in 2‘5F. The ground state. the second and third excited states
were assigned spins and parities of 5 / 2+. 7/.2+ and 9/ 2+, respectively, based on shell
model calculatirms. Two excited states at. 3810 and 2900 keV that deexcite by a
. ., . 0- . ,, g 7 . .
cascade of gamma-rays at 910 and 2900 keV in ~3F have been reported by Bellegulc
et al. [37] in 368 fragmentation reactions. These two states were assigned as 7/2+
and 9/ 2+. respectively, by com1;)arrison to the shell model. ;\lichimasa et al. recently
. .° . 9-. . . . .
reported studies of the excited states in “5F using three kinds of reactions. nan'iely
I 6 . . 7 0t 6 I . I. .' .. r)" . _
4He(220. 239,-). iHe(-3F, 23F7) and lHe(2'F. ~3F7) [H]. The resulting gamma—ray
decay scheme. shown in Fig. 1.10. was established up to 7 MeV based on gamma.-
gamma coincidence 111ez-rsurements. In the most recent work. the 2268 and 40.59 kev

energy levels were assigned to spins and parities of 1/2+ and 3/2+. respectively. The

spin assigmnent. for the state at 4.05 .\IeV is inconsistent with Orr et al. work. The
spin and parity for other states are unknown and no negative parity states in 23F

have been observed at present.

1.6 Present Work

The present work focused on the lmta-delayed neutrons and gamma-rays from 22N
and 230 to establish the neutron unbound and bound energy states in 220 and 23F,
res1.)ec.tively, at particular interest were the negative parity states in doubly magic
220 nucleus. These states were not exrmrimentally known but were measured in this
work due to the highly selective beta. decay. The beta decay schemes for 22N and 230
have been established and compared with shell model calculations. The accuracy and
precision of the half-lives and total neutron emission probabilities were significantly
improved.

This (’lissertation presents the study of the beta decay of 122-N and 230 using neu-
tron and gamma-ray spectroscopic arrays. The theory of beta decay is discussed in
Chapter 2 explaining the decay modes. The beta decay selection rules are introduced
to assign spins and parities of the observed states. The isotOpe production technique
and the details of instrumentation 1.1tilized to monitor beta particles. neutrons and
gamma—ray events are presented in Chapter 3 including the electronic setup and cal-
ibrations. The details of the analysis of neutron time—of—flight system are. described
including the peak shape and energy. In Chapter 4, data analysis and results are re-
ported with a detailed discussion of the assigmnents of transitions and decay schemes.
F inally. The experin‘iental beta decay properties of desired isotopes are compared with

shell model calculations in Chapter 5.

16

Chapter 2

Overview of Beta Decay

The primary objective of this study was to measure the neutron unbound and bound
states of nuclei near the neutron drip line to understand the structural changes of
those nuclei. The techniques to obtain information on states in neutron-rich nuclei
involve Coulomb excitation, direct and transfer reactions, inelastic scattering and
beta decay. In the present study, beta decay was chosen as the method to populate
states in neutron-rich light nuclei. In light nuclei, the level density is low and high
efficiency neutron and gamma—ray detectors with good energy rrscflution can provide
information on energy level structure of nuclei. The decay of these nuclei is also char—
acterized by large Q-values opening a large energy window to populate a significant
number of states. As one approaches the neutron drip line. the neutron separation
energies decrease while the Q-values are large so that a large fraction of the beta-
decay strength can lead to neutrcm unbound states. Measuring the beta decay. and
delayed neutrons and gamma-rays from a nuclide thus provides information on the
levels, which are populated during the beta decay. This also allows one to calculate
transition strengths, known as the branching ratios. for the particular transitions. The
transition energy coupled with the transition strength can be utilized to calculate the
log(ft) value on the beta decay branch. This in turn can be used as criteria. for as-

signing the properties (spin and parity) of the energy levels of the daughter nuclide.

17

The following sections will include discussions on the theories of beta decay, includ-
ing beta-delayed neutron and gaunma-ray decay and calculations of Gamow—Teller

transition strength.

2.1 Theory of Beta Decay

Beta decay is a radioactive decay process in which a neutron is converted into a proton
or vise versa by emitting an fast electron (beta 1')article) or a positron, respectively.

There are three kinds of beta decay process, which are given below:

,3—dccay : {2.ij —>§+1 l’j$_1 + ,3“ + I" + (235 (2.1)
153+(1ccay : gXA-i Héfll YAT+1 + {3+ + v + Q3 (2.2)
Electron Capture : gXN —>§_1 YN+1 +1! + Q‘s} (2.3)

where A. Z. N, 13‘. ,sj+, it and e are mass. proton and neutron numbers of parcnt(X) or
daughter(Y) nuclei, fast electron. positron. anti—neutrino, and neutrino, respectively.
Q3 'alue is the energy released from the decay process. which is calculated from
the mass difference between parent and daughter nuclei. In .3“ decay, a neutron
is converted into a proton while emitting an electron and anti—neutrino. When the
binding energy of the daughter nucleus is 1.022 l\lev (2111.112) higher than the parei'it
nucleus, 3+ decay may occur by converting a proton into a. neutron with an emission of
a positron and a. neutrino. If their energy condition is not satisfied by the system. the
alternative process of electron capture can occur. Here an atomic electron is captured
to convert a proton into a neutron.

Fermi related the beta decay transition rate (Afi) to the interaction lsz‘) that
causes the transition between the initial and the final states. and the density (p(Ef))
of final energy states. The assumption of the theory is that the interaction which

causes beta decay is a weak perturbation relative to the strong nuclear and coulomb

forces in the nucleus [-5.10]. This relationship for the transition rate can be fornnilated
as:

2a

, ‘2 '1 ,
Aft = 72' <. if? >l [)(I‘.j') (2.4)

For the beta decay. the interaction matrix element (g< Vfi >) in Equation 2.4 can be

written as;

where 1.5.,- and cf are the wavefunctions for the initial and final nuclear states, re-
spectively; ac and on are the wavefunctirms of the emitted electron and neutrino,
respectively; and g is a parameter which describes the strength of the interaction
(coupling constant). The symmetry properties of beta. decay observed in experiments
require that the opera-nor O in Equation 2.5 be a linear combination of a polar vector
and an axial vector operator.

The emitted electron and neutrino are taken to be. free-particle plane wave func-
tions:

ada26flfiwh (2m

61%;“) : (2.37.04.th (27)

where C is a normalization constant and p and q are their momenta. A series of
approximations can be made using the expansions of Equations 2.6 and 2.7 based
on the selection rules of decay to simplify the interaction matrix element. Finally.
the interaction matrix element can be written as Equation 2.8. where < ij > is the

nuclear matrix element for allowed beta decay.

<hfi>zg<efmhg>zg<igi> 98)

The total beta decay rate A is obtained by integrating over the density of states

It)

in the range of energies available to the electron and neutrino, and is given in the

Equation 2. 9.

2 1 . .
_ (1 m' c I < II],- > I.2 /I'mu.r FZ
(

I — 27r2li‘ )

 

p);) ’—(Q 7.411,; (2.9)

where p. mp. Ta and c are the momentum, mass and energy of the emitted electron,
and speed of light, respectively. Q is the energy released in the beta decay which
is shared between electron and neutrino, and F(Z‘, p) is the Fermi function which
describes the shapes of the emitted ii" and {3+ spectra. This function includes the
effects of the, C oulomb field of the nucleus on the elect.r.on

The types of beta. decay can be classified by the angular momentum carried away
by the electron and neutrino. The most prevalent are those for Ale, which are
referred to as “allowed” beta decays. The en‘iitted particles have spin of 1/2 and
therefore, they can be in a singlet (S : 0) or triplet (S = 1) state. The two types
of allowed beta (‘lecay are called Fermi (P) decay (singlet) and Gamow Teller (GT)
decay (triplet). The spin relationship for the angular momenta. of the nuclei for both

decays can be written as,

: Jf +1 for Fermi decoy (2.10)

”Ii : J! + l + l for Cummc — Teller decoy (2.11)

where .l-

, is initial nuclear spin, .1! is final nuclear spin and l is the orbital angular

momentum carried by the electron and the neutrino. The term g2I< Alf, >I2 in Equa-
tion 2..‘-) can be replaced with two nuclear matrix elements and two coupling constants

corresponding to the two types of beta decay types:

92l<\[f1>l2_*(]Il-l\[fiF>l2_lf/:21l<\If/((;ll>l2(2'12)

The weak interaction polar vector (V) and axial vector (A) coupling constants for

the decay of neutron into proton are denoted by gy and 95.1 respectively. The nuclear

20

 

matrix elements in the Equation 2.12. Alp-(F) and h/lfi(Cl'l‘), can be defined with

Fermi and Gamow-Teller beta decay operators as follows

< 11f,(F)>— <uf|wut~ (2.13)

<1lff,’((rfl1 )> (LfILkaIIt' (2.14)

where t is an opera-Ltor which transforms a proton into a neutron and 6 is the usual
Pauli spin operator, the sum being taken over all nucleons in the nucleus. By replacing
Equation 2.9 with two nuclear matrix elen'ients, the total beta decay rate can be
written as

"1:3C4

A:———— 2 ’77? {934 < )If,(F ).> >I2+gQII < rumor) > )2} (2.15)

where f is the phase space integral

anr
f 2/0 F(Z p)p2 (Q— 7.8)2 (1]) (2.16)

The Fermi integral f can be numerically determined by using the atomic number

of daughter (Z’) and beta decay energy (Q) for particular beta decay.

2.1 . 1 Selection Rules

Beta decay is a process which happens only between selective. states governed by
the set. of rules known as the selection rules. These rules are deduced based. on the
principle that the total angular momentum and the parity of the angular momentum
must be conserved during the. transition between the initial and final states in the
beta decay process. The selection rules for Fermi and Ganmw-Tellcr beta decay will
be discussed below.

The beta 1")article and neutrino emitted in both beta decay process have zero

orbital angular momentun'is under the allowed beta decay classification. In Fermi

‘21

decay. the spins of the beta particle and neutrino are anti—parallel (82:0), and the
total change in nuclear spin (AJ) between the initial and final states in the transition
must be zero (AJ 2 0). In Gamow-Teller decay. the beta particle and neutrino are
emitted with their parallel spins (8:1) resulting the total change in nuclear spin zero
or one (AJ : (l or 1). The parity change of the system is defined by A7.- = (~1)’ , where
7r is the parity of the system. Since 1 = (l for the allowed beta. decay, the parity of the

initial and final states should be same for both types of decays.

Table 2.1: Classification of beta decay

 

 

Beta decay type Fermi AJ Gamow—Teller AJ Air log(ft)
Supperallowed U 0 No 2.9 -3.7
Allowed 0 0.1 No 4.4 - 6.0
First. Forbidden 0,1 0,12 Yes 6 - 10
Second Forbidden 1,2 12,3 No 10 — 13
Third Forbidden 2,3 2,3,4 Yes >15

 

 

 

 

 

 

 

W’ hen the beta particle and neutrino are emitted with l 7é O. the decay by an
allowed transition cannot occur. However, this kind of decay does occur, but with
a much smaller probability compare to the allowed decay. Such decays are known
as “forbidden” decays and are classified in order of forl'nddenness based on 1 value.
For example, the first and second forbidden beta (.lecays result from the beta particle
and neutrino emitted with l = l and 2, respectively. The classification of beta decay
transitions based on spin and parities are summerized in Table 2.1. The transitions
can also be categorized with their experimental log(ft) values. shown in Table 2.1,
where f is Fermi integral and t is a partial half—life of the transitimi (see section 2.4).
If the log(ft) value is in the range 2.9 to 3.7 for a beta transition it is generally ‘alled

as superallowed beta (glecay.

22

 

  

Unbound

 

 

stotes T
Sn ................ __ll_v____
A-l
Bound 2+ tY N-2
states
A
2+ lY N-l

Figure 2.1: Sclu‘nentic diagram of Beta-delayed Neutron Decay
2.2 Beta-delayed Neutron Decay

In particularly, the ,13‘ (’lecz-ty of miclei far from the valley of beta stability can have a
high tendency to populate neutron unbound states that are above the neutron separa—
tion energy. since they are characterized by large Q value and low neutron separation
energy. Neutron emission s11liisequent to the beta decay is called beta—delayed neutron
decay. This decay process finally populates the states in the neighboring daughter
(A‘IY), which has a mass number less than one mass unit of the parent. Fig. 2.1
shows beta-delayed neutron decay from parent (AX) to the single beta-delayed neu-
tron daughter (A‘IY). In this case. the parent AX beta decays to one of the unbound
state in the daughter AY and emits a neutron subsequently to feed into the excited
state in the neutron (“laughter A‘W'. which undergoes ganuna—ray decay. The neu-
tron will have a kinetic energy that is cliaracteristic of the energy difference between
the initial and final states. Spectroscopic measurements of the neutrons can therefore

provide information on the structure of the. two nuclei.

2.3 Gamma-ray decay

Neutron bound states. except. for the ground state. in the. (laughter populated by the

beta decay deexcite through an emission of electromagnetic radiz‘rtion, called gannna—

23

 

”E

ray decay. This decay process can only occur when the nucleus is in the excited state.
The excess energy in the nucleus is released as photons (gamma-rays) to relax to
the relatively low energy state or ground state. Based on the conservation of angular
momentum, a photon connecting two nuclear states should carry at least one unit of

angular momentum and must. satisfy the following relationship

where I.-

and I f are angular momenta of initial and final states and l is the multi—
polarity, which is defined as the number of angular momentum units carried by the
photon. Note that l = 0 is a forbidden transition for photon emission.

The change in the distribution of matter and charge during the gamma-ray decay
leads to a change in the electric and magnetic I‘n'operties of the nucleus. Therefore.
gann‘na—ray transitions can be categorized based on the effective electric and magnetic

cl'iaracter. The multipolarity of the photon depends on both the angular momentum

and the type of transition. which can be represented by following relationships;

must) : (—i)’ (2.18)

Aida/1) : (-1)’+‘ (2.19)

where A77 is the parity change between states and. E. M and 1 represent. the electric

and magnetic cluu‘acters and the nuiltipolarity of the transition.

2.4 Gamow-Teller Transition strength

The operator associated with Fermi decay is prt)portional to the isospin raising and
lowering operators (f in ('zquations 2.13%. 2.14). As such. Fermi decay can only connect

analog states and it provides a. test of isospin conservation in the nucleus. The operator

 

associated with Gair'ic‘)\\«'-Telle1' decay also contains the nucleon spin operator ((7 in
equation 2.1-1). In general. this decay goes to many final states as it. produces a
mixture of relative spins. and provides a sensitive test of shell—model configuration
mixing in the nucleus using the beta decay transition strength.

The total decay rate for a given initial state can also be written by summing the

partial beta decay rates (Af,,-) over the total number of final states:

with the branching fractitm (b fl) to a specific final state:

 

.\ ,-
bfl- = i (2.21)

The partial half-life for a particular final state will be denoted by:

r _ T1/2

'1/‘2 _ l
where the beta decay half-life is T1 /.2. The partial half-life for a particular decay
with the calculated Fermi integral (f) is used to obtain log(ft) that can be used to
characterize the transition type. The relationship between Fermi integral and the

partial half-life is given by:

 

Iv
ff 0 I . r r r ‘_ .' (2'23)
1/- | <.«\/f,:1«‘> )3 + (gay/g5-” <g .\/f,i(;1) > l2
where K is defined as:
t 3 T «
. 2, I I 2 ‘ .
I\ : 'r i n( ) (2.31)

m?c’lg,v
Equation 2.25 is derived by the partial beta decay rate defined in the same form
of Equation 2.15 and introduced the partial half—life relationship to the partial beta

decay rate. For 0+ ——> 0+ nuclear transitions. < .\/f,~((;’l‘) >= () and for a transition

between (isospin) T = 1 analogue states < Alf-AF) > = 2. Equation 2.25 is then
reduced to K = 2 fI-l /2. By fitting the exl‘)erimental partial half-lives and Q values
for 0+ —» 0+ transitions of 20 well known nuclei. the “K" constant was found to be
6170(4) s [th lb]. The Gamow—Teller beta decay strength [B(GT)] for a particular
transition is defined as |< Mfi(GT) >l2. For the .23‘ decay of the neutron—rich nuclei,
the relationship between Gamow-Teller strength and the partial half—life of the final

state is expressed as:

ft (5170 s
. O z ‘. V T
U“ (HA/girl2/3(Cll

 

where gA/gy is known to be 1.259(4) [IT].
This equation will be used in Chapters 4 and 5 to calculate Gamow—Teller strengths
for the desired beta decay transitions along with Fermi integrals (f) calculated from

an emlnrical equation given in Ref. [18']:

log( f) = 4.01091? + 0.78 + 0.022 — 0.005(2 — l)fogE (2.26)

where E (keV) and Z are the :3” decay end point energy for the transition and the

atomic nun'iber of the daughter nuclide. respectively.

2.5 Application

The measurement. of beta decay with delayed neutrons and gan‘una—rays allows the
study of the beta. decay strengths to excited states and ground state of the (laughter
nuclide. In the. case of 22N allmved beta decay. the negative parity states in 22
are expected to be populated as the ground state of" QQN is predicted to be 0‘ [IN]
and the ground state of the even—even 220 was found to be 0‘L [ll]. This means

. r): - . . .
the feeding to the ground state of “20 could be less probable as it is a. forbidden

transition. The ground state of 23C) is known to be 1/2‘L [ll] so that one can expect.

26

 

bet a. feeding 1)redominately to excited states as direct feeding to the. ground state of
23F with known J77: 5/2+ would be at. least a first forbidden decay. Beta—delayed
neutron tinw-of-flight spectroscopy has been utilized to observe neutron unbound
states. Particle bound states in the daughter nuclide had observed by employing
traditional gamma—ray spectroscopy. The beta decay events has been measured with
a plastic scintillation detector and time stamped to generate a decay curve. from
which the half-life was deduced. The branching ratios were determined based on the
observed neutron and gamma-ray intensities considering the feeding into the state
and deexciting from the state. The partial half—lives and decay energies to a state
can be used to deduce log(ft) values. which in turn can be used to infer spin-parities
of final states. The beta decay schemes for ”N and 230 have been established with
information on (.lecay energies. spins and parities. and branching ratios states. The
next chapter will explain the techni ral details of the measurements including the

isotope production, beta. gan'nna-ray and neutron detection.

27

Chapter 3

Experimental Setup

Radioactive beams of 22N and 230 were produced using projectile fragmentation at
the National Superctinducting Cyclotron Laboratory‘s (NSCL) Coupled Cyclotron
Facility (C‘C‘F). The interesting isotopes were stopped in an implantation detector
to observe bet.a-(lelaj\_'ed neutron and gamma-ray decay events. A neutron spectro-
scopic array with sixteen scintillation detectors and a gan’nna-ray array with eight,
segmented germanium detectors were employed to measure the neutron and photon
energies, respectively. Radioactive beams of 16C and 17N were also produced and used
to calibrate the neutron detectors. The production of fragments, and the experimen-
tal techniques and equipment used to measure the beta decay of ”N and 230 are

describt-‘d in the following sections.

3.1 Fragment Production

The stable isotope. 1h)Ca, was accelerated to produce the radiozwtive beams of in-
terest. lsC'a vapor was introduced into a Electron C'ycl(_.)t1'on Resonance (IS-CR) ion
source. and ”(7218+ ions were extracted and guided to the K500 cyclotrtm. These
ions were accelerated to 12.3 MeV/A. and then injected into the K1200 cyclotron.

A thin carbon foil was used prior to acceleration in the [(1200 cyclotron to strip

‘28

RT-ECR G‘scu 20 n
ion sources " ‘

 

SC'ECR ‘ WW‘J—r—r-Wj
coupling 9 "‘09”?
line _ - ,'

      

c -' ' quadruple
A1900 magnet
: =='$. image2
\ ""
production 's‘, Q. I
stripping target ‘ g: '|
foil ”'0

Figure 3.1: Schematic diagram of the NSCL Coupled Cyclotron Facility and the
A1900 fragment. separator.
the remaining electrons to produce 48Ca20+ ions. The ions were accelerated to 140
MeV / A Within the K1200. The full-energy ions were extracted and guided onto a 846
mg / cm2 beryllium target at. the object position of the A1900 spectrometer as shown
in Figure 3.1. The thickness of the target. was selected to maximize the production
rate of the 221V isotope based on the LISE code [1‘ l]. The fragmentation reactions
occurred inside the target. usually prmlucing nuclides lighter than ‘lSCa. The mech-
anism of fragment production can be explained as the removal of nucleons from the
projectile by collisions with target atoms. The projectile—like fragments are emitted
with approximately the same. velocity as the primary beam after de-excitation via
emitting neutrons charged particles and gamma—rays [30]. The produced fragments
were directed to the A1900 fragment. separator [Til] where the desired isotope was
separated from the projectile like fragment. cocktail beam by means of two magnetic
bends along with a 825 ing/cm2 aluminum wedge placed at. the Image 2 position of
the separatm'. The A1900 separz-itor consists of four superconducting dipole magnets
and eight. superconducting quadruple triplet magnets as shown in Figure 3.1. The
dipoles separate ions based on their momentum to charge ratio.

The isotopic separation was obtained in three stages. An initial selection of frag-
ments with a specific momentum to charge ratio (mv/q) was accomplished using the

first. two dipole magnets of the A1900 separator. Fragments with a desired HIV/(1

Table 3.1: A1900 magnet settings and beam purity at. the A1900 focal plane.

 

 

Secondary beam 221V 230 16C 17N
Bplqg (Tm) 4.9477 4.4967 4.1730 3.7205
Bp3‘4 (Tm) 4.6970 4.2100 3.9660 3.4635

Beam purity (%) 58.6 16.8 72.7 75.1

Major impurities 25F. 2‘10. 21N 26Ne. 2“1F 17N 180

 

 

 

 

 

 

 

passed through the diploes while others with the incorrect. mv/q were filtered out and
deposited in a catcher bar located inside magnets. The forward moving fragments
with the same mv / q needed to be further separated to produce a beam with a higher
ccmcentration of the desired isotope. This was achieved by introducing a Z (proton
number) dependent momentum shift using a wedge degrader. The fragments pass-
ing through the wedge lose energy based on the Z and velocity (V) as given in the
following equation:
d1? Z2 AZ2

_fi.WX_E (3.1)

where E and X are energy and thickness, respectively. In the present. case, the atomic
charge Q is equal to the nuclear charge Z. The fragment of interest. was finally selected
from the fragments that exited the wedge using the last two dipole magnets of the
A1900 separator. The magnetic rigidities (Bp) of all magnets for the produced beams
are given in Table 3.1 with the beam purities and major impurities.

Each nuclide in the secondary beam was individually identified at the experimen—
tal end station by energy—loss and time-of—flight measureinents. The secondary beam.
optimized for the desired nuclide. was sent to the N4 vault where the desired nuclide
was stepped in an implantatirm detector. A schematic diagram of the experimental
setup at the end station. is shmvn in Figure 3.2. The setup consisted of the implan-
tation detector system, the neutrmi spectroscopic array and detectors from the MSU
segmented germanium array (SeGA). Each component. of the setup will be cxplt-tincd

in the following sectitms.

30

Neutron Spectroscopic
Array

   
  
  

Segmented Germanium
Detector Array

/

Diagnosttc
Chamber

Beam Llne

Figure 3.2: Experimental setup with the neutron and SeGA array
3.2 Implantation Detector System

Secondary beam exited vacuum beam line in N4 vault passed into air through a
kapton window, which had thickness of 0.03 mm. The beam then traveled 135 cm
in air before reaching the implantation detector system. The implantation detector
system consisted of four components: a dE detector, an Al degrader, an implantation
detector, and a veto detector. The secondary beam passed through the dE detector,
which was a silicon surface barrier detector with thickness 200 am and area 300 mm2.
for isotope identification. The energy loss in the dE detector in combination with a
tirne—of—fiight measurementtTOF) derived from the cyclotron resonance frequency and
the time signal of the (IE detector allowed particles to be identified on an event—by-
event basis. The isotopes of interest were stopped in the implantation detector in order
to observe the beta decay. The incoming ions were properly ranged by introducing

an aluminum degrader before the implantation detector, as shown in Figure 3.3. The

31

   
  

Plastic scintillator
Veto detector

AE detector

(0
ON 960 Al degrader

Figure 3.3: Implantation detector system.

Table 3.2: Calculated and actual degrader thickness used to stop the ions.

 

 

Secondary beam SRIM predicted thickness (mm) Actual thickness (mm)
WC 15.845 15.506
17N 10.100 9.704
22N 16.052 15.704
230 11.536 11.412

 

 

 

 

 

thickness of the degrader was adjusted so that the isotope of interest was fully stopped
in the implantation detector. The initial estimates of the degrader thickness were made
based on results from the program SRIM (Stepping and Range of Ions in Matter) [52]
by modeling the all material through the beam path. The thickness of all objects in the
beam path, material types and isotope with its energy were used as input parameters
to the program. Table 3.2 shows the calculated and actual degrader thickness used to
stop the secondary beams. The second silicon surface barrier detector. served as a veto
detector. It was placed after the implantation detector to detect ions that were not
stopped in the implantation detector. The veto detector specifications were similar
to the first detector. The implantation detector was a thin plastic scintillator (3 mm
thick) attached to two Photo-h'lultiplier Tubes (PMT) and located at. the center of
an array of neutron detectors.

Data were collected in a beam-on/l’)eam-oft cycle mode. The beam was pulsed

on for a fixed time period to collect. nuclides in the implantation detector and the

32

Table 3.3: Beam-on/ofl' periods for each beam. the literature half—life and the produc-
tion rate of the important isotope in the beam.

 

 

 

Nuclide Beam-on/oti Half-life Production rate (pps)
T50 2.5 8 0.747(8) s 27
17N 6.5 3 4.173(4) s 86
”N 100 mm 24(5) ms 03
230 300 ms 82(37) ms 7

 

 

 

 

 

beta decay was monitored during the subsequent. beam-off period. The time intervals
were controlled by VME Dual Timer. The beam was interrupted during the beam-off
period by applying a TTL logical gate signal to the r.f.-transmitter on one of the dees
of the K500 cyclotron. At the beginning of each beam-off period, a real—time clock
was started and beta decay events were time stamped to produce decay curves. The
time signal for the time stamp was deduced from two ortect RC014 Real Time Clock
modules operated in parallel with conjunction to CAEN V 993 VME Dual Timer (see
Figure 3.4). The length of time for beam-011 /bea1n-olf cycle was decided based on
the literature half—lives of the implanted nuclides. Table 3.3 shows the beam on and
off time intervals for each radioactive beam along with their reported half—lives and
isotope production rates. The beam-on and beam-off periods was set to approximately

three times the literature half-life of the isotope of interest.

3.2.1 Data Acquisition System

The Data Acquisition System (DAQ) consisted of separate components for the dE.
veto and implantation detectors. the neutron spectroscopic array and detectors from
SeGA. The system consisted of various NIM. CAMAC and VME models. Data were
recorded by mapping the CAhleC addresses into the VME domain controlled by
a DAQ computer. The l'lt’llll‘OIl spectroscopic array and the SeGA array electronics
used VME and CAMAC morilules for digital readout. which will be described in
subsections related to each device. NIM modules handled the trigger logic with the

imMantation detector system clectrrmics. A complete diagram of the electronics setup

33

of the implantation detector. including the. trigger logic. is shown in Figure 3.4. The
output from each PMT of the implantation detector was split. into two signals to
obtain energy and time information. One of the signals was fed to a CAMAC Charge-
to—Digital Converter (QDC) in order to store the energy. while the other was used
as input. to a Tennelec TC-455 Constant Fraction Dist‘rriminator (CFD), which was
used to produce a logic signal. The QDC used was a CAEN Model V792 QDC, which
has 3‘2 channels that integrate the charge deposited within a selected time window.
The time signal from the CF D was recorded by a TDC upon the start signal from the
master gate and also used in trigger logic. The time signals from the two PMTS of the
implantation detector were logically ANDed to discriminate against false events from
the implantation detector or noise in PMTs. The AND signal of was split using a
Fan-In and Fan-Out (FIFO) to produce two trigger signals, which were again AN Ded
separately with beam-on and beam—off gate signals produced by the VME dual timer
model. The two ANDed logic signals were again Ored to produce the master gate
signal. Then, the master gate signal was AN Ded with a computer NOT-busy signal
to define the master live signal. which triggered the computer acquisition to read all
detectors.

The software used to read the data from the electronic modules was based on
the N SCL-DAQ readout program [:33]. This program was responsible for responding
to master triggers and reading out the output. information from the digitizers. Sep-
arate sub—modules were included to the main readout code to read the digitizers of
the neutron array and SEGA. The data events were analyzed to produce the graph-
ical histograms and to apply other analytical operations using the standard SpecTcl

software [:73].

34

20ns 5n 5n

30ns 100ns

5ns .10ns TDC

 

 

 

 

 

1ns 100ns
5ns
Scat
an
I I'
3 2ns 1n -Sca ar Ive
Pm "5 ms ..
U
ns | .
5ns . p
. MGLive
3'“ 5...... u‘" “‘5
Zns E3
FIFO
' -
Scalar1
I
20ns 5ns 5ns

 

 

 

     
   

 

Scalar Inhibit

NIM OUT

 

 

 

 

RC014 Clock ON
R0014 Clock 0N

 

 

Figure 3.4: Electronic setup for the implantation detector. CF D- Constant Fraction
Discriminator, QCD- Charge—to—Digital Converter. FIFO— Fan In and Fan Out, and
PMT— Photo-Multiplier Tube.

3.3 Neutron Spectroscopic Array

Beta—delayed neutron decay is associated with the neutron unbound states in the
beta decay daughter. The energies of the delayed neutrons are measured by means of
time-of-flight measurements using a neutron spectroscopic array. The detailed speci-
fications. energy and efficiency calibrations of the neutron spectroscopic array will be

discussed in following sub-sections.

3.3.1 Detail of the Neutron Spectroscopic Array

The neutron array consisted of sixteen BC41‘2 plastic. scintillator bars with the ap-
proximate dimensions of 157 cm x 7.3 cm x 2.54 cm bent in an arc with a one-meter
radius. The detector design provides an equal flight path for all neutrons leaving a
central implantation detector. This array covered a total solid angle of 1.9 steradians
and had a surface area of array approximately 800 c1112. Detailed information about
the neutron array is available in Ref. [551]. The neutron bars were supported by an
aluminum frame work so the implantation detector was at. the center of each neutron
bar. The time signal originating from the detection of a. beta decay event in the im-
plantation detector served as the start of a neutron time-of—flight measurement for
any of the neutron detectors. Each scintillator bar had a photomultiplier tube (PMT)
at each end of the bar to detect photons resulting from neutron interactions with the
scintillator material. The mean time signal from two PMTS attached to any of the
neutron bars served as the stop for the neutron time-of—flight (TOF) measurements.
The time difference between the start and stop signals was used to deduce the neutron
time-of-flight. and thus determine the neutron energy.

The schematic electronic diagram for the neutron spectroscopic array is given in
Figure 3.5. The delayed output signal of each PMT was split into two signals. One
signal was processed through a QDC. which was gated by the master gate trigger

to get energy information. The other signal was used to produce the time signal.

100ns

 

5ns
Delay QDC QDC Gate
20 100ns 5 IOns
ns ns
LNcu-PMT Splitter I
lOns

 

   

 

 

Corcgister

 

 

 

 

 

 
  

 

 

8H8 5ns
I CF D
1 Gus
ZOns 5ns
RNeu-PMT Splitter
1 00m 1 Ons
5ns
Delay QDC QDC Gate
1 OOns

Figure 3.5: Schematic electronic diagram for the neutron bar array. CF D- Constant
Fraction Discriminator, QCD- Charge—to-Digital Com-terter, F IFO- Fan In and Fan
Out, and PMT -Photo Multiplier Tube.

As shown in Figure 3.5. both logic signals processed by the CF Ds of both sides of
neutron detector were ANDed to eliminate false neutron events or noise from PMTs.
The ANDed signals from each neutron detector were combined with an OR logical
gate and used in trigger logic. The second logic signal from CFD was processed by
the TDC, which was stopped by the master gate.

The neutron spectroscopic array was used to determine the energy of beta-delayed
neutrons as well as the number of neutrons emitted with the beta decay of desired
isotope. Therefore, the individual neutron detectors required calibration for both neu-
tron energy and efficiency. The neutron energy calibration was achieved by calibrating
the TDC modules for their time slopes using a time calibrator (ORTEC 462). The
offsets were determined from the known beta—delayed neutrons of 16C and 17N taken

as calibration beams. Data from beta-delayed neutron decay of these isotopes were

37

 

250

200 .

150 -

Counts / channnel

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 - 1 4i l 1 -
0 500 1000 1500 2000 2500

Channel number

 

Figure 3.6: The time calibration spectrum for the neutron detector.

also used for the efficiency calibration. A Monte Carlo simulation was used to extent
the efficiency calibration to higher energy. The detail procedure of both calibrations

will be discussed in the following sections separately.

3.3.2 Neutron Energy Calibration
Time calibration of the neutron array

The determination of neutron energy using the time-of—flight technique requires two
type of calibrations: calibration of the TDC response of each PMT channel, and the
on-line calibration. which includes the intrinsic response. of neutron detectors. The
time-Slope calibration of each TDC channel was obtained using an ORTEC-462 time
calibrator. The start signal of the calibrator was split and used as an input to the
CFDS of the implantation detector. The stop signal to the calibrator was also split
and used as an input to the CFDs of each PMT of a neutron detector. The period and
range of the time calibrator were set to 10 ns and 32 [(5, respectively. The TDC time

response for each PMT channel was measured indept—mdently. An example spectrum

Table 3.4: Time calibration results for neutron detectm's.

 

 

Neutron Time slope Beta-prompt Neutron Time slope Beta—prompt
detector (rrs / channel) peak centroid detector (ns/ channel) peak centroid

01 25.296 45.4 ()9 25.232 45.4

02 25.256 45.4 10 25.267 45.5

()3 25.271 45.5 11 25.253 45.6

04 25.259 45.4 12 25.286 45.5

05 25.262 45.5 13 25.289 45.5

06 25.239 45.5 14 25.312 45.6

07 25.262 45.5 15 25.273 45.5

08 25.260 45.6 16 25.185 45.5

 

 

 

 

 

 

 

 

from one of the neutron detector calibration is given in Figure 3.6. Calibration plots
(time vs. channel number) were made to derive the time slope (ns / channel) for each
neutron bar, and the results are given in Table 3.4.

The time slopes were used in the SpecTcl code as parameters for time calibration.
SpecTcl produced a histogram (spectrum) for each neutron detector based on recorded
time events and the time calibration. It was essential that the spectra of all neutron
detectors were aligned. since the individual spectra were summed to improve statistics.
The initial time alignment was done by using a. gamma-gamma prompt peak position
in 60Co spectra from each neutron detector. These spectra were obtained by replacing
the implantation detector by a. BaFQ detector with a GoCo source. The final position
adjustments were done using the on-line caliln‘ation spectra generated from beta-
(lelayed neutrons of 16C and 17N.

The beta—delayed energies and emission probabilities of the neutrons of 16C and
17N are known with high precision. The beta. decay of 16C produces neutrons with
energies of 810. 1714 and 3290 keV [55. .36] and 17N beta decays with neutrons of
energies 382.8, 1170.9 and 1700.3 keV [33.57]. In addition. both beta-delayed neutron
time-of-flight spectra produced prompt peaks which can be used as calibration points.
Secondary beams of 16C and ”N were produced in similar manner to that explained
in Section 3.1 with appropriate Al dti‘grader thicknesses (see Table 3.2) to implant the

desired isotope. The beam-on and —off time intervals were adjusted according to their

39

half—lives. The details of beam purity. l’>earrr-on\off and degrader thicknesses are given
in Tables 3.1, 3.2 and 3.3. Beta-gamma prompt peaks of beta—delayed neutron time-of-
flight spectra of 16C and 17N from all detectors were aligned to channel number 45.5
by introducing offset. parameters to the S]_)ecTcl code. The average channel number for

beta-gamma prompt peak from both sriiectra is given in Table 3.4 for each detector.

On-line neutron energy calibration

Orr-line time calibration was carried out. as follows. The neutron kinetic energy, En can
be written in terms of the velocity of the neutron (V1,) with no relativistic corrections

(since the neutron energy is low enough to treat classically)

En 2 $171.13. (3.2)

This equation can be rearranged as shown in Equation 3.3 by substituting the rrrass

of neutron for m:

 

(3.3)

where En is in MeV and V n is in rn/ns. The velocity of the neutron can be obtained
from the time-of—fliglrt of the neutron and the flight path ((1). which is defined as
the distance between the point where beta decay occurred and the point. where the
neutron interacts in the neutron detector. The time-of—flight comes from the peak
centroid (c) of the time-of-flight spectrum, which is calibrated. Finally. the reciprocal

of velocity of the neutron can be written as:

7:: 2 1111+? (3.4)

where p is the TDC offset. According to equation 3.4. the flight path ((1) and the TDC
offset (p) for the neutron array can be determined under the given experimental

conditions lmsed on known neutron energies from beta decay of 1("C and “N. In

40

Table 3.5: Energy calibration results for neutron detectors.

 

 

Neut ron Energy Average Neutron Energy Average
detector slope (1 /1n) distance (in) detector slope (1/1n) distance (In)
01 0.9896 1.011 09 0.9926 1.007
02 0.9908 1.009 10 0.9932 1.007
03 0.9857 1.015 11 0.9891 1.011
()4 0.9898 1.010 1‘2 0.9881 1.012
05 0.9848 1.015 13 0.9890 1.011
00 0.9870 1.013 14 0.9905 1.010
()7 0.9946 1.005 15 0.9805 1.020
08 0.9935 1.007 16 0.9800 1.020

 

 

 

 

 

 

 

 

addition. the centroid of the prompt peak was used as part of the neutron energy
calibration. The most probable beta energies (KE) were calculated by taking 0.33 of

the beta decay energies for a particulzu' decay as:

c2 2

7m;

‘1’ 2 C" 1 __ ‘ 3.5
'5 (KE + mpcl) ( )

wht-rre nu is the mass of electron and C is the speed of light.

 

The spectra. recorded from the beta decay of 16C and 17’N for each neutron detec-
tor were analyzed to determine the peak centroids using the code DAMM (Display,
Analysis and Manipulation Mode) developed at Oak Ridge National Lab [38]. The
peaks were fitted with asyinn’ietric gaussian peaks and a third order polynomial back-
ground. The cnergy slope for each detector and the flight path ((1) calculated from
their slope are given in Table 3.5.

The calibrated time-of-flight spectra were added after aligning the prompt peak to
channel number 45.5 to generate the total spectrum from the neutron array. The total
beta-delayed neutron tin'ie-of-flight spectra. of 16C and ”N. shown in Figure 3.7, were.
fitted using the DAMM code. The peaks were fitted with asymmetric Gaussian peaks
and a third order polynomial liiackground. The F\-\'ll.\l values. asymmetric parameters
and the coefficients of the background were treated as variables throughout. the fitting

prmredure to establish neutron peak and background shapes. Figure 3.7.(a) shows the

-1 1

 

500 ~ 5000

 

 

 

 

 

 

 

 

 

 

 

 

 

1(3) 810 .(b>
1714 6 4000

g» 400" g ” 1171
C ’ (U .
CU _ .C _
'5 300 l. 3 3000 f 01210 E0 1630 110
\ t r ,
(I) U)
E 200— *5 2000»
3 t ' 8 ’ 1700
O 100- 0 1000-

. 32901 .

O "n 1 A O I m 1 A I 4
80 100 120 140 90 100 110 120 130

Channel number Channel number

Figure 3.7: Total neutron time-of-flight spectra of 16C and 17N. Neutron TOF spectra
of (a). 16C and (b). 17N with fitted neutron peaks and the background are shown.
The energies are marked close to the peak in keV.

Table 3.6: Fitting data from 16C and 17N neutron time—of—flight spectra.

 

 

 

16C data jTN data
Peak position Area Error F W HM Peak position Area Error F WHM
81.5 108 9.2 2.28 97.5 3556 4.4 3.11
97.3 1847 3.6 3.68 108.9 23243 1.6 4.83
122.8 3247 2.8 5.98 160.0 648 11.8 12.0

 

 

 

 

 

 

 

 

 

 

beta-delayed neutron peaks of 16C with their energies labeled. The peak without an
energy label is unknown from the beta decay of 16C at. present. The fitted beta-delayed
neutron time-of—flight spectrum of 17N is shown in Figure 3.7.(b) with labeled neutron
energies. The fitting results for both decays are given in Table 3.6 and were used to
establish neutron energy and peak shape calibrations. and to study the background
shape of the neutron time-flight spectrum for the neutron spectroscopic array under
the present exl')erimental conditions.

The total neutron time-of-flight spectrum was calibrated for energy by establishing
a relationship between the neutron peak centroid and the reciprocal of the neutron
velocity. as in Equation 3.4. The second column of Table 3.7 shows the literature values
for neutron energies from beta decay of 16C and ”N. The energies were converted
to velocities using Equation 3.

3. In addition. the prompt peaks were translated into

42

Table 3.7: 1GC and 1’ N data for the energy calibration of neutron array

 

 

 

 

 

 

 

 

 

 

 

    

 

 

 

Nuclide Energy (keV) 1 / Velocity (ns/ n1) Peak position
ITN 1700.3(17) 55.4(3) 97.5(19)
1170.9(8) 66.8(2) 108.9(27)
382.8(9) 116.9(14) 160.0(59)
we 3200(30) 390(2) 81.5(13)
1714(5) 5522(8) 97.3(21)
810(5) 803(2) 122.8(33)
Nuclide Q—values (keV) 1 / Velocity (us/m) Peak position
WN 8012 3.380(1) 45.5(3)
16C 8680 3.374(1) 45.4(4)
120 - 17
* N
100 -
E 80 -
m
C L
2? 60-
8 40 _
F) _[5—Prompt
Z 20 -
w— _ Y=O.9911X-41.3
o -
30 A 610 l 90 l 180 A 15LO A 180

Peak position

Figure 3.8: Energy calibration of the neutron array using 10C and 1"N neutron decay.

the reciprocal of velocity by using Equation 3.5 with substituting KE value as 0.33 of
Q-value corresponding beta decay. The neutron energy calibration was established by
plotting the reciprocal of velocity vs peak position (centroid) as given in Figure 3.8.
The energy calilination C(piation used to derive unknown neutron energies is given
in the figure. The error associated with the calculated neutron energy includml the

fitting uncertainties of the calibration and the error from the peak position.

43

Table 3.8: Neutron peak shape calibration

 

 

Nuclide Peak position (Peak position)1/2 F\VHM Asynnnetric factor
16C 81.5 9.03 2.28 0.2
97.3 9.87 3.68 0.3
122.8 11.08 5.98 0.5
”N 97.5 9.88 3.11 0.3
108.9 10.44 4.83 0.5
160.0 12.65 12.0 0.8

 

 

 

 

 

 

 

3.3.3 Neutron Peak Shape and The Background

It. is important to establish a standard procedure to define peak shapes and the.
background when analyzing a neutron time-of—flight spectrum. A study of such was
carried out using the 16C and 17N beta-delayed neutron time-of—flight spectra. As
mention above. neutron peaks were fitted with asymmetric Gaussian functions having
exponential tails which extended to higher time-of-flight values. The fit functions are

given in Equaticm 3.6

 

—- X —— X' 2
X<X0 YL = .4 =1: E.l‘p(;—T—U—l—)
(7
-- X — 1' 2
X 2 X0 YR = .4 =1: Erp( . ( _ 0&0) ) (3.6)
do + S(.\' — X0)a)

where Y L and Y 11’. are left and right parts of the peak with centroid X0. and 0 and S
are the FVV HM and the asymmetric factor of the peak. respectively.

It is reasonable to add an exponential part to the pure Gaussian peak to produce
neutron peak shape. The neutron response of the detector has a. tail principally due
to a (‘lelayed light. emission in the plastic in the case of low change deposited in the
scintillator bar. The size of the exponential tail was controlled by the FVV'HM and the
asymmetric factor. The calibration spectra were fitted using the DAMM progran'i by
minimizing the reduced \2 values. which were found to be in the range of 0.8 - 1.7.

Table 3.8 shows the peak centroid. with the ('(‘n'respomling F \VHM and asymmetric

44

 

     

  

 

 

 

17
12 - N
10 —
t
8 )—
2 .
I
E 6 ~
u. ' 16
4 ~ C 17N
>160 I17N
2 - Y = 0.3207x2 - 6.423X + 34.072
9 10 11 12 13 14
(Peak position)"2

Figure 3.9: Peak shape calibration

factors obtained from the DAMM fits. The peak shape calibration was determined
for the FVVHM as a function of the square root of the peak centroid in the total
time—of—flight spectrum. Figure 3.9 shows the peak shape calibration plot with the
equation, which was used to define the FVVHM used for fitting in new time—of—flight
spectra. The equation was included to the DAMM program to determine FVV HM
when analyzing a. new Spectrum.

The shape of the background is an inn’mrtant factor in the neutron time—of—flight
spectrum, since it affects the peak area. A study was carried out. to establish a rea-
sonable shape for the l')ackground based on the time-of-fliglit spectra collected from
16C, 17N, 19N and QUN delayed neutrtms. The time-of—flight spectra for 19N and 20N
were taken from the pervious experiment that used the same neutron spectroscopic
array [34]. The spectra. were fitted using the DAMN-l program as explained above with
various functions for the background and the reduced 12 values of the fits were com—
pared. A third—ordcr polynomial function. as shown in Figure 3.10. was selected as
the best match to all backgrmmds of the tin'ie—of-flight spectra. The high backgrounds

under the strong neutron peaks were attributed to the neutron backseatteriug. The

 

 

 

 

 

 

 

 

 

 

500 ~ 600
16C3 17N
400- 400
200- 200
1 . J J l -_‘_v_ ‘Jh‘WK‘L-v
900 150 200 25° 0 200 ' 250 T 300 ' 350
1200

 

 

150-

l
800i
100 -

Counts / channel

400- 50 L

 

 

 

 

 

 

 

 

360A400A560A600

 

30

20

10»

 

    

 

 

100 150 i 200 A 250

Channel

Figure 3.10: Study of neutron background shape. Third-order polynomial background
was fitted for the delayed neutron spectra from 16C, 17N, lQ-QON and 22N.
neutron time-of-flight spectrum of 22N . where the background was fitted with a third-

order polynomial is shown in Figure 3.10.

3.3.4 Time Walk Correction

Good time resolution of the neutron array is important especially when low energy
neutrons need to be detected. The resolution is inversely preportional to the pulse
height of the signal [FWHM :x rise—time / (signal to noise ratio)]. so that the resolution
of a low pulse-height signal will be poorer. In addition. constant fraction discrin‘iina-
tors tend to have a delayed output for low pulse height signals. which is called “walk”.
The typical correlation of pulse-height with time is shown in Figure 3.11 . obtained

using a Am-Be neutron source. If there is no walk the plot should show a straight

46

 

 

Energy (o.u.]

Energy (o.u.)

  
  

    

 

280 580 880 1 180 1460 'l 780

 

.‘: a.“ .—, - "‘
. 1816 2416 3016 3616 .
T1me (Channels) Tlme [Channels]

69*“ ' ‘
16 6161216

Figure 3.11: A scatter—plot of time.vs.energy obtained using an Am—Be neutron source.
(left) The plot deduced with another PMT did not require a correction. (right) The
plot deduced with one of the PMT that required a time walk correction.

vertical line, corresponding to a constant time for all energy neutrons. which is illus—
trated by Figure 3.11(left). The walk is seen as a long tailing at the lower neutron
energies in Figure 3.1l(right). The walk was treated by adding a correction to the raw
time measurement for each PMT. Corrections were derived by fitting the plot of time
versus energy from each PMT as a function of energy pulse height. The line showed
in Figure 3.1] represents data points having the maximum counts. Those points were
used to derive correction functions. The correction functions were applied in SpecTcl
code for all neutron time-of—flight meantime measurements to produce the mean time

of each event:

tmean : {UL — foPH)l 1’ llR — lepfllll/Q (37)

where t L,t R: f L(PH), f R(PH) are left and right time measurements, and the correction
functions, respectively. The different types of functions were tried to get minimum
F WHM for the beta prompt peak. The functions for the PMTs that needed a correc—

tion are given in Table 3.9.

47

Table 3.9: Time walk correction functions

 

 

 

Left—PMT Function Right-PMT Function
number number

()1 33.()*Exp(—PH/20.l)+15.1 01 24.2-0.382*PH
()2 - ()2 22.4*Exp(-PH/l4.0)+29.3
()3 54.8*Exp(-PH/9.0)+‘20.5 O3 14.2*Exp(-PH/18.3)+27.3
04 19.6*Exp(-PH/l2.6)+12.1 04 18.0*Exp(-PH/17.8)+26.9
05 75.1*Exp(-PH/9.6)+19.8 053 19.7*Exp(—PH/17.3)+28.9
06 34.0*Exp(-PH/12.1)+18.8 ()6 ‘28.]*Exp(-PH/15.7)+24.2
()7 38.1—0.310*PH 07 18.0*Exp(—PH/17.8)+26.9
08 - 08 —
(1.9 ‘20.1*Exp(-PH/12.())+1‘2.7 ()9 -
10 18.8*Exp(-PH/11.4)+13.3 10 40.1-().234*PH
11 41.7-O.467*PH 11 18.3*Ex1.)(-PII/14.6)+30.1
12 14.2-0.415*PH 1‘2 -
13 14.53-0.I7G*PH 13 12.1-0.1*PH
14 99.5*Exp(-PH/7.9)+16.0 14 14.0-0.256*PH
15 103.1*Exp(—PH/3.6)+3().(1 15 25.6*Exp(-PH/8.3)+24.7
16 34.8-0.176*PH 1G 26.7*Exp(-PH/6.4)+19.2

 

 

 

 

 

3.3.5 Neutron Efficiency Calibration

The neutron efficicency at. a particular energy was defined as:

A

2 ___P,, * (7101. (3.8)

“n

where A, Pn, and Cm; are the area under the neutron peak. neutron emission proba-
bility and the total number of beta decay events registered at the implantation detec-
tor. respectively. The total number of decay events for particular isotope observed in
the implantation detector was determined by integrating the individual decay curve
throughout the. beam off period. The (ilecay curve contained not only the ('lecay of
the in'iplanted isotopes but also the decay of their daughters and gramldaughters.
Therefore, it was necessary to find the contribution from each isotope to the total
decay curve. This was achieved by fitting the decay curve with an appropriate decay
model. Decay models were developed for the 16C and ”N implantations. as explained

in Appendix A, by incorporating the decay of implanted parents (1°C and 1‘N). the

 

3000

 

         

 

 

 

 

 

 

 

(a) 5000
2500 ’
m m 4000
CEO 2000 (E
N N 3000
\ 1500 \
E . w
c *5 2000
:3 1000 :1
8 . 8 ’
500 16 1000 ~
1 N + Background Background
0 1 1 1 4 L 1 1 1 1 1 O 1 4 1 4 1
0.0 0.5 1.0 1.5 2.0 2.5 o 1 2 3 4 5 6
Time (s) Time (3)

Figure 3.12: Beta (‘lecay curves of 16C and 17N. (a).The fitted beta decay curve of
17N with the background are shown. (b). Neutron TOF spectrum obtained in the
17N experiment is shown with fitted neutron peaks and the background. The neutron
peak energies are given close to the peak in keV.
growth and decay of daughter (IGN), and a flat background. The growth and decay
contributions during the beam on period were taken into account and the fraction of
isotope that was not. decayed within the I.)arti(’-ular cycle was added to the next cycle.
Figure 3.12 shows the fitted decay curves for (a) 16C and (b) ”N with their daughter
and background contrilmtitms. The half-lives of 16C and 17N and the neutron emis-
sion probabilities were free parameters in the fitting procedure and the half—life of
1le, the daughter of 16C. was kept fixed (Tl/‘2 = 1.8 s). The individual decay curves
of 16C and 17N were integrz-ited and total number of decay events were found to be
3.337(6)x1()3 and 2.0-572(14)x1()6 with half-lives of 755(4) ms and «117(7) s. respec-
tively. which have a good agreement with literature [ltl](see Table 3.3). The total
number of 16C and 17.N beta decay events with the number of detected neutrons and
their neutron emission probz-tbilities were used to generate. neutron efficiency function
for the neutron s1')ectroscopic array.

The number of neutrons that had been registered in the neutron array (peak area)
was determined by fitting the total time-of-flight spectra. from 16C and 17N beta ('lecay

(see Figure 3.7). The neutron peak areas from the fits and («irresrmiitli11g neutron

49

_'.
o

 

_'1
'01
I

   
  
 

Simulation

Log(Eh‘iciency)
1'0
0

 

 

 

-2.5-
"N Y=1.711X3-3.063X2+1.619X-1.751
-3.0r
-0.4 -0.2 0.0 0.2 0.4 0.6
Log(Energy{MeV})

Figure 3.13: Neutron efficiency calibration

emission probabilities with their energies from the literature are given in Tables 3.0
and 3.10, respectively. The neutron detection efficiencies calculated using Equation 3.8
are given in Table 3.10 were used to generate the neutron efficiency function for
the neutron spectroscopic array. The function shown in Figure 3.13 used the six
experimental data points in the range of 382 - 3290 keV from beta-delayed neutrons of
16C and 17N and three data points at 1800, 3000 and 4000 keV obtained from a Monte
Carlo simulation using the KSUEFF program [50.6% i]. The function in the high-energy
region had a small SIOpe as seen from the experimental data points in Figure 3.13.
Therefore. the simulated data points were moved to match the experimental data
points in flat region while keeping the slope generated by (‘-(nmect.ing three points
constant. The logarithmic values of neutron energy vs efficiency were fitted to a third
order polynomial. given in Figure 23.115. which was used to determine the neutron
efficiencies. The lowest. detection limit for energy was determined to be approximately
360 keV by extrapolating the low energy part. of the efficiency function to the energy
axis. The right side shoulder of the prompt peak in the time-of-fiight spectrum forms

the limit. for the detection of high-energy neutrons. and was estimated to be 8000

Table 3.10: Efficiency calibration of neutron array using 16C and “N beta decay.

 

 

 

 

 

 

 

 

 

Nuclide Energy (keV) Emission probability (‘1) Area (Ei‘r()1“/t:) Efficiency
rec 1714(5) 15.5(17) 1847(30) 0.035(4)
810(5) 83.5(17) 3247(28) 0.0117(4)
3200(30) 1.0(2) 1()8(9.2) 0.032(7)
17x 1700.3(17) 0.9(1) 3556(4.4) 0.025(4)
1170.9(8) 50.1(13) 2324306) 0.0226(7)
382.8(9) 38.0(13) 618(117) 0.0008(1)

keV.

3.4 Segmented Germanium Detector Array

Beta-delayed gamma transitions are particularly important to establish the neutron
bound states in a level scheme. The detection of beta-delayed gamma-rays required
high resolution and efficient gamma—ray detectors in a close geometry to the im—
plantation detector. The l:)eta—delayed gamma—rays were detected using eight n-type
high-purity germanium (HpGe) detectors from the MSU Segmented Germanium Ar-
ray (SeGA) [til]. The detail geometrical arrangement of SeGA with their energy and

efficiency calibration will be discussed in following sections.

3.4.1 SeGA detectors

Each flpGe SeGA detector has a cylindrical shaped germanium crystal with a length
of 8 cm and a diameter of 7 cm. The crystal is a closed-end coaxial crystal with a
lithiinn-diffused central contact to produce the full energy signal. The outer surface of
the crystal is doped with p-type contact. to make four azimuthal and eight longitudinal
segments. giving a total of 32 segments. Only the central contra-t output from each
detector was used for this experiment. The cryostat of the crystal is mounted at a
450 angle to the liquid nitrogen dewar. Eight, HpGe detectors (75ft. relative efficiency)
from NSCL-SeGA were placed in a ring structure with the detector crystals parallel

to the beam axis and made a distance of 14 cm from the. beam axis to each detector

Beam pipe

   
 

Segmented
germanium
detector

Veto
detector

Figure 3.14: Schematic diagram of the implantation detector and SeGA array.

crystal surface. The distance from the implantation detector to the front surface of
the detector crystal along the beam axis was 19.2 cm. A schematic view of the HpGe
detector array setup is shown in Figure 3.14.

Each HpGe detector has two outputs from the central contact, which were used for
an energy and a timing signal. The timing signal output from each detector was sent
to a T0455 NIM CFD module and subsequent outputs were used as an input to a
LeCroy 380A Multiplicity logical unit to combine all signals. The electronic diagram
for the HpGe detectors is shown in Figure 3.15. The combined signal (OR signal)
was used for the master gate logic. The second output signal from the CFDs was
the stop for a Phillips 7186 T DC. The TDC was started by the master trigger. The
energy signals from the central contact were amplified using ORTEC 572 amplifiers

and digitized using ORTEC 413A ADCs.

3.4.2 SeGA Energy Calibration

All HpGe detectors were calibrated for energy using spectra obtained with a Standard
Reference Material (SRM) 4275C source. containing 12581). 1541311 and 1551311, along
with single sources of 60C0. 1521311. 2"“Am and 207Bi. In addition, the gamma-ray

energies from known daughter decays from the implanted isotopes and the natural

52

I Scalar I

 

 

 

5115
60115
3ns lOns
TFA
Time 2ns
5ns lOns
Energy lOns

 

Figure 3.15: Schematic electronic diagram for SeGA array.

background gauu'na-ray peaks from 40K and 208T] were used to extend the energy
calibration up to 6200 keV. The sources were placed at the location of implanta-
tion detector and gamma-ray spectra were collected for all detectors. The gamma—ray
peaks were fitted with Gaussian functions using the. DAh‘Ih‘I program. Two energy
calibrations for low and high ge-urnna—ray energy ranges were established by weighted
fitting the photopeak centroid versus the known gamma—ray energy for each detector.
The low and high energy ranges were chosen as 60 - 1500 and 1500 - 6200 keV, respec—
tively. to achieve the best. fit. to the experimental data. Energy data points at 1275.
1298, 1333, 1406, 1460, 1596, 1633 and 1770 keV were used in both calibrations to
obtain a smooth transition between two calibrations. The low-energy range calibra-
tions were fitted to second order polynomials and the high energy range calibrations
were fitted to straight lines for all detectors. The residuals. which were defined as the
difference between the literature energy and the calibrated energy. are given in Fig-
ure 3.16 and were within :t0.6 keV for all detectors. Energy calibrated spectra from
all detectors were added to produce the total gamma—ray spectrum, which was used
for further analysis. The errors for gannna—ray energy were estimated by accounting
for the errors from the calibration tit and the errors in the peak position given by

DAMM code.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0~-—-— -—_-~w~-—————-- 1,0
SeGA01 SeGAOZ
0.5- 0.51
0.0 -7.-,L 00pm“! h!“ r r 1
-05 -o.5l ., ll 1
1 0F:—:::~ “T f:_::_:f__:i 10 ______ —“‘“"'——-‘ "w‘
SeGA03 SeGAO4
0.5t 05+
L
A 00* _* 0.0»
a
it, -0.5 -0.5i
a 1.0—- ________ .___. , a—-—-~—
.8 SeGA05 1 0 SeGAOG
'35 05r 0.5[
0 ,
m 0.0 0,0 Ten—r1
1.0 L“ ‘ 1.0
i SeGA07 SeGA08
0.5» 05.
La. 0.01 L.-- T
-O.5F -0.5»
-1.0l___. ___.J_.__._._..__l—__.n__l -1“) 1 i . i
0 1000 2000 0 1000 2000
Energy (keV)

Figure 3.16: Residuals of the energy calibration for seGA detectors

3.4.3 SeGA Efficiency Calibration

The gamma-ray coincidence efficiency measurements for the full energy peak were
carried out using the radioactive sources off-line as well as with the beta decay of
well-known daughters from the on—line measurement. For the off-line measurements,
a N al scintillation detector was used as a trigger with same electronic setup replacing
the implantation detector signal. The 60Co, 1521311 and 20‘!Bi sources were placed both
in front. and in back of the implantation detector to minimize the effect. coming from
the implantation detector thickness for off-line efficiency calibration. The energies

of the photons from each source are given in Table $3.11. The aluminum degrader

Table 3.11: Off-line coincidence efficiency calibration data for SeGA.

 

 

 

Source N a1 Nal Energy Coincidence Peak Efficiency
gate (keV) Count (keV) fraction area
152Eu 1408 2.46E+5 122 1 6673 2.7(3)E-2
152Eu 867 1.28E+5 241.2 0.427 2078 3.81(5)E2
1521311 344 1.89E+6 268.2 0.00287 216 3.9(3)E2
152136 779 4.92E+5 341 0.65 11906 3.72(3)E,2
1521311 344 1.71E+6 364.4 0.0315 1901 3.52(4)a2
1521311 344 1.75E+6 407.8 0.083 5420 3.74(3)E—2
1521311 122 1.20E+5 441.2 0.0458 203 3.69(1)E—2
20431 1064 4.51E+5 570 1 14001 3.11(2)E—2
15213311 344 1.45E+6 583.4 0.0171 767 3.09(4)a2
1521311 344 1.41E+6 675.7 0.0172 689 2.8(4)E—2
1521211 344 1.41E+6 710 0.0034 139 2.9(14)E—2
152nm 344 1.36E+6 776.4 0.4703 16553 2.6(2)E—2
204131 570 1.03E+6 1064 0.8412 19579 2.3(2)E-2
152Eu 344 1.27E+6 1086.3 0.0628 1757 2.2(4)E—2
152136 122 8.57E+4 1112.1 0.2204 388 2.1(7)E—2
6000 1333 1.24E+5 1174 0.9992 2770 2.2(2)E—2
1521311 122 8.50E+4 1210 0.0229 39 2.0(5)E—2
1521311 344 1.22E+5 1298.3 0.059 1429 1.9(2)rr2
6006 1174 1.49E+5 1333 1 2937 1.9(2)a2
152Eu 122 8.56E+4 1406 0.3389 594 2.0(7)a2
204131 570 8.86E+5 1770 0.0691 932 15(1)}3—2

 

 

 

 

 

 

 

 

thickness of 15.704 mm, which was used in the 22N experiment, was placed in to
perform the calibration under the same geometry.

The off-line coincidence efficiency was established by measuring gamma—ray events
registered in the HpGe detectors triggered by the Nal detector. A software gate was
placed on one of the peaks detected in the Nal detector and applied to the total
gamma-ray spectrum to generate the coincidence spectrum for the sum of all SeGA
detectors from a particular source. The peak areas of this gated spectrum were ob-
tained by a Gaussian fit. The total number of triggered events in the Nal detector
was determined by integrating the background subtracted area under the gated re-
gion of the peak. The gamma-gamma coincidence emission probability for a particular
gamma-ray pair was calculated by considering the gamma-ray cascade properties of

the decay scheme. Table 3.11 shows data from the coincidence measurements using

55

Table. 3.12: On-linc coincidence efficiency calibration data for SeGA:22N experiment.

 

 

 

 

 

 

 

 

Beta Decay Energy Emission Beta decay Peak Efficiency
nuclide (keV) 1")1‘obability (‘71. ) events area
22F 1274.537 100 28573 576 20(1)}3—2
2'21? 2082.6 81.9 28573 348 1.5(1)E—2
‘22 2166.1 61.6 28573 230 1.3(1)E—2
21F 350.725 89.55 18598 635 3.8(2)E-2
20F 1633.602 99.99.95 9955 168 1.7(2)s2
25515. 974.72 14.95 34545 123 2.3(6)E-2
IGN 6125.41 67.2 10622 49 6.9(5)E-3

 

 

off-line sources and the coincidence efficiencies calculated by the division of the SeGA
peak area by the total number of triggered events and the corresponding gamma—
gannna coincidence emission probability.

In addition to the off-line efficiencies. the well-known daughter/ granddaughter
decay of implanted isotopes provided a set of efficiency data points measured under
the experimental conditions. The beta decay of 22F, 21F 20F and 25Na provided
strong gannna—ray peaks with well-known gannna—ray emission probabilities, given in
Table 3.12. from the 221V implantation. The decay of 16N also provided a gamma—
ray peak at 6125.41 keV from the 16C implantation, which was used to extend the
gamma-ray efficiency to high energy. Aluminum degrader thickness of 15.506 mm
(0.198 mm thinner than used in the 22N experiment) used in the 16C experiment.
did not make a significant difference to the efficiency as the attenuation is small at
high energies. The on-line efficiencies given in Table 3.12 were calculated using the
peak area, the total number of beta deer-1y events derived from the. decay curve fitting
and the gaunma—ray emission probability. The on-line and off—line efficiencies were
used to establish the mincidence efficiency curve. shown in Figure 33.17. for the 221“
experiment analysis. The efficiency function for the ”N ex1')eriment was fitted to the
fourth order polynmnial given in the same figure.

The low energy part of the efficiency function is highly sensitive to the absorber

. , . . 4)! .
thickness that blocked some of the incoming 0annna—ravs. In ~30 ex )ernnent. an A]
b ('3 4

.1.
o

 

 

 

 

_1 2 ' Y: -0.154x4 + 2.144x3 -11.19x2 + 25.24x - 22.08
3: .
O
.5 ~14 —
.9 _
40.)
a, -1.6 —
U
c t
g 1 8
.6 '- _ -
C h
'5
9,-2.0 -
C3
O .-
_J
-2.2 -
-24 1 m 1 1 1 . 1 a
2.0 2.5 3.0 3.5 4.0

Log(Energy (keV))

,. 4‘ . . 4 . . . . . 9 .
Flgure 3.17: Comcidence efficlency calibratlon for SeGA:2~N expernnent.

-1.0

 

1 2 ' Y = —0.346x‘ + 4.297X3 - 19.912x2 + 40.279x - 31.265

-1.4 —

-2.0
1

Log( Coincidence efficiency)

-2.2 —

 

 

_2.4 1 . 1 1 1 . 1 1
2.0 2.5 3.0 3.5 4.0

Log(Energy (keV))

 

. , 7‘ . . _ -, . . . . -‘ , -)-’ .
Figure 3.18: C. oincrdence efficlency calibration for beGA:-*“O experiment.

C1
\1

Table 3.13: Orr—line coincidence efficiency calibration data for SeGA:23O experiment.

 

 

Beta Decay Energy Emission Beta decay Peak Efficiency
nuclide (keV) probability (‘74.) events area
”N 870.71 3.3 2085015 1553 2.3(1)E—2
171\’ 2184.48 0.34 2085015 72 1.0(2)E-2
26575. 1128.6 58754 840089 795 1.64(9)EQ
201w]. 1811 99.08 840089 10816 1.33(3)E2
23% 438.3 32.9 171285 1885 2.41(9)E-2
21F 3488 89.55 10775 355 3.7(3)E—2

 

 

 

 

 

 

 

 

degrader thickness of 11.412 mm (4.202 nnn thinner than the thickness used in the
previous calibration process) was used to ensure implantation into proper detector.
Another efficiency calibration was established using the on-line efficiency data points
to analyze 230 experin‘iental data. The peak efficiencies of gamma—rays associated
with beta decay of 26Na. 23Ne and 21F. shown in Table 3.13, were used alone with
the efficiency data measured from the beta decay of 17'N and 16N . to produce the effi—
ciency function, which had a similar shape of the function generated with the off—line
efficiency data points. The coincidence efficiency calibration "for the 230 experiment

is shown in Figure 3.18 with its calibration function.

58

Chapter 4

Data Analysis and Results

4.1 Anaysis of The 22N Beta Decay Experiment

The 22N radioactive beam was produced by fragmentation of a 140 MeV/ A 48Ca beam
on a 846 mg/cm2 9Be target. The purity of the beam was analyzed at two places along
the beam path. The beam was analyzed the dE detector just before the implantation
detector. 22N was produced as part of a cocktail beam with impurities of 25F, 24O,

20C, 10~12Be. 89Li and 6He. Figure 4.1 shows part of the particle identification (the

 

 

 

281 341 401 451 521 581 541
<— Time-of—Flight (on)

Figure 4.1: Identification of nuclides produced in 22N experiment. The particle identi-
fication was done using the (IE detector before implantation and part of the spectrum
is shown.

energy loss verses the RF time-of-flight) spectrum obtained from the dE detector
and the particles are labeled in the spectrum. Very light. particles are not shown in
the figure. The composition of the beam was also checked at the focal plane of the
A1900 before the implantation runs and is given in Table 4.1. The composition of
nuclides stopping in the implantation detector was analyzed with help of the dB and
Veto detectors by making apprOpriate gates on the particle IDs to apply on the Veto
detector, and vise versa. The number of particles reaching the Veto detector was used
to obtain the number of particles stopped at the implantation detector. The purity
of the beam at the implantation detector and literature half-lives of the constituents
are summarized in Table 4.1. The analysis of the gated particle ID spectra generated
from dB and veto detectors showed approximately equal number of 2OC particles in
both spectra. This concluded that the 20C nuclei passed through the implantation
detector with negligible implantation of 20C.

The beta decay of 22N produces the beta decay daughter 220, the beta-delayed
one neutron daughter 210, and granddaughters of 22F and 21F as was indicated in
Figure 1.8. In addition, the beta decay chains of 25F and 24O, which were impurities
of the beam, were observed in the same experiment and they will be addressed sep—
arately. It is important to know whether all daughters and granddaughters produced
from the beta decay of the parent have achieved their saturation activities under the
experimental conditions, as the activities of the daughter decay chains were used to
calculate the beta decay branch to the ground state and total neutron emission prob-
ability. Simulations were carried out to demonstrate the saturation of the activities
during the experiment.

The 22N beta decay chain was modeled by using the Bateman equations [01]
including beam-on / off mode effects. The simulations were done at. a constant implan—
tation rate of 100 pps during the beam—on time. Hence. the activity of the parent
grows during the beam—on period and the activity then decays to daughters and sub-

sequently to granddaughters during the beam-off period. The activity that did not

60

Table 4.1: Beam of composition of 22X experiment. after the A1900 and at the im-
plantation detector.

 

 

 

 

 

N uclide Purity at A1900 Purity at implantation Half-life
(C70)1 detector (‘70) (ms)
TN 498 51.8 24(5)?
2517 27.6 35.6 90(9)3
240 8.1 12.6 65(5)4
200 3.5 - 14(+6—5)5

 

 

 

110alQBe, 819Li and 6He contributed to the remaining 11%
2Average from Refs. [518,112,411]

3From Ref. [10]

4From Ref. [031]

5From Ref. [318]

decay during the previous cycles was added to the next cycle in addition to the growth
and decay of nuclei produced during the present cycle. For example, the nth cycle has
the decay contributions from all previous (n-1) number of cycles in addition to the

H1. cycle. The activities were added to find the final

growth and decay during the n
activity. The relationship between the beta—delayed neutron daughter decay chain and
the direct beta decay chain was established based on the literature neutron emission
probability. Figure 4.2 shows how the total activity varies with time for all nuclei in
the decay chains. The growth and decay of 22N during the first 4000 ms is shown in
Figure 4.2(a) and the decay curves of 22O and 22F are shown in Figure 4.2(b) and (c),
respectively. The figures indicate that the activities of the daughter and the grand-
daughter approach saturation after the first 40 s of the experimental time. One can

conclude that the parent and daughter activities in this decay series were saturated

given that each data taking run was approximately 30 minutes long.

4.1.1 Total Number of Beta Decay Events

The calculation of the neutron and gamma-ray transition probabilities required knowl-
edge of the total number of beta decay events registered in the implantation detector

from a particular decay. In general, the integration of decay curve during the exper-

61

(a) (b)

 

 

 

 

 

 

 

 

 

 

 

A 120 —w~———~ —~—~——-——#, ’\80.fl.__m.1___mgw____
z; 100 :3 70
g ‘ a 60'
V 80' v50
3. 60 3140
“H -H 30
40
34 .3 20
5 20 ‘6 10
a: , g -1 n: , _ A
1000 2000 3000 4000 5 10 15 20
Time (m8) Time (s)
(C)
A 80
5 70»
' 60
f0
”’50
5140
g 30 .
-r-1 20
8 10
Kt _.___ .L_._____.. A A
10 20 3O 40
Time (s)

Figure 4.2: Growth and decay curves for the 22N decay series calculated using a decay
model with a production rate of 100 pps for the parent of the decay series. The beam
on/off modes were included in the calculation. (a)22N activity curve, (b)22O activity
curve and (c)22F activity curve are plotted as a function of time.

imental run time can be used to deduce the total number of beta decay events. The
individual decay contribution from a particular nuclide was extracted by fitting a
decay model to the decay curve. The decay model was developed as explained above.
The Bateman equations were written for all implanted nuclei and their decay chains
including the beam-on/off effects to model the beta decay events observed at the im-
plantation detector. The fit to the beta decay curve was performed using this model,
where four parameters, namely the half-life, the total neutron emission probability
and the initial activity of 22N, and a flat background, were allowed to vary freely.
The ratios of implanted radioactive nuclides measured from the dB and Veto detec-
tors were used to fix the initial activity ratios of the impurity nuclei. The half-lives of
all daughters and granddaughters. which are reported in the literature [1%)] ( values are
given in Appendix A). were kept as constant through fitting procedure. The half-lives
of 25F and 24O. which were deduced in this work to be 73(11) and 53(8) ms. respec-

tively, from the gamma-ray gated decay curves. were included in the model as fixed

62

 

 

1000 5' fi“ ' ~:.-m-.;-:, Jittw
E Daughter decay + Backgorund

 

 

 

 

(I)
E I
a
o- 100E
\
w W
E . 240
D
O 10 y
0 E
C l l l n l L 1 A
20 4O 60 80 100
Time (ms)

Figure 4.3: Ungated beta decay curve of the 22N experiment. The individual decay
contributions from the implanted nuclei are shown with the total decay contribution
from daughters and granddaughters and the background.

values. The reported neutron emission probabilities of 23(5)% [16] and 58(12)% [:58]
for 25F and 240, respectively, were also used. Figure 4.3 shows the individual decay
contributions from each implanted nuclide, their daughters and granddaughters, and
the background to the total decay.

The individual components to the total decay curve fitting in Figure 4.3 were in-
tegrated through the beam-off period to determine the total number of detected beta
decay events, which are given in Table 4.2. The half-life of 22N, given in the same
table, was a result of the fitting procedure, since the, other half-lives were taken to
be fixed values. The total number of beta decay events corresponding to the individ-
ual nuclide decay were used to calculate the l:)eta—delayed neutron and gamma-ray

emission probabilities.

63

Table 4.2: Detected beta decay events from the 22N experiment.

 

 

 

Nuclide Total number of Half-life Literature Half-
beta decay events (ms) life (ms)
221V 5.58(2)><10‘I 21(7) 24(5)
25F 3.84(4)x104 73(11) 90(9)
240 1.37(4)x103 53(8) 65(5)

 

 

 

 

 

4.1.2 The analysis of the neutron time-of-flight spectrum

from 22N cocktail beam

The analysis of the neutron time—of—flight spectrum included the identification of the
beta-delayed neutrons with their energies and emission probabilities. Figure 4.4.(a)
shows the beta-delayed neutron time—of—flight spectrum from the 22N experiment,
which was generated by adding individual neutron spectra of all 16 neutron bars.
The prompt peak, which results from relativistic electrons from the beta decay and
travel from the implantation detector to neutron detectors, was centered at channel
45.4 for all neutron detectors. These electrons traveling at. a velocity near the speed
of light were used to establish a time reference for the neutron time-of-flight measure-
ments. The small peak marked as “Cosmic-ray peak” is the result cosmic-rays passing
through the neutron detectors first and the implantation detector. The peaks to the
right of the prompt peak in Figure 4.4.(a), which are expanded in Figure 4.4.(b), are
considered to be neutron peaks from the beta decay of the implanted nuclei.

The neutron peak shapes were defined based on the peak shape calibration dis-
cussed in Chapter 3. The coefficients of the peak shape calibration, given in Figure 3.9,
and appropriate asymmetric factors were used in the DAMM program to define the
peak shape at. a given. peak position. In addition, the channel number regions of 80-
95 and 105—120 were tested with giving different positions as initial gausses for the
peak positions and changing the number of peaks for the region to check for other
combinations that. might fit. the spectrum under the given peak shape constrains.

A tliird-m‘der polynomial function was used to fit. the background as discussed in

(34

1 00 50

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

. to b
* A/Cosmic-ray peak (a) ' lg ( )
a; 80 - — 4o _ "
C 8 :2
g B-yprompt peak g 8 no N
'5 60 - .: 30¢ 1 3 K:
\ N k 0 co F5 .. " "
m eutron pea s \ m a, N R’ ii I l
H '— ('3
g 40 - ‘2' 20 Pm g N ‘ i I g 8
0 i 8 y l .l ll 1 ' . '- "
O O i ll “Ll lv V "'3
20+ 10 » ll 1 . A,
l .41 i L l A I . I o . 1 A J . l A L L l L L
40 60 80 100 120 140 160 180 80 90 100 110 120 130
Channel number Channel number

Figure 4.4: Neutron time-of-flight spectrum from the 22N experiment. The (a) Beta-
delayed neutron time-of-flight spectrum shows the prompt, Cosmic-ray and neutron
peaks. The (b) Neutron peaks were fitted with ten asymmetric Gaussian functions
and a background. The neutron energies are given in keV above the peaks.

Chapter 3. Figure 4.4.(b) shows the fitted neutron time-of—flight spectrum, where the
best minimum reduced X2 value was achieved with ten asymmetric Gaussian peaks
and the background. The peak fitting results given in Table 4.3 were used along with
the neutron energy and efficiency calibrations to determine the neutron energies and
the associated number of neutrons originated from the beta decay, respectively. The
calculated neutron energies and the number of neutrons for each neutron peak in
Figure 4.4(b) are. given in Table 4.3 were used to assign the neutron energy groups to
the beta decay.

The assignment of a delayed neutron transition to a particular beta decay parent
is generally done based on the half-life. The half-life curves gated on neutrons were
generated for this purpose. The statistically significant decay curves were fitted with
a single decay constant and flat background. The half-life, the initial activity and the
background were free parameters of the fit. Figure 4.5 shows the fitted neutron-gated
decay curves along with the neutron energies in keV and resulting half-lives in ms.
The neutron-gated decay curves generated from the neutron peaks of 2791, 3274 and

4069 keV, which are not. well resolved, were not analyzer] due. to their poor statistics.

Table 4.3: The neutron time-of-flight data from the 22N beta decay experiment. neu-
tron energies and neutron gated half-lives.

 

 

 

 

 

 

 

 

Peak Area (Error%) F WHM Energy Gated Number of
position (Error%) channels (keV) half-life (ms) neutrons
73.9 53(17) 3.55 5178(24) 18(4) 1808(36)
78.1 44(19) 3.80 4069(15) — 1437(13)
82.2 55(17) 4.04 3274(11) — 1621(14)
85.6 51(20) 4.50 2791(8) - 1762(3 5)
89.3 121(11) 4.50 2370(6) 22(5) 3688(51)
95.6 223(8) 5.72 1845(4) 22(4) 7127(72)
101.5 144(11) 6.65 1498(3) 16(5) 5130(61)
108.2 148(12) 7.81 1212(2) 68(16) 6400(83)
114.1 98(17) 9.17 1021(2) 20(5) 5341(62)
125.4 68(29) 11.50 763(1) 18(6) 6589(70)

 

 

The analysis of these data shows that neutron energy groups of 763, 1021, 1498,
1845, 2370 and 5178 keV originated from the same beta decay as their half-lives are
in reasonable agreement. Moreover, these neutrons have been assigned to the beta
decay of 22N, since the average gated half-life of 19(2) ms agreed within uncertainties
with the average literature half-life of the 22N beta decay [10]. The neutron peak at
1212 keV had a gated half-life of 68(16) ms, which is clearly different from the half-
lives of the other neutron groups. A comparison of the half-life with the literature
half-lives of the implanted nuclei indicated that this neutron group could originate
from either 25F or 240 beta decay. Further assignments of neutron groups were made
based on the intensity requirement by the desired decay scheme and will be discussed

below.

4.1.3 Gamma-ray Identification

The total beta-gamma coincidence spectrum obtained from the 22N cocktail radioac-
tive beam, shown in Figures 4.6 and 4.7, contains beta-delayed gamma—rays events
from the 22N, 25F and 24O decay chains observed during the beam—off time period.
The identified gamma transitions are labeled based on their parent decay. The gamma-

ray assignments were made based on the half—lives obtained from gamma-ray gated

66

 

 

 

20 , 24 20

I = -
15. E" 363 20. En'1021 16’ En =1212
12 {10'1“6) 16’ + t1,2=20(5) ("2:53am
. l

  
   

 

 

 

 

 

 

 

 

 

00 20 40 60 80 10000
28.
24_
20

 

 

 

  
    

En= 1498
t1,2=16(5)

   

 

 

 

 

 

 

 

 

 
 
    

(D
E
:16»
$12> f
5 °’
0 3’ . 1+. . 0
0204060801000204060801000020406080100
20
En=5178
16-
Mafia“)

12

4r

 

 

 

00 20 in 60 so 100
Time (ms)
Figure 4.5: Neutron gated decay curves from the 22N experiment. The neutron ener-

gies in keV and half-lives in ms are shown.

decay curves, the experimentally known gamma-ray transitions and intensities, dif-
ferences between experimentally known energy levels of possible daughters, and the
observation of peaks in the beta-gamma—gamrna triple coincidence spectra. In addi-
tion, the gamma-ray transitions from the beta decay of long lived isotopes such as
60Co, 40K and 208T1 were also observed in the unshielded detectors and are labeled
in Figures 4.6 and 4.7.

The gamma-ray transitions with energies 637, 708, 918, 944, 1863,1874 and 2501
keV were compared with the observed gamma-ray transitions in the 220 beta decay
studies reported by Hubert. et al. [65] and Weissman et al. [66]. The agreement of
the gamma-ray energies and their intensities leads to the conclusion that the above
gamma-ray transitions can be attributed to the beta de(.:ay of 220, which is the
daughter of the 22N beta decay. The summary of all observed gamma-rays with their
intensities and assignments are given in Appendix B. The known gamma-ray peak

at 72 keV from 220 was not observed in the spectrum reported here due to the

67

 

200

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_37 349 438
76 25 278 21,: 492
c 1 _. Ne 386 23
6 100 i ”°
W .
E 50
8
O 0
_ 200
0’ .
E
m 150
‘5
\ 100
.59
5 50
8
0
3 1057 e 1275 1386
E120 r1017 20 “fps 2 , 1312 22N
m 623 0 pea F ' 1395
.1: F 1071 1236 24o 1369 1451
\ l 25Ne 22N 25': N8 ' 21F
.03 r _ \\ l
g 40 ,1 ,
O 1. 1‘
0 O l l l I 1
1000 1100 1200 1300 1400 1500
- 75 16231634 1701 1703 1863
0:J 1616 1731 17881820
C 25 25F 2'F 23 25F 21o 231: 0
«350. F\ 1674 R/ 21o 1332 137
'8 1613 22 . 1751 j 240 20
£2
E 25
3 1
o
o O l l l
1 500 1 600 1700 1800 1 900

Figure 4.6: Total beta-gamma coincidence spectrum from the 22N experiment: Part.
I. Gamma-rays are labeled with their parent nuclei and energies in keV.

68

80

 

 

 

 

 

 

 

 

E 11885 1918 1983 2084 2090 2167 2203
c 60 .210 23 24 22F 25 F
g 1901 F F F2127 2187 25MB Escapefi
g 40 _ 22F 23,.- 251= peak
.9 .
S 20 .
o
0 l l l i
1900 2000 2100 2200 2300
40
a _ 2756
c 24 3198
C 30 _ 2501 Na
2 . 220 Escape 1 2992 3002 2214
o 20 Peak 22 24o 3312
\ - F
a \ \ / 22N
S 10
0 ~ * , ~, .
O ' ' 1
0 1 l L l l
2400 2600 2800 3000 3200 3400

Figure 4.7: Total beta-gamma coincidence spectrum from the 22N experiment: Part
II. Gamma-rays are labeled with their parent nuclei and energies in keV.
low energy threshold limits (about 78 keV) of the SeGA detectors. The gamma-ray
transitions from the beta decay of 22F, the granddaughter of 22N, reported by Davids
et a1. [67] were found at energies 1275, 1901, 2084, 2167, 2992 an 4372 keV and their
relative intensities agreed with those published in Ref. [67]. The rest of the gamma-ray
transitions from the beta decay of 22F reported by Davids et al. were not observed
here due to their low intensities.

A beta decay study of 210. the beta-delayed single neutron daughter of 22N, was
reported out by Alburger et al. [68.]. They observed gamma-ray transitions at ener-
gies 279.92(6). 933.2(3). 1450.5(2). 1729.2, 1730.28(8).

1754.74(8). 1787.16(8),

1884.01(9), 3179.43(10). 3459.38(13), 3517.40(10), 4572.2(4) and 4.5835(3) keV.
The highest absolute intensity of 45.6(6)% for the 1730.28 keV gamma-ray transi-

tion was reported in the 210 beta decay. The transitions at 278(3), 933(3), 1451(6).

69

1731(5), 1751(5), 1788(5) and 1885(4) keV were observed in the present work, shown
in Figures 4.6 and 4.7, and assigned to the beta decay of 210 based on the energies
and intensity ratios (given in Appendix B) that match with the reported values within
uncertainties. The other known transitions did not. have significant intensities to ob-
serve in this spectrum. The granddaughter of the A = 21 decay chain is 21F, which
was first studied by Harris et a1. [69] and later, by VVarburton et al. [70] has fifteen
known gamma—ray transitions (see in Appendix B). The most intense gamma-rays
with energies at 351 and 1395 keV were observed in this work.

Apart from the gamma-rays associated with the direct beta decay chain and the
beta-delayed single neutron daughter decay chain of 22N, gamma-rays attributed to
the A = 20 mass chain, which was not implanted in this experiment, were found
in the beta-gamma coincidence spectrum. The only mechanism that leads to the
A = 20 mass chain is the emission of two neutrons from the beta decay of 22N.
Note that 21O is not a delayed neutron emitter to feed the A = 20 mass chain. The
gamma-ray transitions observed here with energies at 1057 and 1634 keV agree with
those having energies 1056.78(3) and 1633.602( 15) keV reported in the beta decay
studies of 200 and 20F, respectively. shown in Figures 4.6 and 4.7. They are the only
major transitions originated from these beta decays and have emission probabilities
of 99.975% and 99.9995%, respectively. The consistency of energies and emission
probabilities for these respective transitions in this experiment with the corresponding
reported values suggests that the above transitions originated from the beta decay of
200 and 20F, respectively. The identifications were confirmed by their gated half-lives.

The assignment of the gamma-ray transitions to levels of 220 following beta decay
of 22N was carried out based on the 1.)revious knowledge of gamma—ray decay in the
nucleus. The 1386, 3198 and 3312 keV gamma-ray transitions shown in Figures 4.6
and 41.7 and cited in Refs. [21,371.22L‘J‘3] were also observed in the present study. The
rest of the gamma-rays attributed to 220 were not observed in the present. work.

In addition, the 1221 keV tremsition. which was reported by Stanoiu et al. [21] as

70

 

 

 

 

 

 

 

  
   

8 -
«n 4 .
E r
V 0 . . . .
B 0 20 40 60 80 100
*1; 16
o ’ E = 3198
Q 12 -

11,2 = 24(3)

 

 

    
     

0 20 A 40 60 l 80 100
Time (ms)

 

o b m
' I

Figure 4.8: Two gamma gated half-lives from the 22N beta decay with gamma-ray
energies in keV and the gated half-life in ms.

belong to the gamma-ray decay in 210, was identified in this work. The gamma-rays
at 881, 1845, 2133. 3026 and 3070 keV presented in the gamma-ray decay scheme
of 210 [21] were not visible. However. the observed gamma—ray at 2129 kev, which
matched with the 2133 keV energy within uncertainties, was assigned to the beta
decay of 23F based on the relative intensity ratios in the same decay. The 1675 keV
transition was identified as a gamma—ray in 200 as reported in Ref. [21,31]. There
were no other reported gamma—rays related to the 20O gamma-ray decay scheme were
observed. Decay curves in coincidence with gannna—rays at 1221 and 3198 keV, given
in Figure 4.8, yielded an average half—life of 24(3) ms which is consistent with the
literature value for 22N beta decay [10]. The decay curve gated by the 1675 keV

transition could not be evaluated due to poor statistics.

4.1.4 Beta Decay Scheme of 22N

The beta decay scheme of 22N determined from the present. work is shown in Fig-
ure 4.9. The following presents the neutron and gannna-ray assignments to establish
this decay scheme. The gated decay curve. analysis on the neutron time—of—fiight spec-
trum showed six neutron peak with energies at 763, 1021, 1498, 1845, 2370 and 5176

. . . 4 r) . . .
keV had half-lives consistent with the l,)e.ta. decay of 2"N. In a.(.l(htlon, the gamma—ray

71

22
20(2) ms
N‘ Q =22750 keV

———49'6”6 /° 13298

._'_,

12121237 7649

W 6510

4 4
"3% 3728
1513)%
<31.6%

 

1011')
p, = 571519. P1,. = 33131% P2n =12131%
[0-,l-,2‘)
-—--—> ............ K
3.21 61% 20839
5178132)

‘. $2,311; 50:"); o,’.’-: .9664
" "“ ' " ‘ 4.2791131)

 

(07172 ’ 102119.61

 

5128 1674 2+
‘ ' 12674122) 0,

 

 

 

 

 

(0' 1‘2 2) 237°“ 61200 6,, = 3806

 

 

 

 

 

 

 

11/2")
..‘.°.:.‘.:?.’...‘_i’\i‘5“~k 1 2210-001 ‘2'“ 62 1
763112) 2, S 06850
3312120) 2: O =
1138617) 2+
3198124)
1

 

 

22(:)

Figure 4.9: Beta decay scheme of 22N. The average half-life in ms, which was deduced
from all neutron and gamma-ray gated half-lives, single and two neutron emission
probabilities are given. The neutron transitions shown with dashed arrows have un-
certainties in their placements due to the possibility of interchange their assignments.
The heights of the shaded boxes in 200 represents the limits that level can be varied
due to the interchange of neutrons. The average energies of these levels are given. The

transition probabilities for the neutrons and the gamma-rays are given in parenthesis
with their energies in keV.

transitions at 1221, 1386, 1674, 3198 and 3312 keV were identified as belong to the
22N beta decay. The gamma-ray at 1221 keV. which has been placed to the level at
1221 in 210, (see Table 4.4), was based on the knowledge of the gamma-ray decay
scheme [21] of particular nucleus. This gamma-ray transition required the feeding of
7.0% from the total 22N beta decay based on the observed gamma—ray intensity. This
requirement could be satisfied by the neutron transition of 2370 keV based on an in-
tensity match, therefore, the 2370 keV neutron transition was tentatively assigned to
the state at 10545 keV in 22O as shown in Figure 4.9. The analysis of the gamma-ray
activities of 210 beta decay showed that the single neutron emission probability is
33(3)% for the 22‘N beta decay. This requires feeding of 26(3)% to the ground state of
210. Note that the parent and daughter activities in this decay series were saturated
during the 30 minute-long runs as showed in the simulation, hence, it was reasonable
to determine the absolute emission probabilities from the daughter activity. The neu-
trons with energies 763 and 1845 keV were placed as depopulating levels at 7649 and
8782 keV in 220, respectively. Such placement order is necessary to feed the ground
state of 210 as they cannot fulfill any other intensity requirement of a state in 22O.
The observation of a 1674 keV gamma-ray with an intensity of 2.2% in 200 suggested
beta-delayed neutron decays to neutron unbound states in 210 which subsequently
decay to 200 as shown in Figuer 4.9. Note that the mass chain A = 20 was not im-
planted. The energy levels of 200 are well-known from previous experiments [21,31]
and the observed 1674 keV gamma-ray was identified as depopulating the 1674 keV
state in 200. The difference of 9.8(4)% between the gamma-ray feeding to the ground
state of 200 and the number of 200 beta decay events derived from daughter gamma-
rays suggested some feeding to the ground state of 2”O. Two neutrons with energies
of 1021 and 1498 keV emitted in sequence match the feeding requirement to the
ground state of 200 as they have the same neutron emission probability (9.6(16) and
9.2(10)%, respectively). The neutron triple coincider’ice events were not, observed to

establish the sequence. However, there were two possible ways to place these neutron

73

decays. One way was to assign the 1021 keV neutron as depopulating a 13298 keV
state in 22O and place the 1498 keV neutron to a state at 5379 keV in 210. The second
way was the interchange the order of emission. The proposed energy of 5379 keV state
in 210 would then be lowered by 501 keV while the energy of the proposed 13298
keV state in 220 would remain unchanged. The 5379 keV state in 21O is presented
in Figure 4.9 as 5128 keV, which is the average energy of the above mentioned limits,
and the uncertainty of the state is shown by the shaded box. Feeding to the state at
1674 keV in 200 was possible with the sequential emission of the 5178 keV neutron
and one of the neutrons with energy 2791, 3274, or 4069 keV, since they have similar
emission probabilities. However, the sequential neutron transitions of 5178 and 2791
keV were assigned to feed the 1674 keV state in 200 based on the available energy
window. The 2791 and 5178 keV neutrons were assigned to the states at 8411 keV
in 21O, and at 20839 keV in 220, respectively. These assignments are also subject
to an interchange of the order of emission, which would increase the energy of the
proposed 8411 keV state by 2506 keV. The average energy of 9664 keV is represented
the 8411 keV state in 210 in the figure and the uncertainty is shown by the Shaded
box. The summary of the neutron assignments is given in Table 4.4. In addition, the
gamma-ray transitions with energies 1386, 3198 and 3312 keV were placed, as given
in Table 4.4, in the 220 levels to be consistent with the previous work [21]. The beta-
delayed gamma-gamma coincidence events were not useful for placement due to poor
statistics.

Figure 4.9 shows decay to the single-neutron daughter. 210, with a single neutron
emission probability of 33(3)% and to the two-neutron daughter, 200, with a two-
neutron emission probability of 12(3)%. The total neutron emission probability (P,,)
for the beta decay of 22N was 57(5)% and was deduced by adding the weighted neutron
emission probabilities of both daughters [Pn = 1P1" + 21’2"]. The beta branching
ratios given in Table 4.5 have been calculated by considering the intensity flow through

the (ilecay scheme. The transititm probabilities for both neutrons and gz'imina-rays

Table 4.4-: Assigmnents of gamma-ray and neutron energies for beta decay of 22N.

 

 

 

 

 

 

 

Gamma-ray Emission N uclide Energy
energy (keV) probability (%) level(keV)
1386(4) 3.0(16) 22o 4584
319818) 21(3) 220 3198
3312(5) 211) 22o 6510
1221(3) 7.0111) 2lo 1221
1674(3) 2.2(12) 200 1674
Neutron Emission Nuclide Energy
energy (keV) probability (%) level(keV)
763(1) 1213) 220 7649
1845(4) 13(1) 220 8782
2370(6) 6.6(7) 220 10545
102112) 1 9.6(16) 210 4878 2
5178(24) 3 3.216) 220 20839
149813) 1 9.2(10) 220 13298
2791(8) 3 3.1(6) 210 84114

 

 

 

1The order of emission could be interchanged.
2This could terminate at the level at 5378 keV.
3The order of emission could be interchanged.
4This could terminated at the level at 10917 keV.

are given in parentheses following the transition energy. The energy levels shown in
the shaded boxes represent the uncertainty introduced by the interchanging of the
order of the sequential neutron emission. The neutron decay of the highest observed
energ level in 220 has been displayed with dashed lines due to uncertainties in these
assignments. The average half-life of 20(2) ms shown in Figure 4.9 was deduced from
the neutron and gamma-ray gated decaycurves given above. The apparent log(ft)
values given in Table 4.5 were calculated as explained in Ref. [71] using the Q-value
of 22750 keV [19], the half-life of 20 ms and the observed beta decay branching
ratios. Five states in 22C) were assigned negative parity while the observed neutron
bound states were assigned positive parity based on the log(ft) values and beta decay
selection rules. The possible spins for the negative parity states are 0. 1 or 2 assuming

allowed beta (‘lecays from the 0‘ or 1‘ ground state of 22N [18]. All bound states

\I
L“!

Table 4.5: Properties of the 22N beta decay.

 

 

Energy Branch Log(ft) Spin B(GT)
level (keV) (%) parity
0 < 31.6 5.82 0+ 0.006
3198 15(3) 5.79 2+ 0.006
4584 7(3) 5.95 3+ 0.004
6510 2(1) 6.24 2+ 0.002
7649 1213) 5.30 0~, 1-, 2- 0.020
8782 1311) 5.26 0-, 1—, 2— 0.022
10545 6.6(7) 5.08 0‘, 1‘, 2“ 0.033
13298 9.6(16) 4.52 0-, 1-, 2- 0.12
20839 3.2(6) 1.67 0‘“, 1‘, 2" 84

 

 

 

 

 

 

 

observed in present work of 22N beta decay were known by several experimental
work. The spins of the positive parity bound states in 220 should be 0, 1, 2 or 3
to satisfy the selection rules of the first forbidden decay. However the spins of the
bound states, shown in Figure 4.9, were assigned based mostly on previous work. The
spins and parities of the observed states in 22O are given in Table 4.5. The spins
and parities for states in 210 and 200, shown in Figure 4.9, were adOpted from the
literature [21,34]. The Gamow-Teller strengths for beta. decay to the observed states
in 220 were calculated as explained in Chapter 2 and reported in Table. 4.5 for later

comparison with shell model calculations.

4.2 Beta Decay of 25F

The largest contaminant of the implanted beam was 25F. The beta decay of 25F
populates levels in 25Ne, which can provide indirect information on the existence of
N = 16 shell gap in the Ne isotopes. The shell structure of 25Ne has two valence
protons in the 0(15/2 orbital and one valence neutrons in the ISI /2 orbital. It. has been
argued that the assignment of 1/2+ to the ground state of 25Ne with a negligible
contribution from the 0d3/2 orbital provides evidence a the large energy gap between

the ISI /2 and 0113/2 single particle states [16. 72.]. The recent n'ieasurement of 25F

76

beta decay and comparison with USD shell model calculations by Padgett. et. al. [16]
claimed the location of 0(13/2 moves closer to the fp shell increasing the N = 16 shell
gap for the Ne isotopes. This work also showed a considerable discrepancy in the shell
ordering between the experimental and the USD calculated energy levels for the first
3/2+ and 5/21L states. However, it is important to accurately determine the energy
states in 25Ne in order to understand the N = 16 shell gap in the Ne isotopes.

The half-life and total neutron emission probability of the 25F beta decay were
first reported to be 59(40) ms and 15(1)%, respectively, by Reeder et al. [39]. An-
other experiment was carried out using four Ge detectors and 42 He proportional
counters by Reed et al. [63] and reported a half-life of 50(6) ms and a total neutron
emission probability of 14(5)%. This work also reported four gamma-ray transitions
of 574.7(5), 1613.4(12), 1702.7(7) and 2188.6(1.3) keV associated with three energy
levels at 1702.7(7), 3316.1114) and 38908115) keV in 25Ne. The recent beta decay
study by Padgett et al. ['16] published three gamma—rays at 1234, 1622 and 2090 keV
associated with energy levels at 2090 and 3324 keV in 25Ne. The half-life of 90(9) ms
was reported in the same work, which is much longer than previously reported values
except for the value of 70(10) ms measured by Penionzhkevich [62]. The reported
total neutron emission probability of 23.1(4.5)% from the work of Padgett et al. is
reasonable agreement. with the previous values. Although the average total neutron
emission probability of 17% was reported from all measurements, the beta-delayed
neutron energies leading to neutron unbound states are not. known at present for the
2"3F beta decay.

The energy level structure of 25N e was first investigated by Wilcox et al. [73] using
the reaction 26l\tlg(7Li, 8B)25N e. Five excited states up to 4.7(1) MeV was observed.
Woods et a1. [71] had studied the reaction 26Mg(13C, 1"10)25Ne and measured four
excited states in 25Ne including a level at 628(5) MeV, which is 2.7 MeV above
neutron separation energy. A study based on a single step fragmentation experiment

by Belleguic et al. [75] reported two cascading gamma—rays of 1617(5) and 1707(4)

77

 

 

 

 

 

 

 

 

 

 

 

Figure 4.10: The 25F beta decay chain. Beta decay chains end with stable 24Mg and
25Mg shown in black squares.

keV associated with the 1707 and 3324 keV levels. The recent investigation using
the direct one—neutron knockout reaction by Terry et al. [72] reported three gamma-
rays corresponding to three energy levels in 25Ne with their spectroscopic factors. In
addition, the spins and parities for the first three excited states in 25Ne have been
assigned as 5 / 2+, 3 / 2+ and 5 / 2+, respectively. The ground state of 25Ne was reported
to be 1/2+ in all experiments. No neutron unbound states except the 6.28 MeV state
and no negative parity states were observed in 25Ne.

The beta decay of 25F produces the beta decay A = 25 daughter chain and the
beta-delayed neutron A z 24 daughter decay chain has shown in Figure 4.10. The
variations in the activities during the experiment were checked by a decay model
incorporating all decay chains under the experimental conditions similar to that for
22N discussed above. Details of the model and the method are given in the 22N ex-
periment. section and Appendix A. The simulated activity curves for nuclei in the 25F
beta decay chains, shown in Figure 4.11. shows that all daughters and granddaughters
reach their saturation activities within the first 400 s of the experiment. The input
parameters for the simulation such as half-lives of all decays and the total neutron

emission probability of 23F were taken from literature [19] and also are. presented in

78

 

 

 

 

 

 

 

 

A120____,_,,,,,,1,, A80>———— —’ -fl11’m
:3 100] :5 70
.3 a 60
:1 6O 3‘40
r-i -r—1 30
401
Z 1 .3 20
8 20 S 10
<C _ __4_ ._-._..._.1_.__H WW4 4: _ ____4_ - __
1000 2000 3000 4000 5 10 15 20
Time (ms) Time (s)
(C)
A 80 ~——»~«~
5 70
m 60
“’50
5:40
g 30
-'-1 20
8 10
Kt ___l

 

 

 

100 200 300 400
Time (s)

Figure 4.11: Growth and decay curves for the 25F decay series calculated using a
decay model with a production rate of 100 pps for the parent of the decay series for
(a)25F activity curve, (b)25Ne decay activity and (c)25Na activity curve.

The beam on / off modes were also included in the calculations.
Appendix.B.

The assignment of gamma—ray transitions to the 25F beta decay chains was per-
formed based on the knowledge of those beta decays and the extracted half-lives from
the gamma—ray gated decay curves. Ganuna—rays with energies 87, 981, 1071 and 2203
keV were associated with the beta decay of 25Ne (see Figures 4.6 and 4.7). Gamma-
rays at 386, 583, 976 and 1613 keV from transitions in 25Mg following the beta decay
of 25N a were also present. The intensities of transitions agreed with previous measure-
ments, thus confirming their assignments. In addition to the beta decay mass chain
of A = 24 introduced by the implantation of 240, the beta-delayed neutron decay
daughter chain of 25F also prmluced 2"Ne and 2‘lNa from subsequent. beta decays.
Therefore, the 1983 keV level in 2‘1Ne. which is the only reported state in 2'1Ne. has
two feeding patlnyays, namely, the direct beta decay of 2‘11: generated from the A =
24 mass chain and feeding from the beta—delayed neutron decay of 25F. In addition,

the gamma-ray at 1983 keV from the 2"IF beta decay, 474 and 876 keV from the. 2‘lNc

 

 

16' E = 572
’ 11,2 = 65113)

  

 

 

 

 

 

 

 

 

Counts I4 ms

 

12- E=2090
1,,2=79(19)

  

 

 

 

4.

0 L 4% J g l A P

0 20 40 60 80 100
Time ms

Figure 4.12: Gamma gated half-lives for the 2BF beta decay. The gamma-ray energy
in keV and the respective gated half-life in ms are given.

beta decay, and 1369 and 2756 keV from the 24Na beta decay were observed and
are shown in Figures 4.6 and 4.7 confirming the A = 24 decay chain. All gamma-ray
energies, intensities and their decay assignments are given in Appendix B.

The 1703, 2090, 1616, 1236, 572 and 2187 keV gamma-ray transitions associated
with the beta decay of 25F were observed in the present experiment, which reconfirms
the observations reported in Ref. [16]. The gamma-ray gated decay curves displayed
in Figure 4.12 were created for transitions that had reasonable statistics and were
well resolved. The half—lives were determined from a fit using a single exponential de-
cay constant and a flat background. The resulting half-lives were consistent with the
literature values confirming their placement in the level scheme of 25Ne. The present
work did not observe new gamma—rays associated with decay of 25F compared to the
Padgett et a1. work. Therefore, the gamma-ray decay in 25Ne, shown in Figure 4.13,
was established to match the work of Padgett et al. Note that no beta-gamma-gamma
coincidences were observed in present work. The assignments are summarized in Ta—
ble 4.6 along with their gamma-ray emission probabilities.

The beta decay scheme of 25F, shown in Figure 4.13, was generated from all

80

Table 4.6: Gamma-ray and neutron energies assignments for the 23F beta decay.

 

 

 

 

Gamma Emission N uclide Energy
energy (keV) probability (%) level(keV)
572(3) 1212) 25N8 3889
1236(3) 712) 25Ne 3326
161614) 11.2138) 25NC 3315
162314) 10.6138) 25Ne 3326
170313) 3115) 25Ne 1703
209015) 2514) 25NC 2090
2187(4) 512) 25N8 3889
198315) 19.4120) 24Ne 1983
Neutron Emission Nuclide Energy
energy (keV) probability (%) level(keV)
121212) 1712) 25Ne 7426

 

 

 

 

 

 

gamma-rays discussed above and the neutron transition identified from this work.
The following will be discussed the neutron identification. The analysis of the neu-
tron time—of—flight spectrum in the 22N experiment suggested that the neutrons with
energies 1212, 3274 and 4069 keV could originate from 25F or 240, as they could not
be assigned to the 22N beta decay. The high uncertainty of the neutron gated half-life
of 68(16) ms for the 1212 keV neutron could match the half-lives of either 25F or
240. However, the assignment to 25F was based on the intensity requirement for the
25F beta decay neutron daughter branch from the independent gamma—ray measure-
ments. The only known state at 1983 keV in (“Ne [76,133, 16] can be populated either
by the decay of 24F (100% of beta goes to this state), the daughter of 240, or by
delayed neutrons from 25F decay. The contribution from the 21F beta decay to the
1982 keV state in 24Ne was reasonably well known from the neutron emission proba-
bility of 2‘10 (see the beta decay of 2"10). The feeding requirement to this state from
the l.)eta-delayed neutron decay of 25F has been calculated by taking the difference
between the total number of ol‘)served 1982 keV gamma-rays and the contribution
from the beta decay of 2'40. Moreover. the neutron feeding was also calculated inde—
pendently from the gamma-ray activities of 25Ne. which agreed within uncertainty

with the above calculation. By considering both values, the average total neutron

81

emission probability of the 25F was found to be 19(2)% from the gamma-ray activity
analysis. This value agreed with neutron emission probability of 17(2)% for the 1212
keV neutron energy group and with all reported P", values within uncertainties [16].
Combinations of other neutron paths were considered but they failed to satisfy the
feeding requirement by the state at 1983 keV in 24Ne. Therefore, the neutron energy
of 1212 keV depopulates the neutron unbound new state of 7426 keV in 25Ne as given

in Table 4.6 and Figure 4.13.

25F 73111) ms

{— 115/2+) Q =13330190] keV (2n = 19(2191,
.__, 7426 3/2+.5/2+,7/2+)

 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

17(2)% 1212117)
2+
1983
1983119)
5 =4180
19131176...”n ......... . ,,,,,,,,,,,, 0+ 0
7514—12 3326) 157204) (5,25
° I
3315 1623111) 1616112)
1 7( 41% 123617) +
»———> 2090 ' 11 [ 1372,)
-—> (5/2 )
8161°/o [703 209024
( ) 1703136)
<21110)/o 0 f 112*
25Ne

Figure 4.13: Beta decay scheme of 25F.

The beta branching ratios were deduced by considering the. intensity sum rules.
The apparent log(ft) values, given in Table 4.7, were deduced using the method de-
scribed in Ref. [71] along with the reported Q value of 1333(9) MeV and the average
half-life of 73(11) ms deduced from all gated decay curves related to the 25F beta
decay. The spins and parities for the observed excited states were assigned based

on the beta decay selection rules assuming the spin and parity of the ground state

82

Table 4.7: Properties of the 25F beta decay.

 

 

Energy Branch Log(ft) Spin B(GT)
level (keV) (%) parity
0 <21110) <5.36 1/2+ >0.017
1703 8(6) 5.48 5/2+ 0.013
2090 1714) 5.08 3/2+ 0.033
3315 0 - — —
3326 1814) 4.80 5/2+ 0.062
3889 1913) 4.65 3/2+, 5/2+, 7/2+ 0.088
7426 1712) 3.72 3/2+, 5/2+, 7/2+ 0.75

 

 

 

 

 

 

 

of 25F to be 5/2+. Five allowed beta decay transitions were observed along with a
new neutron unbound state at 7426 keV. The spins and parties for states at 1703,
2090 and 3326 keV given in Table 4.7 were independently assigned and reconfirm the
values given by the works of Padgett et al. and Terry et al.. An upper limit of the
beta decay feeding to the ground state of 25N e was determined by taking the differ-
ence between the number of 25Ne beta decay events deduced from the corresponding
gamma-ray activities, and number of gamma-rays feeding from the excited states to
the ground state. The B(GT) values, given in Table 4.7, for the observed beta decay
transitions were calculated as explained in Chapter 2 for later comparison with shell

model calculations.

4.3 Beta Decay of 24O

24O was one of the contaminants that. was implanted during the 22N experiment.
The beta decay of 240 heads the decay mass chain of A = 24 and has a beta-delayed
neutron daughter in the mass chain A = 23. shown in Figure 4.14. The daughter
24F decays to the 24Ne granddaughter and subsequently, to the great-granddaughter
24Na. Finally, 2‘1Na decays to the stable nucleus 2’1 M g. In the case of the beta-delayed
neutron daughter chain, stable 23N a nuclei are produced from subsequent decays of
23F and 23Ne. The activity of nuclei originating from the 24O decay chain during

the first 1000 8 period of the experimental run were simulated to check whether they

83

 

 

 

 

 

 

 

240

 

 

 

Figure 4.14: 240 beta decay chain. The stable isotopes are shown in solid squares.

become saturated using the model described in Appendix A. The simulation used the
half-lives of all beta decays in the 24O decay chain as given in Appendix A. Figure 4.15
shows the activity build up of 240, 24F and 24Ne obtained from the simulation with
a production rate of 100 pps for 2"10. The activities become saturated after 1000 s.
The results from the simulation assured that the daughter gamma-rays could be used
to extract absolute gamma-ray intensities.

The heaviest bound oxygen isotope, 2"‘10, beta decays to 2’1F thus allowing the
study of the structure of 24F that has very little known information. The beta decay
of 24O was first studied by Mueller et al. [10] using a 471' neutron detector in coinci-
dence with a Si(Li) beta detector. They reported a half-life of 6115133 ms and a total
neutron emission probability of 58(12)%. In contrast to this measurement, Reed et
al. [63] obtained 65(5) ms and 18(6)% for the half-life and the total neutron emission
probability, respectively, from an experiment that implanted 9000 240 ions in a Si
telescope at GAN IL. The ganuna—rays were measured with four large Ge detectors
and neutrons with 42 He proportional counters. Although the half—lives agreed within
uncertainties, the total neutron emission probability has a large discrepancy. Three

gamn'ia-ray transitions with energies 521.5(3), 1309.5(5) and 1831.6(5) keV associated

84

 

 

 

 

 

 

 

 

 

 

 

 

 

”‘120r—————~ — fl 80r‘—~- e—eeeee~~—~—~ a
5 100- 5 g0
m _ m 0
a. 80 ~,50
3w 60> 3140
.H ‘H 30
40
.5 .3 20L
‘5 20 810
<12 A - - d: _ - -
1000 2000 3000 4000 5 10 15 20
Time (ms) Time (s)
(c)
”‘80
5 70
'60»
m
~'501
3140
g 30
-r-1 20'
‘5 10
Kt A A -
250 500 750 1000
Time (s)

Figure 4.15: Growth and decay curves for the 24O decay series were calculated using
a decay model with a production rate of 100 pps for the parent of the decay series
for (a)24O activity curve, (b)24F activity curve and (c)24Ne activity curve. The beam
on / off modes are included to the calculation.

with the 522 and 1832 keV levels in 24F were reported by Reed et al. and it is the only
information on excited states in 24F. The spins and parities of 2+ and 1+ have been
assigned to the 522 and 1832 keV states, respectively, based on comparison with shell
model predictions. In addition, the shell model calculations using the USD, SDPOTA
and CW(Chung and Wildenthal) interactions predicted other 0+ and 1+ states in
24F in addition to the previously reported states, such low spin states with positive
parities favored by allowed beta decay, but were not observed in the previous work.
Gamma-rays from these states might be observed in the present experiment because
the states are expected below the neutron separation energy.

The beta-gamma coincidence spectra from 22N cocktail beam are shown in Fig-
ures 4.6 and 4.7, where the gamma-ray peaks are labeled by their parent nuclei. As
explained in the analysis of the 25F beta decay, gamma-rays associated with beta de-
cays of 24F, 24Ne and 24N a were observed, and the energies and intensities are given

in Appendix B. Seven gamma—rays attributed to 23F decay and a single gamma—ray

 

 

 

 

 

 

 

 

 

 

12E- 5:520 12; E=1832
U)
E
V .
9 . . . . . oh . 1 - . .
g 0 20 40 1460 80 100 O 20 40 60 80 100
8 12: E = 3002

,0; t,,2=47(11)j

 
   

---.---.-++
o 20 4o 60 80100
Time(ms)

 

 

 

Figure 4.16: Gamma gated decay curves of the 240 beta decay. The gamma-ray
energies in keV and the gated half-lives in ms are shown.

at 439 keV from 23Ne decay were identified thus confirming the beta-delayed neu-
tron daughter chain of 240, since the A = 23 mass chain was not implanted. The
reported 520, 1312 and 1832 keV gamma-ray transitions in 24F have been observed
in the present study and the assignment of the 520 and 1832 keV transitions to the
decay of 240 was confirmed by half-life results from the gated decay curves shown
in the top panels of Figure 4.16. A new gamma-ray transition with energy 3002 keV
in 24F was also identified based on the half-life obtained from the gated decay curve
in Figure 4.16. A single weak gamma-ray at 2243 keV, which could be associated
to gamma—ray decay in 23F known from our experiment using 230 cocktail beam
(see analysis of 230 beta decay) was observed in present work. However, the peak at
2243 keV might also be the single escape peak of an intense gamma-ray at 2754 keV
produced from the beta decay of 24Na. The peak was assigned to 23F. The observed
gamma-ray emission probabilities for observed gamma-rays are given in Table 4.8.

The tentative beta. decay scheme of 240 is shown in Figure 11.17. The level assign-

86

Table 4.8: Gamma—ray and neutron energies assignments for the beta decay of 240

 

 

 

 

 

 

 

 

 

Gamma Emission Nuclide Energy
energy (keV) probability (%) level(keV)
520(3) 14(4) 7‘11? 520
1312(5) 13(5) 24F 1832
1832(4) 30(5) 24F 1832
3002(6) 14(4) 24F 3002
Neutron Emission N uclide Energy
energy (keV) probability (%) level(keV)
3274(10) 12(2) 24F 9515
4069(15) 11(2) 24F 8102

 

ments for the observed gamma-rays in 2"F were based on the knowledge of gamma-ray
decay in 24F from the work of Reed et al. [(33] and comparison to a shell model cal-
culation given in the same work. The new gamma-ray at 3002 keV was attributed
tentatively to a new state at 3002 keV in 24F. This new assignment fills in the pre-
viously missing allowed beta decay to a state at. 3000 keV predicted by shell model
calculations using the CW interaction, which has good agreement with the other
observed states.

The analysis of the neutron tiIne—of-flight spectrum for implantation during the
22N experiment revealed six neutrons energies that assigned to the beta decay of 22N
and a 2730 keV neutron attributed to the same decay (22N) based on the intensity flow
arguments and available beta decay energy window in 220. The neutron with energy
1212 keV was assigned to the 25F beta decay. The two remaining unassigned neutrons
were candidates for the beta decay of 240 since they did not satisfy intensity sum rules
in either 221V or 25F beta decays. The gated decay curves for these neutrons did not
produce half-lives due to low statistics. The neutron emission pr(_)l:)abilities of the 3274
and 4069 keV neutrons were found to be 13(2)% and 11(2)%. respectively. with respect
to the total number of 2‘0 beta decay events. However. the gz’umna-ray activity of
23F beta decay required 39(8)% feeding to the ground state of 23F. Since 23F was not
implanted, this feeding had to be fulfilled by beta-delayed neutron decay of 240. The

gamma—rays associated with the energy levels in 23F were not observed as discussed

87

 

24
O 5351”“; o = 11400 keV pn = 39(8) %

M° 8102 .. . 49:;1?‘

___. 7272 - - - - '- - 4069(105)
l2(2)°/o ‘

“

32 74(1 1 .9)

 

 

 

 

 

 

 

14(4)o/ -S-r1-?--3--8-f?-6- ----------- a—- 0 (3/2‘,5/2.)
1——>° 3002-—— (031’) 23F
3002(14)
44(7)°/o 1832 1832(301 1+
1312(13)
520 "
<3(6)°/o 0 v 152ml”
24F

Figure 4.17: Beta decay scheme of 24O. The transition energies in keV and emission
probabilities in parenthesis are given close to the arrow representing the transition.
The tentative assigned neutron transitions and their states are displayed in dashed
lines.

above. Hence, both neutrons have been placed to feed the ground state of 23F as
shown in Figure 4.17. The neutrons with energies 3274 and 4069 keV depopulate
levels at 7272 and 8102 keV states in 24F, respectively. In addition to these states,
the decay associated with the neutron unbound states that were not observed in this
experiment was 16% of the total decay, which was estimated from the feeding and
decay of the 24F ground state.

The total neutron emission probability of the 240 decay was found to be 39(8)%
from the gamma-ray activity in 23Ne, the decay of beta-delayed neutron daughter.
The beta branches, shown above the horizontal arrows in Figure 4.17, were calculated
to satisfy the feeding requirements of each state. The upper limit of the beta branch
to the ground state of 24F was calculated as 3(6)00 by considering the total neutron
emission probability and the beta decay feeding to the neutron bound states in 24F.
The state at 520 keV in 24F had no feeding within the uncertainties. The transition
energies with their emission probabilities in parenthesis are also given in the same

figure for both gamma—rays and neutrons. The apparent log(ft) values and B(GT)

88

Table 4.9: Properties of the 240 beta decay.

 

 

 

 

 

Energy Branch Log(ft) Spin B(GT)
level (keV) (%) parity
0 <3(6) >571 0+, 1+ >0.008
520 0 — — —
1832 44(7) 4.15 1+ 0.28
3002 14(4) 4.38 0+, 1+ 0.28
7272 11(2) 300 0+, 1+ 4.0
8102 12(2) 2.61 0+, 1+ 9.7
>3856 <16(4) - - -

 

 

 

 

values, given in Table 4.9 were calculated as explained in previous sections. The beta

feeding to all observed excited states were categorized as allowed beta decay based

on the apparent log(ft) values, and except for the 1832 keV state, were tentatively

assigned spins and parities of 0+ or 1+ assuming that the ground state of 24O is 0+.

The 1832 keV state was given a lJr to be consistent with the work of Reed et al. and

the shell model calculations. The spin and parity for the ground state of 24F was not

given as the feeding is negligible.

4.4 Analysis of 230 Deta Decay Experiment

 

1987 — 26

) -—>

1687

1387

dE [0.0

1087—

 

787
875 925

 

975

1025

      

1075 1125 1175

 

4— Time-of-Flight (o.u.]

Figure 4.18: The identification of implanted nuclides. The identified particles from
the 23O cocktail beam are labeled.

89

Table 4.10: Beam purity of the 230 exI-ieriment from the A1900 and the implantation
detector.

 

 

Nuclide A1900 Implantation Detector Literature
Purity1(%)2 Purity3(%) half-life4 (ms)
230 16.8 14.2 82(37)
26Ne 62.2 83.1 192(6)
24F 7.4 2.1 400(50)
21N 1.5 06 85(7)

 

 

 

 

 

 

1At the A1900 focal plane from the TOF and energy loss measurement.

2 25F, 27Ne, 10’11’12413Be, 748v9Li and 6H9 contribute to the remaining 12.1%.
3Taken from the difference in counts from the dB and Veto detectors.
4Taken from Ref. [10].

The secondary beam of 230 was produced by fragmentation of a 140 MeV / A 48Ca
beam with the same target and wedge as in the 22N experiment, but the settings of the
A1900 magnets were change to optimize 23O. The beam was analyzed for purity at the
focal plane of the A1900 before the implantation runs. The secondary beam from the
A1900 separator was a cocktail beam consisting of 230, 26Ne, 24F and 21N as major
constituents, and 25F, 27Ne, 10~11’12J3Be, 7+819Li and 6He as minor constituents. The
percentage compositions of the beam at the focal plane of the A1900 are given in
Table 4.4. A part of particle identification spectrum generated using the dE detector
is shown in Figure 4.18, where major constituents are labeled and the light particles
are not shown. The purity of the implanted beam, also given in Table 4.4, was deduced
by applying gates on particle identification plot and taking the difference in counts
between the dB and Veto detectors. The implanted beam consisted of only 230, 26N e,
24F and 21N. The reported half—lives for the implanted nuclei are given in the same
table.

The beta decay of 230 produces the A = 23 mass chain, which includes the
daughter decay of 23F and the granddauighter 23Ne decay to the stable 23Ne. The

beta-delayed neutron branch of 230 decay introduces the A = 22 decay chain with

90

 

 

A 120 -__n_-_____‘ '- ----——~— - e» a A 80 —— —~— J—— — —4 —— ——
:5 100 :i 70

g 6 60

v 80 v 50

51 60 340

.H q... 30 .

40

3. .3 20

8 20 8 10'

<1: _‘___é_‘ ~~‘Mg___ __.____‘ d:

 

 

 

1000 2000 31000 4000775000
Time (ms)

 

 

80~—"_~~—
70’
6O
50
4O
3O
20
10

)

(a.u.

Y

 

 

 

 

Activit

#—

l200 400 600 800
Time (s)

 

Figure 4.19: Growth and decay curves for the 23O decay series were calculated using
a decay model with a production rate of 100 pps for the parent of the decay series
for(a)230 activity curve, (b)23F activity curve and (c)23N e activity curve. The beam-
on / off period of 300 ms are included to the calculation.

22F decay to the stable 22Ne. Figure 1.9 shows all decay chains for 230 beta decay. All
of these decays could be observed in addition to the decays of the implanted impurity
beta decay chains. The analysis of the beta decay of 26Ne, the major impurity in the
implanted beam, will be given in a separate section.

The analysis of the 230 beta decay data for determining absolute transition inten-
sities requires the knowledge of whether activities of daughters and granddaughters
become saturated under the experimental conditions and were needed to determine
the beta decay feeding contribution from directly implanted parent nucleus. The sim-
ulations were performed as explained in the section of the analysis of the 22N data.
The Bateman equations [til] were written for the growth and decay of all decays dur—
ing the beam—on/off periods. The detailed explanation of equations and the fitting
function are given in Appendix A. The nuclei that did not decay during the beam-off
period were added to the next cycle. The growth of the beta-delayed neutron decay

chain was established by means of the neutron emission probabilities given in Ap—

91

pendix A. Figure 4.19 shows the sin‘iulated decay curves obtained for a production
rate of 100 pps for 23O. The growth and decay of 230 during the first 5000 ms period
of the experimental run is shown in Figure 4.19.(a) and the activity variations of 23F
and 23Ne are shown Figure 4.19.(b) and (c), respectively. The simulation confirmed
that 230 and the daughter activities were saturated after 200 s from the beginning

of the experimental run.

4.4.1 Total Number of Beta Decay Events

 

 

 

 

     

10000:
: Daughter decay + Background
0) ’M
E ' e
8 1000 .
o' : 23o
\ 5
0)
g 100 E 24
O F
O ’ 21
10 E N

 

 

 

o 50 100 150 200 250 300
Time (ms)

Figure 4.20: Ungated beta decay curve for the 230 experiment. The total fit to the
decay curve, the individual decay components of the implanted 26Ne, 230, 24F and
21N, and the background plus all decay contributions of daughters and granddaughters
decay are shown.

The total number of beta decay events from a particular nucleus detected by the
implantation detector was determined by integrating the beta decay curve. Beta decay
events were time stamped from the start of beam-off period to produce an overall
beta decay curve. This curve had contributions from the decays of all implanted

nuclides and their decay series. The decay curve shown in Figure 4.20 was fitted with

a function that. describes the decays of all implanted nuclides and their decay chains

92

Table 4.11: Detected beta decay events from the 230 experiment

 

 

N uclide Total number of Half-life
beta decay events (ms)

230 1.47(4)x10‘°T 102(23)I

26Ne 8.61(2)x105 192(4)2

24F 221(7) x104 384(16)2

21N 653(5) x103 85(14)3

 

 

 

 

 

‘ By fitting the decay curve, see the text.
2Gamma—ray gated half—lives from the present work.
3Taken from Ref. [70].

including the growth and decay during the beam-on and off periods. As explained
in the analysis of the 22N experiment, a function was composed for each implanted
decay series using the Bateman equations [04] for beam-off period and included the
growth and decay contributions during the beam-on period. A detail explanation for
the fitting function is given in Appendix A. The implantation purity ratios, taken
from measurements in the dB and Veto detectors, were used to fix the initial activity
ratios of the implanted isotopes. The half-lives of all daughters and granddaughters,
and the half-life of 21N, which are reported in literature [11)](see Appendix A), were
kept constant through out the fitting procedure. The half—lives of 26N e and 24F, which
were deduced from the gamma-ray gated decay curves (see below) were also taken
as fixed values. In addition, the neutron emission probabilities of 24F and 21N were
also included by using the values of 5.9% and 81%, respectively, as reported in the
literature [19]. Four parameters were left to vary: the half-life of 230, the implantation
rate of QGNe, the neutron emission probability of 230 and a flat background. The
individual contributions to the decay curve from each implanted nuclide are shown
in Figure 4.20 with the total daughter and granddaughter contributions plus the
background. The number of beta decay events extracted by integrating the individual
components are given in Table 4.4.1 with half-life and their uncertainties taken from
appropriate sources as cited. The half-life and P", value for 230 were deduced to be

102(23) ms and ll(9)%, respectively. The large number of activities present in the

93

detector does not allow more precise measurement of the half-lives in the bulk activity.

4.4.2 Beta-delayed neutron time-of-flight measurement

 

   
 
 
 

 

 

 

100000 {
«— p - y prompt peak
76 10000 g
: E Cosmic-ray peak
: -
(D 1000 g-
5 a
7, 100 E A Q): Sn -
E . 1‘ '
3 1o '
o . “UWMIE'll “1"“)th
1 9

 

50 100 A 150
Channel number

Figure 4.21: The beta-delayed neutron time-of-flight spectrum of 230 obtained by
adding the data from all neutron detectors in the array. The peak due to cosmic-ray
interaction with neutron detectors and the prompt peak are labeled. The upper limit
of the beta decay energy window (Q 73-372) to the neutron unbound states is indicated
by the arrow.

The total neutron time-of-flight spectrum measured during the beam-off period
and corrected for the constant-fraction discriminator (CFD) walk in all of the de
tectors in the neutron spectroscopic array is shown in Figure 4.21. The position of
the prompt peak provided the time zero reference point for the time-of-flight spec-
trum. Cosmic-rays predominately propagate in the opposite direction through the
detection system and trigger the electronics at a shorter time relative to the prompt
peak to produce the cosmic-ray peak in Figure 4.21. No neutron peaks were observed
within energy detection limits. The lower and upper energy detection limits are ap—
proximately 360 and 8000 keV, respectively. Since the energy window available for
beta decay into the neutron unbound states is limited to 3750 keV (channel number

112). the energies of neutrons are well within the upper detection limit... It is possible

94

800

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7;, . 84 153 232 473
E 600 _ zeNe fsNe 25114 23Ne 24 493
2 I 350 Ne 23
o * 21 404 y F
g 400 - 1 1 F 26Ne ?
E t I l 1 511
O 200
O
0 L n I n I n I n J
100 200 300 400 500
300 Channel number
'5 1 911 12371274 1279
E 250 l- 816 230 1003 10171129 230 22F 26N
2 l. 638 23 874 25 23F 26Na 9
200 Na
3 ( 230 24MB
.9 150 - l \ \ \ \
g .
50 .—
0 b I n I 1 i J J 4 I n I n I 1 I a
600 700 800 900 1000 1100 1200 1300
200 Channel number
1411 1716
E .1365 3:68 25M 1621 1637 1701 230
.1: r 1 I 1 \ 1731
3100 - , 210
*9 l l
S
8 50
0 7 . r . 1 a 1 . l
1300 1400 1500 1600 1700

Channel number

Figure 4.22: Beta-gamma coincidence spectrum for 230 experiment: Part I. The peaks
are labeled with the parent nucleus and the energy in keV.

that low energy beta—delayed neutrons from the decay of 230 were below the lower
energy detection limit of the neutron spectrosc0pic array or there are no neutron
emission from this decay. To determine whether this could be the case, a search for

the gamma—rays that originated from the beta-delayed neutron daughter decay was

undertaken.

200

 

 

 

 

 

 

 

 

 

— 1809 2243
2 +1775 ”N 2219 230
g 150 '26Na ‘— a 1898 1982 2132 ZBNe ,
5 ’ 1822 ”Na 24F 2083 ”F
B100 » 23F 1 2,920 l 22,: 2166
E 5 I J F l 2"’1:
351/U * 4
0 - 1 r 1 l . 1 1 I 1 m L g
1800 1900 2000 2100 2200 2300
60 Channel number
6 . 2316 2415 226526 36542 2673 i734 2926
E I. 23F 23F 2486 Na Na 23 F 2754 230
.: Ne\ a
o _ /
(I)
E520
3
O
o

 

1 I 1 1 I 1 I e I

O 1 I 1 ‘ ,
2300 2400 2500 2600 2700 2800 2900 3000
40 Channel number

3367 3432 Escape 3848 4066

 

 

 

 

 

3 ' ak
E 30 - 23o ”F De) 3383‘ 23o 3863 23o
g _ \ F 230
\ 20 - . /
a, , ,
g 1 . 1 I ‘ , . t l 1 l I - i
O 10 " ' l' ‘ ‘ (I .| I x ‘ ‘ .
o . ~ ~
0 1 L n i n L 1 I 1
3000 3200 3400 3600 3800 4000

Channel number

Figure 4.23: Beta-gamma coincidence spectrum for 230 experiment: Part II. The
peaks are labeled with the parent nucleus and the energy in keV.

9G

4.4.3 Beta-delayed gamma-ray measurement

Figures 4.22 and 4.23 show the total gamma—ray spectrum obtained in coincidence
with the beta decay of the 230 cocktail during the beam-off period. The peaks are
labeled with their assigned parent. nucleus and energy in keV. The beta decay of
230 leads to the A = 23 decay chain, which produces gamma-rays from decays of
23F and 23Ne. The gamma-ray transitions with energies 493, 816, 1017, 1701, 1822,
1920, 2132, 2316, 2415, 2734, 3432 and 3831 keV were assigned to the beta decay of
23F based on previous measurements [76]. The assignments were reconfirmed based
on resulting half-lives from gamma-ray gated decay curves for those peaks that were
statistically significant. Two gamma-rays from 23Ne beta decay, the granddaughter
of 230, were observed with energies 440 and 1637 keV and emission probabilities
of 33.0% and 1.1%, respectively. These observations were in good agreement with
literature values [76]. The gamma-ray transitions from the decay of the impurities in
the cocktail beam, such as 26Ne, 24F and 21N, and their daughters and granddaughters
are shown and labeled in Figures 4.22 and 4.23. The gamma—ray transitions associated
with the A = 26 decay chain will be addressed separately below. In addition, a gamma
ray with energies 1983 keV was assigned to the beta decay of 24F, which was also
reported in Ref. [76]. The half-life extracted from the gamma-ray gated decay curve
was 384( 26) and confirms this assignment. A few gamma-rays from the A = 21 decay
chain determined in previous experiments are also shown and labeled in Figure 4.22.

Although beta-delayed neutrons from 230 were not observed, gamma-ray peaks
associated with the beta decay of 22F, the beta-delayed neutron daughter of 230
were observed with energies 1274. 2083 and 2166 keV. These weak transitions had
an intensity ratio ()f 524:3. This observation leads to the conclusion that at least one
of the 22F states is populated by beta-delayed neutron decay of 230, since nuclides
with A = 22 were not implanted during the experiment. Excited states in 22F were
studied previously in beta decay of 220 [66]. and the 22Ne(3He. t) and 22:\7e(7Li. 7Be)

reactions [77]. A weak gamma-ray at. 638 keV associated with energy levels in 22F was

97

observed in present work. The known gamma-ray energy 72 keV attributed to 22F
gamma—ray decay and expected to observe in cascade with a 638 keV transition was
not seen here due to the threshold of the SeGA detectors. Although neutrons were not
observed as discussed above, the observation of the A = 22 decay chain and a weak
transition in 22F indicate a total beta-delayed neutron emission probability at the
level of 7(2)%, which was calculated from the total beta decay of 22F derived from the
observed gamma-ray activities in 22Ne. Note that the parent and daughter activities
in this decay series were saturated during the 30—minute long runs, as discussed in

the previous section.

 

 

30, 4°
to . 1621 keV 3243 “V
E ] 46196125) 30% 5101(9)
oz 7 . l 4H4
N I 1 1 ‘1'. I 1 ,
E - 1 + 20 1‘ ' ]]‘
c ’ l
a 1 . 1 5
8 - 1o

 

 

 

 

 

 

 

0 50 100160 200 260 0—5‘0160150200260

 

 

 

16» 2673 keV t3868 keV
3 [ . _ _ t1rz= 35120) 12. 1,2=98(20)
: r101] 011.1 8 .‘TlII-lll .
£3 ‘ -. - “,1- l;
S 7 ‘ 7]]1Ll 4 [TL ]
8 '1 1+ 1 TI]

 

 

 

 

 

 

50 100 150 200 250 00 50 160 150 zoo 250
20
4066 keV

 

  

11,2: 95(20) 16’ .
12- l

 

 

 

 

 

Counts/7 9 ms
+ ”5
-+ . ..__ ‘
___';__ 7
’13—!—
5g
.5 on

 

 

oo 50 100 150 200 250 00 60 100 150 200 250

Time (ms) Time (ms)

Figure 4.24: Gamma gated decay curves of 23O. The fitted single exponents are shown
for the statistically significant peaks corresponding to beta decay of 230. The gated
gamma-ray peak energies and corresponding gated half-lives are given in keV and ms,
respectively.

The relatively strong gamma-ray transitions with energies 1621, 2243, 2673, 2926,

98

Table 4.12: Gamma-ray assignment for the beta decay of 23O

 

 

Gamma Gated half-life Emission Nuclide Energy
energy (keV) (ms) Probability (%) level (keV)
911(4) — 2.7(12) 23F 3837
1237(4) — 3.1(9) 23F 4604
1621(6) 106(25) 5.7(10) 23F 3866
1716(6) — 2.1(6) 23F 5553
2243(8) 101(9) 51.5(12) 23F 2243
2673(9) 86(20) 5(1) 23F 5599
2926(10) 95(20) 7(2) 23F 2926
3367(13) — 4.5(10) 23F 3367
3868(15) 98(20) 10.1(16) 23F 3866
4066(16) 92(17) 17.1(17) 23F 4066
638(3) — 1.5(8) 22F 710

 

 

 

 

 

 

 

3868 and 4026 keV were assigned to the beta decay of 230, which agree with previous
work [37, 43]. The half-lives were obtained from gamma-ray gated decay curves by
fitting a single exponential plus a flat background, as shown in Figure 4.24. The
deduced half-lives gave a weighted average value of 97(8) ms. Although the half-life
of 21N a is 85(7) ms, the above gamma-ray transitions cannot be attributed to the 21Na
beta decay since the number of implanted 21N nuclei were not sufficient to produce
such intense gamma-ray peaks. Four gamma-rays with energies 911, 1237, 1716 and
3367 keV were also attributed to the 230 beta decay based on the work of Belleguic et
al. and Michimasa et al. [37,43]. The transitions at 911, 1237, 1716 and 3367 keV also
matched within uncertainties with the reported transitions in Refs. [37,43]. Gamma-
ray peaks at 2003, 3445, 3985 and 4732 keV reported in the nuclear reaction study

were not observed in the present work.

4.4.4 Beta Decay Scheme of 23O

The proposed beta decay scheme of 230 based on the observation from present work
is shown in Figure 4.25 and the details of assignments will be discussed following.
The assignment of gamma-rays to the energy levels in 23F was based on the previ-

ously known energy levels and gamma-ray transitions, since the beta-delayed gamma-

99

230 97(8) ms

 

 

 

 

        
 

  

 

   
  

 

 
   

  
  
  

 

+ 9,: 11290 keV
1/2
P,,=7(2)°/o {“~~-_. +
‘~~~ ' 710 3
---------------------------- v 2 o 4
8n = 7540 22F
5'2110’% . 5599 (”2:303
‘2,1(o)/., l 1 5553 (1/2 ,3/2 1
31(9)?o - l + +
4604 (1/2+ ,3/2 1
17.111 1% 123 3.1) 406 3/2 + +
3866 (1/2 ,3/2 )
15.8(1 3837
3367
2926
1621 7) +
1—> 2243 ”2
45.8(17)%
3367(45)
29260.2)
3868001)
4066071) 22431515)
- o 5/2+
23
(A) F

Figure 4.25: Beta decay scheme of 23O. The gamma-ray decay was given in vertical
arrows with the transition energy and emission probabilities in parenthesis. The hor-
izontal arrow shows the beta decay feeding to the level with the beta branch and the
corresponding uncertainty in parenthesis.

gamma coincidence events were not evident. due to poor statistics. The gamma-ray
transition with energy 638 keV was placed to deexcite an energy level at 710 keV in the
neutron daughter 22F following Ref. [77]. The gamma-ray transitions at 2243, 2926,
3367, 3868 and 4066 keV were assigned to feed the ground state of 23F as reported
in Ref. [43”] and shown in Figure 4.25. The gamma-rays of 912, 1237 and 2673 keV
were placed to depopulate the known states at 3837, 4604 and 5599 keV, respectively.
in order to be consistent. with the gamma decay scheme in 23F as given in Ref. [133].
The gamma-ray with energy 1716 keV has been placed depopulating the known state

at 5553 keV. This tentative placement is reasonable because it matches with the dif-

100

Table 4.13: Preperties of the 230 beta decay.

 

 

 

 

 

 

 

Energy Branch Log(ft) Spin B(GT)
level (keV) (%) parity
2243 47.8(17) 4.29 1/2+ 0.20
2926 0 — - -
3367 0 - - -
3837 0 - - -
3866 16.5(19) 4.33 (1/2+, 3/2+) 0.18
4066 17.9(17) 4.24 3/2+ 0.23
4604 3.2(9) 4.82 (1/2+, 3/2+) 0.06
5553 2.2(6) 4.68 (1/2+, 3/2+) 0.08
5599 5.2(1) 4.28 (1/2+, 3/2+) 0.21

 

 

ference in known energy levels and the intensity flow. Although the gamma-ray with
energy 1621 keV was not seen in previous experiments, it was assigned to the 3866
keV state in 23F based on the energy difference between the known energy levels at
2243 and 3866 keV. Table 4.12 shows the observed gamma-rays with their uncertain-
ties, the half-lives, the gamma emission probabilities and the energy level assignments
for the beta decay of 23O.

The absolute beta decay branching to each level was deduced from the difference
between gamma-ray intensity into and out of each level, normalized to the total decay.
The gamma-ray energies and their emission probabilities in parenthesis are given on
the vertical arrows in Figure 4.25. The comparison of total gamma-ray feeding to the
23F ground state and the total gamma-ray activity in the 23F beta decay showed
a negligible beta decay feeding to the ground state. Beta decay branching was not
deduced for the states at 2926, 3367 and 3837 keV since the feeding and deexcitation
intensities balanced within uncertainties. The observation of the 638 keV gamma-ray
in 22F suggested that beta-delayed neutrons pOpulate excited states in 22F as shown
in Figure 4.25.

The apparent log(ft) values were determined for the bound states in 23F using
the method explained in previous sections. Table 4.13 shows the calculated beta

decay branches, log(ft) values and Gamow-Teller transition strengths [B(GT)] for the

101

observed bound states along with their spin and parity assignments. B(GT) values

were calculated according to Ref. [331] using the present log(ft) values. Six allowed

beta decay states were assigned the spin and parity of 1/2+ or 3/2+ based on the

measured log(ft) values and the selection rules of beta decay and considering the 230

ground state has a 1/2+. The states at 2243 and 4066 keV were given spin and parity

assignments of 1/2‘L and 3/2+, respectively, to be consistent with the corresponding

assignments given by Michimasa et al. [43].

4.5 Beta Decay of 26Ne

,+ 233.6

1+_82_.5

3+ ———— ——
(O)

-+_2723

1 _____

1+ 1511_

2+ 400M
25.2335

1+2§;§2

+.- -___
3 (b)

26.27.

_2559_
2290
:2186‘

2048

 

1996

_429__
2+_241__

1+ 88
+ .__

 

(C)

 

 

(d)

3+_181W_

1+ 0
(e)

 

Figure 4.26: Known level scheme of 26Na. The observed energy levels in 26Na by
(a)Dufour et al. [78]. (b) \Veissman et al. [79], (c) Pearce et al. [81 l], and (d) Lee at
al. [8]], and the calculated allowed beta decay levels by (e) Wildenthal et al. [15'] are.
shown. The energies are in keV.

102

Shell model calculations have been successful in reproducing the shell structure
of nuclei close to the valley of stability. However, there are cases where significant
differences between shell model predictions and experimental data occur. One such
case is the beta decay of 261V e, which was recently re—measured by Weissman et al. [79]
to check the discrepancy between theory and experiment. Weissman et ah reported
the beta decay feeding to three lJr states at 82.5, 1511 and 2723 keV, and two 2+
states at 233.5 and 406 keV in 26Na compare to the previously measured two 1+
states at 82.5 and 233.6 keV by Dufour et a1. [78] as shown in Figure 4.26. This
leads to a contradiction for the spin assignment of the 233.5 keV state based on the
beta decay experiments. In contrast, the USD shell model calculations performed by
Wildenthal et al. [18] predicted five 17L beta decay states in 26Na, with four below
2.8 MeV. The weakest beta branch among four of them was predicted to be 0.7600
to the state at 2538 keV. These predicted levels were also presented in Ref. [79]. The
predicted fourth 1+ state was not observed by the previous beta decay experiments
including the work of Weissman et al., which had a sensitivity of 0.4% for the beta
branch. The nonobservation of the predicted 1Jr state below 3 MeV in 26Na shows a

clear discrepancy between the experimental and theoretical values.

 

26NO

 

 

 

l3”

 

26Ne

 

 

 

Figure 4.27: Zf’Ne beta decay chain. The stable isotope is shown in the solid square.

The energy levels of 26Na. have been studied by Flynn et. al. [82] using the 261\Ig(t,3He)

reaction up to 4702 keV assuming a spin and parity assignment of 3+ for the ground

103

 

. E = 153 keV
60 5 11,, = 192(4)

 

 

 

60 0 50 100 1 50 200 250

 

 

 

(D

E

‘3’.

(‘0

:2

C

8 . . .

O 300 50 100 150 200 250

l E = 1212 keV
20 - 1,,2 =190(10)

 

 

 

 

Figure 4.28: Gamma gated half—lives of 26Ne beta decay. The energies in keV and
Half-lives in ms are given.
state of 26Na. Other investigations carried out by Pearce et a1. [80] and Clarke et
al. [76] using the same reaction reported a few more levels in addition to the previ-
ously observed ones. and assigned spins and parities to a few of the new levels in 26Na.
Figure 4.26 summarizes the experimental and calculated energy levels in 26Na. The
14C(14C,d) reaction was used by Lee at al. [81] recently to observe even a few more
levels in 2(Na. This reaction confirmed the spin and parity assignment of 1‘L to the
82.5 1511 and 2723 keV states and 2+ to the 233.5 and 406 keV states later reported
by Weissman et. al. Since 26Ne. was the largest contaminant in the 230 cocktail beam
with a high production rate, it was interested to remeasure the beta decay of 26Ne
to check the controversy between previous beta decay measurements and shell model
calculations.

2“Ne decays to 26N a, which subsequently decays to stable. 26Mg as shown in F ig—
ure 4.27. The beta-delayml gan'nna-ray spectrum observed within the beam-off time

period in the 230 experiment, shown in Figures 4.22 and 4.23. displays the gamim-i-ray

104

 

lines from the 26Ne parent decay. The gamma-rays energies at. 1003, 1129, 1365, 1411,
1775, 1809, 1898, 2526 and 2542 keV were assigned to the 26Na decay, the daughter
of 26Ne, and are in agreement with a. pervious experiment [19]. The gamma-ray tran-
sitions in 26Na were assigned as 84, 153, 232, 404, 1212, 1279 and 2486 keV based on
the knowledge from the previous 26Ne beta decay experiment [79] and present decay
curve analysis. Gated decay curves were generated for gamma—rays assigned to 26Ne
decay that were statistically significant. The half-lives were determined by fitting a
function that included a single exponential decay with constant background to the
decay curves. The gamma-ray gated decay curves associated with the 26Ne beta de-
cay are shown in Figure 4.28. The weighted average half-life for the 26Ne beta decay
was deduced as 192(4) ms in present work, consistent with the reported half—life of
192(6) ms from the beta decay experiment and the theoretically estimated half-live
range of 162 - 170 ms [79]. A weak gamma-ray energy 2219(4) keV could be the same
as the observation of 2232(15) keV gamma-ray transition in 26Na by Lee et al. [8'1].
The gamma-ray emission probabilities, given in Table 4.14 were calculated using the
total number of 26Ne beta decay events and the gamma-ray efficiency. The emission
probability of the gamma-ray at 84 keV was not determined, because this energy
was below energy threshold in some of the SeGA detectors. The gamma-ray emission
probability was taken from literature for this transition [‘79].

The proposed beta decay scheme was given in Figure 4.29. The gamma—ray place-

Table 4.14: Gamma-ray assignment for the beta decay of 26Ne

 

 

Gamma Emission Nuclide Energy
energy (keV) Probability (%) level (keV)
84(3) 95 26516 84
153(3) 3.4(2) 26Na 234
232(2) 4.4(2) 26Na 234
404(3) 0.4(1) 26Na 404
1212(3) 1.2(3) 26516 2723
1279(3) 5.4(2) 26516 1513
2219(4) 0.6(2) 26Na 2453
2486(4) 0.7(2) 26Na 2723

 

 

 

 

 

 

 

 

Fl

2°Ne 192(4) ms

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+
0 o, = 7330 keV

1.9[4]°/o 2486(0.7) 2723 (0+. 1+)

5 . 2453 10+, 1+)
0.6(2)°/o .

221506) 12120.2)
4.2(4)¢. J. 1279(54) ,, 1513 10+, ,4.)
0.4(1)/o : [12:23:44]!” 404 (0+.1+. 2+]
1.1 4)°/ Y 1717 - 2+
, 1 15313.4] {2334 1+
91,6(2)% r r84l951 0 3+

26NO

Figure 4.29: Beta decay scheme of 26Ne. The gamma-ray decay is given in vertical
arrows with the transition energy and emission probabilities in parenthesis. The hor-
izontal arrow shows the beta decay feeding to the level with the beta branch and
the respective uncertainty in parenthesis. The dotted arrow shows a new gamma-ray
transition.

merit in the decay scheme of 26Ne was constructed based on the knowledge from
gamma-ray decay in 26N a from Refs. [79, 8 I]. All gz'u’nma-rays except for a new tran-
sitions at 2219 keV were placed among the energy levels in 26N a as in Ref. [79]. The
assignments of these gamma-rays are given in Table 4.14. The new 2219 keV gamma-
ray was tentatively placed to the known 2453 keV state [81] as a feeding to the 234
keV state to match the shell model calculations. which will be discussed in the next
chapter. The beta branching was calculated by taking the difference in intensity flow
into and out of a specific. level. The beta decay branch to the ground state of 26Na

was negligible as the summed intensities of gamma—rays feeding from excited states

106

Table 4.15: Properties of the 26Ne beta decay.

 

 

 

 

 

 

 

Energy Branch Log(ft) Spin B(GT)
level (keV) (%) parity
0 _ _ 3+ _
84 91.6(2) 3.84 1+ 0.57
234 1.7(4) 5.72 (0+, 1+, 2+) 0.008
404 0.4(1) 6.11 (0+, 1+, 2+) 0.003
1513 4.2(4) 4.73 (0+, 1+) 0.07
2453 0.6(2) 5.23 (0+, 1+) 0.02
2723 1.9(4) 4.6 (0+, 1+) 0.10

 

 

to the ground state and 26N a beta decay events deduced from daughter gamma-ray
activities were similar. The apparent log(ft) values given in Table 4.15 were calculated
for observed states using the method given in Ref. [71]. Four allowed beta decay tran-
sitions were found based on the beta decay selection rules. They were assigned with
0“L or 1+ spins and parities considering the ground state of 26Ne has a 0+, except
for the 84 keV state, which was given a 1"L to agree with previous work. The feeding
to the states at 234 and 404 keV was categorized as the first forbidden decay based
their log(ft) values and the spin and parity assignments are shown in Figure 4.29.

The B(GT) values given in Table 4.15 were calculated as explain in Chapter.2.

107

 

Chapter 5

Discussion

5.1 Beta Decay of 22N

The results of the beta decay of 22N (Figure 4.9) showed that allowed beta decay
feeds five neutron unbound energy states in 22O. The total feeding to those states is
44(4)% of the total beta decay of 22N. The first forbidden beta decays, which account.
for 56(4)% of the total beta decay, were observed with three excited states and the
ground state of 220. Note that the observed first forbidden decays go to neutron
bound states in 22O. In addition, three gamma—rays transitions in 22O and a single
gamma-ray transition in each of the neutron daughters of 21O and 200 were confirmed
from previous works. Beta-delayed neutrons of 221V leading to the single neutron and
two neutron daughters were observed yielding neutron emission probabilities of P1,,
2 33(3)% and P2,, 2 12(3)%. The total neutron emission probability was found to
be 57(5)% from gamma-ray analysis of the daughter decay activities. The half-lives
and the total neutron emission probabilities of 22N beta decay from the. present work
and literature are shown in Figure 5.1 for conu:>arison. The total neutron probability
deduced in the present. work are in agreement. with values reported by Yoneda et
al. [10] and Penionzhkevich et al. [62] but disagreed with the value re}.)orte(.l by

Reeder et al. [1’19]. Note that the upper limit of the two neutron emission prolmbility

108

 

 

 

 

 

 

 

 

o\°
505 *9 3 133* i
A - Experiment 3'3 ' '
g 40I c 5 *i g :3." d Theory
v - 1———>
a: 30. 1c ‘1 '
“—1: . if *h '3 50'.
m .
£20: ] lb die' Th ' El 40; b] C .9
eo
. (i) *3 20» Experiment f (ii)
0 g 10

 

 

 

Figure 5.1: The comparison of half-life(i) and neutron emission probability(ii) of 22N.
The values are taken from works of (a) Mueller et al. [38], (b) Reeder et a1. [39], (c)
Penionzhkevich [62], (d) Yoneda et al. [40], (e) present work, (f) Groote et al. [41],
(g) VVapstra et al. [45], (h) Wildenthal et al. and (i) New shell model calculations.
The experimental and theoretical values are labeled for both cases.

of 13% reported by Yoneda et al. agrees with our measurement. The average half—life
derived from the gated decay curves was found to be 20(2) ms, which is in agreement
with all previously published values [19]. Shell model calculations that are discussed
below were also performed to compare the results of the 22N beta decay.

The new shell model calculations for the allowed beta decay of 22N used the WBP
interaction in the spsd shell model space. Since the energy gap between the 0‘ ground
state and the 1‘ excited state in 22N is predicted to be small [48], the calculations
considered the feeding of 0“, 1’ and 2‘ states in 220 assuming the ground state of
22N as either 0‘ or 1‘. The beta decay half-life of 22N was calculated to be 39.8 and
24.5 ms for the 0‘ or 1" ground states, respectively, and both agree with the adopted
value. Figure 5.2 shows the calculated allowed beta decay schemes of 22N for both the
0‘ and 1“ ground states. Note that these schemes show only the beta decay branches
higher than 1%. In the case of the 1“ ground state, the allowed beta branch of 9.56%
feeds only one state below the neutron separation energy, and the rest of the allowed
beta decay feeds the neutron unbound states resulting in a predicted total neutron
emission probability of 90.4%. In contrast, the calculations for the beta. decay of the

0‘ ground state of 22N predict that. all allowed decay feeds neutron unbound states

109

22N 24.5 ms 22N 39.8 ms

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0‘)

14157 0'
13584 0‘
12226 0: 2.86% 118651"
11865 1 ‘ .. o = 11650]-
10852 1" 1383/54, 189132 1'

""""" 1224 - l'
9831 ‘3- . .. 100521'
9259 2 W 8991 1‘
8260 2' O
7513 1" 63-9 4°; 7513 1'
7395 2'

---------- s,=6850 556850
5953 0'

22 0+ 22 0+
0 0

Figure 5.2: Theoretical beta decay scheme of 22N. The beta decay schemes shown
in the left and right are calculated considering the ground state of 22N is 1‘ or
0‘, respectively. The allowed beta decay branches higher than 1% are shown. The
calculated half—lives in ms, spins and parities, and energies in keV are given.

making the total neutron emission probability of 100%. However, the predictions for
neutron emission probabilities could change dramatically as the estimated energies
of the negative parity states have about a 1 MeV uncertainty. In the extreme case,
the states close to the neutron separation energy could move closer and even into the
neutron bound region, reducing the total neutron emission probability to about 36%.
Although this theoretical lower limit become closer to the observed single neutron
emission probability of 33% by lowering the energy levels, the present experiment
did not. observe any bound state fed by the allowed decay. Therefore, one can expect
that there should be a considerable contribution from the first forbidden decay in 22N

decay which is consistent with our results.

110

 

0‘ ____14157

0 ————13584 (0 .1 .2) 13298
0' ____12226 _
1 11865
1‘ —‘—11865 1-:11650
1' —————10852 1'——— 10852 (0'.1‘.2‘)
0' ____10224 12—10492 ““— 10545
1' ——9931 I ———-— 10052
2 ——9259 ,- 899] ______ (011-2-, 8782
2— 8260 - (0',1‘,2') 7649
‘_ -—5--— 75131 _—__75)3 ...... ~———- +
2 7395 2+ 4 __ 6936
‘— 6510 2+—— 6509
0 5953 (011 ')_ 5800
3+ o+__._ 4909
458“ 3++——+-- 4582
+
2 3198 2+ 3,99
- 22 ..
[22N gs. =1 ] [ Ngs. =0]
0+ _‘ 0+——-——— 0 Q——+ 0 0+____. 0

(i) Shell Model (ii) Shell Model (iii) Present work (iv) Previous work

Figure 5.3: Comparison of the 220 energy levels. Shell model calculated energy levels
that are fed by the allowed beta decay of (i) 1‘ or (ii) 0‘ 22N ground state are shown.
The observed levels from (iii) present work and the known levels in 220 (iv) from the
works of Stanoiu et al. and Cortina-Gil et al. are shown. All energies are given in keV.
The likely energy levels are connected with the dashed lines.

The energy level scheme of 220 obtained in the present work and the negative
parity states predicted by the shell nrodel considering the 1‘ or 0‘ ground states for
22N are compared in Figure 5.3 along with the known energy levels from previous
works of Stanoiu et al. and Cortina-Gil et al. The observed energy levels are closely
matched with the predicted levels that were calculated from beta decay of the 0‘
22N ground state compared to the beta decay of 1‘ state. The likely energy levels
are connected with dashed lines as shown in the figure. The observed levels higher
than 8782 keV are not compared due to the complexity of the shell model predictions.
The positive parity bound states that are observed in this work were measured by
previous experin’rents. However, the. only known negative parity bound state at 5800
keV in 220. which is favored by bet a (1(_.‘(f'd}°'. was not observed in this work.

The experimental Gamow—Teller strengths for 22N beta decay are compared with

111

 

II:

the corresponding values calculated by considering either a 0‘ or 1‘ ground state of
221V and are shown in Figure 5.4. The experimental values shown in the figure include
the observed allowed and first forbidden beta decay transitions. In contrast, the shell
model predictions, shown in the figure, are associated only with the allowed beta
decay. The figure shows the B(GT) values corresponding to the energy range 7 - 11
MeV derived assuming the 1‘ ground state for 22N are in reasonable agreement with
the experimental values. However, the overall comparison between the observations
of the 22N beta decay with the shell model calculations for both cases is poor due
to the large strengths at high energies that are not reproduced by shell model. Large
beta decay strengths for states at high excitation energy is one of the signatures of
the halo structure as discussed in Chapter 1. Figure 5.4 shows large B(GT) values
to states at 13298 and 20839 keV in 22O supporting the halo structure of 22N. The
distribution of B(GT) values from the beta decay of 22N is similar to the beta decay
of 11Be and 11Li as given in Figure 1.6. Although the above facts support the 22N
halo structure, a study of the one-neutron knockout reaction for 22N is required to

confirm the nature of the structure.

5.2 Beta Decay of 23O and Energy States in 23F

The weighted half-life of 97(8) ms for beta decay of 230 measured in this experiment
is consistent with the half-life reported by lvlueller et al. [11)]. However, the new shell
model calculations using the USDB interaction [Nil] and free-nucleon Gamow-Teller
operator predicted a half-life of 160 ms for 230 beta decay. Thus, the 230 beta
decay rate is enhanced relative. the theory. In cmitrast, the shell model calculations
for 220 [Ni] and 26Ne (.lecay using the same interaction produced half-lives of 1.4 s
and 114 ms. both shorter than the experimental values of 2.3(1) s and 192(4) ms,
respectively. The hindrance of experimental relative to theoretical half—lives for beta

decay is typical, but. the enhancement of the (’1xperimental 230 beta decay is not

112

 

IE“

 

0.12

_ Exp %
0.10 ,_ -SM(0-)
_ msmm

 

 

 

 

 

 

o ' 5 l‘ W 10 ' 15
Level energy (MeV)

Figure 5.4: Comparison of Gamow-Teller strengths between the experiment values
and the shell model calculated values for the beta decay of 22N. Gammow-Teller
strengths are shown for the observed (Exp) and the predicted (SM(0‘) and SM(1’)
states in 22O.

understood. The total neutron emission probability of 7.2(18)% from present work is
inconsistent with both experimental values in the literature and also with most of the
theoretical predictions except for that of Wildenthal et al. and the new shell model
calculations (about 2%).

Shell model calculations were performed for the allowed beta decay of 230 using
the USDB interaction in sd-shell model space assuming a 1/2+ ground state for 230.
In addition, the gamma-ray decay scheme of 23F was calculated in order to construct
the complete 230 beta decay scheme. Figure 5.5 shows the theoretical 230 beta decay
scheme for the allowed beta decay branches greater than 0.5%. These calculations
predict that nine states are fed by allowed beta decays with branches greater than
0.5%. Two of these states are neutron unbound, leading to the total neutron emission
probability of 1.7%. However, the uncertainty of about 1 MeV associated with the
shell model predicted energy could move a few levels above the neutron separation

energy, which yields the upper limit for the total neutron emission probability of

113

 

230 l60 ms

 

 

 

 

 

  

 

o = 11290 keV
W“ B
Pn = 1.7%

o +
0.9/6 mm 317]::. l/ 24“
0.5% ________ 99,223 r: a as. {39%.11‘; 3?:- }

QZdagar—Wo'oo' Sn=7540 22
O 50/ <50 0“! 731.7355 + F
—‘..-"-> 9:: a s a -690‘ 3/2+
5.6 /0 mg or 61 v 6567 3/2
=0 0 6500 1 2*
54/0 3 or / +
3.9% A '__ 6139 3/2
A?
39‘ +
-2?) 5164 5/2
VI
366: 4532 7/21
'3—3°7°" % 4479 3/2+
_——9 g 3975 3/2+
25.3% 3691 9/2
3147 5/2+
2795 7/2+
+
, 54 30; 1990 1/ 2
. o A A
E?“ r: 5 g 3,
C 2, Cl 9‘. Q
g e, a :2 8’
l\ v— '— 0‘ C)~
(\j cf) ‘0 (‘0 r— +
0 5/2

23F

Figure 5.5: Theoretical decay scheme of 230. The decay scheme was constructed with
a minimum limit of 0.5% for the beta branch and 0.2% for gamma-ray emission.
12.9%. The calculations indicate major beta branching of 54.3% and 25.3% to the
states at 1990 and 3975 keV. The overall agreement between the experimental and
theoretical decay schemes is reasonable within the experimental detection limits.
The level scheme for 23F from the present work in Fig. 5.0 can be compared
with the shell model calculations in sd-shell model space and previous experimental
work. The thick lines in Fig. 5.0 show the predicted levels in 23F that have beta
decay feeding greater than 0.5%. The first experimental 1/2+ state located at. 2243
keV is about 253 keV higher than the shell model predicted state at 1990 keV. The

likely experimental and calculated states are joined with the dashed lines in the

114

 

figure. The level at. 4000 keV was previously associated with the first 3/2+ state
based on spectroscopic factors measured by Michimasa et al.. This assignment was
also supported by recently calculated spectroscopic strength for the 4He(220, 23F7)
reaction by Brown ['15]. Note that the analysis of the theoretical spectroscopic factor
for the above mentioned reaction shows the state at 3975 keV contains about 50% of
the d3/2 spectroscopic strength, which is supported by the observation of the highest
cross-section going to this level in the work of Michimasa et al.. The next higher shell
model state with the spin and parity of 3/2+ at 4479 keV should be associated with
the 4604 keV state. There are no other low spin states near 3.8 MeV in the sd model
space calculations that can be associated with the 3806 keV state. Thus, this could

be an intruder state. Its observation in beta decay may be due to a strong mixing

3/2+ 6901 __

 

 

 

 

 

372: 6567 _ ._ 2233*
1/2 6500— , -__
772++ 6357 * 6365 @-
3/2+ 6139 __
5/2 6030 (1/2+,3/2+) 5599 5534“
1/2+ 5493 (1/2+,3/2+1 5553 ~5‘54?”
5/2+ 5164 ““— 4923 __ 500_0
5/2+ 4875 ll/ gig/2+) 4604 :3239:
7/214532F_, . — ' 4618
3/2 4479 41/211929 131254059 4090.
3/2+ 3975 ...—”(W 243/27L 3_866 ::: 9644: 3810
“3837“" ‘ ——~»3858 — ,_ -H
3833
+ -.__.. T 3367 -3378 _
5/2 3147 __ ,,,______ __________ .-2‘LQQ 37—39
7/2“ 2795 ~--~-— 2926 2920
(17 2+1 2243 (1/_2__*_1___2_268 22:12
1/2+1990——"'
5/2' ________ _§/2_‘__ _ _____ _ __ _ __
(1) Shell model (II) Present (1") (IV) (V)

Figure 5.6: Comparison of 23F levels from the present experiment along with shell
model calculations and previous works. Shell model predicted (I) allowed beta decay
states in thick lines and forbidden beta decay states in thin lines, and the energy
levels from the present work (II) and work of Michimasa et al. (III), Belleguic et. al.
(IV) and Orr et al. (V) are shown. The likely calculated and experimental states are
con'lbined with the dashed lines. All energies are. given in keV.

 

 

 

    

   

 

 

 

 

     

0.6 . ’ - Shell model calculations
» 5°" 7 m Experimental data
0.5 1- ‘ a
r 040 1- a
0.4 " i > g
r: 1 g 530 2
9 0'3‘ a? 5 .
m ' 9‘ 1:120. a
0.2 " 5‘ 5 r,
1 ‘2 ' E a:
0 1 ~ 3? 10 r a 22
' rr . s 22
' ’5 fi 0 ,
0.0 5" I. 54 4
0 2 4 6 8 10 o 2 4 8 8 10

Excitation Energy (MeV)

Figure 5.7: Comparison of beta decay branching (right) and Gammow-Teller strengths
(left) between shell model predictions and the experiment values for the beta decay
of 23O.

with the sd-shell state. The experimental beta decay branching and B(GT) values
compared with corresponding predicted values from the same reference are shown in
Fig. 5.7. The experimental values for beta decay branching and B(GT) to the first
1/2+ state agreed reasonably with shell model predictions. The beta decay feeding to
the state at 3866 keV and above is not consistent with the theory. The inconsistency
is highlighted by the difference of the B(GT) values.

Fig. 5.8 shows the energies of the lowest 5/2+, 1/2+ and 3/2+ states in odd—
mass fluorine isotopes. The ground state of odd-mass fluorine isotopes have a single
proton in the d5/2 shell. Neutrons are added to the d5/2 shell as the mass of the
isotope increases. The systematic variation of the lowest 1/2+, 3/2+ and 5/2+ levels
in the fluorine isotopes shows a sudden increase in the splitting of the 5/2+ and
1/21’ levels in 23F as shown in Fig. 5.8. This observation could be an indication of
the appearance of N = 14 shell closure in this region. Moreover, the lowering of the
observed 3/2‘L state in 23F relative to the 3/2+ state in 17F illustrates the influence
of the monopole interaction and it can be further explained in following. The analysis

of the experimental spectroscopic strengths for 23F taken from h-Iichimasa et al. [43]

116

 

3/2'

 

 

 

 

 

 

‘50
(3/2 )
P40
l—3.0
l /2‘
3/2. '1 — 2-0
3/2‘ .
,' '- l.0
l /2‘ .'
3‘ 5/2. 1/2' '
.1?— ‘~.L&.-" 5/2’ L2- -0
17F l9F 21F 23F MeV

N=8 N=lO N=l2 N=l4

Figure 5.8: The location of experimental energy states in odd—mass fluorine isotopes
as a function of neutron number. The neutron number corresponding to each isotOpe
is given at the bottom.

and for 17F taken from Yasue et al. shows that the energies of the first 3 / 2+ states in
both structures represent the location of the d3 /2 proton single particle states. Note
that 23F has a structure with a fully occupied neutron d5/2 orbit in contrast to the
empty neutron d5/2 orbit in 17F. Therefore, the orbital split between the proton d5/2
and d3/2 is affected by the m0110pole interaction where additional neutrons in 23F

relative to 17'F causes a reduction of (15/2 — d3/2 energy gap at. 23F.

5.3 The 1‘L Excited States in 26Na

The previ(,)us measurement of 26Ne beta decay observed three 1+ excited states in
QGNa at 82.5, 1511 and 2723 keV. The shell 1110(l0l predicts four 1+ excited states
below 3 MeV with relatively strong beta branr’fhes. Based on a conmarison between
the. experimental data and the theory. Lee et al. [81.] argue that the nonobservation
of one of the 1+ state in 26Na was a clear disagreement. The similar situation was
observed with the beta decay of 28Ne reported in Ref. [\1. 81]. Three allowed beta

decay states with 1+ at 0, 2218 and 2714 keV in ”Na was observed compare to

117

 

 

 

2t’Ne 114 ms

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. ~57
0 32'
(I) O
8 .9

AM o—- CO +
0.7% QQHAAA 4085 I

(\l o (D 00'—

“339:9: , ,
“—7" 951% $533!: 2677 1* ..... 2723 (0 l l
0'2/0 : 8801 3 + +
.__.3 9°/ 2450 1 ----- 2453 (0 l l

. O
2059 2*
:5.
0')
9.: . 1513 10*,1*1
SR
W F'— l28l ll,"
. 0
K7 5.
”(KT 9" Q + + +
0 to l\
" NA.— ‘. 404 (0,1,2)
L334. ‘2'; L325 2‘3" [0“1+ 2*)
02 co l08 22..” 234 ' '
F ‘6 84 1"
‘—"" :T v 4 1. +
82.9% 26 0 3+ 26 0 3
No No
Theory Experiment

Figure 5.9: Theoretical beta decay scheme of 2GNe. The decay scheme is constructed
with a minimum limit of 0.1% for the beta branch and gamma-ray emission prob-
ability. The observed states from present work are connected to the corresponding
calculated states with the dashed lines. All energies are given in keV and the calcu-
lated half-life is 114 ms.

four allowed states in similar energy regime predicted by USD shell model for the
beta decay of 28Ne. Therefore, the discrepancy was explored for the observed energy
levels in 26Na. The theoretical beta decay scheme for 26Ne, shown in Figure 5.9, was
constructed using the USDB interactions in sd-shell model space to search for the
missing 1Jr state. The beta decay feedings greater than 0.1% are shown in the figure

with the possible deexcition gamma-rays associated with each state. The calculated

r

energies for states in 26Na have a reasonable agreement as shown in Figure 5.9.
However. the calculated gamma-ray decay intensities in 26Na. especially for higher-
lying states, showed a disagreement. with the observations. The observation of the
84(3), 1212(3), 1279(3) and 2486(4) keV gamma-rays originated from the 1+ states

at 84. 1513 and 2486 keV in the present work confirmed previous work of \Veissman

et al. In addition, we observed a weak gamma—ray at 2219(4) keV identified similar to

118

 

 

 

 

 

 

 

  
  

 

 

 

 

    

 

 

 

 

 

 

105’, 21:120 1
A E £1001 1.
3104.! “,5,5 1 /l
75 3; ‘8 80- -..-c
10 L. l - —O—N
E r Q 50r 1 +0
5102' S 1 -4-r=
I E. .g 401- : .-V.—Ne
1. '- ’ 'fit—x
1°? 5'3 2°: l //
10°’*LAJ-+eL3--I-- EO-s..a~et¢§: ......
31012141618202 ‘3' 8 1012141618 20 22
z

Neutron number Neutron number

Figure 5.10: Variation of half-lives and neutron emission probabilities with neutron
number.

the observation of a 2232(15) keV gamma-ray in 26Na by Lee et al. They assigned the
2232 keV gamma-ray to an excited level with a direct feeding to the ground state [81].
However, this transition is unlikely in the beta decay of 26Ne as the ground state of
26Na has 3“L and the allowed beta decay feeding states have 0+ or 1+. As well, the
shell model does not predict any gamma—ray transition from 1+ high energy states to
3+ ground state making the placement of the 2232 keV state uncertain. Therefore,
we assigned the 2219 keV gamma—ray to the known 2453 keV level feeding to the 234

keV state which matches with the shell model calculations.

5.4 The Half-lives and Total Neutron Emission Prob-
abilities of N eutron-rich Light Nuclei

The variation of the experimental half—lives with increasing neutron number in neutron—
rich light nuclei is shown in Figure 5.10 (left). The half-lives of 22N, 23O, 25F, 240
and 26N e were taken from the measurements of present work and the rest of half—lives
were obtained from Ref. [19]. The general trend of decreasing half-life as the neutron

number increases is seen, as expected, due to decreasing binding energy. The discon-

119

tinuities peaks at N = 14 for oxygen and neon isotopes are obvious and indicate a
possible shell closure in these isotopes. Figure 5.10 (right) shows the total neutron
emission probabilities taken from Ref. [19] and from the present work for 22N, 25F,
2"10 and 23O isotopes. There is a discontinuity at N = 10 for carbon and nitrogen
isotopes due to the influence of the N = 8 closed shell. The beta-delayed neutron
daughters of 16C and 17N (isotopes at the tip of peaks) have higher stability relative
to the surrounding isotopes due to the magic number N = 8. The peak at N = 14
for nitrogen isotopes (21N) cannot be explained based on the argument that N = 14
closed shell has an extra stability as the neutron daughter of 21N does not belong
to closed shell configuration and this peak could be due to measurement error. The
peaks shown at N = 16 for oxygen and fluorine isotopes can also be explained by the
extra stability due to N = 14 shell closure. The isotopes 24O and 25F located at the
tip of the peak have beta-delayed neutron daughters of 23F and 2‘1Ne, respectively
that have extra stability due to N = 14 shell closure and, hence, more feeding to
high lying states in the daughter that lead to a large neutron emission. The overall
analysis showed the influence of shell closure at N = 14 on the beta decay properties

particularly with oxygen and fluorine isotopes.

5.5 Conclusion and Summary

The beta decay measurements of 22N and 230 have been performed to investigate
the shell structure evolution in the region close to the oxygen drip line. The exotic
fragments were produced by frgmenting a 1401\IeV / A ‘18Ca beam in a Be target. The
A1900 fragment separator provided isotope selection. The desired isotope were im—
planted into a thin plastic scintillator to measure beta decay events. Beta-delayed
neutrons using the neutron spectroscopic array and beta—delayed gamma-rays us-
ing eight detectors from SeGA have been n'leasurer‘l in coincidence with beta. decay

events. The neutron spectroscopic array was calibrated for energy and efficiency using

120

well-known beta—delayed neutrons from 16C and 17N beta. decays. The beta—gamma
coincidence efficiency and energy calibrations for SeGA detectors were produced us-
ing the known gamma-rays from the daughters of the implanted nuclei and the offline
60Co, 2078i and 152En sources. The cocktail beams of 22N and 230 also produced a
significant amounts of 25F, 24O and 26Ne impurities, allowing the study of the beta
decay of these nuclei as well.

Half-lives and total neutron emission probabilities were determined with improved
precision and accuracy for beta decays of 22N, 23O, 25F, 240 and 26N e. Single and two
beta-delayed neutron emissions were observed from 22N decay with probabilities of
33(3)% and 12(3)%, respectively, in good agreement with literature. Five new negative
parity states and three previously known positive parity states were observed in 22O,
confirming the shell closure at N = 14 for oxygen isotopes. The observation of large
beta decay strength at high excitation energies in 220 indicates the indirect evidence
for the halo structure of 22N. The total neuron emission probability of 230 beta decay
was found to be 7(2)%, which was inconsistent with literature values. Systematic
increase in the energy of the first 1/2+ state in 23F relative to 21F indicates an
existence of N = 14 shell closure for the fluorine isotopes. New beta decay schemes
were established for 22N and 230. New transitions and unbound states were added
to the existing beta decay schemes of 25F, 240 and 26Ne.

The new results were compared to new shell model calculations particularly for
22N, 23O and 26Ne. The overall agreement between the experimental and theoretical
values for both 230 and 26Ne beta decay is reasonable with the experimental detection
limits. However, the results from 22N beta. decay have a poor agreement. with the shell

model predictions.

 

1F

 

Appendix A

Beta Decay Fitting Model

The fr.)llowing explains how z-rctivities associated with the implanted nucleus and its
decay chain vary with time during the experimental run. The activity variations of
only the parent, daughter and granddaughter will be explained the simplicity. Beta
decay experiment was performed in beam-on / off mode where the desired nucleus was
implanted during the beam-on period and the beta decay was monitored during the
beam-off time. Consider that the desired nucleus is produced at a constant rate of
p (s‘l) during the beam-on time of T (s). The initial activity of the parent nucleus
is taken to be zero at the first. cycle of the experiment. The activity variation of the
parent within the first four cycles is shown in Figure A.1. The growth of the parent
activity and the decay activities of the daughter and the granddaughter produced from

the decay of implanted parent are given in Equations A.1, A.2 and A3 respectively;

:11 =p(1— (3‘21!) (Al)
Bl 21).!)(1— (,—/\1t)((,—/\11_ (ii—A?!) (A2)
('1 = A2)\3p(l — (~741’)(ar’\1’ + sir—42’ + «Kg—43’) (.43)

where A1, A2 and A3 are decay constants for the parent. the daughter and the grand-

daughter. respectively. The basic forl’nulas for the grmvth and decay of nuclei in the

122

 

\ \

 

 

 

 

 

 

 

 

 

 

 

\ \
Time (S)‘___ T____, e—T—v ‘— T_, +-—’ TH—a <— T—-—+ +— T——> <——T——> <——T
Cycle «— n=1~——++—--— n=2 ““4 F‘— r1=3—-——~——n=4

Figure A.1: The growth and decay of the parent. nucleus. The first four cycles are
shown and cycles are numbered by n. In each cycle, the activity is grown during the
beam-on time of T s and then decay during the beam-off time of T s.

decay series are adopted from the Bateman equations [61]. The notations D, a, f} and

7 are defined by following equations.

 

 

(I:

(>12 — A1W3 - A1)

1

13 =
(/\;1 - AgllAs — *2)

 

:1
1' =-
(41 - 4311.42 — 43)

 

The activities produced during the beam-on period of the first cycle decay during
the beam—off time of T s. The decay curve of the parent during the first cycle is shown
in Figure A1 in addition to the other few cycles. Equations A.4. A6 and A.7 illustrate
how activities of the parent, the daughter and the granddaughter are varying with

time during the beam-off time, respectively.
(11 : [)(l — (JTAITV—AlU—T) (A4)

/

bl = p.1)(1—6—MT)[(r—/\1(’—T)-e‘A-sz—Tl) (A5)

+(r-'“’\1(T) — a“/\2(’I’))w-AQU—Tll

123

 

 

(‘1 = *2*3P(1— r?*’\1fl(ma"\1(”T) + sr-‘*2(’“T) + yo‘*:i(l—T)) (A6)
+p.D(l — c**17')(..-*1’1' _ €—*2T)DI((,/\2(f—T) _ e—A3(t—T))

-AITTM—AlTdee—AQT “843756—7130—7‘)

+/\2/\3p(1 — e )

The notation D1 is defined by;
_ *2
F *3 — *2

DI
The activities produced during the beam-on period of the second cycle consist of
the activities due to the implantation explained in the first cycle and the activities

that. have not decayed from the previous cycle. Both activities are added to derive the

total activity corresponding to each nucleus, given in Equations A7, A.9 and A.10.

 

gt
A2 :1)(l — e—’\1(t—2T)) +1.1(1 - e_’\1T)c—’\l (tTT) (A.7)
32 = p.D(l — e—*1(‘—‘3T))(a—*l(’-2T) _ e—*2(’—271) (A.8)
+1).D(1— (acne—men _ ...—8211411)

+1.).D(l — e_)‘1(T))(e’—’\1(T)_ p—/\2(Tl)(.*2(f—T)

C2 = A2/\3p(l — e—A1(t_2T))(nc_’\1“—271)+l’3c‘)‘2(t—2T)+ 7(r—A3(t_2T)) (A.9)
+A2A3pu —--e-’\1T)(rre—’\1(t—T)+,£3(c_’\2(t—T)+ 769364))
+p.D(1— e‘“*1T)(a‘*lT _ .1—*2T)Dl(..A2(l—T)_ ..—*3(f-T))

_’\17‘)((1c—/\1T +1’fc_)‘2T + 7(‘—’\3T)c_’\3(1_7‘)

+/\2A3p(l —— c

As ill previous cycle, the )‘rroduced activities are dem-ryed during the beam—off
period and the total activity corresponding to each nucleus is taken by adding the
decay of the activity produced in the present. cycle and the ('lecay of the remaining

activity from the previous cycle. The variation of activities with time for the parent,

124

the daughter and the granddaughter are given in Equations All), A12 and A13.

(22 :— p(l — (%TA1(T))('-’\1(t—3T)+p(1 —— 6,—A1'I‘)(,—A1(t—T) (A.10)
b2 : p.D(l — ('_)‘.1T)[(e”’\1(f-3T)—- e_)\2(f"3T)) (A.11)

+(€,—A1(r—»7’)_ e—A2(t—T)) + (541(7) _ (712(7))

(C—A1(t—T)_ e—A-2(r—T))]

c2 = A2A3p(l — e—AIT)((1e_’\1(t—3T) + ,1‘"3c.-)‘2(t~3T) + 7r2_’\3(t‘_3T)) (A12)

r V

“My,“_€—A1T)W—A1(r—T)+_3(,—/\g(r—'I')+.,,€-~A3(1—1))
+p.D(l — .;‘*1'T)(c—*1T — e‘*27’)

DlKeAQu—r) _ c—A3(t—T)) + (e—A2(f—3T) _ €,—/\3((—3T))]
“2%,,“ _C—,\1T)( —A1T+l,3e—A2’I‘ —,\3T)

are + 7e

X(e—A3(t—’1‘) + €-)\3(t—3T))

The variation of activities with time corresponding to each nucleus can be written

’ h cycle expanding the algorithm discussed above. The activity of any nucleus

for the 11
during the beam—on period contains the activity due to the. implantation or its decay
in the present cycle and activities decaying from n-l number of previous cycles. Note
that the 11m cycle begins after spending of 2T(n-1) s time from the beginning of the

experimental run. The activity relationship with time for the parent, the daughter

and the granddaughter are given ill Equations All}. :\.15 and .416.

 

. .. ,. _ _,/\1'3']‘(n.—l)
fin. : p(l — c—All‘) + ])(l -— (’—’\11‘)e_’\l(f+1)(1 (' \1'71' > (A13)
l— c” V “

 

8,. = p.0(1—r—:—*1’)(e—*1’—e—*2’)+p.D(1—c—*1T) (.414)

[€_/\1(t+,1.) 1_ €/\12F(n—-1) — C—A2(1+T) 1_ eAgQTUi—J)
I 1 — e*12T ' 1 _ CA2”

 

, . Ar “27(11—1)
——/\ r ,—,\. T ,—/\1 t+T 1-6 2
H. 11 1_, 21 1“. 21 )( 14W ))1

C” = A2A3p(l — e—Alt)(ae—’\1t+fie_’\2t + ’y'cTA3t) (A15)

, —/\12T(n—l)
. _ —All" ..—/\1(1+T) 1—0
+A2/\3p(1 c. )[oc . 1 — €_/\12,1.

 

—/\! 2T —1 _A 27" ’_1
+.%—*2(1+T) “E 2 (n ) +79—43(12+T) 1-e 3 f" l
'1 ' 1—e_’\22T ’ 1_e—A32T

+p.D(1 ——r1—)‘IT)(c—’\IT— 17*27”)D1

—A 1 0" — i r1 1’...
—*2(1+T) 1_€_ 227(71 1) ._ -—A3(t+T) 1_e A321(n 1)
i9 9 e
l— e"*2-T 1_ (21321

+A2/\3p(1 — c_)‘1T)(ae_’\1T + (361—2271 + “ye-A370
...—4311+?) (1 - E'"A32T("”1*)
—)\ 2T
1 — e 3
At the beam-off period of nfh cycle, The activities produced from all previous
cycles and the implanted activity during the beam-on period of the present cycle are
decay to yield the total activity of the desired nucleus. Equations A16. A18 and
A19 represent how the activities of the parent, the daughter and the granddaughter

t h

vary with time during the beam-off period of n cycle, respectively.

A 2TH
,_, _—AT—,\tl-€1
(1]),—I)(1_ 6 1 )C 1 (W) (A.16)

126

f

, ., _ A12Tn
bn : p.D(I — e_’\17 )[c_)‘lf (1—€———> (A.17)

CAQQT
__ A22Tn
><€_)‘ t(1 e , ))]
—)\ 2TH
—A T —)x t 1‘8 1
on = A2A3p(1—e 1 )[ae 1(W) (A..18)
...—4.1 1.133371 ,. , 4.1 2.3.333. J
-"‘ 1__e—A22T 16’ 1_c—A32T

+p.D(1— e_)‘1T)(e_)‘1T — e_’\2T)D1

—)\ 2Tn —/\ 2T7;
.44.____ _. 2 )_ .—4__.__ _. 3 )1
. 1 _ e_,\22T 1 __ e—A32T

+A2A3p(1 — e—AITXae—AIT + ,1’3e—A2T + ’ye—A3T)

X(1_)‘3t (w)
1 _ e—‘A32T
The beta-delayed neutron branch of the decay series is included by incorporating
the total neutron emission probability (Pn) to equations, where the production ac—
tivity is replaced with the product of the initial activity and Pan, value. The data used

in fitting and simulation procedures are given in Table A1

Table A1: Decay curve fitting parameters.

 

 

N uclide Half-life Pn Purity Nuclide Half-life Pn Purity

(%) (%) (%) (%)

22N 24 ms 67 51.8 24Ne 3.38 min

220 2.25 s 24Na 14.9590 h

22F 4.23 s 24o 53 ms 58 12.8

210 3.42 s 24F 384 ms 5.9 2.1

21F 4.158 s 23F 2.23 s

200 13.51 s ‘ 23N€ 37.24 s

20F 11.163 8 23o 82 ms 14.2

“251? 73 ms 23 35.8 ”We 197 ms 83.1

25Ne 802 ms 26.51.. 1.07128 s

‘25Na 59.1 s ‘21N 85 ms 81 0.6

 

 

 

 

 

 

 

 

 

 

127

 

Appendix B

Gamma-ray Spectrum Analysis

{ 1’
.2

The beta-Gamma coincidence s ectrum from 2 N ex reriment was analyzed to reveal
O .

gamma—ray energies and their emission probabilities using respective calibrations.

 

Since this spectrum contained gamma-ray transitions from all beta decays associated
with the beta decay chains of 22N, 25F and 2’10, the gamma-ray identification was
done based on knowledge from previous experiments and by extracting gated half-
lives for gamma-ray peaks, which had significant statistics. The analysis of gamma—ray
s111ectrum includes the determination of energy. emission probability and assignment.
The summary of the gamn'ra-ray spectrum analysis and the literature information on

relevant beta decays are presented in Table B5.

y
A

- 9
Table B1: Ganu’na-ray measurements and literature data for 2-N (I)

 

 

 

 

 

 

Experimental Literature
Gamma-ray Energy Emission Gamma-ray Energy Emission
(keV) Probability (%) (keV) Probability (%)
22N beta decay Half-life: 24(5) ms
1221(3) 7.0(11) 1383(4) 43(8)
1386(4) 3.0(16) 2354(6) 20(7)
1674(3) 2.2(12) 3199(8) 100(15)
3198(8) 21(3) 3310(90) < 17
331‘._(5) 2(1) 3710(00) 15(7)

 

 

 

 

 

 

 

Table B.2: Gamma-ray measurements and literature data for 22N (II)

 

 

 

 

 

 

 

 

 

 

 

 

 

Experimental Literature
Gamma-ray Energy Emission Gamma-ray Energy Emission
(keV) Probability (%) (keV) Probability (%)
220 beta decay Half-life: 2.25 s
637(3) 96(5) 72 100
708(4) 9(3) 638 98(10)
918(3) 33(3) 918 33(5)
1863(4) 59(4) 944 3(1)
1874(4) 8(3) 1862 63(3)
2501(4) 3(1) 2499 1.5(10)
22F beta decay Half-life: 4.23 s
1275(4) 101(6) 1275.54(3) 100
1901(4) 10(3) 1900.0(6) 8.7(4)
2084(6) 84(5) 2082.6(5) 81.9(2)
2167(5) 58(5) 2166.1(5) 61.6(14)
2992(7) 5(3) 2987.7(9) 7 .0(3)
4372(9) 11(3) 3983.5(10) 1.2(2)
4247.9(10) 1.0(2)
4366.1(10) 11.3(6)
210 beta decay Half-life: 3.42 s
278(3) 13(3) 279.92(6) 324(12)
933(3) 6(3) 933.2(3) 127(12)
1451(6) 11(6) 1450.5(2) 216(12)
1731(5) 42(4) 1729.2 90(12)
1751(5) 9(4) 1730.28(8) 1000(12)
1788(5) 13(3) 1754.74(8) 248(12)
1885(4) 8(3) 1787.16(8) 311(12)
1884.01(9) 150(12)
3179.43(10) 115(12)
3459.38(13) 65(12)
3517.40(10) 338(12)
4572.2(4) 104(12)
4583.5(3) 116(12)
21F beta decay Half-life: 4.158 s
349(3) 1(3) 350.725(8) 10000
1395(4) 12(5) 1395.131(17) 1713(30)
1745.8 86.4(15)
1890.4(3) 020(3)
1989(1) 0.022(6)
2779.4(3) 0.177(17)

 

 

 

 

129

 

 

Table 8.3: Gamma-ray measurements and literature data 22N (III)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Experimental Literature
Gamma-ray Energy Emission Gamma-ray Energy Emission
(keV) Probability (%) (keV) Probability (%)
21F beta decay Half-life: 4.158 s
2793.94(5) 020(3)
3384.6(2) 0.039(6)
3533.2(4) 0.326(17)
3735.2(5) 0.278(26)
3883.9 0.107(14)
4174.1(3) 357(7)
4333.52(25) 5.31(14)
4525.84(24) 1.06(3)
4684.27(25) 313(11)
200 beta decay Half-life: 13.51 s
1057(2) 100(2) 325.73(14) 0. 0001(1)
653.2(3) 0. 0001(1)
656.00(3) 0.0002(2)
983.53(4) 0.0011(2)
1056.78(3 ) 99. 975(3)
1187.70(6) 0.0001(1)
1309.17(3) 0.0023(1)
1644.50(8) 0.0020(2)
1843.74(3) 0.0018(1)
2179.09(4) 0.0025(2)
2431.43(99) 0.0019(8)
2504.54(18) 0.0010(1)
3488.13(4) 0.0196(68)
2UF beta decay Half-life: 11.163 8
1634(2) 100(3) 1633.602(15) 99.9995
3332.54(20) 0.0082(60
4965.85(20) 0.00005(2)
23F beta decay Half-life: 2.23 s
492(2) 6(2) 492.9(7) 11(3)
819(4) 8(3) 815.2(5) 25(5)
1017(2) 9(3) 1016.7(5) 20(6)
1701(3) 32(6) 1701.44 100(5)
1820(3) 17(4) 1822.25(21) 47.4(26)
1918(4) 7(4) 1919. 3(5 ) 19.3(25)
2127(5) 24(7) 2128. 8(7) 68(11)
2314. 2(8) 7.7(27)
2414. 3(4) 15(3)
2515.9(13) 2.9(10)

 

 

 

130

Table 8.4: Gamma-ray measurements and literature data for 22N (IV)

 

Experimental

Literature

 

Gamma-ray Energy

Emission

Gamma-ray Energy

Emission

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(keV) Probability (%) (keV) Probability (%)
23F beta decay Half—life: 2.23 s
2734.2(5) 11.9(18)
3431.4(4) 25.4(18)
3830.7(4) 8.8(9)
Y3Ne beta decay Half-life: 37.24 s
438(3) 32(2) 439.988 33.0(13)
1635.96 100(4)
2075.91 0.101(8)
2541.92 0.027(2)
2981.85 0.038(2)
240 beta decay Half-life: 61(26) ms
520(3) 14(4) 521.5(3) 14.3(20)
1312(5) 13(5) 1309.5(5) 12.0(28)
1832(4) 30(5) 1831.8(5) 28.3(30)
3002(8) 14(4)
24F beta decay Half—life: 400(50) ms
1983(4) | 1981.5 ] 100
24Ne beta decay Half-life: 338(2) min
474(2) 101(7) 472.202 100
878(3) 5(3) 874.41 8.0(3)
24Na beta decay Half-life: 14.9590(12) h
1389(4) 100(5) 998.82 0.0014(2)
2758(4) 99(8) 1388.833 100
2754.028 99.944(4)
2889.50 0.0003(1)
3888.19 0.052(4)
4237.96 0.0011(2)
75F beta decay Half-life: 90(9) ms
572(3) 12(2) 574.7(5) 9.5(9)
1238(3) 7(2) 1234
1818(4) 11.2(38) 1813.4(12) 11.8(18)
1823(4) 10.8(38) 1822
1703(3) 31(5) 1702.7(7) 39.1(28)
2090(5) 25(4) 2090
2187(4) 5(2) 2188.8(13) 7.2(18)

 

 

 

 

Table B.5: Gamma-ray measurements and literature data for 22N (V)

 

Experimental

Literature

 

Gamma-ray Energy

 

Emission

Gamma-ray Energ

 

Emission

 

 

 

 

 

 

(keV) Probability (%) (keV) Probability (%)
25Ne beta decay Hal4—life: 602(8) ms
87(3) 89.53 95.5(6)
981(4) 18(4) 979.77 18.1(19)

1071(3) 2(1) 1089.30 2.3(4)
2203(4) 3(2) 1133.00 0.4(3)
2112.00 0.62(19)
2202.00 1.1(3)
3219.00 0.53(15)
3597.00 0.22(18)
3687.00 0.96(24)
25Na beta decay Hal4-life: 59.1(6) s
388(2) 10(3) 389.70 97.5(17)
583(4) 12(2) 585.03 100.0(14)
978(4) 15(4) 838.84 0.800(20)
1813(4) 10(3) 974.72 115.0(17)
989.85 1.280(24)
1379.53 1.78(4)
1811.711 72.9(11)
1984.53 1.128(17)
2216.32 0.719(16)
2801.30 0.380(12)

 

 

 

132

 

 

 

The radioactive bean'i of 230 was implanted with impurities of 26Ne, 2"117 and 21N
in 230 experiment. Thus. the beta—gamma coincidence spectrum from 230 experiment
contains gamma-ray decay events from beta decay of impurities and their decay series
in addition to 23O decay series. The results of the analysis of the beta-gamma—ray
coincidence spectrum are shown in Table B.7 and compared with relevant literature

values.

Table B.6: Gamma—ray measurements and literature data for 230 (I)

 

 

 

 

 

 

 

Experimental Literature
Gamma-ray Energy Emission Gamma—ray Energy Emission
(keV) Probability (%) (keV) Probability (%)
730 beta decay Hal4-life: 82(+45-28) ms
638(3) 1.5(8) 913(7)
911(4) 2.7(12) 1240(12)
1237(4) 3.1(9) 1696(25)
1621(6) 5.7(10) 1706(21)
1716(6) 2.1(6) 1711(8)
2243(8) 51.5(12) 2003(12)
2673(9) 5(1) 2268(12)
2926(10) 7(2) 2644(49)
3367(13) 4.5(10) 2920(3)
3868(15) 10.1(16) 3378(11)
4066(16) 17.1(17) 3445(54)
3858(24)
3985(41)
4059(11)
4732(59)
2313‘ beta decay Hal4-1ife 2.23 s
493(2) 3.1(7) 492.9(7) 11(3)
816(4) 7(3) 815.2(5) 25(5)
1017(2) 6.5(12) 1016.7(5) 20(6)
1701(3) 33(2) 1701.44 100(5)
1822(3) 18(4) 1822.25(21) 47.4(26)
1920(4) 8(2) 1919.3(5) 19.3(25)
2132(5) 24(2) 2128.8(7) 68(11)
2316(7) 3(1) 2314.2(8) 7.7(27)

 

 

 

 

133

 

 

 

Table B.7: Gamma—ray measurements and literature data for 230 (II)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Experimental Literature
Gamma-ray Energy Emission Gamma-ray Energy Emission
(keV) Probability (%) (keV) Probability (%)
23F beta decay Hal4—life: 2.23 s
2415(6) 4(2) 2414.3(4) 15(3)
2734(7) 5(1) 2515.9(13) 2.9(10)
3432(8) 9(1) 2734.2(5) 11.9(16)
3831(11) 3(1) 3431.4(4) 25.4(18)
3830.7(4) 6.8(9)
23Ne beta decay Hal4-life: 37.24 s
439(3) 33(1) 439.986 33.0(13)
1636(3) 1.2(4) 1635.96 100(4)
2075.91 0.101(6)
2541.92 0.027(2)
2981.85 0.038(2)
22F beta decay Hal4—life: 4.23 s
1274(3) 99(7) 1275.54(3) 100
2083(6) 73(12) 1900.0(6) 8.7(4)
2166(5) 56(13) 2082.6(5) 81.9(2)
2166.1(5) 61.6(14)
2987.7(9) 7.0(3)
3983.5(10) 1.2(2)
4247.9(10) 1.0(2)
4366.1(10) 11.3(6)
2(’Ne beta decay Hal4—1ife: 197(1) ms
84(3) 95 82.5 100
153(3) 3.4(2) 151 3.3(7)
232(2) 4.4(2) 232.5 4.9(10)
404(3) 0.4(1) 408 0.4(2)
1212(3) 1.2(3) 1211 1.3(4)
1279(3) 5.4(2) 1278 5.9(10)
2219(4) 0.6(2) 2489 1.1(3)
2486(4) 0.7(2)
2bNa beta decay Hal4—life: 1.0'128(25) s
1003(2) 1.1(1) 1002.61(12) 1.282(8)
1129(2) 5.9(2) 1128.89(13) 593(3)
1365(2) 037(6) 1365.21(15) 0.3517(15)
1411(3) 2.3(3) l411.32(16) 2.466(7)
1775(3) 1.7(2) 1775.08(20) 157(4)
1809(2) 97(2) 1808.71(20) 100
1898(3) 21(4) 1898.78(22) 2.074(7)
2528(5) 1.2(2) 2524.1(3) 143(3)
2542(5) 2.2(2) 2541.6(3) 239(5)

 

 

134

 

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