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dissertation entitled

'Ground State of 10L! and 13Be'

presented by

Shigeru Kennedy Yokoyama

has been accepted towards fulfillment
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Ph . D. degree in _Eh¥s_Lcs_

 

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mm:

 

GROUND STATE OF 'OLi AND l3Be
By

Shigeru Kennedy Yokoyama

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department Physics and Astronomy

1996

ABSTRACT

GROUND STATE OF 'OLi AND 12Be
By

Shigeru Kennedy Yokoyama

llLi nucleus is known to have the structure of a 9Li core and a two-neutron halo and is the
heaviest particle stable Li isotope. The ground state study of 10Li is important to understand
the structure of 11Li since it has information on the n +9Li interaction which determines a
significant part of the 11Li three body structure. A direct mass measurement of 10Li is im-
possible since it has very short lifetime (~10'21 3). Previous experimental studies have
shown conflicting results for the 10Li ground state. l3Be information is also crucial for un-
derstanding of 14Be structure similar to the 10Li and 1 1Li case. The goal of the current work
is to determine the ground state properties of 10Li and 13Be.

The technique of sequential neutron decay spectroscopy (SNDS) was employed around
0° for the present study. The nuclei IOLi, and 13Be were created via fragmentation. They
decayed immediately in the target and emitted a neutron and a fragment (9Li and 12Be)
which were separated with magnets and detected. The relative velocity spectra were created
from the experimental information. Monte Carlo simulations were performed and the re-
sults were compared with the data. The limit of the decay constants for each isotope were
extracted via x2 analysis.

The low-lying s-wave ground state was established for 10Li at E, .~. 50 keV or as z -40
fm. The result of 13Be could be either interpreted as a low-lying s-wave state or the tail of

the known state at 2.0 MeV.

To my wife, Kelly

iii

ACKNOWLEDGMENTS

First, I would like to thank my advisor, Michael Thoennessen. He has always been a
great help to me. His perspective always helped me stay on the right track and showed me
the way to proceed. I could never have come this far without his help.

I thank professors Pawel Danielewicz, Michael Harrison, Wayne Repko, and Brad
Sherrill for being my guidance committee. I also thank professor Gregers Hansen for in-
sightful discussions and providing the scattering length calculations. As a collaborator, I re-
ally enjoyed having discussions with professor Aaron Galonsky.

I learned a lot from a former post-doc of our research group, Robert A. Kryger. He es-
pecially contributed to the improvement of my computer skills a great deal. Peter Thirolf,
a former post-doc, was a good example to me in his way of being unintimidated with having
too many things to do. His solid way of handling complicated tasks influenced my attitude
toward the thesis writing.

It was very lucky for me to be able to work with Easwar Ramakrishnan, Afshin Azhari,
Thomas Baumann, and Marcus Chromik as colleagues. I believe we were one of the best
‘teams’ in the NSCL. I would like to thank Afshin Azhari and Mike Fauerbach for their
proofreading of my thesis drafts.

It was really enjoyable interacting with the people in the NSCL including John ‘Ned’

Kelley, Raman Pfaff, Don Sackett, Larry Phair, Mike Lisa, Wen-Chen Hsi, Tong Li, Eu-

gene Gualtieri, Stefan Hannuschke, Q. Pan, Damian Handzy, Jim Brown, Magic Hellstrom,
Chris Powell, Jon Kruse, J ing Wang, Phil Zecher, Mathias Steiner, Sally Gaff, Barry Davis,
Heiko Scheit, Thomas Glasmacher, Jac Caggiano, N jema Frazier, Corn Williams, Richard
Ibbotson, Roy Lemmon, Gerd Kunde, Razvan Popescu, Luke Chen, Renan Fontus, and Ky-
oko Fuchi.

I would like to thank all the staff of the NSCL, especially Raman Anantaraman, Reg
Ronningen, Richard Au, Ron Fox, Barbara Pollack, John Yurkon, Dennis Swan, Dave
Sanderson, and Craig Snow. They saved me from many troubles I encountered while I con-
ducted experiments and research in the NSCL.

My experience at the NSCL gave me the privilege to meet international visitors such as
Toshiyuki Kubo, Yoshiyuki Iwata, and Akos Horvéth. Meeting and working with people
from all over the world was a very unique and valuable experience.

I also would like to thank my computer at home PowerMacintosh 7500/ 100, Zip drive,
and 28.8kbps modem for their stable operation. I wrote the thesis with this system. At the
beginning of 1996, 100MHz clock speed and 28.8kbps modem was kind of fast but I’m sure
that readers will find it ridiculously slow in the very near future.

I would like to thank my friend Dr. Frederick 1. Kaplan for his encouragement and help
in my life in Michigan.

I am also thankful for my friendship family in Michigan, Roy and Elaine Pentilla. Their
hospitality was very heart warming especially during the cold holiday season in Michigan.

I thank my family in Japan and my brother Naohiko in LA. for all sorts of support. I’m
glad that all of my family could visit me in East Lansing while I was studying at Michigan

State University.

Finally I thank my wife Kelly Yokoyama Kennedy for her love and support. In finally
reaching this goal I deeply thank all those people around me in Michigan. I will never forget

the people and the beautiful campus of Michigan State University.

vi

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................ ix
LIST OF FIGURES ........................................................................................................ x
Chapter 1
Introduction ...................................................................................................................... 1
Chapter 2
Neutron Halo Nuclei ...................................................................................................... 3
2.1 The Two-Neutron Halo Nucleus 11Li ....................................................... 3
2.2 10Li And “Li Three-Body Models ........................................................... 6
2.3 Recent Reports of The loLi Ground State ............................................... 13
2.4 14Be Three-Body Models and 13Be Ground State .................................. 22
Chapter 3
Experimental Details .................................................................................................... 25
3.1 Experimental Method .............................................................................. 25
3.2 Mechanical Setup .................................................................................... 27
3.3 Neutron Detectors ................................................................................... 31
3.4 Fragment Telescope ................................................................................ 33
3.5 Electronics and Data Acquisition ............................................................ 37
Chapter 4
Data Analysis ................................................................................................................. 41
4.1 Overview ................................................................................................. 41
4.2 Calibration of Detectors .......................................................................... 42
4.2.1 Calibration of the Fragment Telescope ........................................ 42
4.2.2 Neutron Detector Calibration ....................................................... 51
4.2.3 Time Calibration ........................................................................... 53
4.3 Coincidence Fragment Spectra ............................................................... 55
4.3.] He group ....................................................................................... 57
4.3.2 Li Group ....................................................................................... 58

vii

4.3.3 Be Group ....................................................................................... 60

4.4 Simulation of Experiment ....................................................................... 61

Chapter 5
Results and Discussion ................................................................................................ 65
5.1 Selection of The Valid Events ................................................................. 65
5.2 The Relative Velocity Spectrum of 7He .................................................. 65
5.3 The Relative Velocity Spectrum of 10Li .................................................. 69
5.3.1 The s-wave Case ........................................................................... 75
5.3.2 The p—wave Case .......................................................................... 80
5.4 The Relative Velocity Spectrum of 13Be ................................................. 82
5.4.1 The s-wave Case ........................................................................... 84
5.4.2 The d-wave Case .......................................................................... 88

Chapter 6
Summary and Conclusions ......................................................................................... 92
BIBLIOGRAPHY ......................................................................................................... 94

viii

4.3.3 Be Group ....................................................................................... 60

4.4 Simulation of Experiment ....................................................................... 61

Chapter 5
Results and Discussion ................................................................................................ 65
5.1 Selection of The Valid Events ................................................................. 65
5.2 The Relative Velocity Spectrum of 7He .................................................. 65
5.3 The Relative Velocity Spectrum of 10Li .................................................. 69
5.3.1 The s-wave Case ........................................................................... 75
5.3.2 The p-wave Case .......................................................................... 8O
5 .4 The Relative Velocity Spectrum of 13Be ................................................. 82
5.4.1 The s-wave Case ........................................................................... 84
5.4.2 The d-wave Case .......................................................................... 88

Chapter 6
Summary and Conclusions ......................................................................................... 92
BIBLIOGRAPHY ......................................................................................................... 94

viii

LIST OF TABLES

Table 3.1 A example of an output file of the INTENSITY [Win92] calculation for
an 80 MeV/nucleon 8O beam (intensity = 10 pnA) with a 94 mg/cm2
9Be Target. ................................................................................................... 29

Table 4.1 Calibration beam energies for different target thicknesses. ......................... 42

ix

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

LIST OF FIGURES

[Kob88] (a) Transverse-momentum distributions of 6He fragments from the

reaction 8He + C. The solid lines are fitted Gaussian distributions with a re-

duced width of 0'0 = 59 MeV/c. (b) Transverse-momentum distributions of 9Li
fragments from reaction 11Li + C. The solid lines are fitted distributions with
two Gaussian components. The dotted line is a contribution of the wide com-
ponent in the 9Li distribution. The reduced width of the two components are
0'0 = 71 MeV/c and 0'0 = 17 MeV/c, respectively ........................................... 5

[Han87] The calculated relations between the matter r.m.s. radius and Zn sep-
aration energy with mass parameters corresponding to 11Li and 6He by Hans-
en and Jonson. The experimental values for radii and Zn separation energies

were taken from [Tan85] and [Wap85]. ......................................................... 7

[Ber91] The dependence of the 11Li two neutron separation energy to the 10Li
1171/2 state energy predicted by Bertsch and Esbensen. The solid line and
dashed line show correlated and uncorrelated neutron cases, respectively. ...8

[Tho94] The comparison of the calculated 9Li core momentum distributions
from 11Li fragmentation by Thompson and Zhukov and the experimental data
by Orr et al. (square) and Kobayashi et al. (star). The calculation includes s-
wave potential as well as p-wave potential in n-9Li interaction. .................. 10

[Tho94] The calculated relation between 11Li binding energy, Vp1/2 resonance
energy, and vsm scattering length. The horizontal solid line shows the ob-
served two-neutron binding energy of 11Li by Kobayashi et al. [Kob92]....11

[Wil75] The energy spectra of 8B was obtained from the following reactions
using 121 MeV 12C beam. (a) 12C(9Be,83)13B is for an energy calibration, (b)
9Be( Be,8B)loLi is from singles events, and (c) 9Be(9Be,gB)mLi is from co-
incidence events with 9Li from the breakup of the recoiling 10Li. The angle
was at 14° in the laboratory. ......................................................................... 13

[Ame90] The spectrum of protons produced in absorption of stopped 1f me-
sons by 11B nuclei. The arrow shows the resonance at E, = 0.15 i 0.15 MeV
and l" < 0.4 MeV. .......................................................................................... l4

Figure 2.8

Figure 2.9

Figure 2.10

Figure 2.11

Figure 2.12

Figure 2.13

Figure 2.14

Figure 3.1

Figure 3.2
Figure 3.3

Figure 3.4

Competition between 31 ,2 and pl ,2 levels among N=7 nuclei [Tal60]. The lev-
els are shifted to match the lowest pl ,2 state. Extrapolation implies the non-
normal parity ground state of 10Li [Bar77]. .................................................. 14

[Boh93] Energy spectra of 12N from the reaction of 9Be(13C,12N)10Li by
Bohlen et al. The ground state (E, = 0.42 MeV) and the first excited state at
E, = 0.38 MeV (E, = 0.80 MeV) are not completely resolved. .................... 15

[You94] The energy spectrum from the transfer reaction llB(7Li,gB)loLi by
Young et al. It shows a strong evidence of the state at E, z 500 keV. ......... l6

[Kry93] The relative velocity spectra of 9Li + n coincidence events obtained
with sequential neutron decay spectroscopy by Kryger et al. The dashed line
is a simulated spectrum with the parameter by Wilcox et al. (E, = 800 keV, l
= 1) superimposed on the Gaussian background (dotted). The solid line is a

simulated spectrum with the parameter by Amelin et al. (E, = 150 keV, l = 0)
plus the Gaussian background. ..................................................................... 17

[Zin95] Radial momentum distributions of neutrons from 10Li breaku re-
ported by Zinser et al. 10Li was created by one proton stripping from 1Be
(top) or by one neutron stripping from 11Li (bottom). In the top figure, the top
dotted line assumes an I: 1 resonance at 0.05 MeV. The two sets (as = -5 and
-50 fm) of the calculations were shown with the 9Li recoil widths (IQ = 100
MeV/c (solid) and 0Q = 0 MeV/c. In the bottom figure, two contributions
were considered in the theoretical curves. One is diffraction (1/3 intensity)
and the other is the intermediate state of 10Li (2/3 intensity) which was as-
sumed to be a pure s state. ............................................................................ 19

[Ost96] Spectra of the 10Be(12C,12N)wLi reaction by Ostrowski et al. Al-
though the state reported by Bohlen et al. [Boh93] at E, = 0.42 MeV was as-
sumed to be there for fitting, it is not resolved from the ground state at E, =
0.24 MeV. The state reported by Wilcox er al. at 0.8 MeV was not observed
in these spectra. ............................................................................................. 21

[Kor95] The proton spectrum from the reactions CD2(12Be,p) (solid) and
C(12Be,p) (dotted). The lowest state extracted reliably is at E, = 2 MeV. ...23

Kinematic diagram of the sequential neutron spectroscopy for the 10Li de-

cay. ................................................................................................................ 25
.Floor plan of the National Superconducting Cyclotron Laboratory. ............ 28
Top view of the experimental setup. ............................................................. 30

The dimensions of one neutron detector and the configuration of the whole de-
tector array. The gray area shows the neutron sensitive part. ....................... 32

xi

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

Figure 3.10

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Simulated efficiency curve of the neutron detector with a sideway geometry.
It was calculated with the code KSUEFF [Cec79]. ...................................... 33

Efficiency plot of the neutron detection for the 10Li neutron decay for the de-
cay energy range of 0.00 MeV < E, < 1.00 MeV. The energy dependent solid
angle coverage of the neutron detectors, the energy dependent neutron detec-
tor efficiency, and fragment detector acceptance are folded as a total neutron
detection efficiency. The upper abscissa indicates a corresponding decay en-
ergy. .............................................................................................................. 34

Schematic of the fragment telescope. ........................................................... 35

Front view of one of the AE Si detectors. The gray area shows the sensitive
region. The crossed lines on the gray area indicates the segmentation
lines. .............................................................................................................. 36

Structure of CsI(Tl) E detector array. Each of the nine crystals were wrapped
with white blotter paper independently to optically isolate them from each
other. ............................................................................................................. 37
Diagram of the electronics. ........................................................................... 38
Two dimensional histogram of energy loss in the AE2 detector’s quadrant
number 1 versus time of flight of the fragments. m/q = isotopes are selected
using the A1200 mass analyzer ..................................................................... 44
Two dimensional histogram of energy loss in the AE2 detector’s quadrant
number 1 versus total energy in the E3 detector of the fragments. The large
square gate in the plot was applied to select the valid signal for

a projection .................................................................................................... 44

Energy spectrum of the calibration beam with an A/Z = 3 gate. .................. 46

Quadratic fitting for energy calibration of the 6He fragment for each E detec-
tor. The E2 detector was omitted due to its nonlinear behavior. .................. 47

Quadratic fitting for energy calibration of the 9Li fragment for each E detec-
tor. The E2 detector was omitted due to its nonlinear behavior. .................. 48

Quadratic fitting for energy calibration of the 12Be fragment for each E detec-
tor. The E2 detector was omitted due to its nonlinear behavior. .................. 49

Energy loss spectrum of the calibration beam with AlZ=3 gate ................... 50

Timing diagram of the neutron signals and the QDC gate. Shaded areas show
the integrated part of the neutron signal. ...................................................... 51

xii

Figure 4. 9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 4.13

Figure 4.14

Figure 4.15

Figure 4.16

Figure 4.17

Figure 4.18

Figure 5.1

Figure 5.2

Two dimensional plot of the neutron detector signal. A 239Pu— Be source was
used to supply y—rays and neutrons along with6 Co y-ray source. ............... 52

Compton edges of a 60C0 source and a 239Pu-Be source in a one dimensional
plot of the neutron total signal. It was obtained by using the y—ray condition
established in the two dimensional plot (Figure 4.9). ................................... 53

The relation of the fragment time signal, the neutron detector signal, and the
RF time signal. The earliest and latest possible neutron signal have margins

of ~ 25 us from the edge of the fragment signal to take a fragment time spread
into account. .................................................................................................. 56

AE_1 (first quadrant of AB) vs. E3 plot of He group. The oval contour shows
a 6He gate. ..................................................................................................... 57

AE_1 (first quadrant of AE) vs. TOF (thin plastic time) plot of He group. The
contour gates show the 6He reals gate and the 6He randoms gate. ............... 58

AE_1 (first quadrant of AB) vs. E3 plot of the Li group. The contour shows a
9Li isotope gate. ............................................................................................ 59

AE_1 (first quadrant of AE) vs. TOF (thin plastic time) plot of Li group. The
contour gates show the 9Li reals gate and the Li randoms gate. ................. 59

AE_1 (first quadrant of AE) vs. E3 plot of the Be group. The contour shows a
12Be isotope gate ........................................................................................... 60

AE_ 1 (first quadrant of IAE) vs. TOF (thin plastilc2 time) plot of Be group. The
contour gates show the 2Be reals gate and the 2Be randoms gate. ............ 61

sz versus neutron TOF resolution plot. xvz is for the fit of the 7He neutron
decay simulation and the data. The minimum xv 2of (best fit) 18 at tmes~ ~.0 70
ns. .................................................................................................................. 63

The relative velocity spectrum for 6He + n coincidence events. The circles
with the error bars are the data. The dashed line shows the estimated back-
ground. The dotted line is the simulated decay of ground state of 7He without
the background and the solid line is a sum of the background and the simula—
tion. ............................................................................................................... 66

The Breit-Wigner lineshapes of 7He state at Er = 440 keV with the width of
l" = 160 keV. The solid line shows the actual case with the angular momentum
l = 1. For the comparison, I = 0 case is shown with the dashed line. The low
energy region of the peak for the l = 1 case is suppressed compared to the

l = 0 case. .............................. . ....................................................................... 68

xiii

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10
Figure 5.11

Figure 5.12

Figure 5.13

Figure 5.14

Figure 5.15

The relative velocity spectrum simulation of 7He -) 6He + n decay for the dif-
ferent time resolutions. The dotted line shows a case of perfect resolution (out
= 0.00 ns, out = 0.00 ns). The solid line shows a case of a current experimental
resolution (<3tn = 0.70 ns, Otf = 0.057 us). The dashed line shows a case of the
experiment by Kryger et al. (th = 0.89 ns, 0“: 0.89 ns). ........................... 70

The relative velocity spectrum of 10Li -—> 9Li + n. The convention of the data
point and the Gaussian background are the same as the 7He spectrum. The
dashed side peaks are the simulation of the p-wave state at E, = 538 keV re-
ported by Young et al. The dashed central peak 18 the simulation withl= 0,
E,= 50 keV, F0: 241keV. This 15 the fit at xvz minimum for the s-wave neu-
tron. ............................................................................................................... 72

The level diagram of the possible two cases of the neutron decay of 10Li. ..74

The valid region of the Er and F space based on the x2 analysis and Wigner
limit for s- wave initial state of1 i. ............................................................. 76

The result of the calculations with the Faddeev three body function for the

11Li binding energy as a function of 1pm resonance energy and the scattering
length of the 131,2 low- -lying state. The current result a = -40. 0 fin is indicated
with the solid line. ......................................................................................... 78

The 10L1 lineshapes used for the best fit of the simulation to the data. The rel-
ative population of the s-wave and p-wave is 33% and 67%, respectively. .79

The valid region of the E, andl" space based on the x2 analysis and Wigner
limit for p-wave initial state of 8Li. ............................................................. 81

The relative velocity spectrum of the 12Be + n coincidence events. ............ 83
The level diagram of the possible two cases of the neutron decay of ”Be. .85

The valid region of the E, and [‘0 space based on the x2 analysis and the Wign-
er limit for s-wave initial state of Be. ........................................................ 86

The 13Be lineshapes used for the best fit of the simulation to the data. The rel-
ative population of the s-wave and d—wave is 44% and 56%, respectively. .87

The valid region of the E, and 1'}; space based on the x2 analysis and Wigner
limit for d-wave initial state of1 Be. The case (a) in Figure 5.11 18
assumed. ........................................................................................................ 89

The result of x2 analysis 1n the case of d—wave state in 13Be as an initial state
and the first excited state of1 2Be as a final state. ......................................... 90

xiv

Chapter 1

Introduction

The field of exotic nuclei is currently one of the most active areas studied in nuclear phys-
ics. Recent advancements of equipment and facilities have provided unique opportunities
to study nuclei near and beyond the neutron and proton drip lines. There are two major mo-
tivations to study exotic nuclei. One reason to study exotic nuclei is for nuclear astrophys-
ics. The stellar evolution process begins with H and He atoms from the big bang [R0188].
Starting out with hydrogen burning, the more complex atoms were formed via various nu-
clear reaction cycles such as the CNO (carbon-nitrogen-oxygen) cycle [Won90]. Exotic nu-
clei often play an important role within these reaction cycles and the information on those
nuclei is crucial to explain the abundance of the elements and to determine the age of stars.
Another motivation to study exotic nuclei is that unique tests of the fundamental laws of
physics and nuclear models can be carried out by studying the properties of those nuclei.
Exotic nuclei are either neutron or proton rich. The current work is a study of 10Li and
13Be, which are light nuclei on the neutron dripline. The nuclei 11Li and 9Li are known to
be bound nuclei and 11Li is the heaviest particle stable Li isotope. The nucleus 11L1 is also
known to consist of a two-neutron halo around a 9Li core. Unlike other nuclei which have
an uniform nuclear matter density, halo nuclei have a lower nuclear matter density region

. (halo) around the normal nuclear matter density region (core). The recent experimental ef-

2

forts to study the halo nuclei also stimulated the interest of theorists. Various model calcu-
lations for the halo nuclei have been reported. For the 11Li case, structure information of
10Li, which is an unbound nucleus, turns out to be crucial for the theoretical calculations as
a subsystem of the halo nucleus llLi. One of the goals of the current experiment was to
measure the ground state energy level of 10Li. Since it is particle unbound, it is impossible
to measure the energy in a direct way. We employed the technique of neutron sequential
decay spectroscopy at 0° and extracted the ground state energy and width of 10Li.

The situation in Be isotopes is similar to the Li isotopes. The nucleus 14Be is the heavi-
est stable isotope and also considered a two-neutron halo nucleus whereas 13Be is particle
unstable. Again the n-12Be interaction, or 13Be is important for the understanding of 14Be.
Previous work and the relations of the 10Li structure to the 11Li model as well as 13Be and

14Be are discussed in the next chapter.

Chapter 2

Neutron Halo Nuclei

2.1 The Two-Neutron Halo Nucleus llLi

llLi is the heaviest particle-stable nucleus among the Li isotopes. It has been known as a
neutron drip-line nucleus since 10Li is unbound toward one neutron decay and 12Li is not
bound either. 11Li has a half-life of 8.2 ms for B decay to 1lBe. Tanihata et al. [Tan85]
measured the interaction cross sections (0,) of lithium isotopes (6Li, 7Li, 8Li, 9Li, and llLi)
and beryllium isotopes (7Be, 9Be, and 10Be) on the targets of Be, C, and A1 at 790 MeV/
nucleon using the novel technique of exotic isotope beams produced through projectile
fragmentation in high energy heavy ion reactions. The extracted root mean square (rms) nu-
clear radii from the 0’, showed that 11Li has an unusually large radius (R, = 3.14 fm) com-
pared to neighboring nuclei (R, == 1.2 fm x A“3 [Kra88] (= 2.5 fm for 9Li)). It was
interpreted as a large deformation and/or a long tail in the matter distribution due to the
weakly bound neutrons.

To investigate the nature of the large matter radius of 11Li, different experiments were
performed, for example momentum distribution measurements. Previous studies showed
that the momentum distribution of fragmentation products have a Gaussian distribution

which is isotropic in the projectile rest frame [Gre75]. The width of the Gaussian

4

distribution 0' is related to the Fermi momentum or the temperature corresponding to the
nuclear binding energy [Gol74] and the momentum distribution inside the projectile
[Hiif81]. Goldhaber [Gol74] parameterized the width 0' of the Gaussian shape momentum
distribution by a single parameter 0'0 (reduced width) defined as

F _
= 06%? <3»

62

where F is the mass number of the fragment and A is the mass number of the projectile.
Kobayashi et al. [Kob88] measured the transverse momentum distribution of 9Li from
the fragmentation of 11Li on a C target to investigate the structure of 11Li. The secondary
beams of 11Li, as well as 8He, and 6He of 790 MeV/nucleon were fragmented on a C, and
a Pb target and projectile fragments were measured at zero degrees with a magnetic spec-
trometer. The transverse-momentum distribution of 6He fragments from the reaction 8He +
C (Figure 2.1 (a)) exhibited a Gaussian shape. For the He data, a reduced width of 00 ~ 60
MeV/c was extracted. The momentum distribution of 9Li from the reaction 11Li + C (Figure
2.1 (b)) showed a different structure. Two Gaussian distributions were superimposed in the
11Li spectrum. The reduced width of the wider component was 0'0 = 71 MeV which is sim-
ilar to the value of 12C fragmentation data (0'0 z 78 MeV) by Greiner et al. [Gre75]. The
second component had an extremely narrow reduced width of 00 = 17 MeV. The momen-
tum distribution of one-nucleon-removal fragments reflects the momentum distribution of
the removed nucleon at the surface of the projectile [Htif81]. The idea was extended to a
several-nucleon-removal channel to interpret the two components in the momentum distri-
bution of 9Li. The narrow component was considered to originate from the removal of the

two weakly bound outer neutrons in llLi. The broader component was interpreted as a re-

sult of the removal of normally bound neutrons, decay of excited 9Li, and the decay of 10Li.

 

(’1
O

do/dpj [orb]

 

 

 

 

 

 

 

 

0
50
'3'
E.
63
'b
\
-8
0 . I 1 l L i J‘..
'200 -100 0 100 200
P, [MeV/c]

Figure 2.1: [Kob88] (a) Transverse-momentum distributions of 6He fragments from re-
action 8He + C. The solid lines are fitted Gaussian distributions with a reduced width of 60
= 59 MeV/c. (b) Transverse-momentum distributions of 9Li fragments from reaction 11Li
+ C. The solid lines are fitted distributions with two Gaussian components. The dotted line
is a contribution of the wide component in the 9Li distribution. The reduced width of the
two components are 00 = 71 MeV/c and 60 = 17 MeV/c, respectively.

6

A large root mean square radius, small momentum distribution width component in the
projectile fragmentation, and a small separation energy of the two outer neutrons (S, =
295keV [You93]), suggest the existence of a large two-neutron halo around the 9Li core in
llLi. This structural characteristic has subsequently been found in many other light neu-
tron-rich nuclei (6He, “Li, “Be, 14Be, etc.) [Han95, Tho96].

Before the experimental discovery of the neutron halo, Migdal [Mig73] suggested that
the force between two neutrons may lead to a bound state of the two neutrons and a nucleus
even if a combination of the two do not form a bound state. Hansen and Jonson [Han87]
interpreted Migdal’s suggestion on l'Li as a quasi-deuteron consisting of a 9Li core cou-
pled to a dineutron [2n]. A radial square well potential was assumed for the 9Li core and the
binding energy of the dineutron was assumed to be zero. The external wave function of the
dineutrons outside the core was approximated for the small binding energy B between the

9Li core and the dineutron by

- -1/2CXP[-r/P] exp[R/p]
yo) — (21:9) r [(1+R/p)1/2] (3.2)

 

where R is the radius of a square well potential, r is the distance between the 9Li and the
dineutron. The decay length p in Equation 3.2 is defined as p = 71/0118)”2 where u is the
reduced mass of the system and B is the binding energy. This simple model agrees well

with the experimental results for the radius and the Zn separation energy (see Figure 2.2).

2.2 10Li And llLi Three-Body Models

After Hansen and Jonson’s two-body calculation [Han87] for 11Li, a number of three-body
model calculations were performed to obtain a more detailed understanding of 11Li. For the

three-body calculations of 11Li, detailed information about the 10Li states are essential

 

    
   
 
    

r 1 r I 1 r I I

square—mu. potential.

 
 
  

"L

4.0 — "Li experimental. my. -

   

2.5 -

 

 

 

10" 10° . 10'
Zn 3W0" energHMeV)

Figure 2.2: [Han87] The calculated relations between the matter r.m.s. radius and Zn
separation energy with mass parameters corresponding to 11Li and 6He by Hansen and Jon-

son. The experimental values for radii and Zn separation energies were taken from [Tan85]
and [Wap85]. '

input parameters.

Bertsch and Esbensen treated llLi as a three-body system consisting of two interacting
neutrons together with a structureless 9Li core [Ber91]. They used a two-particle Green’s
function technique to describe the two-neutron wave function. A Woods-Saxon potential,
with a kinetic energy operator and a spin-orbit interaction were used for the single particle
Hamiltonian. The numerical test was performed assuming the ground state of 10Li to be a
me state (see Figure 2.3). The result was compared with the available experimental data
of the 10Li ground state energy at 0.8 MeV [Wil75] and they obtained a two-neutron sepa-
ration energy of 0.20 MeV which is approximately consistent with the available experimen-
tal value of 0.25 i 0.01 MeV [T hi75, Wou88] at that time.

Bang and Thompson [Ban92] performed three-body calculations for 11Li by applying

the Faddeev three body equations [Lav73] using the super soft core potential SSCC

 

 

62“ (MeV)
16
r
\

 

 

 

0
.—-UI
e
i-

- O -O.5 O 0.5 1.0 1.5

6 (MeV)
p112

Figure 2.3: [Ber91] The dependence of the llLi two neutron separation energy to the
10Li 1pm state energy predicted by Bertsch and Esbensen. The solid line and dashed line
show correlated and uncorrelated neutron cases, respectively.

9

[Tou75], or the Reid soft-core potential RSC [Rei68] for the neutron-neutron potential Vnn.
Choosing parameters to give a 1pm level at the energy of the 9Li neutron separation energy
(-4.1 MeV) and varying 1pm resonance energy between 0.4 and 0.7 MeV, a Woods-Saxon
potential and a spin-orbit term, or a Woods-Saxon potential and a pairing term were used
for the core-neutron potential Vcn. Although they reproduced the main features of the halo
in their results, some inconsistencies were found for fitting both the energies and the radius
of 1‘Li simultaneously.

Thompson and Zhukov [Tho94] performed a second Faddeev three-body calculation
for 11Li. It was shown that the presence of a near-threshold s-wave virtual state in the 9Li
+ n two-body potential within the three-body calculation for 11Li had an explicit effect on
the calculated structure of the 1]Li halo. A Woods-Saxon potential was considered for the
neutron-9U potential where the s- and p-wave strengths V s and VP along with the spin-orbit
strength V30 were varied to fit a particular 23 scattering length while maintaining the 1 p1 ,
2 resonance energy between +0.15 and +0.50 MeV. The lp3,2 energy was kept constant at
-4.1 MeV which is the neutron separation energy of 9Li. Assuming a nearly 50% s-wave
motion between the halo neutrons and the core, their results agreed very well with the ex-
perimental data obtained by Kobayashi et al. [Kob88] and Orr et al. [Orr92], see Figure 2.4.
The interaction of the halo neutrons was accounted for by using the realistic super-soft-core
on potential (SSC). Figure 2.5 shows the results of this calculation and it will be compared
with the experimental results presented in Chapter 5.

At the time of these calculations, the only available experimental data of the 10Li
ground state were the measurements by Wilcox et al. [Wil75] and Amelin et al. [Ame90].

Wilcox and collaborators studied 10Li using the 9Be(9Be,8B)10Li reaction with a 121 MeV

10

 

 

 

 

4
2.3
.E 3
a
E
E 2
2
U 1
o i i : : C.’OOO'?ONOOO"0~U”M

   
  
  
 
  

d

b

_ Po'v.=vp

‘0

E3 _ ' --- Pa,ao=-27fm(1s) "
.e' 3%.". 61, a0 = -13 I!“ (03)

g ‘2‘. e MSU p"

g 2 . \. e LBL p, (deconvoluted) ‘
E .

d
'

 

 

 

 

0 ‘ L F!*.W
0 20 40 60 80 100 120 140
p (’Li) (MeV/c)

Figure 2.4: [Tho94] The comparison of the calculated 9L1 core momentum distribu-
tions from 1lLi fragmentation by Thompson and Zhukov and the experimental data by Orr
et al. (square) and Kobayashi et al. (star). The calculation includes s—wave potential as well
as p-wave potential in n-9Li interaction.

ll

 

   

 

 

 

 

EG'OV.=VO .l.’
010 LA' """"" A-tttmtsscatteringiength l.’ .
:G--e-1atm ‘1'
A :0—0'27Im ’0’
z 0.00 v- th ,,- .
g . —-— Obsewedbue ’o’
>. . ....... A
9 .010? ,/ ................. .
g , o’"de ....................... ‘.“oo
.8 '0-20 :- ................ 0“ -t
u r ..........
.g l ............
’3 -O.30 -
' : A.
-0.40 f 0
’ l
-0.50

0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0p,,2 resonance energy (MeV)

Figure 2. 5: [Tho94] The calculated relation between llLi binding energy, me reso-
nance energy, and vsm scattering length. The horizontal solid line shows the observed
two-neutron binding energy of Li by Kobayashi et al. [Kob92].

12
9Be beam on a 0.68 mg/cm2 9Be foil. The ground state was observed at 5,, = -0.80 i 0.25

MeV with a width of F = 1.2 :I: 0.3 MeV (see Figure 2.6). Amelin et al. used the absorption
of stopped it mesons by 11B nuclei and observed the energy spectrum of protons near the
kinematic limits of the reaction to study 10Li. The resonance parameters of E, = 0.15 i 0.15
MeV with a width of F0 < 0.4 MeV were extracted assuming an s—wave state by fitting the

Breit-Wigner resonance shape using the x2 test, see Figure 2.7.

2.3 Recent Reports of The 10Li Ground State

Shortly after the first measurement of 10Li by Wilcox, Barker and Hickey [Bar77]
discussed the ground state configuration of loLi. The 10Li structure was compared to the
l'Be configuration since both nuclei contain the same number of neutrons. The ground
state of 11Be is known to have a non-normal parity state (1” = 1/2+) and is considered to
have 1s41p62s structure. The lowest normal parity state (J’r = 1/2') is at 0.32 MeV above
the ground state which is considered to have a 1541p7 configuration. Since the energy of the
lowest non-normal parity state relative to the lowest normal parity state increases as Z
increases for the nuclei with N = 7 and z > 4 (1.67 MeV for 12B and 3.09 MeV for 13C)
[Tal60] (Figure 2.8), the ground state of 10Li was expected to have non-normal parity state
(1" = 1‘ or 2') by extrapolation. A ground state level of the 10Li was estimated using the
available experimental data [Che70] of an T = 2 isobaric analog state of 10Be. The result
showed that it was expected close to 9Li + 11 threshold and lower than the experimental data
of the 10Li state at 0.8 MeV by Wilcox et al. which was attributed to the lowest normal
parity state.

The more recent experimental data reported by Bohlen et al. (Figure 2.9) [Boh93] and

Young et al. (Figure 2.10) [You94] established the existence of a p-wave state around 500

13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20 .. (a) T f i I f T If ‘
121 MeV ’3. "er ’a.. '3) "a
15 - am- '4' ”60 FC .t
,0 , (348,371) j
30'. (b) .
’ee Veda) '°Li
singles
20 - 6950 ac ~
In
3 10 r
O
U
o 1 l 1 1 1
(cl 1o . ’Be( 'Be. ‘8) '°Li
'0 b L' 9" coincidence ‘
l escape
'Lien
.Lie 2n "
5 n . I cl
— l
,
o 1 L [I 1 l l
6 70 so 90

Porticle energy (MeV)

Figure 2.6: [Wil75] The energy spectra of 8B was obtained from the following reac-
tions using 121 MeV 12C beam. (a) 12C(9Be,8B)13B is for an energy calibration, (b)
9Be(9Be,8B)lOLi is from singles events, and (c) 9Be(9Be,8B)10Li is from coincidence
events with 9Li from the breakup of the recoiling 10Li. The angle was at 14° in the labora-

tory.

l4

3 2 1 06,.Mev

 

I H T— j

 

 

 

a J r I .gfl/

l u x
92 9b 96 5,, MeV

 

10 ’ ‘ protons/MeV per 1r‘ meson

Figure 2.7: [Ame90] The spectrum of protons produced in absorption of stOpped n'
mesons by 11B nuclei. The arrow shows the resonance at E, = 0.15 i 0.15 MeV and I" <
0.4 MeV.

 

 

 

 

 

 

 

MeV
4 r
3.09
3 _ -/——- 51/2
_ /
2 __ 2.62 /1//
X 2-
1 __ 1.674...—
/095 2+
P1/2(l+,2+) 032 pm// ' O
0__,{x0—-q— ........... x~~_, ----- P1/2
.__ — 1
? {= “ 31/2 0
_1_ Sl/2(l'.2‘)
10Li7 ”Be, 1237 13C7

Figure 2.8: Competition between 31,2 and pl ,2 levels among N=7 nuclei [Tal60]. The
levels are shifted to match the lowest pm state. Extrapolation implies the non-normal par—
ity ground state of 10Li [Bar77].

15

 

 

TH - T'TIFTTI _ 4.05Mev
60} l C
: 9.5.
984.9(‘3‘C.‘2N)‘°Li 5° 0.38' c
noL I
336 MeV I
140
3.3°—4.3° 30;”
120
100

 

 

80

 

 

 

Counts

 

60

 

4O

20

 

‘WVIIITTTVUUI'IUITIUIUrYl'T—TI'TUITTYrT
JLJLLLLILLLlAAll

 

 

 

 

 

Figure 2.9: [Boh93] Energy spectra of 12N from the reaction of 9Bc(13C,12N)10Li by
Bohlen er al. The ground state (E, = 0.42 MeV) and the first excited state at E1, = 0.38 MeV
(E, = 0.80 MeV) are not completely resolved.

16

keV in 10Li. Bohlen and collaborators [Boh93] used two different transfer reactions,
9Be(‘3c,‘2N)‘°Li at Em, = 336 MeV and 13C(1“c,‘7F)‘°Li at Em, = 337 MeV, to study
the states of 10Li and concluded that E, = 0.42 i 0.05 MeV, I‘ = 0.15 i 0.07 MeV is the l+
ground state and E, = 0.80 i 0.06 MeV, F = 0.30 i 0.10 MeV is the 2* first excited state.
Young and collaborators [You94] observed a p-wave state at E, = 0.54 i 0.06 MeV, F =
0.36 _+_ 0.02 MeV using the reaction ”13(7Li,3B)'°Li at Em, = 130 MeV. Evidence for a
low-lying state in loLi was also seen at E, > 0.100 MeV and I“ < 0.23 MeV.

Kryger er al. [Kry93] employed the method of sequential neutron decay spectroscopy
(SNDS) at 0° and observed a central peak in the relative velocity spectrum of 9Li + n
coincidence events which indicates an existence of a low decay energy process (see Figure
2.11). loLi was created via fragmentation of an 80 MeV/nucleon 18O beam on a 10 mg/cm2

C target. The fragmentation products and the primary beam were separated from the

 

 

 

 

 

 

 

 

 

20p 7 7 V V I Y Y T Y I T Y Y 1 I T Y Y r
-3. (let!)
L 1 I I I
,_ r r I 1 1 ,
15- 3 2 t 0 —
I- I“ 4
“a P I. 4
3 _ “e(’u.'e)“u at. ,
p+evevem
Ill —4
E ”T ------ peeve at .0 j
S .
8 1 I " 4
‘ 4
:11 i -' _
E . l
. \
\
- ~_ ].I
b \' .
o u l - . l - l . a WI
200 220 zoo 200 250

Figure 2.10: [You94] The energy spectrum from the transfer reaction llB(7Li,BB)mLi
by Young et al. It shows a strong evidence of the state at E, z 500 keV.

l7

 

-

400 ITIITITTfiIl’IIIrIIIIIITI

300

200

Counts

100

IrIIlIIIIITIIIIfiIII]
IIILIILiJlLllLllllll

 

 

 

Figure 2.11: [Kry93] The relative velocity spectra of 9Li + n coincidence events ob-
tained with sequential neutron decay spectroscopy by Kryger er al. The dashed line is a
simulated spectrum with the parameter by Wilcox er al. (E, = 800 .keV, l = l) superimposed
on the Gaussian background (dotted). The solid line is a simulated spectrum with the pa-
rameter by Amelin et al. (E, = 150 keV, l = 0) plus the Gaussian background.

18

neutrons using a set of quadrupole magnets and a dipole magnet. The fragments and the
neutrons were detected in coincidence. Since this method is only sensitive to the Q-value
of the decay, the central peak in the spectrum could represent a decay from an excited state
of 10Li to an excited state of 9L1, as well as a decay from the ground state of 10Li to the
ground state of 9Li. Thus, this observation does not prove the existence of a low-lying
s-wave state, however a limit on the decay parameters for each I (= 0 or 1) could be
extracted assuming the central peak to originate from the decay to a 9Li ground state. The
results reported by Kryger et al. [Kry93] for the p-wave case were E, < 200 keV for a width
F0 less than 500 keV and E, < 300 keV for the width [‘0 more than 500 keV and less than
1500 keV. For the s—wave case, E, < 300 keV for the width F0 less than 500 keV and E, <
450 keV for the width more than 500 keV and less than 1500 keV.

Zinser et al. [Zin95] used one nucleon stripping reactions of 11Be and 11Li to investi-
gate the states of 10Li. The secondary beams of 280 MeV/nucleon for 11Li and 460 MeV
for 11Be on a 1.29 g/cm2 carbon target were used for the reaction. The fragments were de-
tected after a separation with a magnetic spectrometer. Neutrons were detected in coinci-
dence with the fragments. The neutron data from the events 11Be + C —-) AZ + n + X and
11Li + C —-) 9Li + n + X were selected and recorded as a distribution of the radial momentum
p,. Figure 2.12 shows the results of this experiment. As a first order approximation, the one
proton stripping from the 10Be core of the one neutron halo nucleus 11Be most likely did
not disturb the initial state of the s-wave halo neutron and it became an unbound neutron in
loLi. Thus it was suggested that the 10Li state seen by Kryger et al. and the narrow momen-
tum distribution in the results were attributed to the s-wave neutrons in loLi. Also, one neu-

tron stripping from the 11Li beam, to create 10Li, could be considered not to affect the 9L1

19

 

 

 

 

 

 

 

 

 

“Be... ‘3C->n+°IJ+X,
1 ..° . i
9- ’ '-.
ch
:1.
11
ab
3
«3° 0.1 :-
r
0.01 ‘
0 10 20 30 40 60
pr (MeV/e)
fir I f T F
“Ltd-”C-rn-ri'u-i-X
1 _ .V 1
i ' I
i .
e- 1
'°.. 9.
o. '- t
\ ‘f
3 0.1 ~ 0 fm -
u - 20 .
a--50frn Ii'af
0.01 ‘ ‘ ‘ ‘ " ,
o lo 20 3o 40 50 60
p, (MeV/c)

Figure 2.12: [Zin95] Radial momentum distributions of neutrons from loLi breakup re-
ported by Zinser et al. 10Li was created by one proton stripping from llBe (top) or by one
neutron stripping from llLi (bottom). In the top figure, the top dotted line assumes an I:
1 resonance at 0.05 MeV. The two sets (as = -5 and -50 fm) of the calculations were shown
with the 9Li recoil widths (IQ = 100 MeV/c (solid) and O'Q = 0 MeV/c. In the bottom figure,
two contributions were considered in the theoretical curves. One is diffraction (1/3 inten-
sity) and the other is the intermediate state of 10Li (2/3 intensity) which was assumed to

be a pure s state.

20

core because of the weak binding between the halo neutron and the core. Thus it was very
unlikely to excite the 9Li core to the 2.7 MeV first excited state and the observed state must
have been due to the ground state of 10Li. The parameter I" of a two—dimensional Lorentzian
was used to parameterize the distribution, and the results from both 11Be and 11Li beams
showed the same F = 36 MeV/c. The Woods-Saxon single-particle potential-well model
was used for the fit and the depth of the p well was fixed to reproduce a resonance at 0.42
MeV [Boh93].

Ostrowski et al. (Figure 2.13) [Ost96] recently reported four states in 10L1 at E, = 0.246
MeV, 1.458 MeV, 4.191 MeV, and 4.631 MeV and widths of I‘ = 0.137 MeV, 0.107 MeV,
0.128 MeV, and 0.43 MeV, respectively. The 10Be('2C,'2N)10Li was employed to populate
the states of 10Li. The energy of the 12C beam was around 20~30 MeV/nucleon. A
Breit—Wigner lineshape was used to fit the peaks in the spectra. The state reported by
Bohlen et al. [Boh93] at E, = 0.42 MeV was assumed to be the first excited state and the
parameters were included in the process of fitting even if it was not clearly observed in the
experimental spectrum (see Figure 2.13). The spins were assigned for the ground state (E,
= 0.24 MeV) and the first excited state (E, = 0.42 MeV) to be 1+ and 2", respectively, which
were both the Vp1/2 configuration. Although the fitting parameter for the E, = 0.42 MeV
was taken from the Bohlen’s result [Boh93], Ostrowski’s result is contradicting from the
Bohlen data, since the state at E, = 0.8 MeV which was assigned to J“ = 2+ in the Bohlen’s
report [Boh93] was not observed.

No defining parameters have been set for the ground state of 10Li. The state at about
0.50 MeV with a p-wave emission reported by Bohlen er al. [Boh93] and Young et al.

[You94] are at least in agreement, however the energies and/or angular momentum

21

 

counts ,

__ 4.63
-—-—J 4.19
-—. 12.321
.._.. 0.50 “t
0.24 .. 1

...l 1.45

P. .

 

Ak

 

. ! l
to [Mu] with \‘l . ..I'iiti in

 

 

 

 

 

 

 

 

o ‘l
O
”E’ 0'4 <
1 Sn ,
i t
401- ‘
L i
l
1 t
20' ‘
' 1
o J-‘
i
l [“1
, k - - L
' eo eo too 120
m

Figure 2.13: [Ost96] Spectra of the 10Be(12C,12N)10Li reaction by Ostrowski et al. Al-
though the state reported by Bohlen et al. [Boh93] at E, = 0.42 MeV was assumed to be
there for fitting, it is not resolved from the ground state at E, = 0.24 MeV. The state report-
ed by Wilcox et al. at 0.8 MeV was not observed in these spectra.

22

assignments of the lower-lying state are still controversial.

2.4 14Be Three-Body Models and 13Be Ground State

Similar to 1lLi, a 14Be nucleus is considered to have a two neutron halo structure which
consists of a 12Be core and two weakly bound halo neutrons [Tho96]. The ground state of
13Be has the same importance to the theoretical models of 14Be as the structure of 10Li does
to the 11Li three-body calculations [Tho96].

Ostrowski et al. [Ost92] performed an experiment to study l3Be using the
double-charge-exchange reaction 13C(14C,140)13Be, ELab = 337.3 MeV. A highly enriched
(98%) 13’C target as well as a 12C target were used in the (14C,14O)-reaction. The 12C target
was used to calibrate and to determine the background. The states observed were at 2.01
MeV, 5.14 MeV, 8.53 MeV above 12Be + n and F = 0.3 MeV, 0.4 MeV, 0.9 MeV,
respectively. R-matrix calculations of the line width suggested the probable spin state for
the lowest observed state to be J” = 5/2+ or 1/2'. A theoretical calculation by Poppelier et
al. [Pop85] using the (0+1)h(0 shell-model, and a prediction by Lenske [Len9l] using a
Woods-Saxon potential with a density dependent pairing interaction, supported the I" = 5/
2+ assignment for the state at 2.01 MeV. Although the latter calculation also predicted a
low-lying 1/2+ ground state at around 0.9 MeV, it was not observed in this experiment. It
was argued that the ground state was not observed in the spectrum, because of the low cross
section of the 231,2 neutron-shell in multi-nucleon transfer reaction and the large s-state
level width.

Penionzhkevich [Pen94] reported states in 13Be using the 14C(1 lB,12N)13Be reaction.

A new state at 0.9 MeV was observed as well as the previously reported state at 2.0 MeV.

23

 

w r r I r r

T Y

(10 MeV)

(7 MeV)
(5 Me
2 MeV

 

 

ooooo

Counts
8

20

    

,.

l " l

L l L L A

0 ..
4-2 0 2 46 81012141618

10

 

 

 

E "_123., MeV

Fi re 2.14: [Kor95] The proton spectrum from the reactions CD2(lzBe,p) (solid) and
C( 2Be,p) (dotted). The lowest state extracted reliably is at E, = 2 MeV.

However, this ground state has not yet been confirmed by other experiments.

Korsheninnikov [Kor95] used a secondary beam of 12Be from an 180 primary beam on
a 5 mg/cm2 thick CD2 target to study the states in 13Be p0pulated via the neutron transfer
reaction d(12Be,p). Figure 2.14 shows the results obtained in this experiment which exhib-
its clear evidence for the known 2 MeV state as well as states at 5 MeV, 7 MeV, and 10
MeV above the neutron decay threshold. However, background due to the carbon in the tar-
get (dotted line in the figure) did not allow for a reliable measurement in the low-energy
region of the spectrum.

Descouvemont [Des94] performed a 12Be + n microscopic cluster model calculation
for 13Be. The Volkov force [V0165] V2 and V4 were used for the nuclear part of the nucle-
on-nucleon interaction. The result of the calculations showed the existence of a slightly

bound low-lying 1/2+ state at E = -9 keV for V2 and at E = -38 keV for V4, which are both

24
lower than the 5/2+ state (E = 2.01 MeV) reported by Ostrowski et al [Ost92]. It suggests

that the inversion of vd5/2+ and vsl/2+ occurs.

As in the 11Li [Tho94] case, Thompson and Zhukov [Tho96] performed similar
three-body calculations of 14Be. While the simple shell model predicts a v(1d5,2)2
configuration for the ground state of 14Be, an admixture of v(sl,2)2 and v(c15,2)2
configurations were assumed and the neutron-core interaction potentials for both 31,2 and
d5,2 was considered. First, it was shown that a d-wave state at 2.1 MeV on 13Be alone did
not lead to the bound l4Be nucleus which contradicted the experimental result (bound by
1.34 MeV [Aud93]). Among several combinations of the 2s and 1d neutron resonances,
only a combination of a 2s virtual state with a large scattering length (aS z -l30 frn) and
another d-wave state at E z 1.3 MeV which was lower than the known 2.1 MeV d-wave
state, reproduced the experimental values of the two neutron binding energy and the matter
radius of the 14Be, simultaneously. More experimental results are awaited to confirm the

low-lying structure of the 13Be as an important step in the 14Be three-body calculation.

Chapter 3

Experimental Details

3.1 Experimental Method

The primary goal of the present work was to determine the ground state energy of 10Li. The
technique of sequential neutron decay spectroscopy [Dea87] (SNDS) was employed to
fragmentation products produced near 0°. Figure 3.1 shows a kinematic diagram of the 10Li

—-> 9Li + n decay. If a 10Li nucleus is produced by fragmentation, it initially has a non-zero

DCUII'OD

  

 

Center of Mass

9Li
Figure 3.1: Kinematic diagram of the sequential neutron spectroscopy for the 10Li de-
.cay.

25

26

momentum. V is the initial velocity vector of the 10Li created by fragmentation in the lab-
oratory system. IOLi is a neutron unbound nuclei and has a very short lifetime (~ 10'21 3),
thus if the initial velocity is at ~40% of speed of light (0.4c z 12 cm/ns), one can assume
that the decay, 10Li —> 9Li + n is instantaneous since it can travel only ~1.3 x 10'12 111 com-
pared to the flight path (~ 5 m). The velocity vectors of the decay products neutron and 9L1
are V,” and megm in the laboratory system. VnCM and megCM are the velocity vectors
of the neutron and the 9Li nucleus in the center of mass system. Conservation of energy in

the centre of mass system yields,
m c2 = m9 c2+m 02+T9 +T (3.3)
10L1 Li H Li 9

where c is the velocity of light, 111, represent the rest masses of each particle, and Tx is the
kinetic energy of each particle in the center of mass system. The kinetic energies are related

to the decay energy (E ,) via:
E, = T9Li + Tn (3.4)
For a two particles system, we can write,

1
E, = iluv2 (3.5)

rel

where 1.1 is the reduced mass of the system and V,e, is the magnitude of the relative velocity

vector between the neutron and 9Li. Using the relationship given in Figure 3.1, we get:

vrel = anM — VfragCM (3'6)

VnCM _ VfragCM = vnlab _ Vfraglab (3'7)
If the decay direction is nearly parallel to the center of mass velocity, Equation (3.6) and

(3.7) can be written with a scalar relationship,

27
vrel = anab — Vfraglab (3'8)
where V,,,ab and Vf,ag,a,, are the magnitude of the corresponding vectors.
During the actual data analysis, the relative velocity spectrum was obtained from the
velocity information of the 9L1 and the neutrons. This information was then compared to

Monte Carlo simulations to extract the mass of 10Li.

3.2 Mechanical Setup

The experiment was performed at the National Superconducting Cyclotron Laboratory
(NSCL). Figure 3.2 shows a floor plan of the NSCL. An 180 beam with a kinetic energy of
80 MeV / nucleon was provided from the K1200 cyclotron. The primary beam bombarded
a 94 mg / cm2 thick 9Be target located in front of the last quadrupole-dipole magnet
combination in the beam transport system of the NSCL. Fragmentation in the target created
various nuclei. Table 3.1 shows a example of a prediction of fragmentation products by the
code INTENSITY [W in92] for the present case. Since the INTENSITY calculation does
not include unbound nuclei, 10Li is not included in Table 3.1. Figure 3.3 shows the
schematic of the experimental setup. The mLi nuclei break up immediately after their
creation in the target into one neutron and a 9Li fragment. The dipole magnet was used to
bend the primary beam and the fragments, respectively, away from the straight flight path
of the neutrons into two properly adjusted separate beamlines. The first one at 11° was for
the fragments and had a telescope detector array at the end. The primary beam then bent
into the 14° beamline and was collected in a shielded Faraday cup at a distance of ~ 25 m
to reduce the background. The neutrons from the breakup were detected by a liquid

scintillator array located ~ 5 .8 m down stream at 0°. The neutrons were extremely forward

28

68883 55296 maze—Duaeouoanm 3:232 05 we 52m 80E ”Nm Semi

Tl— EQQ? Bum—ab Enos 2: coho—93 82M
8 S we 5:me 295 52 2E.

deified mmnE CONE.

  

 

 

 

 

 

 

 

 

.55

 

29

Table 3.1: A example of an output file of the INTENSITY [Win92] calculation for an
80 MeV/nucleon 18o beam (intensity = 10 pnA) with a 94 mg/cm2 9Be Target.

 

Fragment B-rho Energy Rate

(charge) [Tm] [MeV/A] [#/s]

3He(2+) 1.8448 70.320 3449
4He(2+) 2.4620 70.441 10734
6He(2+) 3.6962 70.561 4368
8Hc(2+) 4.9305 70.621 42
6Li(3+) 2.4587 70.260 26191
7Li(3+) 2.8701 70.337 27933
8Li(3+) 3.2816 70.396 1 1892
9Li(3+) 3.6930 70.441 2147
“Li(3+) 4.6118 73.424 7
713e(4+) 2.1468 69.973 18431
9Be(4+) 2.7640 70.158 63463
lo13e(4+) 3.1089 71.833 33108
”Be(4+) 3.4534 73.201 7810
1213e(4+) 3.7976 74.340 891
l4Be(4+) 4.4856 76.127 2
813 (5+) 1.9583 69.664 3940
1013 (5+) 2.4813 71.510 103566
“13 (5+) 2.7570 72.912 147398
12B (5+) 3.0326 74.079 95884
13B (5+) 3.3079 75.064 30550
”8 (5+) 3.5831 75.908 5137
1513 (5+) 3.8582 76.638 495
9C (6+) 1.8315 69.340 254
1"C (6+) 2.0618 71.112 5530
“C (6+) 2.2917 72.556 48809
12C (6+) 2.5214 73.756 185978
13c (6+) 2.7510 74.770 326916
”C (6+) 2.9804 75.637 284789
15c (6+) 3.2097 76.388 133050
16c (6+) 3.4389 77.043 35185
”c (6+) 3.6681 77.622 372
12N (7+) 2.1554 73.373 6501
13N (7+) 2.3522 74.420 64781
14N (7+) 2.5490 75.315 300347
15N (7+) 2.7456 76.090 698891
16N (7+) 2.9421 76.767 897715
17N (7+) 3.1386 77.363 692143
18N (7+) 3.3350 77.892 15899
”N (7+) 3.5314 78.365 120

30

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31

focused due to the high primary beam energy. 9Li fragments were detected in coincidence
with the neutrons at the end of beam pipe bent by 11° with respect to the central neutron
fright path. The fragment flight path distance from the target to the fragment telescope was
~ 6.0 m. The quadrupole magnets and the dipole magnet were tuned to optimize the
detection rate of 9Li and other charged nuclei with a mass-to-charge ratio equal to three
(6He, 12Be, 1513).

The detector system and the signal processing electronics are described in the following

sections.

3.3 Neutron Detectors

Five liquid scintillator (NE213) detectors were used to detect the neutrons. Each neutron
detector had a cylindrical shape, and Figure 3.4 (a) shows their dimensions. Figure 3.4 (b)
shows the arrangement of five detectors.

The intrinsic efficiency of the neutron detectors was energy dependent. It was estimated
with the code KSUEFF [Cec79] and the result is shown in Figure 3.5. The efficiency over
the energy range of the current experiment is ~ 10%.

The solid angle coverage of the neutron detectors in the laboratory was 1.15 msr. How-
ever neutrons from the breakup were forward focused and the solid angle coverage of the
detectors in the center of mass frame of the neutron decay system was much higher than in
the laboratory frame because of the high incident energy of the primary beam. In the case
of the 10Li breakup, the solid angle coverage of the neutrons in the center of mass frame of
a neutron and a 9Li is 100% of 41: up to decay energy of E, z 18 keV decreasing to 0.8%

of 4n: at decay energy of E r z 1000 keV.

32

 

“'3 W51
(no [.71

 

 

 

 

(a) Neutron detector dimension

neutrons

 

side view

 

(b) Neutron detector array configuration

Figure 3.4: The dimensions of one neutron detector and the configuration of the whole
detector array. The gray area shows the neutron sensitive part.

33

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00
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—-{

 

 

 

 

>5
0
5
.g 025 _ ............................................................ _
8::
en 02 a ......................................................................... _
.9. “
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8 E i w in m‘ 2
o ' - ' ' eta. w
'c 0.1 _ .................................................................................... .......... ’....:i:.’;-:;: .......... _
‘3 2 z s s =
g a a z E
5 0.05 _ ......... ....................... ........................ ....................... ...... . ................. ........ _
2 a E i i

o L ......... z ........................ : ......................... z ........................ : ......................... : ......... J

20 40 60 80 100

Neutron energy [MeV]

Figure 3.5: Simulated efficiency curve of the neutron detector with a sideway geome-
try. It was calculated with the code KSUEFF [Cec79].

There was a geometrical constraint on the location of the neutron detectors by the iron
core aperture of the dipole magnet. The configuration of the neutron detectors were chosen
to maximize the coverage of the solid angle of this window. The sensitive part of the neu-
tron detectors covered 76% of the window area.

The energy dependent solid angle coverage in the center of mass and the energy depen-
dent intrinsic efficiency were folded with the fragment acceptance (see Chapter 4) and ob-
tained as an efficiency plot by the simulation code (see Chapter 4). Figure 3.6 shows the

folded neutron efficiency curve for 10Li decay in the form of the relative velocity spectrum.

3.4 Fragment Telescope

The fragment telescope consists of a fast plastic timing detector, three fourfold segmented

silicon AE detectors, and nine CsI(Tl) scintillator crystals with a photo diode readout for

34

 

 

 

 

 

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MF‘FO ownooowma Ol‘v-‘M
gass§2~~ ~~2§esa§ ErlkeVl
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E _ _
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Vn - Vf [cm/ns]

Figure 3.6: Efficiency plot of the neutron detection for the 10Li neutron decay for the
decay energy range of 0.00 MeV < E, < 1.00 MeV. The energy dependent solid angle cov-
erage of the neutron detectors, the energy dependent neutron detector efficiency, and frag-
ment detector acceptance are folded as a total neutron detection efficiency. The upper
abscissa indicates a corresponding decay energy.

35

 

 

 

 

 

L 22.9 cm J
[t fl
End of 11° I Tm - '
. n lasttc I
Pipe ' timing AB l E
.. detector I I
- - — - .+_ ———————————— — \A- * - E — - _
" ® I Si C 101)
Kapton quadrant 8
window Cu collimator segmented

Figure 3.7: Schematic of the fragment telescope.

each of the crystals. Figure 3.7 shows the schematics of the telescope. The end of the 11"
beamline was sealed with a 0.0279 mm thick Kapton® window and the telescope was
operated in air.

The thin plastic timing detector consisted of a 0.0254mm thick fast scintillating plastic
foil (BC400, Bicron Corp.) with a plexi glass light guide frame coupled to a photomultiplier
tube.

A copper collimator was placed after the timing detector. With a thickness of 2.54 cm
it left a square opening of 5.0 cm x 5.0 cm. It was placed in front of the AE and E detectors
to eliminate events which were glazed or reflected from the beamline pipe. It also allowed
to maximize the good event rate in the AE and E detectors during the tuning of the magnets.

Three quadrant segmented Si detectors were used to measure the energy loss. They

were. located at a distance of 12 cm behind the timing detector. They had an effective area

36
of 5 cm x 5 cm and an effective thickness of 1016 um (AE1), 486 um (AE2), and 478 pm

(AE3), separately (Figure 3.8). The detectors were tilted by 7° with respect to the central
fragment trajectory in order to avoid ‘channelling’ of the fragments in the crystal layers.
Three detectors were used to get a sufficient isotope separation for the Beryllium frag-
ments, 10Be,1 1Be, and 12Be in the AE - E plot by adding up the individual energy loss pulse
heights.

Nine 1.7 cm x 1.7 cm x 5.0 cm CsI(Tl) detectors were used to stop and detect the total
energy of the fragments (Figure 3.9). Each of them was wrapped with white reflective
blotter paper (HATF107l0, Millipore Corp.) on the long sides and the polished front face
was covered with a 1.5 um thick aluminized Mylar® foil. The thickness of the aluminum
layer was less than 0.1 um. Photo diodes (83590-03, HAMAMATSU) were attached with

silicone rubber glue (RTV615, GB) at the back end of each crystal and covered with white

 

 

 

 

5.0 cm

 

 

 

 

 

 

 

 

 

 

 

Figure 3.8: Front view of one of the AE Si detectors. The gray area shows the sensitive
region. The crossed lines on the gray area indicates the segmentation lines.

37

aluminized

 

Figure 3.9: Structure of CsI(Tl) E detector array. Each of the nine crystals were
wrapped with white blotter paper independently to optically isolate them from each other.

Teflon® tape for light sealing and for improving light reflection.

3.5 Electronics and Data Acquisition

Figure 3.10 displays the schematics of the electronics used for the signal processing. The
photo diodes attached to the CsI(Tl) crystals E detector had a full depletion voltage of 70
Volts and a maximum voltage of 100 Volts. They were reversely biased with 80 Volt
through the preamplifiers. The signal picked up by the preamplifier was passed to the linear
amplifier with a 3 [is shaping time. The peak height of the outputs of the linear amplifiers
was proportional to the kinetic energy of the detected projectile fragment. These energy
signals were recorded with a peak sensitive ADC (AD81 1, ORTEC). The fast time signal
outputs of the linear amplifier were sent to Constant Fraction Discriminators (CFD: TC455,

TENNELEC) to create TDC stop signals relative to the K1200 cyclotron RF time and to

38

 

 

 

 

 

 

 

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Figure 3.10: Diagram of the electronics.

39

create a bit for each E signal.

Basically the same signal processing was used to operate the three quadrant AE Si de-
tectors. The shaping time of the linear amplifiers was set to 1 us for the AE detectors. AEl,
A52, and AE3 detectors were biased with 90 Volts, 30 Volts, and 42 Volts, respectively.

The fast plastic timing scintillator was attached to a photomultiplier tube. The signal
from the tube was fed to a CFD, and one of the outputs was used as part of the fragment -
neutron coincidence condition. The pulse width of the CFD output for the fast plastic
timing detector signal, which was fed to the coincidence AND, was ~ 200 ns. The other
outputs of the CFD were used to set a bit for each event detected in the fast plastic detector
and to generate a stop signal for a TDC to measure the time of flight relative to the cyclotron
RF and the neutron time signal, respectively.

The neutron liquid scintillator detectors were also equipped with photomultiplier tubes.
The signals from the tubes were split into an energy and time branch. The energy signal
from each detector was integrated in two separate charge sensitive ADC (QDC) channels.
Two differently gated signal charge integrations (tail and total) were necessary to achieve
pulse shape discrimination between y—rays and neutrons. Details of this technique will be
discussed in Chapter 4. In the time branch, the signal from the neutron detectors were sent
to a CFD and created time signals. They were passed to TDC stops and bits for each neutron
detector as well as a bit for downscaled neutron singles. A short (~ 5 ns) signal was also
created from the time signals and was fed to the neutron-fragment coincidence AND. Since
it was much shorter than the other coincidence condition signal from the thin fast plastic
detector (~ 200 ns), time of the neutron - fragment coincidence signals was dominated by

the neutron time. The downscaled singles formed one event type of the master gate, togeth-

40

er with the main event type of coincidence events.

The RF time signal from the K1200 cyclotron was used as a time reference. The original
RF signal had a sinusoidal shape and a frequency of 18.4 MHz, leading to repeated beam
bursts at At = 54.4 ns. The RF signal was used to start all of the TDCs except the TDC for
the TNORP (see 4.2.3) signals, in coincidence with a “master gate” signal consisting of the
neutron singles and neutron-fragment coincidences. A veto signal blocked the data acqui-
sition during the busy time of the frontend processor.

Finally, accepted events were written to 8 mm tapes and analyzed online, using the

standard NSCL data acquisition system [Fox89, Fox92].

£-

 

 

Chapter 4
Data Analysis

4.1 Overview

The off-line analysis of the data was performed with the NSCL data analysis program
SARA [Fox89, Fox92]. The experiment consisted of four parts. First, fragment singles
were recorded for energy calibration of the E detectors and gain matching of AE detectors.
The second part included neutron singles runs for gain matching of the neutron detectors
and calibration of the neutron times. In the third part, coincidence events of neutrons and
fragments were measured to obtain the relative velocity spectra. For the forth part, shadow
bar runs were conducted to measure the neutron background. The calibration of the ener-
gies (E), energy losses (AE), and time of flights (TOF) were performed off-line. Subse-
quently, calibrated AE-E particle identification (PID) histograms were created. Software
gates were drawn for three different elements (He, Li, and Be) on the AE-E particle identi-
fication (PID) plot and the data was filtered into three sets based on these gates. Individual
isotope (611e, 9Li, and 12Be) gates were obtained from the filtered data using both the AE-
E and the AE-TOF plot. Neutrons were separated from 'y-rays by pulse shape discrimination
technique (see section 4.3.1). A relative velocity spectrum of 7He -—> 6He + n was created

from the filtered data. The neutron decay energy and the width of 7He are well known

41

42

[Aj288] and thus could be used as a calibration reaction. The time zero constants for the
neutron TOF of each neutron detector in the data analysis code were adjusted to match the
centers of the spectra with the simulations. The relative velocity spectra of 10Li —) 9Li + n
and 13Be -> 12Be + n were then obtained from the filtered data and compared to the Monte

Carlo simulations to extract the decay energies and the widths.

4.2 Calibration of Detectors

4.2.1 Calibration of the Fragment Telescope

The resolution of the E detectors was crucial because the energy information of the frag-
ments was used to calculate the fragment velocity and also indirectly the neutron velocity.
For the energy calibration of the CsI(Tl) energy detectors and the gain matching of an en-
ergy loss in the Si quadrant segmented detectors, calibration beams of isotopes with mass-

to-charge ratio equal to three (6He, 9Li, and 12Be) were used. The calibration beams were

 

 

 

 

 

 

 

 

 

Table 4.1: Calibration beam energies for different target thicknesses.
27 Al target Kinetic energy of a fragment [MeV]
thickness Bp [TOm]
[mg/cmz] 6He 9Li 12Be
370 3.797 445.8 668.7 891.6
247 3.834 454.2 681.4 908.5
177 3.865 461.5 692.2 922.9
81 3.909 471.6 707.4 943.2
33 3.929 476.1 714.2 952.2
3.4 3.941 479.1 718.6 958.2

 

 

 

 

 

 

 

43

created by fragmentation of a primary 180 beam with a kinetic energy of 80 MeV/nucleon
on various Al targets. The A1200 mass analyzer was used to separate isotopes with mass-
to—charge ratio equal to three. A momentum slit located at imagel in the A1200 was used
to limit the momentum spread of the calibration beam to 0.25% (FWHM) and 1.0%
(FWHM). This corresponds to 0.5% (FWHM) and 2.0% (FWHM) spread in energy.

Six 27Al targets with different thicknesses were used to produce six different energies
of calibration beams. The magnetic rigidities (Bp) of the secondary beam were calculated
using the code INTENSITY [W in92]. The different 27Al target thicknesses, the Bps of the
A1200 mass analyzer, and corresponding total kinetic energies of the fragments of the cal-
ibration beam are shown in Table 4.1. The total kinetic energy of the calibration beam was
calculated using the relation between kinetic energy T [MeV], mass number of the nucleus

A, atomic number of the nucleus Z, and Bo [T-m],

 

2
T = A Juana—9919252) -..A (4.1)
where
u = 931.49432 [MeV]. (4.2)

Two-dimensional histograms of the fragment energy loss versus the fragment time of
flight which was measured between the cyclotron RF and a thin plastic timing detector
(AEl ,2,3 vs. TOF), and the fragment energy loss versus the fragment total energy (AE1,2,3
vs. B) were created from the data to identify the isotopes in the calibration beam. Examples
are shown in Figure 4.1 and Figure 4.2. For the AE detectors, the number of charge carriers
created within a detector of small thickness Ax is proportional to the specific energy loss
dE/dx and Ax [Kno89]. The specific energy loss of nonrelativisitic charged particles of

mass m and charge Ze is expressed in Bethe’s formula:

12 _§ —‘
Be ? 'F llBe

9Li

~r.

“a 1 ’1— 8L1
6He i—v '
é-F
<— Time of flight

 

 

V

Figure 4.1 Two dimensional histogram of energy loss in the AE2 detector’s quadrant
number 1 versus time of flight of the fragments. m/q = isotopes are selected using the
A1200 mass analyzer.

 

t<-—“Be

 

 

 

 

 

V

Figure 4.2: Two dimensional histogram of energy loss in the AE2 detector’s quadrant
number 1 versus total energy in the E3 detector of the fragments. The large square gate in
the‘plot was applied to select the valid signal for a projection.

45

dB mZZ E
Ex- = CITIDCZ’; (43)

where C1 and C2 are constants. It shows that the energy loss is very sensitive to the m22
value but only mildly dependent on the particle energy E. For the E detectors, it is obvious
that the number of charge carriers created within a detector is proportional to the total ki-
netic energy E of the incident charged particles. This different dependence of the signal in
the AE and E detectors allowed the isotope separation.
The A1200 selects isotopes according to their momentum over charge ratio. The force
FMAG on a charge q moving with velocity v in magnetic flux B is,
FMAG = M (4.4)
where FMAG, v, and B are all perpendicular to each other. This charged particle moves
along the circular trajectory with a radius p because of this force and the centripetal force

Fee“ of circular motion can be expressed in the form:

2 .
FCC" : Ev— (4.5)
P
Since FM AG = FCC“,
2
M = B (4.6)
P
which leads to
Bp = ’13 = 3. (4.7)
q q

The centroid of the velocity distributions are equal for all the isotopes in a secondary beam.
For a given Bp value of the A1200 isotopes with the same mass-to—charge ratio m/q have
the same velocities v. For example, isotopes with m/q = 3 were selected and they all had
the same time of flight (the same velocities v) as shown in Figure 4.1.

In the figure, some isotopes with m/q at 3 are also observed (8Li, llBe, etc.). In the 8Li

case, the mass number is 1 less than the chosen mlq = 3 groups. From Equation 4.7, the

46

velocity v of 8Li has to be greater than the chosen group to yield the same Bp to be selected.
8Li was observed in Figure 4.1 at the shorter time of flight (higher velocity v) side than 9Li.
The energy of those particles are expressed as E = p2/2m and as can be seen in Figure 4.2,
8Li has larger energy since the selected 8Li group has lower mass number than 9Li and the
same momentum as 9Li.

A projection of the two dimensional gates on m/q = 3 isotopes on the E axis is shown
in Figure 4.3. The location of the peaks for each isotopes for the six different energies were
fitted quadratically by a least square method as a function of the kinetic energy of the cal-
ibration beams to extract calibration constants for 6He, 9Li, and 12Be isotopes, individually.
The energy resolution of the E detectors was ~ 0.5% (FWHM). These fits are shown in Fig-
ure 4.4, 4.5, and 4.6 (6He, 9Li, and lzBe). The energy detector E2 showed an abnormal be-

havior and it was thus omitted from the later data analysis.

 

 

 

 

 

 

 

 

 

I
E 6H6 9Li
I l 1 12Be
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100 l 1 i I. H.“ 111" 1 ,
50 70 90 110 130 150 170 190

Energy [a.u.]

Figure 4.3: Energy spectrum of the calibration beam with an A/Z=3 gate.

47

 

 

   

 

 

 

 

 

 

 

 

 

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ppPP—-~_——b-—-h~p—hhpu

 

 

Hm

coo

Sb

coo

00¢

Energy [MeV]

Quadratic fitting for energy calibration of the 9Li fragment for each E de-

tector. The E2 detector was omitted due to its nonlinear behavior.

Figure 4.5

49

 

 

 

  

 

 

 

 

 

 

 

 

 

 

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a
CI.
§ § § s s s s s a s s s
"‘ d H fi fi fi

Energy [MeV]

Figure 4.6: Quadratic fitting for energy calibration of the 12Be fragment for each E de-
tector. The E2 detector was omitted due to its nonlinear behavior.

50

102 j
100 . I - l l:
50 100 150 200 25

0

Counts

 

 

 

 

 

Energy loss [a.u.]

Figure 4.7: Energy loss spectrum of the calibration beam with A/Z=3 gate.

The code STOPX [Oak92] was used to calculate the energy loss of the calibration
beams in the AE detectors. Peak channel positions in the one dimensional AE spectra of
6He, 9Li, and 12Be isotopes were recorded (Figure 4.7) and fitted quadratically as a function
of the calculated energy loss by the least square method. The calculated energy loss of the
three isotopes were used together to align the peak positions of the same isotope between
the all AE detectors. Using the constants obtained from the fitting, pseudo parameters were
created in the data analysis code for each AB], 2, and 3 signals to align the peaks of the
isotopes on the one dimensional pseudo parameter plots. Then the plots of AB] , AE2, and
AE3 pseudo parameters were added to obtain a total AE information and used for the par-

ticle identification in the two dimensional plots (AE-E, AE-TOF).

51
4.2.2 Neutron Detector Calibration

The scintillation material (NE 213) in the neutron detectors is sensitive to both neutrons and
y—rays. We used pulse shape discrimination [He188] to identify neutrons and y—rays. The to-
tal pulse (total) and the tail of the pulse (tail) from the photomultiplier tubes of neutron de-
tectors were integrated separately (Figure 4.8). The same gate width of 400 ns was used to
integrate the charge of those two channels but a different part of the signal was integrated
by delaying one signal with respect to the other by 60 ns (see Figure 3.10). Because of the
difference of the interactions in the scintillation material, a neutron signal has a larger tail
compared to a y-ray signal with a similar pulse height. This difference separates two parti-
cles on the two dimensional plot of tail vs. total signals. A 239Pu-Be neutron-y-ray source

(0 ~ 10 MeV for neutrons and 4.44 MeV for y-rays) and a 60C0 'y-ray source (1.173 MeV

 

 

Tail charge integration

(original signal)

 

 

Total charge integration
(delayed by 60 ns)

 

QDC gate

 

 

 

Figure 4.8: Timing diagram of the neutron signals and the QDC gate. Shaded areas
show the integrated part of the neutron signal.

52

and 1.332 MeV) were used to obtain the two dimensional plot shown in Figure 4.9 and the
tail gate time and attenuation ratio of total signal were adjusted to maximize the separation
of the two groups.

The gains of the five individual neutron detectors were matched with a 60C0 y—ray
source (1.173 MeV and 1.332 MeV) and a 239Pu-Be neutron-y-ray source (4.44 MeV). The
projection of the condition around the 'y-ray group of the two dimensional plot on the ener-
gies is shown in Figure 4.10. The high voltage biases were adjusted to match the compton
edges of the five neutron detectors for the 60Co (0.963 MeV and 1.118 MeV) and for the
239Pu-Be (4.198 MeV). Those were -1440 v (N1), -1400 v (N2), -1450 v (N3), 4400 v
(N4), and -1400 V (N5). For the experiment the neutron detector signals were then attenu-
ated to be able to accommodate the highest neutron energy signals (~ 80 MeV) within the

dynamic range of the QDC.

'8 r
[—
neutrons

 

 

 

V

Total

Figure 4.9: Two dimensional plot of the neutron detector signal. A 239Pu-Be source
was used to supply y—rays and neutrons along with 60Co 'y-ray source.

53

   
       
       

 

   

 

1000“—
800 ——
m discriminator threshold
‘5 l
:3 600 —-—
O
U unresolved
400 -— compton edges compton edge of
of 60Co source 239Pu-Be source
200 __ l l
0 l l l l A..__| I I

o 20 4'0 60 so loo— 120 1210>
Energy [a.u.]

Figure 4.10: Compton edges of a 60C0 source and a 239Pu-Be source in a one dimen-
sional plot of the neutron total signal. It was obtained by using the y—ray condition estab-
lished in the two dimensional plot (Figure 4.9).

4.2.3 Time Calibration

All TDCs were calibrated with a time calibrator electronics module which created a cali-
brated time signal (multiple of 10.0 ns) over the TDC range (~ 200 ns). Six positions of the
calibration peak for each TDC were recorded and linearly fitted as a function of time in ps.
All TDCs had a time gain of ~ 100 ps/ch. The fragment time information was used for the
particle identification.
The ‘or’ of all neutron detectors started a TDC which was stopped by a coincidence
fragment in the thin fast plastic detector and recorded in a TDC (TNORP). If tn is a neutron
TOF and tf is a fragment TOF, then TNORP is defined as
TNORP = (tf + Cf) - (tn + C“) (4.8)

where Cf and Cu are constants. Rearranging this equation yields,

54
In = [f - TNORP 4" Cf - C“ (49)

Equation 4.9 was used to calculate the TOF of the neutrons (tn) in the data analysis code.
This method had an advantage over the neutron TOF relative to the RF signal of the K1200
cyclotron, because the RF time resolution was larger than 1 ns.

To determine the constants Cf and Cn for each neutron detector, the following proce-
dures were taken. First, the constants Cf are all zero since the fragment time tf was an ab-
solute flight time of the coincident fragment from the target to the fragment telescope. The
fragment time tf was calculated from the known fragment flight distance (597.0 i 1.0 cm)
and the fragment velocity v which was calculated from the fragment energy information Ef
from the E detectors. Ef is expressed as,
mc2(‘y - 1) (4.10)

y = —1—— (4.11)

1(2)

where m is the particle rest mass, v is the particle speed in the lab frame, and c is the speed

Er

of light. Solving Equation 4.10 and 4.11 for the velocity v, we get

2 2
v = °([ ..(___m° ) . (4.12)
Ef+mc2

This calculated fragment velocity v was also used in Equation 3.8 as meglab to obtain the

 

relative velocity Vrel.

The constants Cn for each neutron detector were determined by observing the peak po-
sition of the time reference 'y-rays in the RF-neutron TOF spectra in the neutron singles
mode. The primary beam bombarded a thick Cu beam stopper and emitted the y-rays in-
stantly at the time of the incident beam. Since a ‘y-ray travels at the speed of light and the

flight distance between the target and the neutron detectors (580.0 i 1.0 cm for N1 and N3,

55
579.0 3: 1.0 cm for N2 and N4, and 592.0 i 1.0 cm for N5) are known, we could calculate

the time offset of the TDC’s.

4.3 Coincidence Fragment Spectra

All the neutron-fragment coincidence data was filtered into three groups (He, Li, and Be)
and were copied to three 8 mm tapes, one for each group. Filtering conditions were estab-
lished in two dimensional plots of the gain matched energy loss versus the calibrated ener-
gy (AB-E) for each fragment group since each isotope, 6He, 9Li, and ”Be had its own
energy calibration constants, respectively. No gate was applied to the two dimensional plot
of the neutron detector signal (tail vs. total) for the filtering.

When coincidence events are recorded, it is inevitable to record chance coincidence
events (randoms) simultaneously since the coincidence gate triggered by the fragments is
~ 200 ns wide and once it is opened, any type of neutron detector signal can satisfy the co—
incidence condition (see Figure 3.10 and 4.11). The RF signal from the K1200 triggered a
TDC start for measuring the fragment time only when a master gate trigger existed. The
master gate consisted of coincidences of neutrons with fragments or downscaled neutrons
where the time was determined by the neutrons. The neutron detector signal times could
have a ~ 200 ns range to be considered as a coincidence event and the gate for the RF was
~ 100 ns wide (see Figure 4.1 1). If the fragment time spread is considered, the possible neu-
tron time range to satisfy the coincidence condition would be ~ 150 ns. The time relations
(Figure 4.11) show that one of four different RF triggers could start the TDC. The most
prominent peak (reals) in the fragment TOF spectrum contained the fragments from both

real and random coincidence events. Reals and randoms gates for the each isotope (6He,

56

200 ns

 

 

 

- ..._!L.

 

31’
: W'

100 ns

 

 

 

 

 

delay .__.

 

100 ns

 

 

354.4 nsi delay 9
:4——>:

 

 

 

 

 

_V—V_V—V_VVV
1111

four possible TDC start triggers

fragment time

earliest possible
neutron time

latest possible
neutron time

earliest possible
RF gate by
master gate

latest possible
RF gate by
master gate

RF time

Figure 4.1 1: The relation of the fragment time signal, the neutron detector signal, and the
RF time signal. The earliest and latest possible neutron signal have margins of ~ 25 ns from
the edge of the fragment signal to take a fragment time spread into account.

57

9L1, and 12Be) in AB vs. TOF plots as well as individual isotope gates (611e, 9L1, and 12Be)
in E vs. AE plots were established using each filtered data sets. It was necessary to subtract
the randoms from the reals to extract the shape of the relative velocity spectrum only from

the real coincidence events.

4.3.1 He group

The filtered data of the He group was used to observe the known state of 7He. To select the
6He group from the one neutron decay of 7He, energy loss versus total energy plot (AE—E,
Figure 4.12) and energy loss versus time of flight plot (AB-TOF, Figure 4.13) were used.
The 6He isotope gate, the 6He reals gate, and the 6H6 randoms gate are indicated in the fig-
ures. The 6He nucleus has a long enough lifetime (~ 807 ms) to be observed in the fragment

telescope. The neighbors of the 6He (5He and 7He) are both unbound which makes it easy

 

 

 

A
80 —
60 -—
=3
.3 40 _
2O —
0 1 1 1 1 1 ,
280 360 440 520 600 680
E [MeV]

Figure 4.12: AE_1 (first quadrant of AE) vs. E3 plot of He group. The oval contour
shows a 6He gate.

58

 

 

A
80 — reals randoms
._. l l
560 — « . ‘
4o — ' ' ‘ * . ,
20 —
O _ I I I l l;
0 40 80 120 160 200
TOF [ns]

Figure 4.13: AE_1 (first quadrant of AE) vs. TOF (thin plastic time) plot of He group.
The contour gates show the 6He reals gate and the 6He randoms gate.

to isolate the 6He group in the two dimensional plots.

4.3.2 Li Group

To study 10Li states, the coincidence events of a neutron and a 9Li were separated from the
other events. Similar to the 7He case, energy loss versus total energy plot (AB-E, Figure
4.14) and energy loss versus time of flight plot (AB-TOF, Figure 4.15) were used. 10Li itself
was not observed on the AE-E and the AE-TOF plot because it is a neutron unbound nucle-
us. 8Li and 9Li have long enough lifetimes (~ 838 ms and ~178 ms) to be detected in the
fragment telescope. Like in the 7He case of the previous section, the reals and the randoms
of the 9Li were selected by the gates in the AE-TOF spectra.

The AE-E plots were handled similar to the 7He case except that E5, one of the CsI(Tl)

E detectors was excluded since it did not have a sufficient isotope separation between the

120 —-
110 —-

90—
80—
70—
60—
50—

AE [a.u.]

 

30

 

59

 

520

r

I
640 680 720 760

E [MeV]

Fi re 4.14: AE_1 (first quadrant of AE) vs. E3 plot of the Li group. The contour shows

a Li isotope gate.

 

 

 

 

120“—
reals randoms
1 l
100—
=5
.3 80—
60—
40 J J I 1 I E
104 120 136 152 168 184 200
TOF [ns]

Figure 4.15: AE_1 (first quadrant of AE) vs. TOF (thin plastic time) plot of Li group.
The contour gates show the 9Li reals gate and the 9Li randoms gate.

60

8Li and 9Li group. This was probably due to abnormal scattering at the center of the AE
detectors (see Figure 3.8), since the E5 detector was located right behind the center crossing
of the segmentation lines of the AE detectors (see Figure 3.9). Thus, the E5 related Li data

was omitted in the later analysis.

4.3.3 Be Group

The filtered data of the Be group was used to select neutron decay events of 13Be. Energy
loss versus total energy plot (AE-E, Figure 4.16) and energy loss versus time of flight plot
(AE-TOF, Figure 4.17) were used to select thelzBe group from the one neutron decay of
13Be. Unlike 13Be, the neighbors 11Be and 12Be have long enough lifetimes (~ 14 s and ~
24 ms) to be detected in the fragment telescope. The E5 related Be data were also omitted

in the later analysis from the same reason mentioned in the Li section.

190l—
170 ~—
,_ 150 -—

:2130—

|—"110—
% 90

70—

 

 

50 1 1 1 | 1 1 1 g
457 571 686 800 914 1029 1143 1257

E [MeV]

Fi ure 4.16: AE_1 (first quadrant of AE) vs. E3 plot of the Be group. The contour shows
a 2Be isotope gate.

61

   

 

A

170 —

150 —-
"T
=1 130—
:6
hi
2 110 _

90 _ f 7‘
reals randoms
| l l l l l -

 

70 -
104 120 136 152 168 184 200
TOF [ns]

Figure 4.17: AE_1 (first quadrant of AE) vs. TOF (thin plastic time) plot of Be group.
The contour gates show the Be reals gate and the 12Be randoms gate.

4.4 Simulation of Experiment

Monte Carlo simulations were performed to calculate the relative velocity spectrum for the
one neutron decay of 7He, 10Li, and 13Be, respectively. The decay of each fragment was
initially considered in the center of mass (CM) frame of the daughter fragment and the neu-
tron. The decay direction was assumed to be isotropic in the CM frame and a Breit Wigner

lineshape of the form [Lan58]
do = F(E)

 

—— —— (4.13)
dB (E—E,)2+},IF(E)12
where
E — ”’05) 414

was used. P,(E) was the l-dependent neutron penetrability function, and F0 = F(E = E,) was

62

the width at the resonance energy E ,.

The decay energy of each event was transformed into the center of mass velocity of the
neutron and the fragment, and then into the laboratory frame velocity of the neutron and the
fragment. In the next step, the decay direction of the fragment in the laboratory frame, was
compared with the data in an acceptance file which was calculated using the RAYTRACE
[Kow87] code. It contained the data of valid directions of the fragment velocity in the lab-
oratory frame at the target to reach the fragment telescope. The magnet settings of the qua-
drupole and the dipole, the location of the 11° beam pipe and the Cu collimator (see Figure
3.3, 3.7) were considered in the calculation. The events which had fragment velocity direc-
tions outside this acceptance were excluded. The direction of the neutron velocity in the
laboratory frame was checked and only the events which hit the neutron detector array were
used to calculate the relative velocity. The neutron detector efficiency was taken into ac-
count for the histogramming of the relative velocity spectrum by looking up an efficiency
file which contained efficiency factors for each neutron energy. This file was created by the
KSUEFF [Cec79] code.

A simulation for the neutron decay of 7He was executed first to set the parameters of
the Monte Carlo simulations and constants in the data analysis code, since 7He has a well
established ground state energy (E , = 440 :l: 30 keV) and width (F0 = 160 i 30 keV)
[Ajz88].

The input parameters of the simulation were set in the following way. The TOF
resolution (0' = 0.057ns) of the daughter fragment 6He was calculated from the energy
resolution of the CsI(Tl) E detectors because it was calculated from the energy information.

The centroid of the momentum distribution (2733.3 MeV/c for 7He) and the width of the

 

63

scattering angle (70.47 mrad for 7He) of the fragmentation product at the target (9Be, 94
mg/cmz) were predicted using INTENSITY. The momentum spread of the fragmentation
product (0' = 3.54% for 7He) for the simulation was set to match the actual spread of
experimental data of the coincidence runs. After setting these parameters, the TOF
resolution of the neutron was found by reduced chi-square (x3) minimization of the fit of
the calculated relative velocity spectrum to the measured spectrum. Figure 4.18 shows the
minimum of a neutron TOF resolution at 0' ~ 0.70 ns.

For the decay of 10Li to 9Li + n and 13Be to 12Be + n, the simulations were carried out
for different combinations of decay energy, width, and angular momentum. The TOF
resolution of the fragment and the neutron were fixed to the value which was established
from the 7He neutron decay simulation. The centroid of the momentum distribution (3901.9

MeV/c for 10Li and 5068.8 MeV/c for 13Be) and the width of the fragment scattering angle

 

 

 

 

 

 

0.8 IILIIIIIIIIIJIIIJLIIIIIJ IIPL
0.9 1 1.1

 

0.8
n [ns]

"68

Figure 4.18: xvz versus neutron TOF resolution plot. xvz is for the fit of the 7He neutron
decay simulation and the data. The minimum xvz of (best fit) is at tnres ~ 0.70 ns.

64
(53.90 mrad for 10Li and 42.38 mrad for l3Be) were also calculated by INTENSITY. The

middle of the momentum distribution of the fragmentation products (0 = 3.38% for 10Li

and 0' = 3.22% for 13Be) were obtained in a same way as in the 7He case.

 

Chapter 5

Results and Discussion

5.1 Selection of The Valid Events

The valid events for the relative velocity (V re, 2 Vn - Vf, Equation 3.8) spectra were select-
ed with the AE-E isotope gates, with the AE-TOF isotope gates for reals and randoms, and
with the neutron gates on the two dimensional plot of the neutron signals (see previous
chapter). Relative velocity spectra were obtained for each isotope, for each neutron detec-
tor, and for reals and randoms by scanning the filtered data for the same Z group. The rel-
ative velocity spectra of randoms were subtracted from the reals, and all the subtracted
spectra for the different neutron detectors were summed to obtain the total relative velocity

spectrum for each isotope.

5.2 The Relative Velocity Spectrum of 7He

7He has a Vp3/2 ground state with a neutron separation energy of Sn = -440 :l: 30 keV and a
F = 160 :l: 30 keV width [Ajz88]. Figure 5.1 shows the relative velocity spectrum for 6He
+ n coincidence events which were collected simultaneously with the 9Li + n and the 12Be
+ 11 events. The open circles with the error bars in the figure represent the data and the solid

line is the simulated decay of the ground state of 7He (dotted) superimposed upon an

65

66

 

 

 

 

400—111rlr1T1lIIIIITIIIIITII r111—

: 0 ‘ u :

300 — ,, ‘0 __.

‘— 0‘ .J _,

3 L I ~
g — "11.: f/\ I
o 200 — 1 I I \U __
.. u ' _

U L— ! \ j, \ .1
: 11 I " 0 I 11 :

10° .— '- . . ‘ .111?! " 1‘1, i

1- ' 1i? 0“ \ l - . . \f? —

” 3413.!” 'i/ \ ' ' - 1‘25!" 7

0 .1” 1 1 _l.|.L 1’14 1 1 1 1 1411 1 1 1\1 >1 4LT". --._.

-3 —2 —1 0 1 2 3

Vn - Vf [cm/n8]

Figure 5.1: The relative velocity spectrum for 6He + n coincidence events. The circles
with the error bars are the data. The dashed line shows the estimated background. The dot-
ted line rs the simulated decay of ground state of 7He without the background and the solid
line 1s a sum of the background and the simulation.

 

67

estimated background (dashed). The known decay energy and width were used in the
simulation. The two peaks in the relative velocity spectrum correspond to forward (positive
Vn-Vf) and backward (negative Vn - Vf) emitted neutrons. Vn - Vf = 0.0 cm/ns indicates
zero decay energy (Q-value is zero).

The precise source of the background for the neutron-fragment coincidence events is
unknown. The background has previously been investigated using the distribution for a
thermal neutron source of the form fiexp(—E/ T) [Dea87]. This thermal source lead to a
near-Gaussian shape background in the Monte Carlo simulation, thus Heilbronn [Hei90]
treated them in general as a simple broad Gaussian which had a centroid at some nonzero
relative velocity value. This approach was also adapted in the present case. The parameters
of the background Gaussian were obtained by fitting the data to the simulation which as-
sumed to be a sum of a broad Gaussian and the ground state decay simulation of 7He, leav-
ing the centroid, width, and amplitude of the Gaussian and the amplitude of the decay
simulation as fitting parameters.

In Figure 5.2, the solid line shows the calculated lineshape by the Breit-Wigner form
(Equation 4.12) with the l-dependent neutron penetrability factor, which was used for the
simulation of the ground state decay of 7He. The neutron separation energy of Sn = -440
keV, width of F = 160 keV, and l = 1 were used for the calculation. The result for the l = 0
with the same parameter as the l = 1 case is shown in the figure with the dashed line for
comparison. The lower energy part of the l = 1 lineshape is clearly suppressed compared to
the I = 0 case because of the 1 dependent penetrability factor.

Previously, Kryger et al. [Kry93] employed the same experimental method of sequen-

tial neutron decay spectroscopy (SNDS) at 0° to investigate the ground state of 10Li. Kryger

 

68

 

 

 

 

 

1- I I I I I I I T T I I I I I 7 I T

H. 25 9
=1 :
cu _
“E: 20 :-
5 Z
.n 15 —
a :
'8 :
1.. 10 —
=1- :
g» 1:
o 5 —
o :
a _

0

0.0 0.2 0.4 0.6 0.8

Decay energy E, [MeV]

Figure 5.2: The Breit-Wigner lineshapes of 7He state at E, = 440 keV with the width
of I‘ = 160 keV. The solid line shows the actual case with the angular momentum l = 1. For
the comparison, I: 0 case is shown with the dashed line. The low energy region of the peak
for the I = 1 case is suppressed compared to the l = 0 case.

 

69

et al. used the cyclotron RF as the start for the TOF for both the neutrons and the fragments
to calculate the neutron velocity Vn and the fragment velocity Vf and obtained the relative
velocity Vrel (= Vn - Vf). The time resolution for the neutron TOF and the fragment TOF
were both Om = Otf = 0.89ns. The current experiment used the fragment energy information
from the E detectors to calculate the Vf to utilize the superior energy resolution (0.49%,
FWHM), corresponding to a fragment TOF resolution of Otf = 0.057ns. The fragment TOF,
calculated from the energy, and the TNORP were used to calculate the TOF of neutrons
yielding a resolution of cm = 0.70 ns. The resolution was thus significantly improved for
the current experiment. The width of the peaks of 6He + n coincidence events were also
used to confirm the experimental resolutions. Figure 5.3 shows a comparison of the relative
velocity spectrum calculation using the different timing resolution. The dotted line shows
the perfect resolution case (neutron TOF resolution; O'm = 0.00 ns, fragment timing resolu-
tion; 0'“ = 0.00 ns). The dashed line shows the spectrum with the resolution of the setup
used by Kryger et al. (0’m = 0.89 ns, one = 0.89 ns). The solid line shows the spectrum with
the resolutions of the current experiment (0'tn = 0.70 ns, C“ = 0.057 ns). As one can see from
the figure, the width of the peaks in the relative velocity spectrum of the data is broadened
by an finite experimental time resolutions. The current experiment clearly shows the im-

provement in the resolution of the relative velocity.

5.3 The Relative Velocity Spectrum of 10Li

The first measurement by Wilcox et al. was reported in 1975 observing a lowest 10Li un-
bound state at E, = 800 i 250 keV and F = 1200 i 300 keV. Then the presence of a p-wave

state at E, = 420 i 50 keV and l" = 800 i 60 keV was reported by Bohlen et al. [Boh93]

 

7O

 

 

 

 

250 _ I I I I I I I I I I rj I I 1 I I I I I I I I I I I I _,

200 —— —_

3 Z :
g: 150 b —
=3 : ‘
O — 1
U _ s
100 :— ‘j

50 _— “

_ 4

0 b—l l [A l I ‘1

_3 3

 

Vn - Vf [cm/ns]

Figure 5.3: The relative velocity spectrum simulation of 7He —) 6He + n decay for the
different time resolutions. The dotted line shows a case of perfect resolution (0'tn = 0.00 ns,
otf = 0.00 ns). The solid line shows a case of a current experimental resolution ((5m = 0.70
ns, 0'“ = 0.057 ns). The dashed line shows a case of the experiment by Kryger et al. (0'm =
0.89 ns, 0'“: 0.89 ns).

 

71

and interpreted as the ground state. However, a low-lying s-wave state at E, = 150 keV and
F0 < 400 keV by Amelin et al. [Ame90] and also by Kryger et al. [Kry93] were reported
as the 10Li ground state. Young et al. [You94] observed a p-wave state similar to Bohlen’s
value (E, = 538 :t 60 keV) and, in addition, evidence of the lower lying state (E, ~ 100 keV).
Ostrowski et al. recently reported a new value (E, = 240 keV) as a p-wave ground state
[Ost96]. Our newly obtained data allowed us to determine if this state could potentially cor-
respond to the state observed by Kryger et al.

Figure 5.4 shows the relative velocity spectrum of the 9Li and neutron coincidence
events. The dotted line indicates an estimated broad Gaussian background. The dashed
lines show a simulated p-wave state (side peaks) at E, = 538 keV, [‘0 = 358 keV, corre-
sponding to the result reported by Young et al. [You94] and a simulated s-wave state (cen-
tral peak) at E, = 50 keV, F0 = 241 keV. The positions of the side peaks in the data matches
the simulation with the Young’s value quite well, however the statistics is not sufficient to
extract the values from a fit to the data. The p-wave state reported by Bohlen et al. (E, =
420 keV) was also tried for the simulation and yielded similar side peaks in the relative ve-
locity spectrum as the Young’s state (E, = 538 keV). Therefore, we consider these two
states as one state. In the new report by Ostrowski et al. [Ost96], this state was also assumed
as a first excited state for a fitting purpose. Thus the state at E, = 538 keV (Young’s value)
was assumed and included in the subsequent x2 fitting procedures.

To extract the decay energy and the width of the initial state for the central peak, sim-
ulations were performed and fitted to the data. For the 10Li initial state, neutron decays cor-
responding to states of l = 0 case and l = 1 case were considered. Each central peak

simulation had a certain combination of the decay energy E ,, the width F0, and the I value

 

72

 

500IIIIIIFHIIIIIIIIIIIIIIII VIII

TIWI

    

400

300

Counts

200

IllilJlllIIllllIlllL

100

 

=IIII|IIIFIIIjIIIIII|

.
I‘l‘

\.

 

Vn ' Vf [CID/11S]

Figure 5.4: The relative velocity spectrum of 10Li —) 9Li + n. The convention of the
data point and the Gaussian background are the same as the 7He spectrum. The dashed side
peaks are the simulation of the p-wave state at E, = 538 keV reported by Young et al. The
dashzed central peak is the simulation with I: 0, E, = 50 keV, F0 = 241keV. This is the fit
at xv minimum for the s-wave neutron.

I .

73

of the initial state neutron in 10Li. The output file of the central simulation was used along
with the pl ,2 state at 538 keV for the fitting. The amplitude of these two simulations and
the parameters of the Gaussian background (amplitude, centroid, and width) were set to be
free parameters and the best fit was searched to minimize the reduced chi-square x3, with
a computer routine [Bev69].

x3 surfaces as a function of F0 and E, were extracted in Figure 5.6 and 5.9. The overall
minimums of the reduced chi-square ximm are indicated with x. The reduced chi-square
value x3 = xgmin + 0.5 was considered to be a tolerance limit of a good fit. The upper lim-
its of the width F0 for each decay energy E, were calculated by setting the spectroscopic
factor 6,2 to the theoretical limit which is unity in a formula of a broad resonance [R0188],

r,(E) = %§(2Tl€)1/2P,(E,Rn)af (5.1)
n
where E = E, in this case since F0 = F(E = E,) was used for the simulation parameter, R, is
the nuclear radius, and P, is the 1 dependent penetrability factor. This limit is referred to as
the Wigner limit. The solid lines shows the Wigner limit and the dashed lines correspond
to constant x3, values of xemm + 0.5 , 13min + 1.0, and xemm + 1.5 as indicated in the fig-
ures.

In the relative velocity spectrum, the distance along the abscissa from 0.0 cm/ns is
directly related to the relative decay energy E, as described in Equation 3.3. Therefore, the
existence of the central peak inside the two side peaks of the 538 keV p-wave state in the
relative velocity spectrum implies another state with a lower decay energy than the p-wave
state and/or with a very broad width.

The widths of the peaks in the relative velocity spectra are related to the width of the

initial state and the final state of the decay as well as the experimental resolution. For the

 

74

final states, only the bound states matter for the analysis. 9Li has only two bound states
which are the ground state and the first excited state (E, = 2.691 MeV). As final states of
thelOLi neutron decay, the widths of these two states are very narrow [Ajz88], and their
contribution to the width of the peaks in the relative velocity spectra were negligible
compared to the contribution from the width of initial states and the finite experimental
resolution.

The present experimental method was only sensitive to the Q—value of the reaction and
not to the quantum numbers of the observed state, thus the single central peak of the data
in the spectrum could be interpreted in more than one way. Figure 5.5 shows a level dia-
gram of different possible cases of 10Li to 9Li + n decay to interpret the result. The first
scenario is illustrated in (a). The central peak could be a decay from a state of 10Li to the

ground state of 9Li. In the second scenario which is illustrated in (b), the central peak could

 

 

 

 

10Li 9Li + n l loLi 9Li + n
| ?
2691 keV . ‘b 2691 keV
I
V1P1/2 _________ L _ _ V1P1/2
- 33 keV . | 538 Re g.s.

(a) (b)

Figure 5.5: The level diagram of the possible two cases of the neutron decay of 10Li.

 

75

be due to the decay from an excited state of 10Li to the first excited state of 9Li at E x = 2.691

MeV.

5.3.1 The s-wave Case

If the initial state of the decay is assumed to be an s-wave, the minimum of the reduced chi-
square is xemm = 1.034 at E, = 50 keV and a decay width of F0 = 241 keV (see Figure 5.6).

If the case (a) of the Figure 5.5 is assumed, the decay energy E, would be equal to the
neutron separation energy 5,, of the lOLi. Then the limits established in Figure 5.6 can be
compared to the limits determined by Kryger et al. [Kry93] which are also indicated in the
figure as vertical and horizontal solid lines. The current result yields a more stringent limit
than Kryger’s result because of the improved experimental resolution and the consideration
of the Wigner limit. The present result is consistent with a recent measurement of the break-
up of llBe [Ish96]. This reconstructed spectrum for 10Li could be explained with an s-wave
at E, = 350 1 150 keV and a width of 2.2 +0350 MeV.

Since a broad resonance was assumed for the central peak and the side peaks in the rel-
ative velocity spectrum, the Breit-Wigner lineshape was used for the analysis of the current
data. However, s-wave neutron decay does not have a barrier and thus is not a real reso-
nance. Therefore the low-lying s-wave state was also analyzed using the scattering length
as a parameter. Zinser et al. measured the one neutron stripping of 11Li and measured the
transverse momentum distribution of the neutrons in coincidence with 9Li. They interpret-
ed their result as evidence of the s-wave ground state of 10Li and described the result with
an s-wave scattering length of as = -20 fm or less, equivalent to an excitation energy below
50 keV. The current result of the resonance energy at E, = 50 keV and F0 = 241 keV cor—

responds to an s-wave scattering length of as = -40.0 i 5.0 fm. This number was obtained

 

76

 

 

 

 

 

 

 

 

\9

X

5000 I I' I I
— a
I /‘
4000 —— 1
.—1 i 1
> 3000 -— —~
<1) ’ 1
v31, 2 Z
1.? 2000 E— —{
t :
1000 _— ——_
” ////// Kryger’s limit :
0 L/l/fi I l 1 l l I l l l l I l l l l i l l l A -‘

0 200 400 600 800 1000
E, [keV]

Figure 5.6: The valid region of the E, and F0 space based on the x2 analysis and Wigner
limit for s-wave initial state of 10Li.

77

by comparing the widths of the central peak simulation by Hansen [Han96] for the various
scattering lengths to the width of the current central peak simulation at the resonance ener-
gy and the width for the overall reduced chi-square minimum Ximin . The current result of
s-wave scattering length lies within the range of the Zinser’s result (as < -20 frn).

This interpretation of the result as a low-lying s-wave 10Li ground state at E, = 50 keV
and F0 = 241 keV is favored by the reports of theorists by Barker and Hickey [Bar77] and
Thompson and Zhukov [Tho94].

The data are compared to the calculation by Thompson and Zhukov. They used Woods-
Saxon potential [Tho94] for the neutron-9Li interaction and varied the parameters to calcu-
late the 11Li binding energy. The cases for a superposition of (1pm)2 and (251,2)2 config-
urations of the 11Li valence neutrons were calculated. Figure 5 .7 shows a comparison
between their calculations and the current result.

When the fitting parameter space was explored to extract the central peak parameters
for the current analysis, the p-wave initial state for the side peaks were fixed to the value
which were adopted from Young et al. [You94]. It was E, = 538 i 60 keV and F0 = 358 i
20 keV. The most current report of the two neutron separation energy of 11Li by Young et
al. ($2,l = 295 i 35 keV) [You93] is combined with the 1pm resonance energy report by
Young et al. and indicated as a dotted rectangular in Figure 5.7. This experimentally deter-
mined valid region is slightly outside the range of the result of three body calculations by
Thompson and Zhukov [Tho94] (see Figure 2.5). The limits of as = -40.0 i 5.0 fm for the
present work are also indicated as the dashed lines which again were interpolated from the
calculations by Thompson and Zhukov. Thus the scattering length of as = 40.0 i: 5.0 fm

agrees well with the 1pm resonance energy and the 2n-separation energy as shown by the

 

1W

 

 

 

 

 

 

 

 

78
as = -40 fm
-150 I I I I I I I I I I I I I I I I I I I
— ' l l I -
C L
-200 -
§ I
g -
<51 —250 :—
‘4 1-
1K
-300 /
a / / 1
_350 .- l I I l I 1 LJ 1 I I l l l I l l l l I l l l l q
400 450 500 550 600 650

1pm resonance energy [keV]

Figure 5.7: The result of the calculations with the Faddeev three body function for the
11Li binding energy as a function of 1pm resonance energy and the scattering length of
the 131,2 low-lying state. The current result as = -40.0 fm is indicated with the solid line.

 

1W

79

overlap over the valid regions.

The lineshapes of the low-lying s-wave state at E, = 50 keV (as = —40 fm) and F0 = 241
keV, and p-wave state at E, = 538 keV and F0 = 358 keV which were used to simulate the
best fit of the data were plotted in Figure 5.8. The relative population of the s-wave and p-
wave are 33% and 67%, respectively. Although, the p—state is populated strong, due to the
energy dependent efficiency (see Figure 3.6), it appears substantially weaker in the spec-
trum.

The case (b) of the Figure 5.5 is still a possibility, however it is unlikely since the recent
report by Zinser et al. [Zin95] showed strong evidence for the s-wave state in the 10Li to be
close to the threshold. In addition, there are no other reports for a state at E, z 2700 keV

where the state would be if it decays to the first excited state of 9Li.

 

 

 

 

 

 

15.0 I I I I I I I I I I I l I I I I T I I I I I I

; 1 1 1 ' 1 T 3

I s-wave I

'_.' 12.5 7 —:
=§ - A’ p-wave d
‘V Z
>, 10.0 __q
3:: a
'3 7.5 _ —§
8 1 —
a. : 3
>4 5-0 L __.
CU b ..
o . s
a) 1- a
D 2.5 :— _-
I- -1

0.0 .. l J l I l l l I l l l 1 r i i i i 1 i i ‘ 1 J l 4 1 d

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Figure 5.8: The 10Li lineshapes used for the best fit of the simulation to the data. The
relative population of the s-wave and p-wave is 33% and 67%, respectively.

 

 

II

 

80
5.3.2 The p-wave Case

If the initial state of the 10Li neutron decay is assumed to be a p-wave state, the valid region
of the decay energy versus decay width space can be confined as shown in the Figure 5.9.
The overall minimum of the reduced chi-square X31110: = 1.1308, is at E, = 50 keV and a
decay width of F0 =1.6 keV (indicated with the x in the figure). Like the previous section,
the solid line shows the Wigner limit and the dashed line indicates the surface of the re-
duced chi-square at 13 = Xian. + 0.5 , xv = szmun + 1.0, and 13 = 13min + 1.5.

If the case (a) of the Figure 5.5 is assumed, the decay energy E, would be equal to the
neutron separation energy S, of the 10Li. The reduced chi-square minimum is interpreted
as the 10Li p-wave state of E, = 50 keV and r0 = 1.6 keV. The statistical limit

13 < x3,” + 0.5 and the Wigner limit set the limit of the 10Li p-wave state at E, < 64 keV
and F0 < 56 keV. These states of 10Li are much lower than the known p—wave state of 10Li
at E, ~ 500 keV [You94, Boh93] and the newly reported value E, = 240 keV by Ostrowski
er al. [Ost96]. Thus the central peak observed in the current data does not correspond to the
p-wave state at E, = 240 keV observed by Ostrowski et al. The existence of this state cannot
be ruled out, and it could be present in the data. However the resolution is not sufficient to
separate it from the central peak.

Case (b) of Figure 5.5 seems unrealistic. A state at E, z 2700 keV would most likely
have a much larger width since it can decay not only to the first excited state but also to the
ground state. Also, there has been no report for the state at E, z 2700 keV from other ex-

periments [Boh93, Ost96].

 

 

1r

 

 

81

 

 

 

 

 

lid
:5 9.
81+ +
.5 N:
120 : 1 1 1 1 I r 1 1 1 1 r I 1 1 1 1 ] I 1 I
: / /:
: / / _
80 t— / —:
g E / / E "—3
£2 60 E— I 1 N'I':
—1 — . W 1 I /7 "g E
o :— \6® ‘ > ,__
L" 40 Z Q1886 I I F: x
20 : 1 I I I
: 1 1 1 3
0 : 1 1 I 1 1 1 1 I 1 1X1 LI ‘1 1 1 I I I 1:
0 20 40 60 80

E, [keV]

Figure 5.9: The valid region of the E, and F0 space based on the x2 analysis and Wigner
limit for p—wave initial state of “’Li.

82
5.4 The Relative Velocity Spectrum of 13Be

There have been several attempts to measure the ground state of 13Be. Ostrowski et al.
[Ost92] employed the reaction 13C(14C,'40)13Be at ELab = 337 MeV and observed a state
of S n = -2.01 MeV and F0 = 0.32 MeV as the lowest observed state. Penionzhkevich
[Pen94] reported a state at a lower decay energy of 900 keV using the reaction
l4C(l 1B,12N)13Be. The neutron transfer reaction d(12Be,p) was used by Korsheninnikov er
al. [Kor95] and in addition to other excited states the 2 MeV state was observed. Thus, the
state at E, z 2.0 MeV seems to be established, however the existence of the low-lying state
is not confirmed though the existence of an intruder s-wave state at lower energies have
been suggested by theoretical calculations [Len9l, Des94, Tho96].

The relative velocity spectrum of the l2Be + n coincidence events is shown in Figure
5.10. The open circles with the error bars show the data and the dotted line indicates the
estimated broad Gaussian background. The spectrum has a single central peak and evidence
of small side peaks around i 2.0 cm/ns. The simulation for the side peaks was performed
in the same manner as in the 10Li case assuming the d5” state of E, = 2.01 MeV and F0 =
0.32 MeV [Ost92] of 13Be. The dashed line with two side peaks on the spectrum indicates
the simulated d5,2 state. Since the presence of the d—wave state at E, z 2.0 MeV is in agree-
ment with the previous experiments and the peak positions of the simulation and the small
side peaks of the data matches well, the known d5” state was assumed to be in the spectrum
even though the statistics of the data for the side peaks was not sufficient to extract the res—
onance parameters.

Similar to the 10Li case, the central peak in the relative velocity spectrum implies a low-

er energy decay and/or a very wide width of the initial state. It is known that the widths of

 

 

83

 

250IIIIIIIIIIIIIIIIIIIIVIIIIIII

IIII

200

150

Counts

100

50

offing ‘ugfi. h :8. .: =i'.. ........

-3

IIIIIIIIIIIIIIFIIII

 

llllIllllLJILlIUlllllll

 

 

 

ml

Vn - Vf [cm/n8]

Figure 5.10: The relative velocity spectrum of the 12Be + n coincidence events.

84

the ground state, the first and the second excited state of the 12Be are narrow [Aj280]. Thus
the contribution of the final state width to the peak width in the relative velocity spectrum
was negligible compared to the width of the initial state and the width broadening due to
the experimental resolution.

Figure 5.11 shows a level diagram of the decay of 13Be —> 12Be + n. The energy levels
of the 12Be in this diagram were taken from reference [Aj280]. Two decay scenarios can be
considered to interpret the central peak in the relative velocity spectrum of 13Be. They are
illustrated in Figure 5.11. In case (a) of the figure, the ground state of 12Be is considered to
be the final state of the decay whereas in case (b) the first excited states at E, = 2.10 MeV
was assumed to be the final state.

In either case, the initial state was assumed to be an s-wave or d-wave since the 13Be
consists of a 12Be core which has a filled p shell [Tho96] for neutrons. The case (a) or (b)
of the decay process, and s or d—wave state as a initial state of the decay were assumed to
extract the decay energy and the width of a l3Be state from the central peak in the 12Be +
n coincidence events. The x2 analysis and the Wigner limit were employed to obtain the

result as in the 10Li case. The individual cases will be discussed in the following sections.

5.4.1 The s-wave Case

Figure 5.12 shows a result of the x2 analysis if the central peak in the relative velocity spec-
trum was assumed to have a s—wave state as an initial state. The format of the figure is the
same as the 10Li case. The x indicates the reduced chi-square minimum in the decay energy
versus decay width plot. The reduced chi-square minimum position indicates that the state
is at E,= 75 keV and the decay width F0 = 110 keV. The limits extracted from Figure 5 .12

for the low-lying s-wave state are consistent with theoretical predictions [Ost92, Des94,

 

 

 

85

4.56 MeV i I 4.56 MeV

2.71 MeV
V1d5/2 2.10 MeV I

 

 

 
   
 

2.01 MeV

 

 

 

Figure 5.11: The level diagram of the possible two cases of the neutron decay of 13Be.

 

 

 

86

 

 

 

 

\9
W X
”0
~48
_ r 1 1 1 1 1 1 1 1 1 r r 1 1 1 '1
6000 —— I o5 /7 / /
" '1 x / / 2
1—1 p *4 / / ‘
> b / / / / \6) d
._ . / -—
.34) 4000 to“ / / / .sx _
L—l I“ §\3 / KI“
o . 90 / 10‘ _
1- / —
2000 I—' / // / ——
.. / _
/ / /
.— / // / —
_ / // _
/ // _
0 W/ff 1 1 I 1 1 1 m I 1 1 1 1 I 1 1 1 1
0 500 1000 1500 2000
E, [keV]

Figure 5.12: The valid region of the
Wigner limit for s-wave initial state of

111;, and F0 space based on the x2 analysis and the
Be.

 

 

87
Tho96]. Lenske [Ost92] calculated the low lying s-wave state at E, z 900 keV, whereas

Descouvemont [Des94] predicted a slightly bound s-wave state ar E, = -9 keV or -38 keV.
Thompson and Zhukov [Tho96] calculated s-wave state very close to the threshold with a
scattering length of as = -l30 fm (E, < 10 keV). From the constraint of ximsn + 0.5 and the
Wigner limit, the maximum possible value for the state of this case is at E, z 1200 keV and
F0 z 4400 keV.

The lineshapes of the best fit of the low-lying s-wave state at E, = 75 keV and F0 = 1 10
keV, and the known 5/2+ state at E, = 2010 keV and the width of F0 = 320 keV are shown
in Figure 5.13. The relative population of the s-wave and d—wave are 44% and 56%, respec-
tively. Although, the d—state is populated strong, due to the energy dependent efficiency
(see Figure 3.6), it appears substantially weaker in the spectrum. These values are only es-

timates since the efficiency for the decay of the d—wave state is very low.

 

P__jlIrIITTTIIIIIIIIIIIIIIIIIIII

00
O

N
O

 

Decay probability [a.u.]
8

 

 

 

 

 

1.0 1.5 2.0 2.5 3.0
E, [MeV]

00

Figure 5.13: The 13Be lineshapes used for the best fit of the simulation to the data. The
relative population of the s-wave and d—wave is 44% and 56%, respectively.

 

 

 

1T
1

88

Although it can not be ruled out, it is unlikely that the assumed s-wave decays to the
first excited state of 12Be as shown in part 0)) of Figure 5.1 1. It would be dominating decay
to the ground state with a decay energy of ~2200 keV and this would be extremely wide.
Also, the experimental data reported by Ostrowski et al., [Ost92], Penionzhkevich [Pen94],

and Korsheninnikov et al. [Kor95] did not detect any states of 13Be at E, z 2200 keV.

5.4.2 The d-wave Case

The limit of the x2 analysis and the Wigner limit assuming the initial state for the central
peak to be a d-wave state and the final state to be the ground state of 12Be are plotted in
Figure 5.14. The reduced chi-square minimum ximsn = 1.07 indicates the decay energy
at E, = 50 keV with essentially a width of 0 keV. As can be seen in Figure 5.14 there is no
experimental limit on the width of the state. However, the decay energy has to be very small
in order to reproduce the central peak and the corresponding Wigner limit makes this an
very unlikely scenario. Such a narrow state should have been observed in the transfer reac-
tions [Ost92, Pen94].

On the other hand, if the case (b) of Figure 5.11 is assumed and the excitation energy
of the 12Be E x = 2100 keV is taken into account as an offset for the initial state energy level
of 13Be, the overall reduced chi-square minimum is ximsn = 1.07 at E, = 2150 keV. Again
the analysis is insensitive with respect to the width. Figure 5.15 shows the x2 surfaces and
the Wigner limit with the offset of E, = 2100 keV. Within the uncertainties this would be
consistent with the known vd5,2 state in 13Be. The central peak in the relative velocity spec-
trum would then be due to the decay from the tail of the vd5/2 state at E, = 2010 keV in 13Be
to the first excited state of 12Be at E, = 2100 keV. Due to the larger decay energy the re-

striction due to the Wigner limit as in case (a) are not present and the data are consistent

 

 

 

IT'”

 

89

 

 
 

 

     

 

 

 

8 ’- I I I I l I I I I l I ‘ I I I I II I I _
.. V1
_ o' ' ' :
1' N+=I +I | :2 "‘
6 .— ‘E1 1 ' + '7.
'—‘ _ x I 1N5 -
% _ I E .. .
M _ I I I X ._
“e 4T" . 1 1 ‘2 f
L" g 1 I I j 1
2 - 1 I 1 a :1
__ 1 _
- . 09 ' ' 7 .
_ 83% 1 I I Z 1;
O '- 1 l 1 l l 1 II J I I l l |1 LI 1 ll 1 l .-
0 50 100 150 200 250

E, [keV]

Figure 5.14: The valid region of the E, and F0 space based on the x2 analysis and Wigner
limit for d-wave initial state of 3Be The case (a) in Figure 5.11 is assumed.

90

 

 

 

 

V?
e :2-
E N
1500 __: I I I I I . I . I I I l I I I I I I I l/ I I I I

.— wig16111m1t / .1

_ / / _
_ / / - 1n
._. ’ / / ‘ 1‘
% 1000 ~— / / -: NE
E s
as _ / / /_ ,3

1.? — / / / a

- / / / ‘

50° 1 / /

, _

I / / -

” I I I ‘

O l 4 l 1 9L 1 l 1 1 I L | 1 l I 1 I 1 l I l I 1 1 l
2100 2150 2200 2250 2300 2350
E, [keV]

Figure 5.15: The result of xz analysis in the case of d-wave state in 13Be as an initial
state and the first excited state of 12Be as a final state.

 

 

 

91

with the measurement of F = 300 keV [Ost92]. Thus the scenario is a possible explanation
of the data. The branching ratio for the decay to the first excited state and the ground state
respectively have to be extracted from the shell model calculations, however as explained

in the last section the present data is not very sensitive to the strength distribution.

 

 

If

 

Chapter 6

Summary and Conclusions

The sequential neutron decay spectroscopy (SNDS) at 0° was employed to study light nu-
clei beyond the neutron dripline, 10Li and 13Be. The nuclei of interest and the nuclei for the
calibration (7He) were created via fragmentation and decayed immediately to one neutron
and a daughter fragment (9Li, 12Be, and 6He). Neutrons and the daughter fragments were
detected in coincidence and relative velocity spectra were obtained for each isotope from
their information of velocities.

The relative velocity spectra was compared with the spectra created by Monte Carlo
simulations. The simulation code included the decay kinematics, the beam optics, the de-
tector geometry, and the detector efficiencies. The code was tested and adjusted by com—
paring the data of the known decay of 7He and the simulation. Decay parameters of the
observed peaks were extracted with x2 tests.

The result of the 10Li data analysis concluded that the ground state of 10Li is most likely
the low-lying s-wave state. The result obtained suggested the ground state at E, z 50 keV
and F0 z 240 keV or in terms of the s-wave scattering length, as z -40.0 fm. It is consistent
with the recent experimental data reported by Zinser et al. [Zin95] and the three-body cal-
culations for 11Li reported by Thompson and Zhukov [Tho94]. The current work experi-

mentally established the existence of the low-lying s-wave ground state of 10Li which was

92

 

 

 

93
suggested experimentally by Kryger et al. [Kry93], Young et al. [You94], and Zinzer et al.

[Zin95] and predicted theoretically by Thompson and Zhukov [Tho94]. It is unlikely to im-
prove the experimental limits of the low-lying s-wave ground state in near future due to its
wide width for the low energy level, however the p-wave states at 500 ~ 200 keV observed
by Bohlen et al. [Boh93] and Ostrowski et al. [Ost96] still need to be resolved.

The conclusions from l3Be data showed that there are two possible scenarios for the
observed neutron decay of 13Be. The decay was either from a low-lying s-wave ground
state of 13Be to the ground state of 12Be or from a tail of the known 5/2+ state [Ost92] of
”Be to the first excited state of 12Be. The current result does not distinguish those two cas-
es. One way to resolve these two cases in the future would be to measure 'y-rays in coinci-
dence with a neutron and 12Be. If the final state of the decay which caused the central peak
is the first excited state of 12Be, the events would be followed by 'y-ray emissions. Further
experimental information of the 13Be ground state is awaited for the understanding of the

neutron dripline nucleus l4Be.

 

 

 

 

 

BIBLIOGRAPHY

 

[Ajz80]
[Ajz88]

[Ame90]

[Aud93]
[Ban92]
[Bar77]
[Ber91]

[Bev69]

[Boh93]

[Cec79]

[Che70]

[Dea87]

[Des94]

BIBLIOGRAPHY

F. Ajzenberg-Selove and CL. Busch, Nucl. Phys. A 336, 1 (1980).

F. Ajzenberg-Selove, Nucl. Phys. A 490, l (1988).

A.I. Amelin, M.G. Gomov, Yu.B. Gurov, A.L. Il’in, P.V. Morokhov, V.A.
Pechkurov, V.I. Savel’ev, F.M. Sergeev, S.A. Smimov, B.A. Chemyshev,
R.R. Shafigullin, and A.V. Shishkov, Sov. J. Nucl. Phys. 52, 782 (1990).
G. Audi and AH. Wapstra, Nucl. Phys. A 565, 66 (1993).

J.M. Bang and 1.]. Thompson, Phys. Lett. B 279, 201 (1992).

F.C. Barker and GT. Hickey, J. Phys. G 3, L23 (1977).

OF. Bertsch and H. Esbensen, Ann. Phys. 209, 327 (1991).

RR. Bevington, Data Reduction and Error Analysis for the Physical Sci-
ences, McGraw-Hill (1969).

H.G. Bohlen, B. Gebauer, M. von Lucke-Petsch, W. von Oertzen, A.N. Os-
trowski, M. Wilpert, Th. Wilpert, H. Lenske, D.V. Alezandrov, A.S. Demy-
anova, E. Nikolskii, A.A. Korsheninnikov, A.A. Ogloblin, R. Kalpakcheva,
Y.E. Penionzhkevich, and S. Piskor, Z. Phys. A 344, 381 (1993).

R.A. Cecil, B.D. Anderson, and R. Madey, Nucl. Instrum. Meth. 161, 439
(1979).

Y.S. Chen, W.D. Harrison, and TA. Tombrello, Bull. Am. Phys. Soc. 15,
1598 (1970).

F. Deak, A. Kiss, Z. Seres, G. Caskey, A. Galonski and B. Remington, Nucl.
Instrum. and Meth. A 258, 67 (1987).

P. Descouvemont, Phys. Lett. B 331, 271 (1994).

94

 

 

 

[Esb92]

[Fox89]

[Fox92]

[Gol74]

[Gre75]

[Han87]

[Han95]

[Han96]

[Hei90]

[He188]

[Hiif8 1]

[Ish96]

[Kno89]

[Kob88]

[Kob92]

[Kor95]

95

H. Esbensen and G.F. Bertsch, Phys. Rev. C 46, 1552 (1992). See also G.F.
Bertsch and H. Esbensen, Ann. Phys. (N. Y.) 209, 327 (1991).

R. Fox, R. Au, and A. VanderMolen, IEEE Trans. on Nucl. Sci. 36, 1562
(1989).

R. Fox and J.S. Winfield, NSCL Data acquisition system reference guide,
(1992).

AS. Goldhaber, Phys. Lett. B 53, 306 (1974).

DE. Greiner, P.J. Lindstron, H.H. Heckman, B. Cork and RS. Bieser, Phys.
Rev. Lett. 35, 152 (1975).

P.G. Hansen and B. Jonson, Europhys. Lett. 4, 409 (1987).

P.G. Hansen, A.S. Jensen, and B. Jonson, Ann. Rev. Nucl. Part. Sci. 1995
45, 591 (1995).

P.G. Hansen, (private communication).

L.H. Heilbronn, Ph. D. Thesis, unpublished, Michigan State University
(1990).

J .H. Heltsley, L. Brandon, A. Galonsky, L. Heilbronn, B.A. Remington, S.
Langer, A. Vander Molen, J. Yurkon, and J. Kasagi, Nucl. Instrum. Meth.
A 263, 441 (1988).

J. Hiifner and MC. Nemes, Phys. Rev. C 23, 2538 (1981).

M. Ishihara, Contribution to the Gull Lake Conference on Nuclear Physics
Near the Driplines, August 21 - 24, 1996, Gull Lake, Michigan (1996).

G.F. Knoll, Radiation Detection and Measurement, John Willey & Sons,
Inc. (1989).

T. Kobayashi, O. Yamakawa, K. Omata, and I. Tanihata, Phys. Rev. Lett.
60, 2599 (1988).

T. Kobayashi, Nucl. Phys. A538, 3430 (1992).
AA. Korsheninnikov, B. Yu. Nikolskii, T. Kobayashi, D.V. Aleksandrov,

M. Fujimaki, H. Kumagai, A.A. Ogloblin, A. Ozawa, I. Tanihata, Y. Wa-
tanabe, and K. Yoshida, Phys. Lett. B 343, S3 (1995).

 

 

 

[Kow87]

[Kra88]

[Kry93]

[Lan58]

[Lav73]

[Len91]

[Mig73]

[Oak92]

[Orr92]

[Ost92]

[Ost96]

[Pen94]

[Pop85]

96

S. Kowalski and HA. Enge, RAYTRACE manual, Laboratory of Nuclear
Science and Department of Physics, Massachusetts Institute of Technology,
(1987).

Kenneth S. Krane, Introductory Nuclear Physics, John Wiley & Sons
(1988).

R.A. Kryger, A. Azhari, A. Galonsky, J .H. Kelley, R. Pfaff, E. Ramakrish-
nan, D. Sackett, B. M. Sherrill, M. Thoennessen, J.A. Winger, and S.
Yokoyama, Phys. Rev. C 47, R2439 (1993).

AM. Lane and R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958).
A. Laverne and C. Gignoux, Nucl. Phys. A 203, 597 (1973).

H. Lenske, Proc. Int. Symp. on Structure and Reactions of Unstable Nuclei
1991, edited by K. Ikeda and Y. Suzuki, World Scientific, Singapore (1991).

AB. Migdal, Sov. J. Nucl. Phys. 16, 238 (1973).

The formulas and parameters of J .F. Ziegler, The Stopping and Ranges of
Ions in Matter, Vols. 3 & 5, Pergamon Press (1980), coded by OakRidge
National Laboratory, doc. in HHIRF__UBOOK, (1992).

NA. Orr, N. Anantaraman, Sam M. Austin, C.A. Bertulani, K. Hanold, J.H.
Kelley, DJ. Morrissey, B.M. Sherrill, G.A. Souliotis, M. Thoennessen, J .S.
Winfield, and J .A. Winger, Phys. Rev. Lett. 69, 2050 (1992).

AN. Ostrowski, H.G. Bohlen, A.S. Demyanova, B. Gebauer, R. Kalpa-
kchieva, Ch. Langner, H. Lenske, M. von Lucke-Petsch, W. von Oertzen,
A.A. Ogloblin, Y.E. Penionzhkevich, M. Wilpert, Th. Wilpert, Z. Phys. 343,
489 (1992).

AN. Ostrowski, H.G. Bohlen, B. Gebauer, S.M. Grimes, R. Kalpakchieva,
A.A. Korsheninnikov, T.N. Massey, W. von Oertzen, A.A. Ogloblin, Y.E.
Penionzhkevich, CH. Seyfert, Th. Stolla, M. Wilpert, and Th. Wilpert, Pro-
ceedings of the International Workshop XXIV on Gross Properties of Nu-
clei and Nuclear excitations, edited by H. Feldmeier, J. Knoll, and W.
Norenberg, GSI, Germany (1996).

Yu. E. Penionzhkevich, Proc. of the IV. Int. Conf. on Selected Topics In Nu-
clear Structure, edited by V.G. Soloviev, Dubna, Russia (1994).

N.A.F.M. Poppelier, L.D. Wood, and P.W.M. Glaudemans, Phys. Lett.
157B, 120 (1985).

 

 

 

[Rei68]

[R0188]

[Tal60]

[Tan85]

[Thi75]

[Tho94]
[Tho96]

[Tou75]
[Wap85]
[Won90]

[Wou88]

[Wil75]

[Win92]

[You93]

[You94]

[V0165]

97

R. Reid, Ann. Phys. 50, 411 (1968).

Rolfs and Rodney, Cauldrons in the Cosmos, The University of Chicago
Press (1988).

I. Talmi and I. Unna, Phys. Rev. Lett. 4, 469 (1960).

I. Tanihata, H. Hamagaki, O. Hashimoto, Y. Shida, N. Yoshikawa, K. Sug-
imoto, O. Yamakawa, and T. Kobayashi, Phys. Rev. Lett. 55, 2676 (1985).

C. Thibault, R. Klapisch, C. Rigaud, A.M. Poskanzer, R. Prieels, L. Lessard,
and W. Reisdorf, Phys. Rev. C 12, 644 (1975).

U. Thompson and M.V. Zhukov, Phys. Rev. C 49, 1904 (1994).
U. Thompson and M.V. Zhukov, Phys. Rev. C 53, 708 (1996).

R. de Tourreil and D.W.L. Sprung, Nucle. Phys. A 242, 445 (1975).
A.H. Wapsta, G. Audi, and K. Bos, Nucl. Phys. A 432, 1 (1985).

S.S.M. Wong, Introductory Nuclear Physics, Prentice Hall, N.J., USA
1990.

J .M. Wouters, R.H. Kraus, Jr., D. J. Viera, G.W. Butler, and K.E.G. Lobner,
Z. Phys. A 331, 229 (1988).

K.H. Wilcox, R.B. Weisenmiller, G.J. Wozniak, N.A. Jelley, D. Ashery,
and J. Cemy, Phys. Lett. 59B, 142 (1975).

J .A. Winger, B.M. Sherrill, and DJ. Morrissey, Nucl. Instrum. Meth. B 70,
380 (1992).

BM. Young, W. Benenson, M. Fauerbach, J .H. Kelley, R. Pfaff, B.M. Sher-
rill, M. Steiner, J.S. Winfield, T. Kubo, M. Hellstrom, N.A. Orr, J. Steatson,
J .A. Winger, and SJ. Yennello, Phys. Rev. Lett. 71, 4124 (1993).

BM. Young, W. Benenson, J.H. Kelley, N.A. Orr, R. Pfaff, B.M. Sherrill,
M. Steiner, M. Thoennessen, J .S. Winfield, J .A. Winger, S.J. Yennello, and
A. Zeller, Phys. Rev. C 49, 279 (1994).

AB. Volkov, Nucl. Phys. 74, 33 (1965).

 

 

 

[Zin95]

98

M. Zinser, F. Humbert, T. Nilsson, W. Schwab, Th. Blaich, M.J.G. Borge,
L.V. Chulkov, H. Eickhoff, Th.W. Elze, H. Emling, B. Franzke, H. Freiesle-
ben, H. Gissel, K. Grimm, D. Guillemaud-Mueller, P.G. Hansen, R. Holz-
mann, H. Irnich, B. Jonson, J .G. Keller, 0. Klepper, H. Klinger, J.V. Kratz,
R. Kulessa, D. Lambrecht, Y. Leifels, A. Magel, M. Mohar, A.C. Mueller,
G. Mfinzenberg, F. Nickel, G. Nyman, A. Richiter, K. Riisager, C. Sheiden-
berger, G. Schrieder, B.M. Sherill, H. Simon, K. Stelzer, J. Stroth, O. Teng-
blad, W. Trautmann, E. Wajda, and E. Zude, Phys. Rev. Lett. 75, 1719
(1995).

 

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