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This is to certify that the

dissertation entitled

THE ELECTROMAGNETIC EXCITATION OF 6HE AND

NEUTRON CROSS—TALK IN A MULTIPLE—DETECTOR SYSTEM

presented by

Jing Wang

has been accepted towards fulfillment
of the requirements for

Ph.D Physics

degree in

 

 

W

Major professor 6

Date [“20‘ 77

 

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1/98 chlRC/DateDue.p65-p.14

 

THE ELECTROMAGNETIC EXCITATION OF 6HE
AND
NEUTRON CROSS-TALK IN A MULTIPLE-DETECTOR
SYSTEM

By

Jing Wang

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1999

Abstract

Part I: The Electromagnetic Excitation of 6He
by

Jing Wang

In the past, llLi was the focus of physicists who were fascinated by its halo
structure formed by the two valence neutrons extending far from the nuclear core. Even
after intensive studies of “Li, it remained unclear whether some properties found in the
11Li nucleus exist in other weakly bound nuclei near the neutron dripline. To further
study neutron halo nuclei, a kinematically complete measurement of coulomb
dissociation of 6He was performed. In the experiment, a 25 MeV/u 6He beam was

delivered to strike six targets——U, Pb, Sn, Cu, Al and C. The momenta of the fragments

were measured for the 6He dissociation in the six targets.

The 2-n removal cross sections for the six targets were determined. The coulomb
part of the cross sections was extracted using a linear extrapolation and a fitting model.
We found, for example, the coulomb dissociation cross section for U accounts for more
than half of the total 2-n removal cross section. The measured width of the 4H6 parallel
momentum distribution (0' = 40.2 i 2.3 MeV/c) corresponds to a rms radius of 2.95 i
0.17 fm for the 6He nucleus. A target dependence of the momentum spread was observed
in both neutron and 4He parallel momentum distributions. From the 2n-4He coincidence

data, the 6He decay energy spectra were constructed for the six targets. Based on the

decay energy spectrum for the U target, the dipole strength function

 

dB(E 1)
was
dE

determined. The strength function with a Breit-Wigner shape peaks at Ed = 1.9 MeV
with a width 1" = 1.5 MeV, which resembles a soft dipole resonance. However, post-
breakup acceleration was found in the high-Z targets, which does not support the soft
dipole resonance model. The data also suggest that there is little correlation between the
halo neutrons in 6He, and a sequential decay mechanism may come to dominate the 6He

breakup in light targets.

Part H: Neutron Cross-talk in a Multiple-detector System
by

J ing Wang

Two 2m x 2m neutron “walls” were built for experiments with two neutrons in the final
state. Each wall consists of 25 rectangular cells filled with NE~213 liquid scintillator. The
close-packed design of the array makes cross-talk an inevitable contributor to distortion of

measurements with this system. For Bn 5 25 MeV almost all the detection efficiency

comes from n-p scattering, and the simple two-body kinematics can be used as the basis
for identifying cross-talk events. A Monte-Carlo code was developed to simulate the
detection process. We found that most cross-talk events could be distinguished from real
two-neutron events. A test experiment for comparison with the code was performed with
neutrons from the 7Li(p, n)7Be reaction at Ep = 30 MeV. With this reaction all two-
detector coincidences are cross-talk events. Consistency between the experimental data

and the simulation results was obtained.

To my wife and my grandmother, the two most important women in my life.

iv

Acknowledgements

I would like to thank my advisor, Aaron Galonsky. The truth is that without his help, I
could not reach where I am today. Even If I were a native English speaker, words could
not express my gratitude to him. For more than six years, he has constantly provided me
guidance, and passed knowledge to me so unselfishly. It was he who made me become a
PHYSICIST, which I will cherish in my entire life. I learned from him not just about
Physics but also about genuinely great American people. The treasure I am going to take
from him will be with me forever. I would also like to thank Marion for her warmth and

kindness.

I want to thank the other members in my guidance committee: Professor Tim Beers,
Professor Alex Brown, Professor Gregers Hansen, Professor Brad Sherrill, Professor Dan

Stump for sitting in my committee and giving me valuable advise.

I don’t think I could have completed my thesis experiment without the help from my
colleagues: Jon Kruse, Phil Zecher, Ferenc Deak, Akos Horwarth, Adam Kiss, Zoltan
Seres, Kazuo Ieki, Yoshiyuki Iwata. It was a unique experience working with each every
one of them. I may forget how they look like one day, but I will never forget their

stories.

It would have been hard for me to work at the lab days and nights without the lively
conversations with my officemates. By the way, my office was probably the only place

where I did not feel that I was a foreigner because it was truly international. Starting

from Brian Young, the “Rush Linbaugh” guy, then came Mathias Steiner, the “car” guy,
Mike Fauerbach, the “Jing, that is your fault and I am going to tell your wife” guy,
Marcus Chromik, the only German I know wearing a yellow sweater of the Brazilian
National Soccer Team, Sally Gaff, the nicest graduate student ever worked in the office,

Don Anthony, the “J ing, your wife has called” guy. Thanks, guys!

It will make me very uncomfortable if I forget to thank the Cyclotron people. To the
people I worked with or not worked with, I want to say “Thank you!” To me, you are

indispensable for Cyclotron’s every bit of glory.

Special thanks go to my friendship Family, Fred and Charlotte, for their love, their
encouragement and the candles they lighted at my birthdays. In the past six years, they
made every holiday so desirable and so enjoyable. If I haven’t been home sick, it is
because of their care. I will never forget the four days I stayed with them before my oral
defense, the defense that I would like to entirely dedicate to them. Thanks, Fred and

Charlotte, for the past six years and for the many years to come!

I want to thank my parents, Shizhong Wang and Liqiong Peng, for giving us the freedom
to go on with my personal life and for the sacrifice they have made in order for me to

chase my dreams.

I dedicate part of my thesis to my grandmother because she is one of the greatest women
in my life. Not only did she bring me up, but also showed me that love is the single most

beautiful thing in the world. Thank you, grandma! May happiness forever with you in

vi

 

heaven!

I cannot imagine working through the past six years without my wife, Lei. It is her
support, encouragement that made this thesis possible. I want so much to thank her for
never letting me give up, for never letting me lose my confidence, for staying with me
during my ups and downs, for the delicious dishes and most importantly, for being my
lovely wife. I sometimes wonder why I am the luckiest one in the world. For you, dear

Lei!

vii

TABLE OF CONTENTS

LIST OF TABLES .................................................................. x
LIST OF FIGURES ............................................................... xii

PART I: The Electromagnetic Excitation of 6He

1. Introduction ............................................................................... 1
1.1 Neutron Halo ................................................................................ 1
1.2 6He Nucleus ................................................................................. 3
1.3 6He Experiments ........................................................................... 4
1.4 Theoretical Models ........................................................................ 4
1.5 Coulomb Excitation ....................................................................... 5
2. Experimental Setup ..................................................................... 10
2.1 The ‘He Beam ............................................................................. 10
2.2 The Neutron Wall Detectors ............................................................. 14
2.3 The Deflecting Magnet .................................................................. 18
2.4 The Fragment Detectors ................................................................. 22
3. Coulomb Dissociation of 6He ......................................................... 30
3.5 2-n Removal Cross—section .............................................................. 30
3.2 Parallel Momentum Distributions ...................................................... 51
3.3 6He Decay Energy Distribution ......................................................... 62
3.4 Post-Breakup Coulomb Acceleration .................................................. 72
3.6 Neutron Correlation ....................................................................... 84
4. Summary ................................................................................... 90

viii

PART II

5. Neutron Cross-talk in a Multiple-detector System ................................ 94
5. 1 Introduction ................................................................................. 94
5.2. Cross-talk in Neutron Walls .............................................................. 95
5.2 Cross-talk Identification .................................................................. 97
5.3 Experiment ................................................................................. 1 17
5.4 Summary ................................................................................... 126
APPENDICES

Appendix A: Calibration of Fragment Detectors ......................................... 127
A1 Neutron Walls ............................................................................. 127
A2 Scintillator Bar Detectors ............................................................... 131
A3 Si Strip Detectors ........................................................................ 135
Appendix B: Electronics and Data Acquisition ........................................... 139
B. l Neutron Walls ........................................................................... 139
B2 Fragment Detectors ..................................................................... 141
B3 Trigger Logic ............................................................................. 141
Appendix C: Cross-talk Simualtion Programs ............................................ 146
BIBLIOGRAPHY ................................................................................ 148

ix

LIST OF TABLES

Table 3.1. 1 Measured 2n removal cross sections on Si for 6He from ref. [17]. These
data were used for the normalization. ......................................................................... 40
Table 3.1. 2 2n removal cross sections in the experiment. 0'2n is the measured cross
section assuming constant neutron multiplicity. 62,, ’ is the measured cross
section adjusted for neutron multiplicity [40,41]. The calculated cross sections
are from refs. [30] and [37]. ....................................................................................... 42
Table 3.1. 3 Neutron multiplicity for the six targets [40]. ............................................... 42
Table 3.1. 4 Coulomb 2n removal cross sections by the extrapolation described in the
text. The calculated cross sections are from Warner [35,37]. ................................... 49
Table 3.2.1 The widths of the measured parallel momentum distributions ..................... 55
Table 3.4. 1 Average velocity shift <AV> between the 4He and the neutrons from the
6He breakup, and the mean lifetime of the resonance determined from <AV>. ........ 82
Table 5.3. 1 The interactions between neutrons and the nuclei in liquid scintillators
— protons and carbon. GR is the reaction cross section. The data are from the
code by Cecil et a1. [9] ................................................................................................. 98
Table 5.3. 2 The best parameters of the light response function L=ax(1-exp(-b><E°)) +
de + f for protons, alpha particles and carbon nuclei ........................................... 104
Table 5.3. 3 Number of 2—n events detected by the neutron walls when one million
1|Li breakups were simulated. .................................................................................. 113
Table 5.3. 4 Results of the simulation of 11Li breakup for 2-n events between the
two walls. G1 and G2 are the gates set on (COSG)c-(COSG),.[l and ATc-ATm

distributions, respectively, shown in Fig. 5.3.5. C3 is the condition that EP’SEn’,

explained in section 5.5. In experiments, all the 2-n events which fall in G1, G2

and satisfy C3 are rejected as cross-talk events. ....................................................... 116

xi

LIST OF FIGURES

Figure 1.5. 2 Photon distributions n 51 (E 7) for the six targets used in the experiment ..... 8

Figure 2.1. 1 The experimental setup (not to scale). This is the top view of the N4
vault at the NSCL. The neutron walls, one behind the other, were placed 5.00
and 5.84 meters from the target. The plastic scintillator array was mounted inside
the vacuum chamber about 1.8 meters from the target. The silicon strip detectors
were located at the entrance of the magnet, 15.24 cm downstream from the target.
The two PPACs were mounted 38.64 cm and 130.08 cm upstream from the
target. .......................................................................................................................... 1 1

Figure 2.1. 2 The beamline time. The start was given by the scintillator array, and
the stop was given by a plastic scintillator 41.5 meters upstream from the
scintillator array. ......................................................................................................... 13

Figure 2.2. 1 The schematics of a neutron wall. Each of the two Neutron Walls is a
2m x 2m array of 25 individual cells. The cells are 2m long, have rectangular
cross sections, and are stacked vertically to fill the entire 4 m2 area with very little
dead space between elements. Custom-made of Pyrex, the cells are filled with
NE America’s NE-213 liquid scintillator and are read out at each end by a Philips
Photonics 3-inch photomultiplier tube. ...................................................................... 16

Figure 2.3. 1 The experimental setup for the 11Li experiment. The Si-CsI was placed
between the target and the neutron detector arrays. ................................................... 19

Figure 2.3. 2 (a) The deflecting magnet and the mapped middle plane. The poles

cover a dimension of 13 inch x 24 inch. (b) The magnetic field at the middle

xii

plane. The maximum intensity is about 1.5 Tesla. Refer to (a) for the coordinates... 21
Figure 2.4. 1 The setup of the 250nm Si strip detectors. The 16 horizontal strips and
16 vertical strips are shown in detector #2. The 32 strips form 256 pixels, each
with an area of 3.125X3.125 mmz. The strip detectors are 15.24 cm from the
target. There is a 2mm gap between the two detectors. .............................................. 23
Figure 2.4. 2 The top and side View of the scintillator array. The array consists 16
BC408 plastic bars. Each of these rectangular bars has dimensions 40.64 X 4 x 2
cm3. Two photomultiplier tubes (PMT) are attached to the ends of each bar. The
PMTs are covered with magnetic shields. .................................................................. 25
Figure 2.4. 3 The divider of the PMT base designed for the scintillator bar. The
divider was placed in the air to dissipate the heat. The divider is connected to the
socket in Fig. 2.4.4 according to the order from J 1-1 to J 1-16, which can be found
in this figure and in Fig. 2.4.4 ..................................................................................... 26
Figure 2.4. 4 The socket of the PMT base designed for the scintillator bar. The
socket, attached to one end of a scintillator bar, was placed inside the vacuum
chamber ....................................................................................................................... 27
Figure 3.1.1 The light output in the entire 16-scintillator array. ...................................... 32
Figure 3.1.2 Trajectories of a 6He projectile and a 4He ion at 23 MeV/u. This is the
result of a calculation with the mapped magnetic field. According to the
calculation, the 6He hits bar #5, and the 4He hits bar #10. ......................................... 34
Figure 3.1. 3 The light ouput for the eight scintillator bars close to the beamline. The
data were taken with a 25 MeV/u 6He beam incident on a U target. Most of the

beam hit bars #5 and #6. A number of 4He particles produced in the target start to

xiii

appear in Bar #8 .......................................................................................................... 35
Figure 3.1.4 The light ouput for the eight scintillator bars far from the beamline.
Almost all the 4He produced in the target were swept by the magnet to the eight
bars and bar #7 shown in Fig. 3.1.3. ........................................................................... 36
Figure 3.1.5 The n-y discrimination spectra. The top branches are 7 and cosmic rays.
The bottom ones are neutrons. (a) The “Fast” signal versus the “Total” signal.
The data were taken with a Pu-Be source. 0)) The attenuated “Fast” signal
versus the attenuated “Total” signal. The attenuation factor is 4. The data were
taken with a 6He beam. ............................................................................................... 38
Figure 3.1.6 Light output distribution for coincidence events detected on bars from
#8 to #16 for the U target. The solid gate was used to select the 4He fragment.
The tail on the left side of the 4He peak is formed by other light fragments such as
3H and 3He. The small peak on the right side of the gate is formed by some 6He
particles. ...................................................................................................................... 40
Figure 3.1.7 Total 2n removal cross sections for the six targets. The solid line is a
simple model (eq. 3.1.4) to extrapolate the nuclear parts of the cross sections for
the high Z targets. The results are listed in Table 3.1.4 .............................................. 46
Figure 3.1. 8 Coulomb dissociation cross sections of 6He for the four targets. The
data points are the results of the extrapolation shown in Fig. 3.1.7. The solid line
is the theoretical calculations by Warner [35 ,37 ]. ...................................................... 48
Figure 3.1.9 Total 2n removal cross sections for the six targets. The points are the
experimental data. The solid curve is a fitting model to extract the coulomb part

of the cross section (eq. 3.1.7). The results are listed in Table 3.1.4 ......................... 49

Figure 3.2.1 Breakup of 6He into 4He + n +n. The breakup occurs as the 6He
projetile touches the U nucleus. Both the 6He projectile and the 4He fragment are
deflected by the coulomb force from the U nnr‘lens

Figure 3.2.2 Neutron parallel momentum distributions for the 6He breakup. The
parallel momentum is the projection of the momentum on the incident direction
of the 6He beam. The solid curves are Gaussian fits. The widths of the

distributions are listed in Table 3.2.1

 

Figure 3.2. 3 (a) The widths of the 4He parallel momentum distributions for the six
targets. (b) The widths of the neutron parallel momentum distributions for the six
targets

Figure 3.2.4 The 4He parallel momentum distributions for the 6He breakup. The
parallel momentum is the projection of the momentum on the incident direction
of the 6He beam. The solid curves are Gaussian fits. The widths of the

distributions are listed in Table 3.2.1.

 

Figure 3.3.1 Decay energy distributions——d0'm/dEd for the six targets. These are 2n-
4He oincidence events
Figure 3.3.2 Calculated solid-angle acceptance of the detection system. The

simulation is based on the 3-body phase space model.

 

Figure 3.3.4 The dipole strength functions. The dashed curve and the dotted curve

are from two 3-body models [25,46].

 

Figure 3.4.1 Neutron energy distributions for the 6He breakup. The points are In—

4He coincidence events from the experiment. The solid lines are Gaussian fits. ......

Figure 3.4.2 Difference between the average neutron energy and the average 6He

XV

52

55

56

59

63

67

70

74

beam energy per nucleon. The average neutron energy is determined from the
centroid of the Gaussian in Fig. 3.4.1. The average beam energy is equal to the

beam energy at the center of the target. The solid line connects the maximum

energy differences for the six targets .......................................................................... 75

Figure 3.4.3 Velocity (z-component only) difference distributions for the three heavy
targets in the expriment. The top three graphs are the differences between the
4He velocity and the average velocity of the two neutrons, calculated on an event-
by-event basis. The bottom three graphs are the differences between the 6He
center of mass velocity before breakup and after breakup for the same three

targets, respectively. The dashed lines are the centroids of the bottom

distributions. ............................................................................................................... 77

Figure 3.4.4 Velocity (z-component only) difference distributions for the three light
targets in the expriment. The top three graphs are the differences between the
4He velocity and the average velocity of the two neutrons, calculated on an event-
by-event basis. The bottom three graphs are the differences between the 6He
center of mass velocity before breakup and that after breakup for the same three

targets, respectively. The dashed lines are the centroids of the bottom

distributions. ............................................................................................................... 78

Figure 3.4. 5 Average velocity difference between the 4He and the neutrons from the
6He breakup. The data points are determined from the centroids of the top graphs

in Figs. 3.4.3 and 3.4.4. The data are adjusted for the systematic shift (indicated

by the dashed lines in those figures). .......................................................................... 80

Figure 3.4. 6 Schematic view of a 6He breakup. The impact parameter is denoted by

xvi

b. The 6He is excited at point A, the closest approach, then breaks up at point B.
The distance between the U nucleus and point B is r, v is the beam velocity and t
is the mean lifetime of the resonance. ........................................................................ 82
Figure 3.5.1 Angle distribution of the two neutrons from the 6He breakup. These are
2n-4He coincidence events for the six targets used in the experiment. The angle
was calculated in the 2n+4He center of mass frame. .................................................. 85
Figure 3.5.2 Angle distribution of the two neutrons from the 6He breakup. The
points are from the expriment for the U target. The solid histogram is a Monte-
Carlo simulation with the 3-body phase space model. The dashed line is the same
simulation with the dineutron model. The dashed line reaches above 10000 at
c080 = 1 ....................................................................................................................... 86
Figure 5.2. 1 The two types of cross-talk in the neutron walls. Type (a) cross-talk
makes one signal in the front wall and another in the back wall. Type (b) cross-

talk makes both signals in either one of the two walls. .............................................. 96

Figure 5.3. 1 The light response for electrons, protons, alphas and carbon nuclei in
liquid scintillators. l-MeVee is equal to the light produced by a 1-MeV electron.

The data are from Verbinski et al. [8] .............................................................................. 99

Figure 5.3. 2 An example of cross-talk between the front wall and the back wall. The
neutron makes one signal in a cell of the front wall and another one in a cell of
the back wall. The position of each scattering is expressed by (x,y,z). The
scattering in the front wall follows the 2-body kinematics given by eqs. 1 and 2 in
the text. ..................................................................................................................... 101

Figure 5.3. 3 An example of a real 2-n event between the front wall and the back

xvii

wall. If we assume this is a cross-talk event, 0 should be the neutron’s scattering
angle according to 2-body kinematics. However, the positions of the two
scatterings give 9’. Unlike cross-talk events, the two angles are not correlated for
real 2-n events. .......................................................................................................... 105
Figure 5 .3. 4 Side view of two neutrons detected in neighboring cells. Because it is
impossible to determine the exact positions where the neutrons scattered, 0 can
vary from almost 0° to 180°. .................................................................................... 109
Figure 5 .3. 5 The results of a Monte-Carlo simulation in which two neutrons from
11Li breakup are detected by the neutron walls. Given by the solid histograms,
“total” represents all the two-neutron events detected by the walls. Given by the
dashed histograms, “real coin” represents the real two-neutron coincidences. G1,
G2 are the gates used to reject the cross-talk events. (a) (COS9)c-(COSG),m
distribution for the events between the two walls. (b) ATc-ATm distribution for
the events between the two walls. (c) ATc-ATm distribution for the events within

either the front wall or the back wall. ....................................................................... 112

Figure 5.4. 1 Layout of the 7Li(p,n) experiment. The front wall was placed 5 meters
from the target, 35° relative to the beamline. The second wall was 1 meter behind the

first one. The shaded area was a stock of concrete blocks ............................................. 119

Figure 5.4. 2 Time-of-flight spectrum for neutrons detected in cell #7 in the 7Li(p,n)
experiment. The signal of cell #7 gave the start and the downscaled cyclotron radio
frequency signal gave the stop. The sharp peaks are from neutrons produced in the

reactions leading to either the ground state or the first excited state of 7Be. .................. 120

xviii

 

Figure 5.4. 3 Cross-talk distributions for the neutrons under the sharp peaks in Fig.
5.4.3 from the 7Li(p,n) experiment. The experimental data are given by open
symbols. The histograms are the results of our simulation. (a) (COSEDc-(COSG)m
distribution for the cross-talk events between the two walls. (b) ATc-ATm
distribution for the same events in (a). (c) ATc-ATm distribution for all the cross-
talk events. ................................................................................................................ 124

Figure 5 .4. 4 Cross-talk distributions for all the neutrons from the 7Li(p,n)
experiment—those from the 2-body reaction (eq. 5.8) and those from the 3-body
reaction (eq. 5.9). (a) (COSG)¢-(COS0)m distribution for the cross-talk events
between the two walls. (b) ATc-ATm distribution for the same events in (a). (c)
ATc-ATm distribution for all the cross-talk events. ................................................... 125

Figure A. 1 The time of flight (T OF) calibration. The y rays, produced in scintillator
bar #9 by a 18O beam, were detected in the front neutron wall. The flight time for
a y ray between the bar and the front neutron wall is 11.1 ns ................................... 129

Figure A. 2 The position distribution of cell #1 of the front neutron wall. The two
edges give the calibration points for the position of the cell. ................................... 132

Figure A. 3 The energy calibration of scintillator bar #1. The three calibration
points in the graph are from 2.61 MeV 'y ray of a Pb-Be source, 80 MeV and 100
MeV 4He beams, respectively ................................................................................... 134

Figure A. 4 The energy calibration of strip #1 of Si detector #1. The four data points
are from 20 MeV/u and 25 MeV/u 4He, 20 MeV/u and 25 MeV/u 9Li beams,
respectively. .............................................................................................................. 138

Figure B. 1 Schematics of the neutron wall electronics. ................................................. 140

xix

Figure B. 2 Schematics for the Si strip detector electronics. 142
Figure B. 3 The fragment trigger logic. The scintillator trigger logic is in the top

box. The Si trigger is in the bottom box. 143

XX

PART I - The Electromagnetic Excitation of 6He

1 Introduction

1.1 Neutron Halo

The development of radioactive nuclear beams (RNB) around the world has
brought much attention to nuclei far from stability. A series of experiments with RNB
led to the discovery of the neutron halo structure in light nuclei near the neutron dripline.
It started with two experiments performed at the Bevalac of the Lawrence Berkeley
Laboratory to measure the interaction cross sections of He isotopes-3'4‘6'8He [l] and Li
isotopes-6’7’8‘9‘nLi [2] at 790 MeV/u. From these experiments, the interaction radii of
those He isotopes and Li isotopes were deduced. The remarkably large radii of 6He, 8He
and 11Li suggested a long tail in the matter distribution of these nuclei. Later, Kobayashi
et al. [3] found that the transverse momentum distribution of the 9L1 fragment from 11Li
breakup is extremely narrow. The narrow transverse momentum distribution suggested a
large spatial distribution of the nuclear matter. These observations became the central
evidences of the neutron halo [4,5,6] as a special property of light nuclei on the neutron

dripline.

In a neutron halo nucleus, a low-density tail of the neutron distribution is
extended out to a large distance from the center of the nucleus. The long tail is caused by
the small separation energy of the neutrons (~ 1 MeV) compared to 6-8 MeV for stable
nuclei. If we assume that a neutron is loosely bound to an inert core, and the interaction

potential between the neutron and the core is a square well, the s—wave function of the

 

 

neutron outside the potential is expressed as

2 —ll2 -n- m
W(r)=(?”) er [(1+ezdz)"2l’ (1.1.1)

 

where R is the width of the potential; K, which determines the steepness of the density
tail, is related to the neutron separation energy 8 by

(hr)2 = 2,118, (1.1.2)
where u is the reduced mass of the system. The density distribution of the neutron is
written as

6—210-

 

p(r) = I‘I’(r)l2 cc (1.1.3)

r2 '
As K decreases with the decrease of the separation energy a, the tail of the neutron
density distribution extends further. To understand the narrow momentum distribution of

the fragment from a neutron halo nucleus, we take the Fourier transformation of the wave

function:

f(p)= (1.1.4)

p2 + (h x)2
which is the momentum distribution function of the valence neutron. As shown by the
equation, the width of the momentum distribution is related to K. The smaller the
separation energy 8, the smaller the parameter K, therefore the narrower the distribution.

This can be understood from Heisenberg’s uncertainty principle-the wider the distribution

in coordinate space, the narrower the distribution in momentum space.

The large coulomb dissociation cross section in experiments of halo nuclei

impinging on high-Z targets led to a proposition of a low-lying excitation mode called the

 

soft dipole mode (SDM) [4]. In the SDM of 11Li, for example, the 9Li core oscillates
against the neutron halo at a low frequency. So far, whether or not there is a SDM in 11L1
is still under investigation. The large electromagnetic dissociation cross section for 11Li
[7,8,9] seems to favor the existence of a SDM. The experiment by Sackett et al.[10]
suggests a direct coulomb breakup because the deduced mean lifetime of the excited 11Li
is too small compared to the lifetime of a resonance determined from the 11Li dipole
strength function. Since the early experiments, many more experiments have been done
to study these properties of neutron halo nuclei, especially those of 11Li. At the same
time, theoretical models, from the early simple dineutron model to complex three-body
microscopic models, were made to explain the experimental results. Although the
models successfully reproduced either the reaction cross sections, the nuclear radii or the
fragment momentum distributions of some neutron halo nuclei such as 6He and 11Li, the

results about SDM is inconclusive. These models will be discussed in a later section.

1.2 6He Nucleus

Theoretically, one may expect similar exotic structure and properties for all nuclei
near the driplines. The 6He nucleus is one of the lightest and simplest such nuclei. The
study of the 6He nucleus can contribute to the understanding of the properties of dripline
nuclei. Even though both 6He and 11Li are typical examples of the so called borromean
nuclei [11], where none of the binary systems have bound states, compared to 11Li, 6He is

a more ideal system to study the exotic phenomena of dripline nuclei, because the oc-core
is more inert than the 9Li-core and the underlying oc-n interaction is well known. The 6He

nucleus has no bound excited states [12]. When 6He is excited to a state above the 2-n

 

separation energy of 0.975 MeV, a three-body decay may occur (6He —> 4He + n + 11). If
6He is excited to the continuum above 1.87 MeV, another decay channel is open. The
6He nucleus can split into a 5He and a neutron. Because 5He is unbound to neutron
decay, it further splits into a 4He and a neutron. This decay mode is called sequential

decay, which may play an important role in the dissociation of 6He [9,13,14].

1 .3 Experiments

Although 11Li has been studied intensively at many different beam energies and
through the interaction with many kinds of targets, only a very small number of
experiments have been performed on 6HC. Tanihata et al. [1] measured the interaction
cross sections of 6He at 0.79 GeV/u on Be, C and Al targets, from which the nuclear
interaction radius was deduced. Then, Kobayashi et al. [8,15] measured the interaction
cross sections of 6He around 1 GeV/u and the transverse momentum distribution of 4He
from the fragmentation of 6He. Later, the transverse momentum distributions of neutrons
from 6He at 0.8 GeV/u on Pb and C targets were measured by the same group [9]. The
momentum distribution of 4He from 6He fragmentation, detected at 5° in the laboratory
for beam energies near 65 MeV/u, was measured [16]. Not until 1996 were the total
reaction cross sections of 6H6 at intermediate energies (20-40 MeV/u) reported [17]. An
experiment was performed recently to study the one-neutron stripping mechanism of 6He

at 240 MeV/u [14].

1.4 Theoretical models

To understand the properties of 11Li, several models were developed. The
dineutron and cluster models [4, 18] were introduced first. In these models, 11Li is
treated as a cluster in which two neutrons are weakly coupled to a 9Li core. The shell
model by Bertsch et al. went a little further, taking into account the weak binding of the
last neutron in 1'Li. As 6He drew more attention of theorists, more elaborate models were
applied to explain the properties of 6He. The cluster—orbital shell model (COSM)
[12,19,20] assumes a 3-body structure of 4He + n+ n in which the 4He core is treated as
being inert, the valence neutrons are allowed to occupy any high single-particle orbits and
the weak binding of the valence neutrons is also taken into account. Because COSM
does not reproduce the binding energy of 11Li and 6He, a hybrid model combining COSM
and the microscopically extended cluster model [22] was introduced. One of the
interesting results of the hybrid model is that the two valence neutrons stay in shell model
orbits when they are close to the core, but form a cluster (dineutron) when they are far
from the core. In addition to the COSM and the hybrid models, there are other three-
body calculations to study the structure of 6He [13,23-30]. The results of these

calculations will be discussed when the experimental results are presented in chapter 3.

1.5 Coulomb Excitation

Fragmentation of a nucleus is the result of either nuclear or electromagnetic
interaction between a projectile nucleus and a target nucleus. Due to the short range of
the nuclear force, the electromagnetic interaction comes to dominate the fragmentation as

the distance between the projectile and the target increases. Electromagnetic collision

has become a popular way to study nuclear matter since the reaction mechanism is very
well understood compared to a nuclear collision. The reaction mechanism in a relativistic
collision is described by the equivalent photon method, called the Weizséicker—Williams
method. Bertulani et al. [31] provided a detailed review of this method. The key features

relevant to the experiment are presented here.

Let’s consider a target nucleus with a fixed position and a projectile nucleus
passing by with an impact parameter larger than the strong interaction radius. The
projectile can be excited by absorbing one of the equivalent photons surrounding the
target nucleus. For a halo nucleus such as 6He, the absorption of the photon may displace
the neutrons while the nuclear force tries to pull the neutrons back toward the core. If the
motion is repeated, a resonance may be formed, and the oscillation may last for a long
time (long enough for the projectile to be far away from the target nucleus) before the
projectile breaks up. The probability of coulomb excitation at energy E! depends on the
number of photons of energy E, and the probability that the projectile nucleus absorbs
such a photon. For an E1 transition the differential coulomb excitation cross section is
expressed as

do 1
—§‘—=—n5,(E,)af‘(E,), (1.5.1)

dE, E,

where nEl(Ey) is the number of equivalent photons with energy Er surrounding the

target and 0;“ is the photonuclear cross section for the photon energy Ey_ The equivalent

photon number n 51 (E 7) can be expressed as

 

nE= -_-,23-z anze ‘mfi ): jade {128: 8 ——[K ,(877>]’+[K.-.,’(877)]’}. (1.5.2)
7: 7

2

. . . e . .
where Z] rs the charge of the pr0ject11e, a = h—rs the fine structure constant, v rs the
c

velocity of the projectile, e = (sin (0/2))’1 is the eccentricity parameter used to account for

the Rutherford bending of the projectile, Km is the modified Bessel function with
imaginary index (in), K,,,’ is the derivative of Km and

77= Ola/7v, (1.5.3)

2 .1
where (1) is the frequency of the photon ( E y = ha) ), y = (1 ‘1’?) 2 is the Lorentz factor,
c

_ z,z,e2

2

is half the distance of closest approach in a head-on collision and m0 is the
moV

reduced mass of the ions. The photon distributions for the six targets used in our

experiment are shown in Fig.1.1. Furthermore, the photonuclear cross section is related

 

. . - dB E l
to the electric dipole strength function E by
r

)_167r3E7dBEI
7 " 9hc dE

7

 

051(E (1.5.4)

One of the nice features of the equivalent photon method is that it ties the dipole strength

 

 

 

B do
function E] to the differential coulomb cross section E1 through the photon
dE, dE,
spectrum nEl(E,,).
dB 971 1 do
5‘ — C 5‘ (1.5.5)

dE ' 167:3 nE,(E,) dE”

7

Photon Number

Figure 1.5. 1 Photon distributions n 151 (E y) for the six targets used in the experiment.

103

 

  

 

1

1111111

 
  

1111111

  

 

 

Excitation Energy (MeV)

 

 

do

 

 

With measured in an experiment and nE,(Ey)calculated for the target nucleus,
7

dB El . . . . . .

dE can be determined. Other multrpole excrtatrons, such as M1 and E2 excrtatrons,

7'

are neglected in the energy region we are interested in since their contribution is much

smaller.

 

 

2 Experimental Setup

The schematics of the experimental setup are shown in Fig. 2.1.1. I would like to
describe the 6He beam and the three major components of the detection system——the

neutron wall detectors, the deflecting magnet and the fragment detectors.

2.1 The 6He Beam

The average energy of the 6He beam striking the experiment targets was 25.2
MeV/u. The primary reason for choosing this beam energy is that good neutron cross-
talk identification can be achieved in the neighborhood of this energy, which will be
discussed in Part II. Even though lower energy is desirable for cross-talk identification, it
would also significantly reduce the 6He beam intensity and make the quality of the beam
worse. Furthermore, we wanted the 6He projectile to travel fast enough so that its contact

with the target nucleus is “sudden”. This will be explained later in section 3.2.

The °He beam in the experiment was produced by bombarding a 2.0 g/cm2 Be
production target with an 80 MeV/u “0°“ beam from the K1200 cyclotron at the National
Superconducting Cyclotron Laboratory at Michigan State University. The 6He particles
had an average energy of about 60 MeV/u after exiting the production target. They were
later degraded to a beam with an average energy at 25.2 MeV/u by a thick plastic wedge.
The 6He particles were then separated from the other particles at the A1200 Fragment
separator before it was sent into the N4 vault, as shown in Fig. 2.1.1, where our

experiment

10

 

Neutron Walls

 

 

 

 

 

  
   

.: ,: Target . .
Plastic Array Neutron Shielding
1—1 r—r
i/l: :1 / / / / / / / /

Figure 2.1. 1 The experimental setup (not to scale). This is the top view of the N4 vault
at the NSCL. The neutron walls, one behind the other, were placed 5 .00 and 5.84 meters
from the target. The plastic scintillator array was mounted inside the vacuum chamber
about 1.8 meters from the target. The silicon strip detectors were located at the entrance
of the magnet, 15.24 cm downstream from the target. The two PPACs were mounted
38.64 cm and 130.08 cm upstream from the target.

 

 

 

 

\\\\\ljif 1\\
\\\\\\%fl\\

was performed.

The beam which was delivered to the targets has a rate of about 10,000 particles
per second. It consisted of 81% °He and 19% S’Be. The average energy of the 9Be
particles, under the same Bp = 2.16976 as 25.2 MeV/u 6He, was 44.8 MeV/u. The 9Be
particles were separated from °He particles using the time of fight (T OF) between a thin
plastic scintillator placed after the A1200 Separator, and the scintillator array mounted in
a vacuum chamber at about 1.8 meters from the target in the N4 vault. The TOF spectrum
is shown in Fig. 2.1.2. For each particle passing through, the scintillator array gave the
start signal and the delayed pulse from the plastic wedge gave the stop signal. The travel

distance was 41.5 meters. The left peak in Fig. 2.1.2 is 6He and the right one is 9Be.

The experiment was performed with six targets --- U, Pb, Sn, Cu, Al and C,
whose values of thickness are 344 mg/cmz, 384 mg/cmz, 373 mg/cm’, 274 mg/cmz, 237
mg/cm2 and 94 mg/cmz, respectively. We ran the beam about 100 minutes with the U
target, about 40 minutes each for the other targets. We also took a 100-minute run with a
blank target in order to exclude the reactions from anything other than the targets.
During the runs with the blank target, the beam energy was reduced to 22.6 MeV/u to

account for the energy loss in the targets.

The 6He beam was focused by a quadruple about 5 meters upstream from the

target. The size of the beam spot on the target was about 1cm x 1cm. In order to

12

 

 

T

I I I I l I I l I Tll'l TFTTTI l I I I T-

1250 —
).
1000 L ‘6/He
750

9
500 Be

 

TIIITIIIIII

llllillllJllllillll111111

 

250

 

 

l

lllllllllllllngLllllllll

400 800 800 1000 1200

T
J

 

 

h-
l

 

Beamline TOF (channel)

Figure 2.1. 2 The beamline time. The start was given by the scintillator array, and the
stop was given by a plastic scintillator 41.5 meters upstream from the scintillator array.

13

 

the momenta of the fragments (”He + Zn) from the dissociation of 6He, the incident
direction and position on the target of each 6He have to be accurately measured. This
was achieved by placing two position-sensitive parallel plate avalanche counters (PPACs)
upstream from the targets. The PPACs were mounted to the beamline, 38.64 cm and
130.08 cm from the target. The signals in the PPACs were divided into up, down, top
and bottom. From the pulse heights, the particle position in each PPAC was calculated
with a resolution about 1 mm. The detection efficiency of one PPAC for the “He at 25
MeV/u was about 86%, which is the ratio between the number of 6He detected by a
PPAC and that detected by the Si strip detectors. The detection efficiency of the Si

detectors should be 100% for the 6He beam.

2.2 The Neutron Wall Detectors

Neutrons in the experiment were detected by the neutron wall facility at the
NSCL. The facility was originally built as an improvement over an old neutron detection
system [10] in a similar experiment performed in 1991 to measure the coulomb excitation
of 11Li. In that experiment, two arrays consisting of 54 cylindrical scintillation detectors,
each about 7.6 cm thick and 12.7 cm in diameter, were made to detect the two neutrons
from the 1'Li breakup. A few drawbacks of the arrays made us decide to build a new

detection system — a pair of neutron walls. These walls are described in Ref. [32] in

detail. A brief description is given in the following paragraph.

The new facility is composed of a pair of large-area, position-sensitive neutron

walls, one of which is shown in Fig. 2.2.1. Compared to the arrays used in 1991, the

14

walls are larger and use fewer photomultiplier tubes (PMT) per liter of scintillator. The
walls have less dead space and inactive mass to scatter neutrons. The position resolution
is somewhat improved. Each wall consists of 25 rectangular Pyrex cells filled with NE-
213 liquid scintillator. Each cell is two meters long, with an internal cross section of 7.62
cm by 6.35 cm. PMTs are attached to the ends of a cell. The neutron timeeof-flight
(TOF) is obtained from the mean time of the PMT signals. The position of a neutron
detected in a cell is determined from the time difference of these signals. Both time and
position resolution [32] vary with the light output caused by the neutron’s interaction in
the scintillator. For a light output equal to that produced by a 1-MeV electron (defined as

l MeVee), the time resolution (0'!) is 0.8 us. It reduces to 0.4 us for a light output over 4
MeVee. The position resolutions (op) for these light outputs are 6 cm and 3 cm,
respectively. The neutron detection efficiency for one wall is 11% for 25 MeV neutrons
if a threshold of 1 MeVee is set for the two phototubes at the ends of a cell. In
experiments with the neutron walls, many of the neutrons produce less than or the same

amount of light as y rays. Therefore, the walls were built with the capability of pulse-

shape-discrimination to distinguish neutron events from 'y-ray events.

In most experiments, the two walls have been used with one wall behind the other
as shown in 2.2.2. There are two advantages of using this configuration: (1) It enhances
the detection efficiency. (2) It has the capability of detecting a pair of neutrons emitted

with a small relative angle. In order to explain the second advantage, consider the

15

 

 
 
 
 
 
  

25 Cells
A1 Frame

Al Cover

Gas Manifold Blower

Figure 2.2. 1 The schematics of a neutron wall. Each of the two Neutron Walls is a 2m x
2m array of 25 individual cells. The cells are 2m long, have rectangular cross sections,
and are stacked vertically to fill the entire 4 m2 area with very little dead space between
elements. Custom-made of Pyrex, the cells are filled with NE America’s NE-213 liquid
scintillator and are read out at each end by a Philips Photonics 3-inch photomultiplier
tube.

16

 

 

 

 

Figure 2.2. 2 The setup of the neutron walls in the experiment. This is a

simplified picture of the walls without the aluminum cover and the other

accessories.

17

extreme case — two neutrons emitted from a source with zero relative angle. If only one
wall is used, the two neutrons will be detected in the same cell at the same time with a
certain probability. Unfortunately, we cannot distinguish them because what we detect is
just the superposition of two pulses. However, if the two walls are used, it is possible
that one neutron makes a pulse in one wall and the other neutron makes a pulse in the
other wall. Since they are detected in different cells, it is not hard to distinguish them and

to determine their relative angle, even if it is 0°.

The choice of the distance between the target and the wall depends on the neutron
energy, which is measured by TOF, counting rate and the requirement of angular
coverage. In this experiment the front wall, the one closer to the target, is 5 meters from
the target, its energy resolution is about 3% for 25-MeV neutrons, and the wall subtends
an angle of about 23°. A large distance between the front wall and the back wall is
advantageous for good cross-talk identification. The back wall was placed 84 cm from

the front wall.

2.3 The Deflecting Magnet
In the 11Li experiment performed in 1991, a very different experimental setup was
used, as shown in Fig. 2.3.1. The remaining energy of 11Li and 9Li after the silicon AE

detectors were measured with a 6 cm x 6 cm X 1.2 cm CsI(Tl) crystal which was placed

between the target and the neutron detectors. Because all 11Li and 9Li particles stopped in

 

54 Neutron Detectors

  
 
 

PPAC’s

“N

 
 

Si/Csl Telescope
Pb Target

Figure 2.3. 1 The experimental setup for the 11Li experiment. The Si-CsI was placed
between the target and the neutron detector arrays.

the CsI(Tl), lots of background neutrons were produced there. The CsI(Tl) was much

thicker than the 0.52-mm Pb target so that there were more neutrons from the CsI(Tl)
than from the target. Even though data were taken with a blank target to subtract the
background, the background from the CsI(Tl) was a major concern. In order to overcome

the drawback of the old detection system, a magnetic dipole with a pole gap of 7.5” and
pole area of 13”><24” was installed between the target and the neutron walls to deflect

charged particles away from the beamline. The deflected fragments and remaining beam
particles were then detected in a scintillator array somewhat far from the beamline. The

position of the magnet in the detection system can be found in Fig. 2.1. 1.

In order to figure out where to position the scintillator array, we calculated the
trajectories of the beam particles with different energies. To make the calculation
accurate, the field of the magnet was mapped with a Hall probe. Because the field was
expected to be non-uniform along the direction perpendicular to the pole surface at the

area close the pole edge, the magnetic field was measured in five planes—the middle

plane, and the planes which are 1, 2, 3 inches above and 1 inch below the middle plane.

Fig. 2.3.2a shows the magnet poles and its middle plane. The distribution of the
magnetic field in the middle plane is shown in Fig. 2.3.2b. The maximum intensity of the
field is about 1.5 Tesla. The mapped field extends to the area about 15 inches beyond the
edges of the magnet. At the edge of the poles, the field quickly drops to an insignificant
level. The magnet field can be regulated from 0 to 1.5 Tesla in principle. This enabled
us to deflect one charged particle beam into different parts of the fragment array for

energy calibration.

20

 

          

(a)
(0.0)
X
(b)
Midplane Field
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l12-13,
I 1 1-12 !
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E /////III:1(Ilvm'.1“‘1‘“ ‘\ :2:
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Ill/ngl’féfo‘ {0‘39" ' 4 I4-5
g g 3 g 133-4
«g B (3 " 132-3

 

 

,,//', .
. ” I - p
o m $ 9 p - ' z{in] I1-2
“3 a3 ' st :1.“ "‘. q; ‘1" — EO-l
x[in] "ngmé’err —
(”IQ ‘T q," “.7 '
5?

Figure 2.3. 2 (a) The deflecting magnet and the mapped middle plane. The poles cover

a dimension of 13 inch x 24 inch. (b) The magnetic field at the middle plane. The
maximum intensity is 1.5 Tesla. Refer to (a) for the coordinates.

2l

 

2.4 The Fragment Detectors

2.4.1 Si Strip Detectors

In order to identify the reaction fragments, two silicon AB detectors and sixteen
plastic E detectors were used. A big vacuum chamber was built to accommodate the
fragment detectors and the target. The AE detectors were mounted onto an aluminum
flange through which electronic cables were connected to provide bias and to pick up
signals. Each AB detector, 5cm x 50m x 250nm, in Fig. 2.4.1, was a MICRON position
sensitive silicon strip detector, consisting of 16 horizontal strips on one side and 16
vertical strips on the other. Each strip is 3.125 mm wide. The gap between the strips is
about 0.1mm. The 32 strips together form a grid consisting of 256 square pixels, as
shown in Fig. 2.4.1, each of which has an area of 3.125 x 3.125 mmz. The strip detectors
were 15.24 cm from the target in the experiment. The size of the strip causes the
uncertainty of angle to be about 12°. When a 4He particle penetrated the Si detector, it
produced a signal in one strip on one side and a signal in another strip on the other side.
From the position of the pixel defined by the two strips, the direction of the 4He was
determined. The pulse height of the signal in either of the strips measures the AE of the
4He in the Si detector. The two Si detectors were positioned next to each other as shown

in Fig. 2.4.1 to achieve large angular acceptance for the fragments.

Besides the slow signal used for AE measurement, a fast signal was picked up
from the vertical strip for TOF measurement. However, the fast signal was distorted due

to interference from the power supply of the magnet. Signals from the scintillator

22

 

2-mm GAP

 

Si detectors

6He Beam

Figure 2.4. 1 The setup of the 250nm Si strip detectors. The 16 horizontal strips and 16
vertical strips are shown in detector #2. The 32 strips form 256 pixels, each with an area
of 3.125X3.l25 mmz. The strip detectors are 15 .24 cm from the target. There is a 2mm
gap between the two detectors.

23

 

array were used instead for TOF measurement.

2.4.2 The Scintillator Array
The scintillator array consists of 16 BC408 plastic bars. Each bar has a

dimension of 40.64 cm x 4 cm x 2 cm. The 16 bars cover an area of 40.64 x 64 cm2.

The top and side views of the array are shown in Fig. 2.4.2. As shown in the figure, two
photomultipliers (PMTs) were attached to the ends of each bar. These PMTs are 8575
Burle tubes [33] and R317 Hamamatsu tubes [34]. All the PMTs have 12 dynodes and an
anode. Because the phototube is wider than the scintillator, a zigzag positioning of the
detectors was chosen to ensure no dead splace between the scintillator bars. The PMTs
were covered with magnetic shields. High voltage was put on a tube through a PMT base
made for the experiment at the NSCL. The base was a modified version of E934
Hamamatsu bases. The design of the base is shown in Figs. 2.4.3 and 2.4.4. The two
major modifications:

(1) The resistors of the E934 bases were replaced with those with half the
resistance. This was to ensure that the bleeder current ----the current flowing through the
resistors, is much larger than the anode current. The larger the bleeder current relative
to the anode current, the more linear the signals.

(2) Unlike conventional bases, the base for the experiment is divided into two

parts---a divider board and a socket. A divider board includes the resistors of the base

24

 

 

 

Top view Side view

PMT Socket

. i/magnetic shield

Divider box

   

 

Divider boxes

 

Scintillator bars

 

 

 

 

 

 

 

Chamber wall

 

 

 

 

Chamber wall

Figure 2.4. 2 The top and side view of the scintillator array. The array consists 16
BC408 plastic bars. Each of these rectangular bars has dimensions 40.64 x 4 x 2 cm3.
Two photomultiplier tubes (PMT) are attached to the ends of each bar. The PMTs are
covered with magnetic shields.

25

 

 

 

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Figure 2.4. 3 The divider of the PMT base designed for the scintillator bar. The
divider was placed in the air to dissipate the heat. The divider is connected to the
socket in Fig. 2.4.4 according to the order from J 1-1 to J 1-16, which can be found
in this figure and in Fig. 2.4.4.

26

 

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Figure 2.4. 4 The socket of the PMT base designed for the scintillator bar. The socket,
attached to one end of a scintillator bar, was placed inside the vacuum chamber.

27

used to divide the high voltage among the dynodes of a PMT. A socket includes the
capacitors to provide electrons. The socket is attached to a PMT placed in the vacuum
chamber. The divider board is out in the air. By putting the resistors outside the
chamber, we can avoid overheating them and the tube. If the resistors were put inside the
vacuum with the socket, as in conventional bases, the heat generated in the resistors
would be hard to dissipate and might result in damage to the PMTs. Each socket is
connected to a divider board through a 16-pin vacuum feedthrough glued on to the back
plate. Four divider boards are placed in a divider box, which is mounted on the back
plate of the vacuum chamber as shown in Fig. 2.4.1. The signals from the 11th dynode
and anode are picked up from the socket in the vacuum, then transmitted to the electronic

modules through the lemo feedthroughs on the back plate.

The positions of the detectors were not randomly chosen as mentioned before. If
the array was put too close to the target, it would stand between the neutron walls and the
target. Neutrons from the target might then be scattered off the scintillator bars and
become background neutrons for the neutron walls. Furthermore, many neutrons
produced in the scintillator bars could then get into the neutron walls. On the other hand,
if the array is put too far away from the target, its acceptance will be too small to detect
both the 6He and 4He because 4He is deflected more than 6He by the magnet. To take
these factors into account, the center of the array was positioned about 1.8 meters from
the target [see Fig. 2.1.1]. Actually, this distance was not only chosen to accommodate

6He and 4He around 25 MeV/u, but also chosen to accommodate 8He, 6He, 11Li and 9Li

28

around 25 MeV/u because the dissociation of 8He and of 11Li were also studied with the

same experimental setup.

The two PMTs at the ends of a scintillator bar detect light signals produced by the
energy loss of the fragments. The geometric mean of the integrated charges of the signals
from the two PMTs measures the fragment energy so that the effect of light attenuation
can be removed. The signal from the top photomultilier served as the start signal to
measure the TOP of the beam particles between the scintillator bar and the plastic
scintillator placed upstream in the beamline. The beamline TOF spectrum is shown in
Fig. 2.1.2. The top signal also served as the stop signal to obtain the TOP between the
neutron walls and the scintillator bar. The neutron energy was determined from this

TOP.

29

 

3. Coulomb Dissociation of 6He

3.1 Zn Removal Cross-section
The direct approach to calculate the 2n removal cross-section 02,, of 6He is to
count the number of the incident 6He particle—— N 0, and the number of the 4He fragments
produced in the target—N . Then use the equation:
No — N = Noe’az'” (3.1.1)
where n is the target density and t is the target thickness. Although the direct approach is
straight forward, the 2-n removal cross section is determined using the n-4He coincident

events, in which a neutron is detected in the neutron walls and a 4He is detected in the

scintillator array. The reasons are given in the following paragraph.

First, the experiment was designed for a kinematically complete measurement of
6He dissociation. The focus was on the events in which neutrons and a 4He fragment
were detected. Therefore, all the coincidence events were processed and recorded. The
single-fragment events, in which either a cell in the neutron walls or a bar in the
scintillator array fired, were downscaled by a factor of 500 in order to reduce the on-line
processing time. Due to the limited beam time for each target, the number of the
downscaled 4He was very small. With the U target, the number of 4He events was only
43, compared to 2,827 n-4He events. So, the cross section determined from the singles
data can have a very large uncertainty. Second, as we will discuss in sections 3.2 and 3.3,

both the 6He projectile and the 4He fragment can be deflected into large angles by the

30

 

coulomb force from the target nucleus. The limited acceptance of the magnet poles

results in some 4He fragments not being detected by the scintillator array.

Before I show how to determine the 2-n removal cross section of 6He from the n-
4He coincidence data, the 4He fragment and neutrons produced in the experiment have to

be identified.

3.1.1 “He Identification

When 6He is excited by interacting with a target nucleus, the excitation energy
eventually comes from the 6He projectile itself. The energy provided has to exceed the
2-n separation energy of 6H6—O.975 MeV in order for a breakup to occur. The
excitation energy is expected to be in the neighborhood of several MeVs. When an
excited 6He decays, the decay energy (the difference between the excitation energy and
the separation energy) is shared among the fragments—a “He and two neutrons. Since
the decay energy is much less than the incident energy (z 144 MeV), the fragments of the
incident 6He beam are expected to travel at about the same speed as the beam. Therefore,
the “He from the breakup carries about 2/3 of the energy of the 6He. The resolution of the
scintillator array (z 4%) should be good enough to separate the two isotopes. Fig. 3.1.1
gives the energy distribution of the charged particles detected in the entire 16-scintillator
array for the U target. The broad “He peak on the left of the 6He peak can come from two
sources. Other than from the target, the 4He can be produced in the array through a

dissociation of the “He in the scintillator itself. Because a 6He can break up at any time

3]

 

 

 

 

 

 

 

5000 I I I l I I l l l I I I I l I I l I l
C: 4000 .— —:
8 . ‘He Beam ,
I: _ .
g r- -1
\ aooo — —
g - _
e p _
U
V .- —.
g 2000 _— _‘
0-
>‘ - _
1000 — _,
- -l
0 P _l .L J l L l I J l l l -
o 100 300 400
Light output (channel)

Figure 3.1.1 The light output in the entire 16-scintillator array.

32

before losing all the energy in the scintillator, the energy loss could be any value between
2/3 and 100% of the beam energy, resulting in the broad peak in Fig. 3.1.1. We need to

identify the 4He from the target.

With the deflecting magnet, we were able to do the identification. Due to
different mass-to-charge ratios but similar velocities, the “He from the target and the
unreacted “He were swept into different bars of the scintillator array. Since the magnetic
field was accurately mapped, we were able to calculate the trajectory of charged particles
at various energies. Figure 3.1.2 shows the trajectories of a “He ion and a “He ion coming
from the target at 23 MeV/u. In this particular case, the “He hits bar 5, whereas the “He
hits bar 10. In Fig. 3.1.3 and Fig. 3.1.4, the energy distributions for the sixteen
scintillator bars are plotted for the data collected with the U target. As shown in these
figures, the “He beam concentrates on bars 5 and 6. Some “He particles go into
neighboring bars. The spread was caused by the dispersion of the beam and the coulomb
scattering in the target. Clearly, the “He produced in the scintillator array can only appear
in the bars where the “He beam stops. On the other hand, the “He from the target goes
into higher—numbered bars far from the beamline. Figure 3.1.4 shows that almost all the
“He from the target stopped in bars from no. 8 to no. 15. It appears that only an
insignificant number of the “He went into the other bars in the array. So, the 4He particles

detected from bar 8 to bar 16 were identified as the fragments produced in the target.

33

 

 

30 -..-,....,...

Scintillator
60 _ array

 

 

 

 

 

40 P
.G
C) L
G
O— r
“ /
20 — .. ,
o
t a I
a
. 2 I
0 a ‘ Si detectors _

 

 

A4.Alr+lrl...lli...l....l..rl

- 1 0 O 10 20 30 40 50

 

Figure 3.1.2 Trajectories of a 6He projectile and a “He ion at 23 MeV/u. This is the
result of a calculation with the mapped magnetic field. According to the calculation, the
6He hits bar #5, and the “He hits bar #10.

34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

um

mm

M”

1“) fl”

um

 

MD

'I' ' 'I -' ‘l‘ l "60' ""I' IT'HFT'TTFITIT'H‘I"TIII
a— 107 _ 5007
- Bar#1 : Bar #2 Bar #3 2 Bar #4
- 8- . 4007
“.- E 40 t
c: ' i ’ :
g ; “He 67 an:
a 4~ . T
g . 4'— ' 200-
g * ’ 20 ’
:2 2» I . I
5 2E- ’ 100—
t .
A n d- - I A A _..._4 “ 11 A
V 0p _ 7‘03 .v1!jh¥...1.. .%v_4 'Tfi.'...v-%Y
% ' 2500:- 257
'5: 3000- Bar#5 _ Bar#6 Bar#7 i Bar#8
F 2000; 300
r i
zooor 15007 .
. 200
. l- '
_ 1000}
1000~ L 100'
. 500— '
, .
o, l ‘JAALAIG Al ‘JAALLIG'

 

 

 

 

1m) 2“) am

 

Figure 3.1. 3 The light ouput for the eight scintillator bars close to the beamline. The
data were taken with a 25 MeV/u “He beam incident on a U target. Most of the beam hit
bars #5 and #6. A number of “He particles produced in the target start to appear in Bar #8.

35

 

 

     

9VP"' 1 "'l""‘FV""'l ' 'l'"'TV""TI'HTTI'T'TTV’""I""l""lT
’ ‘ T
Bar #9 . Bar #10 ~ Bar #11 , Bar #12
30- 30- so— so~
Q I
a) . .
E 20— 20-
“ . .
'5
\ . .
g 10— to—
8 .
V mi i“: h - II I
{g . . .
Sf Bar #13 C Bar#l4 i Bar #15 i Bar#l6
30

30" 30" 30"

..]fi

 

 

 

 

 

 

- 20 _ 20 -
L 10 L 10 L
100 200 300 100 200 300 100 200 300 100 200 300

Light Output (channels)

Figure 3.1.4 The light ouput for the eight scintillator bars far from the beamline. Almost
all the “He produced in the target were swept by the magnet to the eight bars and bar #7
shown in Fig. 3.1.3.

36

3.1.2 n-y Discrimination

The pulse-shape-discrimination (PSD) capability of the neutron walls enables us
to separate neutrons from y rays (See [32], [38] for details). A brief description is given
below. A neutron is detected mainly through a recoil proton that has scattered the
neutron. Gamma rays are detected by Compton scattering on electrons. The ionization
of the scintillator by protons and electrons generates light. For a majority of organic
scintillators, the light yield curve consists of a fast component and a slow component.
The two components are the results of prompt fluorescence and delayed fluorescence in
the scintillator molecules. The gamma-ray-induced electrons generate a larger fraction of
their scintillation light in the fast component of the light yield curve as compared with the
neutron-induced recoil protons, hence producing different pulse shapes. A special n-y

discrimination circuit was built for the scintillator cells of the neutron walls. The input of
the circuit is the anode signal. The outputs of the circuit are “Fast”, “Total”, “Attenuated
Fast” and “Attenuated Total”. “Fast” is proportional to the fast component of the signal.
“Total” is proportional to the total charge of the signal. In order to cover a large dynamic
range of pulse heights in the experiment, the “Fast” output and the “Total” output were
attenuated by a factor of 4. The attenuated “Fast” and “Total” signals are labeled as
“Attenuated Fast” and “Attenuated Total” respectively. In the top spectrum of Fig. 3.1.5,
the y-axis is the “Fast”, and the x-axis is the “Total”. The spectrum is for one of the 32
cells of the neutron walls used in the experiment. These events were taken with a Pu-Be
source placed next to the neutron walls. The upper branch is from cosmic rays and
gamma rays. The lower one is from neutrons. The bottom spectrum of Fig. 3.1.5 shows

the data taken during the “He runs for the same cell except that the x and y axes are for

37

 

(a)

Qfast

Qfast_att

 

| l I
4 MeVee

Qtotal_att

Figure 3.1.5 The n-y discrimination spectra. The top branches are 7 and cosmic rays.
The bottom ones are neutrons. (a) The “Fast” signal versus the “Total” signal. The data
were taken with a Pu-Be source. (b) The attenuated “Fast” signal versus the attenuated
“Total” signal. The attenuation factor is 4. The data were taken with a 6He beam.

38

attenuated light outputs. To select neutrons with pulse heights less than 6 MeVee (1
MeVee is the light output by a l—MeV electron), a contour was drawn around the lower
branch of the top spectrum for each cell. Any event inside the contour is considered a
neutron event. For neutrons with pulse heights greater than 6 MeVee, a straight line was
drawn between the two branches in the attenuated spectrum (Fig. 3.1.5 (b)). Any event

below the line is considered a neutron event.

3.1.3 n-“He Coincidence Data

Fig. 3.1.6 shows the summed energy spectrum of the “He fragments in
coincidence with the neutron walls for the U target. These are the events detected in bars
from bar 8 to bar 16. As shown in the figure, some other fragments, such as “H and 3He,
form the tail on the left side of the “He peak. There also is a small “He peak on the right
side of the “He peak as a result of the coincidence between the “He and some gamma rays
produced in the scintillator array. A gate was drawn to select the “He. There are factors
making the number of the detected n-“He events—N ’ , less than from the number of “He
produced in the target—N. One factor is the detection efficiency of the neutron walls for
the neutrons—(Kl. The detection efficiency of the scintillator bars should be 100%. The
other factor is the system’s solid-angle acceptance for the neutrons 9,, and for the “He (20,
from the target. The geometry of the field, poles and coils of the magnet and of the
vacuum chamber makes knowledge of the energy dependent Qa impossible to know with
any accuracy. Instead, we write

N’=NOEOQn-Qa=N0f (3.1.2)

39

 

100 l v v u l 1 v
80:
60:
.0:

20

 

 

 

 

 

o . ....|

0 100 200
Light (channel)

 

Figure 3.1.6 Light output distribution for coincidence events detected on bars from #8 to
#16 for the U target. The solid gate was used to select the “He fragment. The tail on the
left side of the “He peak is formed by other light fragments such as H and 3He. The small
peak on the right side of the gate is formed by some “He particles.

 

 

 

 

 

 

Energy 02..
(MeV/u) (barn)
00—) 13.7 0.41 $0.10
13.7 —> 29.0 0.47 i- 0.06
29.0 —) 39.5 0.47 i 0.05
39.5 —> 48.1 0.40 i 0.04
48.1 —> 55.6 0.35 i 0.15

 

 

 

 

Table 3.1. 1 Measured 2n removal cross sections on Si for “He from ref. [17]. These
data were used for the normalization.

4o

Then

N = N”. (3.1.3)

To detemrine the factor f, we normalized our Al data to the Zn removal cross section of
“He on a Si target measured by Warner et al. [17]. Table 3.1.1 lists the measured cross
sections for “He at various energies from ref. [17]. We took the cross section for the
energy range 13.7-29.0 MeV/u, 02" (Si) = 0.47 i0.06b, since the average energy of the
6He beam in the middle of the targets (~24 MeV/u) is in the above energy range. We
took the approximation that the cross-section for Al—oh (Al) is the same as that for Si.
This normalization gives f = 0.0648. To see if this normalization factor makes sense, we
want to know the values 8, S2,, and flu. From chapter 2, we know that the neutron
detection efficiency for one neutron wall is 11% at 25 MeV/u. The two walls, with the
way they were set up in the experiment (refer to chapter 2), have a detection efficiency
around 18%, i.e. e = 0.18. As shown in Fig. 3.3.2, the solid-angle acceptance (2,, of the
detection system as a function of the decay energy for “He is calculated. The average (2,,
for Al is about 0.35 at 1.5 MeV that is where the measured “He decay energy for Al
concentrates, as shown later in Fig. 3.3.1. If (20, is not much less than 1,
f = 5 o S2,l 09,, = 0.063, which is consistent with the value obtained from the
normalization. The 2n removal cross-sections for all the other five targets were
calculated with the same f. The results are listed in the second column, the column
labeled 0'2", of Table 3.1.2. The errors due to statistical fluctuation are put next to the

measured cross-sections.

41

 

 

 

 

 

 

 

 

 

 

 

 

Target 02,, 02,, ’ Warner [30] Ferreira et al. [37]
(bang) (barn) (barn) (barn)

U 1.87 i 0.24 1381- 0.18 1.68

Pb 1.70 i 0.22 1.25: 0.16 1.51 1.80

Sn 1.22 i 0.16 0.95i 0.12 0.91
Cu 0.82 i 0.10 0.72i 0.09 0.62 0.89

Al 0.47 i 0.06 0.47: 0.06 0.45

C 0.36 i 0.05 0.39i 0.05 0.34 0.46

 

Table 3.1. 2 2n removal cross sections in the experiment. 62,. is the measured cross
section assuming constant neutron multiplicity. 62,. '
adjusted for neutron multiplicity [40,41]. The calculated cross sections are from refs.

[30] and [37].

is the measured cross section

 

Table 3.1. 3 Neutron multiplicity for the six targets [40].

42

 

It is an approximation that the detection system has the same efficiency factor f
for all the six targets. The approximation could cause a systematic error in the measured
cross sections because we are actually assuming that the neutron multiplicity for the six
targets is the same. According to a model developed by Barranco et al. [40,41], there are
three reaction mechanisms responsible for the “He breakup: coulomb breakup, diffraction
breakup and stripping. Two neutrons are produced and available for detection in
coulomb and diffraction breakups, whereas only one neutron is detectable in stripping
breakups. Since the coulomb reaction becomes the dominant breakup mechanism for the
high Z targets, neutron multiplicity is expected to increase with charge Z. The calculated
neutron multiplicity [40] for the six targets ranges from 1.3 for C to 1.9 for U, as listed in
Table 3.1.3. The 2n removal cross sections adjusted for the neutron multiplicity (62,,’) are
shown in Table 3.1.3. The adjustment is more significant for the high-Z targets than for
the low Z targets. For targets heavier than Al the unadjusted cross section is larger than
the adjusted one, and for C, it is smaller. For example, for U, 02,, = (1.87i0.24) b vs. 02,,’
= (1.38i0.18) b, for C, 62,, = (0.36i0.05) b vs. 62,,“ = (0.39i0.05) b. One has to be
careful about adjusting the cross sections for the varying multiplicity because the solid—
angle acceptance of our detection system may change the measured multiplicity. For
example, even though a coulomb breakup generates two neutrons, one neutron may go to
the neutron walls and the other one may miss the walls, and this is more likely for a high
Z target, such as U, than for a low Z target, such as C. The reason is that strong coulomb
deflection is involved in many breakups for the high Z targets since the breakups can
only occur when “He is close enough to the target. When a “He nucleus breaks up on U,

it may have been deflected from its incident direction, which is assumed to be

43

perpendicular to the neutron walls. In an extreme case in which one neutron recoils
against the other neutron and the “He, the first neutron may come out with such a large
angle to the incident direction that it may just miss the wall or hit the magnet poles. On
the other hand, the second neutron may come out aiming right at the neutron walls. The
effect causes the measured multiplicity for the U target to be lower. Therefore the
difference between the measured neutron multiplicity for the U target and that for the C

target may not be as big as the theory predicts (1.9 vs. 1.3).

The experimental cross sections with and without the adjustment for the neutron
multiplicity are compared with two theoretical calculations in Table 3.1.2. The
calculation by Warner [35] follows closely that by Bertsch et al. [36] for “Li using the
microscopic independent-particle model. In microscopic theories, the matter densities in
two colliding nuclei and the nucleon-nucleon total cross section are two important input
factors. The calculation is described in detail in the paper [35]. The result given by
Ferreira et al. [30] is quite different. Most of the difference comes from the calculation of
the nuclear cross section, since Warner used the same model as Ferreira et al. to obtain
the coulomb cross section. One factor accouting for the difference is that they use
different rrns radii in their codes. Another factor, pointed out by Warner, is that Ferreira
et al. did not consider core survival while calculating halo disintegration. We note that
the “He energy in Warner’s calculations is 24 MeV/u [37], which is our beam energy,
while the energy in Ferreira et al. is 30 MeV/u. Warner’s calculation is probably the

better one for comparison with our data.

44

3.1.4 Coulomb Contribution

One of the purposes of using both light and heavy targets in the experiment is to
separate the coulomb contribution from the nuclear contribution to the Zn removal cross
section. The significance of disentangling the two is that it can help people further
understand the nature of halo nuclei. Because the unadjusted cross sections better agree
with Warner’s calculation for the heavy targets (U, Pb) where the coulomb breakup is a

major contributor, we use the unadjusted cross sections for the coulomb extrapolation.

In this section, two methods will be introduced to extract the coulomb
contribution. The first method is by extrapolation. For light targets nuclear dissociation
is dominant. An extrapolation of the nuclear cross section to the heavier targets is shown
in Fig. 3.1.7. To make the extrapolation possible, we assume that 1) only the nuclear
interaction contributes to the “He breakup on the C and Al targets; 2) if A is the mass
number of a target nucleus, the nuclear 2n removal cross section is proportional to AU“,
i.e., proportional to the radius of the target. So, the extrapolating line is expressed by

a = a +bA“3 (3.1.4)

nuclear
where a and b are two parameters to be determined. If the extrapolation relies only on
two points, C and Al, it may result in a large uncertainty. So, the third point at A = 0 is
deduced. This point is the nuclear cross section as the target nucleus gets infinitely small.
We know that “He consist of a hard “He core and a neutron halo [40] formed by two

valence neutrons. In a classical picture, we assume the Zn removal cross section results

from a peripheral collision. In the collision the neutron halo is broken by striking the

45

 

 

 

 

 

Figure 3.1.7 Total 2n removal cross sections for the six targets. The solid line is a
simple model (eq. 3.1.4) to extrapolate the nuclear parts of the cross sections for the high
Z targets. The results are listed in Table 3.1.4

46

infinitely small nucleus, leaving the core untouched. If the core is hit, reactions other
than 2n breakup occur. So, the cross-section could be written as the area of the halo. The
thickness of the neutron halo was measured to be 0.87 fm [38]. Using the measured

radius of “He—2.33 fm [38], we get
a,,,,,,,(A = 0) z 2er R(“He) x0.87
= 0.13(b) (3.1.5)
In Fig. 3.1.7, the straight line is the fitting result of the first three points (A=0,12,27),

0' =0.1257+0.1102A“3 (3.1.6)

nuclear
The difference between the points and the line is considered to be the coulomb part of the

cross—section. The coulomb 2n cross section from the extrapolation is listed in Table

3.1.4 and plotted in Fig. 3.1.8. The solid curve is the calculation by Warner.

The second method used to separate the coulomb contribution from the nuclear
contribution is to use the expected dependency of coulomb dissociation on target charge,
Zl'“. The coulomb cross section of “He depends on the strength of the coulomb field of
the target, i.e., on the intensity of the equivalent photons surrounding the target nucleus as
expressed in eq. (1.5.1), so owmmb (Z,E7) oc nE,(Z,E7). If one carefully compares
n5, (Z ,E7) in Fig. 1.1 for the six targets in the region where the dipole strength function is
supposed to concentrate (~2-3MeV), one finds the relationship between photon number
nE,(Z,E7) and target charge Z very close to n5, (Z ,Ey) cc 2““. If we simply assume the
nuclear cross section to be proportional to AU“, then we can express the total 2-n removal

cross section as

47

 

1.5

 

 

62,,(coulomb) (b)

 

 

 

100

 

Figure 3.1. 8 Coulomb dissociation cross sections of “He for the four targets. The data
points are the results of the extrapolation shown in Fig. 3.1.7. The solid line is the
theoretical calculations by Warner [35,37].

48

2.5

 

 

 

 

 

 

 

 

U

2 p‘ T

1.5 Sn CH

ozn (b) 1 C“ y
Al
C

0.5

O l l I

O 2 4 6 8

A1/3

Figure 3.1.9 Total 2n removal cross sections for the six targets. The points are the
experimental data. The solid curve is a fitting model to extract the coulomb part of the
cross section (eq. 3.1.7). The results are listed in Table 3.1.4.

 

 

 

 

 

 

 

 

 

 

 

Target Method 1 Method 2 Warner
(barn) (barn) (barn)
U 1.06 i: 0.24 0.921- 0.24 1.10
Pb 0.92 i 0.22 0.75i 0.22 0.91
Sn 0.56 i 0.16 0.31i 0.16 0.39
Cu 0.25 i 0.10 0.12i 0.10 0.15
Al - 0.03i 0.06 0.04
C - 0.01i 0.05 0.01

 

 

Table 3.1. 4 Coulomb 2n removal cross sections by the extrapolation described in the

text. The calculated cross sections are from Warner [35,37].

0.2n : Unuclear + ocoulomb = (“Al/3 + bZl'S (3’1‘7)
The best fit of the data is shown in Fig. 3.1.9 with a = 0.1625 i 0.0089,
b = (2.692 i 0.294) x107“ . The coulomb cross section

0......” = 2.692 x 10"“2L8 (3.1.8)
is also listed in Table 3.1.4. The coulomb cross sections obtained by method 2 are
smaller than those by method 1 and the calculations by Warner excluding. It also can be

observed that for U and Pb, the coulomb effect contributes about half to the total 2-n

removal cross section of “He.

50

3.2 Parallel Momentum Distributions

3.2.1 Why parallel momentum distributions

Other than reaction cross sections, the momentum distributions of nuclear
fragments from reactions of halo nuclei help us obtain more detailed information about
the structure of neutron haloes. For example, momentum distributions may make it
possible for us to determine the wave function of the valence neutrons removed in the
reaction. The relation between the momentum distribution and the wave function of the

valence neutrons was described in section 1.1.

In this kinematically complete experiment, the momentum of the neutrons and the
momentum of the “He from the 6He breakup were measured. Although the full
momentum was measured in the experiment, the measured neutron and “He parallel
momentum distributions are expected to better reflect the momentum function of the halo
neutrons than the full neutron and “He momentum distributions, because the transverse
parts of the full distributions are distorted due to the following reasons.

For neutron: The solid-angle acceptance of the neutron walls prevents us from
detecting neutrons with large transverse momentum. Let’s estimate how much the
limitation is with the setup in this experiment. The first neutron wall, 2 meters wide and
5 meters from the target, has an opening angle of 0.2 radian on one side. With the above
geometry, the average neutron momentum 210 MeV/c yields a transverse momentum of
42 MeV/c, which actually is the cut-off point for the neutron transverse momentum in

this experiment. The geometric limitation obviously does not apply to the parallel

51

Not to Scale

 

Figure 3.2.1 Breakup of “He into “He + n +n. The breakup occurs as the “He projetile
touches the U nucleus. Both the “He projectile and the “He fragment are deflected by the
coulomb force from the U nucleus.

52

momentum.

For “He: The coulomb deflection of the incident “He and the “He fragment by the
target nucleus distorts the fragment momentum in the following way. The direction of
the incident “He is measured by two PPACs before it enters the target. If the “He is
deflected by the coulomb force as it approaches the target nucleus, the true direction of
the “He right before the breakup is going to be different from the measured direction. In
the extreme case as shown in Fig. 3.2.1, a “He breaks up as it just touches the U target
nucleus. The “He would be deflected by 6.10 from its incident direction. If
we assume that the decay energy shared by the fragments after the breakup is zero, the
direction of “He after the breakup would be changed only by the coulomb force. The
scattering angle of “He would be 97° after it breaks away from the “He. This leads to a
total deflection of 158°. In this case, the true transverse momentum is zero because the
decay energy is zero, but the measured one is obviously not. Coulomb deflection is
expected to cause the transverse momentum distribution to be wider than it should be. To
see how much the coulomb deflection effect could be, let’s assume that the average
deflection angle is half of the maximum value, i.e., 7.9“. At 23 MeV/u, the momentum
per nucleon is about 207 MeV/c. The coulomb deflection of 7.9“ gives a “He transverse
momentum P l (“He) = 114 MeV/c. At the same time, if we use half of the “He deflection
for the neutrons, i.e., 3“, then the neutron transverse momentum P l (neutron) = 11 MeV/c.
In the longitudinal direction, however, the change of the “He parallel momentum is only
about 2 MeV/c with a 7.9“ deflection. Compared to U, the effect of the coulomb

deflection for C is much smaller because the maximum deflection angle is only about

53

5.5“.

3.2.2 Neutron Parallel Momentum Distributions

To help compare different measurements it is desirable to characterize the
distributions by parameters from simple statistical distributions. In Fig. 3.2.2, the neutron
parallel momentum distributions are all fitted with a Gaussian function. The solid curves
are the best fits. The widths of the parallel momentum distributions are represented by
the 0' of the Gaussian function. Graph (b) in Fig. 3.2.3 shows the values of the neutron
parallel momentum distributions against Z of the targets in the experiment. Kobayashi et
al. [9] measured the neutron transverse momentum distributions from “He fragmentation
on C and Pb at 0.8 GeV/u. In their measurement, two components were found in the
transverse momentum distributions. Their narrow component, which is thought to be the
result of the removal of the valence neutrons in “He, is compared with the result of this
experiment. The reported rms width (0') of the narrow component of the neutron
transverse momentum distribution, about 32 MeV/c for C, is somewhat larger than the
width of (26.9i2.2) MeV/c for C measured in our experiment. For Pb, the measured
width 6 z 31 MeV/c by Kobayashi et al. is significantly larger than our result 0' z
(19.8i1.2) MeV/c. The earlier discussion about the difference between the transverse
momentum distributions and the parallel momentum distributions may explain the

difference in the measured momentum widths.

It can be observed from Fig. 3.2.3 that the width of the neutron parallel

momentum distribution decreases with the size of the target. For C, 0' is (26.9i2.2)

54

 

 

Yield (counts/9.4 MeV/c)

 

 

Pb target

'UYU'UT'TIIIUT‘IIYIIIIUII

 

1

150 ‘-

l-
100 "

 
  

 

 

100 160 £00 250 500 350

Al target

0..
I-

v"
- ‘ ,,'H_.,._“

P” (MCV/C)

Sn target

 

b-
160

100

 

 

 

0
100 150 EDD 250 300 350

C target

 

f\?50; “I-Ljnlol
200 150 200 850 800 350

Figure 3.2.2 Neutron parallel momentum distributions for the “He breakup. The parallel
momentum is the projection of the momentum on the incident direction of the “He beam.

The solid curves are Gaussian fits. The widths of the distributions are listed in Table

3.2.1

(unit: MeV/c)

 

 

 

 

 

 

 

 

 

U Pb Sn Cu Al C
op,,(4He) 31.309 324:1.4 33.0:t1.3 33.1:1:l.6 44.6i2.2 40.2i2.3
5,.” (n) 19511.0 19.8i1.2 23.0;t1.3 2193:15 24.7114 26.9:22

 

 

Table 3.2.1 The widths of the measured parallel momentum distributions

55

 

0' (“He)

[71/

 

 

 

 

 

 

 

 

(MeV/c)

40

C Al Cu Sn Pb U (b)

30 i
O p“ (n) i i i ‘ .-
(MeV/c) 20 1 I

10

0 I I I I
0 20 40 60 80 100
Z

Figure 3.2. 3 (a) The widths of the “He parallel momentum distributions for the six
targets. (b) The widths of the neutron parallel momentum distributions for the six targets.

56

MeV/c; for U, 0' has decreased to (19.5i1.0) MeV/c. The change of the momentum
width can be attributed to the following two factors:

1) The Serber model tells us that the fragment momentum distribution measures
the momentum function of the fragment in the projectile. This model is based on the
“sudden approximation.” In this approximation, the target nucleus knocks the fragment
out of the projectile in a very short time so that the fragment remains in the initial state
until the instant of breakup. To qualify for a very short time, the interaction time between
the target nucleus and the projectile has to be much smaller than the time for the fragment
in the projectile to complete a full internal oscillation. In other words, it has to be a “snap
shot” catching the moment of the action. If the interaction is too long, the Serber model
breaks down because the initial state of the fragment can be changed. In our experiment,
for the C target, almost all the “He breakups are due to nuclear interactions. Our beam
velocity of c/4 and an interaction pathlength for the “He projectile of 11 frn (assumed to
be twice the diameter of the C nucleus) yield an interaction time of about 44 fm/c. To
estimate the period of the internal oscillation of a halo neutron, we note that a halo
neutron has an rms radius of about 2.6 fm [38] and a momentum about 25 MeV/c in “He,
hence a period of about 610 frn/c, about 14 times the interaction time. Therefore, the
“sudden approximation” is valid in this case. If we go to heavy targets such as U, whose
coulomb interactions with “He contribute more to the breakup than the nuclear
interactions, the “sudden approximation” becomes less valid due to the long—range
coulomb interaction. Because “He may well be disturbed before it breaks up, what we
measure with the heavy targets may not as well reflect the internal momentum function of

the “He. As a result, the momentum distribution could differ from the light targets to the

57

heavy ones.

2) The target-dependence of the width of the momentum distribution could also be
the result of other reaction mechanism effects. For example, for light targets such as C,
sequential breakup of “He via 5He is thought to be the dominant process [14] because of
the stripping mechanism, while for heavy targets such as U, simultaneous breakup of “He

into “He and two neutrons dominates because of the coulomb breakup mechanism.

3.2.3 “He Parallel Momentum

Figure 3.2.4 and Table 3.2.1 show the “He parallel momentum distribution for
each of the six targets. Their width vs. Z of the target is plotted in part (a) of Fig. 3.2.3.
The width of the “He parallel momentum distribution also shows a target dependence.
The width for Al appears to be larger than the others. The big tail on the left side of the
A1 peak in Fig. 3.2.4 contributes to the abnormality. If the tail were ignored, the width of

the distribution for Al would be in line with the trend in the target dependence.

3.2.4 Valence Neutron rrns Radius

One purpose for measuring the “He fragment momentum distribution is to learn
the wave function of the halo neutrons in the “He projectile. Although the direct linkage
between the parallel momentum distribution and the wave function is a simplification, it
can lead us to see a valence neutron distribution which extends far beyond the nuclear

radius determined from R=1.2A“3 for normal nuclei. We can use the simple zero-range

58

U target Pb target Sn target

 

 

  

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g m : m >I I l’ I I I I I I I I I I I I I I .1
Q as —7 ’
2 3 16 — -I
q r 4
6! 20 -: . .
fl :- .,
H 3 ~ ,
)5 15 1 10 - —
H -I " 1
a -I .. -4
5 10 J ’ ‘
3 2 , ; .1
z s -E I j
_ '1 P -I
o 3 . .
O- o
>1 700 000 900 1000
’3
3 Cu target Al target C target
g 12 :I I I I I I I I I I I I I‘I I“ I I : a :I I I I I I I I I I f1 I I I I I _‘ 5 p T I I I I I I I T I I I I I I I
. .. ,. l' "
lo '— —‘ s :— — i I
g : : : ‘ .— —.
v-t _ _: '— _ 1 3
R ° 1 h a . .
*5 : 1 : . 3
:1 ° . ‘1 3 .— “. .
O r- -1 I- - “
o I : I I 3 ,— f
V 4 :- —_1 2 F— j ,. .
c u- -1 p d : :
T; 2 :_ _: 1 '_ .; 1 :- ‘.
p... : : 1
: : : . 1 _
o — I o l L l L l l l l 1 o I LLL 44 .l I
700 woo 700 000 900 rooo no 000 900 1000
P” (MBV/C)

Figure 3.2.4 The “He parallel momentum distributions for the “He breakup. The parallel
momentum is the projection of the momentum on the incident direction of the “He beam.
The solid curves are Gaussian fits. The widths of the distributions are listed in Table

3.2.1.

59

Yukawa-type wave function first introduced by Hansen and Jonson [4] to obtain the
asymptotic behavior of the wave function. This is the region with the most strength for

peripheral reactions.

1 “w“ 322
III/(fixm r (..)

where p is the range parameter, r is the radial distance between the “He core and the halo
neutrons. After the Fourier transform of the spatial wave function, the momentum
distribution becomes a Lorentzian

F

E cc —,, (3.2.3)
div [p2 + r2/4]

2b
where F = 7. After integrating over the other two transverse dimensions, the parallel

momentum distribution has the form

i —-——F (3 2 4)
dP/l [P//2 + F2/4] ’ I “
with FWHM = F. If this distribution and a Gaussian distribution with the same FWHM

are configured, they are almost identical in the central region. So, the width 0 we

obtained from Gaussian fitting can be used to estimate the size of the halo of “He using
1
the rms halo radius (r2)2 2 % . In the experiment, the width of the “He parallel

momentum distribution depends on the target. We use the width for the C target, 6 =
40.2i2.3 MeV/u (F WHM = 94.6i5.4 MeV/c), since it is expected to reflect the intrinsic

momentum distribution of the halo better than the high Z targets, as explained earlier.

For the C target,

60

 

 

2h
F: FWHM: 94.6+5.4MeV/c=>p=—=4.l7i0.24fm

:><r 2)? ~T=2.95i0.17fm. (3.2.5)

The rrns radius of the neutron matter distribution was determined from “He interaction
cross sections in two measurements which gave very close results: 2.59i0.04 fm [39] and
2.61i0.03 fm [44]. The rms radius determined from the “He parallel momentum
distribution here reflects the tail of the valence neutron matter density, because the
calculation is based upon an asymptotic wave function of the neutron halo. On the other
hand, the rrns radius determined in the two previous measurements reflects the entire
neutron matter density of “He. Therefore, the rms radius determined here should be larger
than the two reported results, by 0.35 fm according to this measurement. It is nice to see
the consistency between the experimental results, considering that the model and the

approach used above are simple.

61

3.3 The Decay Energy Distributions
One of the goals of this experiment was to look for possible evidences of the soft

dipole resonance in “He. In section 1.5, we showed how to relate the dipole strength

function

 

dB E E1
—d(E ') to the differential coulomb cross section d; by using the equivalent

 

for “He, we measured the decay energy distributions

photon method. To obtain (13(51)

for the six targets. The decay energy E, of “He is the difference between the excitation
energy FX and the 2—n separation energy 82,, of “He, i.e. E, = E, —S2n. The decay

energy of “He can be expressed as [10],
1 -2 1 —.2
Ed = Ellyn—4 + allen—n (33-1)

m4 (2mn )

 

m . . — .
where ,a, = #2 = 2" , m4 rs the “He mass, mn rs the neutron mass, V2n_4 rs

m4 + 2m" “
the relative velocity between the “He and the center of mass of the two neutrons, VH is

the relative velocity between the two neutrons. The decay energy was calculated for each

 

. . . . . do .
2n—“He corncrdent event. The measured decay energy distributions— dEm for the srx
(1

targets are shown in Fig. 3.3.1. The distributions were obtained after subtracting the
target-out data from the target-in data in order to exclude the reactions in the Si strip
detectors. A peak at around 1 MeV can be found in all the decay energy distributions.
Before any conclusion can be drawn upon the raw differential cross sections, we have to
know what are the constituents of the distributions and what are the complications

coming from our detection system.

62

U target

,_IIIIIIIIIIIIIIIIIIIIIIIIIIIIL

 

40*—
30—

 

 

 

 

' H—*
l
r.
.
b
lllllllllllllllllllll

 

 

 

_I—O—I
E—o—l
° 50—1

O
H
N
9..
p
0

Cu target

15 ITIIIIIIIIIIIIIIIIIIIIIIIIIIT
.-

 

1

p
I—
b
j—

   

10

Yield (counts/0.6 MeV)

 

>——4

 

 

 

C
III!
:I—-O—I
b-——I
ll LJLlllllllllll

“E

 

. :r—«H

O
p
..
p
N
.
h
w..—
0

25 PIIII'IIIT'IIIIIII—I—IIITIIITIII
D d
II '1

q

20 — —

.1

I I
q

.1

_1

'1

q

q

d

—

1

d

d

.4

—

- -1

u- ...H
q

I:

15

Pb target

 

 

 

 

 

 

 

 

 

 

 

Al target

 

—

TIII'IIIIIIIIIIIIIIIIIIIIIIII
_ ‘

 

 

 

 

 

 

 

 

 

PIKITIIIIIIIIIIIIIIIIIIIlllill-
10.0— —
p ..
.1" .

r- .4
75-? —
- -<

r .1

P -1

b q
6.0-0 ll —
E -1
2.3 —- 1' -=~
)- -I

* d
00? db ‘
' I- _L _L .
I- I .1
llllllllllllllllllll llll

25 IIII'IIIIIIIII'IIIIIIIIIIIIII
-
.-

b 1
20— —
,

 

Sn target

 

 

 

 

 

 

 

 

 

)-
h
I-
.-
.—
I
p
D
u-
n-
.-
p
)-
.
_
I-
b
I-

I

p

a I—- - II
b

J

C target

 

 

 

 

 

 

 

 

 

Figure 3.3.1 Decay energy distributions—dom/dEd for the six targets. These are 2n-“He

oincidence events.

63

Since both nuclear and coulomb interactions contribute to the breakup of 6He into
two neutrons and a 4He, the decay energy distributions in Fig. 3.3.1 are not pure coulomb
differential cross sections. Because we are interested in electromagnetic dipole
excitation, we want to exclude the nuclear part of the distributions. However, the small
number of 2n-4He events prevents us from making any valuable separation of the nuclear
contribution. Fortunately, we think it is a good approximation to assume that only the
coulomb breakup contributed to the decay energy spectrum for the U target. There are a
couple of reasons supporting this approximation. First, based on the 2-n removal cross
sections obtained in section 3.1, the coulomb interaction accounts for more than half of
the total cross section for the U target. The nuclear cross section is about 40% of the total
cross section according to our extrapolation. Second, the reaction mechanisms in nuclear
breakups are diffraction and stripping. The diffraction produces events with two neutrons
in the final state, while in the stripping process, because one neutron is absorbed by the
target, only one neutron is observed. The requirement of two neutrons being detected in
the decay energy spectra rules out the stripping mechanism. Because the stripping
mechanism accounts for more than half of the nuclear breakups [40,41], the nuclear
contribution to the decay energy distribution for the U target could be less than 20%, a
rather small part of the spectrum. So, we do not expect the events from nuclear breakup
to significantly affect the shape of the spectrum for the U target. As the contribution of
the nuclear interactions increases from the heavy to the light targets, the approximation

becomes less reliable.

64

 

Now, let’s explain the complications caused by the detection system. The

(1
measured decay energy spectrum for the U target do”

 

, shown in Fig. 3.3.1, is related to
d

 

do
the true spectrum dE by the following equation:

d

dam
dEd

 

(1
(E) = IEOAEQME; .E. ME; (3.3.2)
d

where £(E;,Ed) is the response of the detection system that represents how much the
detection system distorts the true decay energy spectrum. £(E;,Ed) is a complicated
function of neutron timing (ct = 1.27 ns) and angular resolution (0'a = 04° ), 4He energy
(GE: 2%) and angular resolution (1.2°), energy loss in the U target (E = 6.24 MeV) and

multiple scattering effects, plus the solid angle acceptance of the neutron walls.

The solid-angle acceptance of the neutron walls was limited vertically (~ 1 meter)
by the magnetic poles, horizontally (~ 2 meters) by the length of the cells. So the
maximum vertical neutron angle with respect to the 6H6 projectile direction was only
5.7°. In the horizontal direction, the maximum neutron angle was 113°. The decay
energy distributions are affected by the solid-angle acceptance of the detection system.
The higher the decay energy, the smaller the acceptance because large decay energy
results in higher neutron transverse momentum, making the neutrons more likely to miss
the neutron walls. With decay energies below 0.3 MeV, no neutron will miss the neutron
walls because both neutrons have laboratory angles less than 5.7°. When the decay

energy exceeds 0.3 MeV, some neutrons start to miss the wall in the vertical direction. In

65

 

an extreme mode, in which one neutron recoils against the other neutron and the 4He, the
first neutron will have the maximum velocity. The first neutron will just miss the neutron
walls at Ed = 0.3 MeV if its momentum in the rest frame of the 6He projectile is
perpendicular to the pole faces of the magnet. When the decay energy is over 1.2 MeV,
some neutrons start to miss the wall horizontally. Fig. 3.3.2 shows the calculated solid-
angle acceptance vs. decay energy based on a Monte-Carlo simulation using the 3-body

phase space distribution. The curve starts to fall around 0.3 MeV as predicted.

Because the response function is too complicated, it is not possible to unfold the

do m
response from
dE

 

 

directly. So, models were chosen for do . Each one of the models

(I d
was filtered through the detection system using a Monte-Carlo simulation, and compared

with the measured decay energy spectrum. The one that gave the best fit was considered

. d
the true decay energy spectrum. As shown in eq. 1.5.1, to obtain % , we have to know
d

the photonuclear cross section 0 E] (E). We used the empirical model parameterized

with a Breit-Wigner function introduced in [10]

a1“
“5W m ’ (”-3)
where
r E T E
NE.) = ————-( T"()E() d) (3.3.4)
0

66

Solid Angle Acceptance

 

_L

 

 

 

O
I
0.8 — O
0.6 —
O
0.4 ~ 0
O
O
O
.0
O
0.2 — °.
'0
'0
O...
O
0 l l l l l l l |
0 0.5 1.5 2 2.5 3 3.5 4 4.5 5

Decay Energy (MeV)

Figure 3.3.2 Calculated solid-angle acceptance of the detection system. The simulation
is based on the 3-body phase space model.

67

In eq. 3.3.3, I" is the width, E0 is the resonance energy and a is a normalization factor.
For 6He, the excitation energy E, = E, +0.975 MeV. In eq. 3.3.4, 1"(Eo) is the width at

E0, T(Ed) is the transmission coefficient with the energy dependence of s-wave neutrons

[45]. The energy dependence forces the Breit-Wigner function to be zero at zero decay
energy. In Fig. 3.3.3a, the measured decay energy for the U target is shown again with a

solid line that is the Breit-Wigner model with the resonance parameters E0 = 1.9 MeV
and I‘(E0) = 1.5 MeV. Within statistical errors, the model gives a very good fit to the

data. So, eq. 3.3.3 with the two best parameters is considered our measured photonuclear

function 0,5.I (E) for 6He. The function is plotted in Fig. 3.3.3b. The corresponding dipole

strength function, as shown in Fig. 3.3.3c, was determined from the photonuclear

function 051 ( E) based on eq. 1.5.4.

The dipole strength function is compared with two three-body models, as shown
in Fig. 3.3.4. The model by Danilin et al. was first introduced in ref. [25] to look for the
dipole resonance for 6He. This model is based on hyperspherical harmonics and the
coordinate space Faddeev approach [23]. The model was later used to calculated cross
sections for coulomb dissociation of 6He [30]. The dashed curve is the most recent
calculation obtained from Ian Thompson, one of the collaborators in ref. [30]. In the
other three-body model, by Pushkin et al.[46], the strength function for two-valence

neutron halo nuclei is expressed as

 

dB(E1) E3

dE fl
(ng + E) 2

(3.3.5)

68

 

 

 

 
   

 

 

 

 

 

{III
A 1
h 4
3 Utarget —-
a ' ( )
.o 2 a
a -_
g It
\ —
b I
'0 II
t" l I . I...lIT,'
t:I II ‘II III II'IIIIIIIII:
A ZSE— _:
E E Eo=1.9 may 5
"" m:— r=1.51tev T
23 1 E : (b)
.6—
5 E
Eq‘ 1.0}
H" E
b 0.5:-
E/
¢.o_'
E 0.6}
1": L.
.0 I
0.6-—
3’ 3 (e)
a: :
"d 0.4-
\ :
9 t
B- 0.27-
% .
OoohllllllllllllllljqulllJ
Ed (MeV)

Figure 3.3.3 Decay energy spectrum for the U target. (a) The points are experimental
data. The solid line is the result of a Monte Carlo simulation with a Breit-Wigner
function (E0 = 1.9 MeV and F = 1.5 MeV). (b) The photonuclear spectrum corresponding
to the Breit-Wigner parameters determined from the data. (c) The dipole strength
function determined from the data.

69

dB/dE (Arbitrary Unit)

120

100

80

60

40

20

 

Danilin et al.
Pushkin et al.
This experiment

 

 

1
0 2 4 6 8

 

Illllllllllllllllllllllll

I .

llll‘

 

 

Decay Energy (MeV)

,_-
0

Figure 3.3.4 The dipole strength functions. The dashed curve and the dotted curve are
from two 3-body models [25,46].

70

where S2”: = aSzn is an effective separation energy with a =1.45—1.55. The strength
function for two-neutron halo nuclei is derived from the E1 strength function for one-
neutron halo nuclei by Bertulani et al. [18]. The dotted curve in Fig. 3.3.4 is the result of
the model with a = 150 and $2,, = 0.975 MeV. Even though the shapes of the strength
functions differ quite a bit, they are very well concentrated in the area between 1.5 MeV
and 2.0 MeV. Since excitation energy Ex = E0 + 0.975 MeV, this may indicate a

concentration of the dipole function between E)( =2.475 MeV and E)( = 2.975 MeV.

We can further compare our data with another 3—body model using the coupled-
rearrangement-channel method base on an 0t + n + n cluster model [28]. The calculated
strength distribution had a broad peak at Ex z 2.5 MeV. The width of the peak predicted
in the model is in the neighborhood of 4 MeV, which is very similar to the model by
Pushkin et al. Some authors [25,28] in their papers thought that the broad widths did not
support the existence of a resonance in 6He. They call the peak a reminiscence of a
resonance behavior since the soft dipole resonance is supposed to have a very narrow

width (F31 MeV).

The experiment and the calculations agree that there is a strong concentration of
the dipole strength at low energy Ex ~3 MeV. However, it is not clear whether the 6He
breakup occurs directly or through a resonance state if we base our judgement solely on

the decay energy spectrum. We will look for further evidences in the following section.

71

3.4 Post—breakup Coulomb Acceleration

It remains as an interesting topic whether halo nuclei, such as 11Li and 6He,
breakup in the coulomb field through a soft dipole resonance, or simply break directly
into three pieces—two neutrons and a charged fragment. For 11Li, the post-breakup
coulomb acceleration (PBA) of the 9Li fragment favored the direct breakup mechanism
[10]. It is one of the goals of the experiment to find if PBA can be found in the 6He
breakup as well. First, let’s briefly explain what is PBA using the 6He projectile and the

U target as an example.

Because of the great photon intensity, coulomb excitation is more likely to occur
when the 6He projectile is close to the U nucleus [10]. If the projectile decays
immediately after being excited by the coulomb field, the two valence neutrons fly away
with whatever velocity they have at the moment of the breakup because the neutrons do
not feel the coulomb force. On the other hand, the 4He would be accelerated as it leaves
the coulomb field of the U nucleus. Since the decay energy is small relative to the
incident energy of the 6He, it cannot significantly alter the velocities of the fragments.
Therefore, on average, the accelerated 4He fragment tends to have a higher velocity than
the neutrons if the direct breakup is the dominant mechanism. However, if it forms a
resonance after being excited, the projectile will not break up until the resonance reaches
the end of its lifetime. If the resonance lives long enough, the excited 6He will travel far
away from the U nucleus. As a result, the neutrons and the 4He fragment will have about
the same velocity because the coulomb field at the point of the breakup is too weak to

have any effect on the 4He fragment.

72

3.4.1 Projectile Slow-down

As we can see from the above, the premise for the post-breakup acceleration is
that the 6He projectile has to break up when it is close to the target nucleus. As the 6He
projectile approaches the target nucleus, it slows down when part of its kinetic energy
transforms into potential energy. The closer the projectile is to the target nucleus, the
more kinetic energy it loses, and the lower its velocity. It can be inferred that if the 6He
breaks up at a place close to the target nucleus, the average neutron energy should be
lower than the incident beam energy per nucleon. The energy distributions of the
neutrons from the 6He 2-n removal reactions are shown in Fig. 3.4.1. These events were
n—4He coincidence events. The distributions were fitted with a Gaussian function. The

centroids of the distributions give the average neutron energies. Fig. 3.4.2 shows the

difference AB between the average neutron energies E. and the average beam energies

per nucleon Elm"... The solid line connects points AEm for the maximum slow-down as

the 6He projectile grazes the target nucleus. IfR, and Z, denotes the radius and the change

of the target nucleus, respectively, AEM can be expressed by the potential energy at

zaflé
Aam=——FL-6 can

where R,He = 2.33 fm , R, = 1.2 Am. As shown in the figure, the 6He projectile slows

R=R +a,

6H:

down more for the high Z targets because of the presence of stronger coulomb fields.

73

U Target Pb Target Sn Target

4w 11"IIIIUIIIIIIIIUUIIIIUIU‘ll 20°1IIIIIIIIIIHIIIIIIIHIIIIIII IIUUITIIUI'UUII—I'IIITTIUIIU'I
r -I b ..

I 150'— —
r I

P

[-

 

 

 

J

 

 

 

 

 

 

     

 

 

 

 

 

 

 

 

  

  

- 4
3°°:' ‘: 4
.. q ‘1
: : a
200— —« q
'- -1
9 * 3
too— -—
g E —
N . o ‘
B 0108031406060 OIOEOMQOOBO 0108333406080
H
g ' CTarget
a Cu Target Al Target
8 :UIUUIUTIYIIWIIIIFWUUWIYVTI: soplIIIIFIUIIIIIIIIIIIIlilllllll
126*— —‘ 125
"U : :
"'63 “ ‘
a 100:- —- 100
75—- —_ 75
C I
50:- — so
i I
26— "'1 u
E 1
00102030405000 001080m406060 0102030406000

En (MeV)

Figure 3.4.1 Neutron energy distributions for the 6He breakup. The points are ln-4He
coincidence events from the experiment. The solid lines are Gaussian fits.

74

 

 

 

 

 

(—En _Ebeam) E

(MeV) ‘2 ‘ E ‘

I

C Al Cu Sn Pb U
_4 _ _

—8 t I l I
0 20 40 60 80 100
Z

Figure 3.4.2 Difference between the average neutron energy and the average 6He beam
energy per nucleon. The average neutron energy is determined from the centroid of the
Gaussian in Fig. 3.4.1. The average beam energy is equal to the beam energy at the center
of the target. The solid line connects the maximum energy differences for the six targets.

75

Another observation is that the lower the Z of the target, the closer the slow-down is to
the maximum. This indicates the dominance of the nuclear interactions for the low Z
targets, interactions in which the 6He projectile has to get very close to the low Z targets

in order to acquire sufficient energy to induce a breakup.

3.4.2 Velocity Shift

Although the projectile slow-down proved that the breakup of 6He occurs close
to the target nucleus, it did not tell how the 6H6 breaks up—direct or through a resonance
state. We turned to the difference between the average the 4He velocity and average
neutron velocity for further evidence. For each 2n-4He coincidence event, we determined
the velocity for each neutron and the velocity for the 4He fragment. To rule out the bias
towards any one of the neutrons, we took the average of the velocities of the two
neutrons. The top three graphs in Fig. 3.4.3 show the difference between the 2-
component of the 4He velocity and that of the average velocity of the two neutrons for the
three heavy targets—U, Pb, Sn. It will be explained later why only the z—component is
used. The results for the light targets—Cu, Al, C are shown in the top three graphs in Fig.
3.4.4. The velocity difference is expressed relative to c, the velocity of light. One
concern with the velocity difference between the neutrons and the 4He fragment was that
neutron and 4He velocities were measured by different detectors in the experiment.
Different responses of the detectors could cause a systematic shift in the velocity
difference. This type of systematic error might lead us to a wrong conclusion. In order to
see if a systematic shift exists in our detection system, we calculated the z-component of

the center-of-mass velocity for the 2n+4He system both before breakup and after breakup.

76

U target Pb target Sn target

 

 

 

   
    

 

 

 

 

 

 

 

   

 

 

 

 

 

 

  

      

 

 

 

 

 

 

 

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Figure 3.4.3 Velocity (z-component only) difference distributions for the three heavy
targets in the expriment. The top three graphs are the differences between the 4He
velocity and the average velocity of the two neutrons, calculated on an event-by—event
basis. The bottom three graphs are the differences between the 6He center of mass
velocity before breakup and after breakup for the same three targets, respectively. The
dashed lines are the centroids of the bottom distributions.

77

Cu target Al target C target

 

 

 

     

  
    

 

   

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 3.4.4 Velocity (z-component only) difference distributions for the three light
targets in the expriment. The top three graphs are the differences between the 4He
velocity and the average velocity of the two neutrons, calculated on an event-by-event
basis. The bottom three graphs are the differences between the 6He center of mass
velocity before breakup and that after breakup for the same three targets, respectively.
The dashed lines are the centroids of the bottom distributions.

78

Before breakup, the center-of-mass velocity is determined from the incident beam energy
at the center of the target. After breakup, the center-of-mass velocity is determined from
the measured velocities of the two neutrons and the 4He. Based on momentum
conservation, the difference between the two velocities should center at zero if there is no
systematic error with the measurements. It has to be pointed out that only the 2-
component can be used, because the center-of-mass velocity of the 6He is changed in the
transverse direction due to the interaction with the target nucleus. The z-component, on

the other hand, remains the same since the target nucleus on average recoils at 90° to the

z direction. Therefore, it is a good approximation to assume that the target nucleus gains
zero momentum in the z direction after the impact. Based on momentum conservation,
there should be no momentum change for the 2 component of the 2n + 4He system before
and after the interaction, i.e. the center-of-mass velocity difference should be zero. The
graphs on the bottom in Figs. 3.4.3 and 3.4.4 show the center-of-mass velocity difference
distributions for the six targets. Every peak in the graphs has a center at

(-0.0045i0.0012) c. This indicates that there is a small systematic shift in the detection

system. The vertical dashed lines in the top graphs indicate -0.0045 c. To account for the
systematic shift, the velocity shift was measured from the centroid of the velocity
difference distribution to the dashed line. The result is shown in Fig. 3.4.5. As shown in
the figure, within the statistical uncertainty, the heavier targets produce a 4He fragment

with a higher velocity than the neutrons.

If a resonance state was formed, it would be meaningful to see how long the

excited 6He nucleus remained in the resonance state in order for the observed velocity

79

 

0.05 - -

(Va—Va) 1 I E I E .
(C) 0.00—— —} ———————————————————————— ~

-0.05 *- C Al Cu 511 Pb U ‘

 

 

 

O 20 4O 60 80 100

Figure 3.4. 5 Average velocity difference between the 4He and the neutrons from the 6He
breakup. The data points are determined from the centroids of the top graphs in Figs.
3.4.3 and 3.4.4. The data are adjusted for the systematic shift (indicated by the dashed
lines in those figures).

80

shifts to be produced. Obviously, the longer the lifetime, the smaller the velocity shift.
Sackett et al. [10] showed how to calculate the lifetime of the resonance from the velocity
shift. As shown in Fig. 3.4.6, simplified breakup schematics is used in the calculation.
First, a straight-line trajectory is assumed, since the 6He is only deflected by a few
degrees. Second, the excitation occurs at the distance of closest approach, because the
electric field is the most intense at that point. So, the 6He is excited at point A, then
breaks up at point B. To see the detailed deduction of the formula, please refer to ref.
[10]. The relation between the average velocity shift and the mean lifetime is expressed

as:

z,,,,z,,e2 1
m4V b2 +V2’l'2 ,

 

(AV) = (V4.(°°) -V2..(°°)) = (3.4.2)

where V4z (co) and V2,“ (oo) are the z-component of the measured velocities for the 4He and

the two neutrons, respectively, V is the incident beam velocity, b is the impact parameter

and ”c is the mean lifetime of the resonance. For the U target, (AV) = 002161200045 0

and V = 0.2260 c. If we use a small average impact parameter, b = R(6He)+R(238U)
= 2.33 + 7.44 = 9.77 fm, based on eq. 3.4.2 the mean lifetime of the resonance is

1 =47i18fin/c, which yields a width of I‘=4.2:t1.6MeV. This means that a

resonance state has to have a width 4.2 MeV to be consistent with the measured velocity
shift, which would be much larger than the I‘ =1.5MeV obtained from the decay energy
spectrum in Fig. 3.3.3a. Based on the measured 1" = 1.5MeV , the resonance should have
a lifetime of about 131 fm/c. The velocity shift shows, however, that the 6He projectile

breaks up long before 131 fm/c. This means that the time is too short to form a

81

U target

 

 

 

/ A v’t \

Photon absorbed here Breaks up here

Figure 3.4. 6 Schematic view of a 6He breakup. The impact parameter is denoted by b.
The 6He is excited at point A, the closest approach, then breaks up at point B. The
distance between the U nucleus and point B is r, v is the beam velocity and 1: is the mean
lifetime of the resonance.

 

Target U Pb Sn

 

<AV>/c 0.0216i0.0045 0.0190i0.0055 0.0185i0.0046

 

'c (fm/c) 47:18 50.5i24 18.6i22

 

Target Cu Al C

 

<AV>lc 0.0098i0.0075 0.0019i0.0087 —0.0002i0.0177

 

’t (fm/c) 27i49 100i49 1 mice

 

 

 

 

 

 

Table 3.4. 1 Average velocity shift <AV> between the 4He and the neutrons from the
6He breakup, and the mean lifetime of the resonance determined from <AV>.

82

resonance. So, the velocity shift appears to support a direct breakup mechanism. One
can notice that it is a conservative estimation by setting the average impact parameter at
the sum of the radii of the 6He and U nuclei. With a higher b, the mean lifetime of the

resonance T is even smaller, therefore the corresponding P will be even further from the

measured I‘ =1.5MeV . The mean lifetimes determined from the velocity shifts for the
other targets are listed in Table 3.4.1. For Al and C, eq. (3.4.2) does not stand since E1
excitation is a very small part of the 6He breakup, hence the calculated mean lifetimes
have no physical meaning. The calculated mean lifetimes for the other targets are

consistent within the statistical uncertainties.

83

3.5 Neutron Correlation
3.5.1 Evidence From Neutron Relative Angle

When the neutron halo was found in the nuclei near the neutron dripline, a simple
model of core-plus-dineutron was suggested as the main structure [4]. If the 6He nucleus
does have a dineutron structure, coulomb excitation would cause a two-body breakup, in
which the 4He core is pushed away by the target nucleus, leaving the two neutrons with
the same momentum. As a result, the two neutrons are going to be strongly correlated,
i.e., the relative angle 6 between the momenta of the two neutrons in the rest frame of the
6He should be zero, or cost) should be 1. The measured cosG distributions are shown in
Fig. 3.5.1 for the six targets. Two observations can be made from the figure. First, from
the U target to the Al target, the distributions peak forward at cosO = 1.0. Second, the

forward peak, becoming weak from the heavy to the light targets, is hardly found in the

distribution for the C target.

Again, the response of the detection system might distort the true 0036
distribution. Since the solid-angle acceptance of the system favors the breakups with
small n-n angles, the cosG distribution may be forced to be forward peaked. To take the
response and other geometry effects into account, we calculated the cosG distribution for

the U target in two extreme decay modes by Monte-Carlo simulations. In the first mode
the two neutrons recoil against the 4He core as a dineutron. The dashed histogram in Fig.
3.5.2, which shows the simulation result in the dineutron mode, is strongly forward

peaked. The solid histogram in Fig. 3.5.2

84

 

 

 

 

 

 

 

 

 

 

 

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—t.o —o.5 0.0 o: 1.0 —o.5 0.0 0.5 1.

 

 

cos(9m)

Figure 3.5.1 Angle distribution of the two neutrons from the 6H6 breakup. These are 2n-
4He coincidence events for the six targets used in the experiment. The angle was
calculated in the 2n+4He center of mass frame.

85

 

100 I I l I l l I T ‘l’ l I I l I l i

80

L___—.

60

40— I
_ l'
: m'

l

|

Illllllllll

arbitrary unit

 

 

 

E-‘lllllllJlllJllllllllllllll

O

 

cos(9m,)

Figure 3.5.2 Angle distribution of the two neutrons from the 6He breakup. The points
are from the experiment for the U target. The solid histogram is a Monte—Carlo
simulation with the 3-body phase space model. The dashed line is the same simulation
with the dineutron model. The dashed line reaches above 10000 at cost? = 1

86

 

is for the three-body phase space model. The two neutrons in the phase space decay
mode are uncorrelated. As shown in Fig. 3.5.2, the angle distribution for the phase space
model is only slightly peaked after being folded with the response function of our

detection system. It also appears to be peaked at 0m, = 180°. Figure 3.5.2 only plots the

U data against the simulation results from the two models. We can further compare the
two models with the angle distributions for the other targets shown in Fig. 3.5.1. One can
see that the data suggest the correlation between the neutrons in 6He is in between the two
extreme models. This is consistent with the hybrid model [22] introduced in section 1.4.
In this model, the two valence neutrons of 6He stay in shell model orbits when they are
close to the core, but form a cluster (dineutron) when they are far from the core. If the
6He nucleus breaks up when the neutrons are far from the core, the neutrons tend to be
strongly correlated. If the 6He breaks up when the neutrons are close to the core, the
neutrons tend to be uncorrelated. The tendency of the neutrons to be uncorrelated from
the heavy to the light targets may be caused by the dominance of the sequential decay of
the 6He through the 5He. In the sequential decay mode, the first neutron knocked out
from the 6He projectile has no correlation with the second neutron, which is later
separated from the unstable 5H6. Only after all these decay modes are taken into account,

can the cost) distributions for the six targets be reproduced theoretically.

3. 5.2 Evidence From Neutron Momentum
One indirect method to find the n-n correlation in 6He is to compare the width of

the 4He parallel momentum distribution with that of the neutron parallel momentum

87

0,.” (4He)

 

 

 

 

 

 

 

(MeV/c)
Orv/(n)
(MeV/C)
2.5
2,
4H §
————0””( e) 1.57 5 i z i i
UPI/(n) 1 z
1
0.5
o . .
o 20 4o 60 80 100
Z

Figure 3.5.3 (a) The width of the 4He parallel momentum distribution for the six targets.
(b) The width of the neutron parallel momentum distribution for the six targets. (0) The
ratio of the 4H6 momentum width to the neutron momentum width. The data, the same as

those in Fig. 3.2.8, are from n—4He events. The dashed line indicates J2 .

distribution. The theory is based on momentum conservation in a projectile as in the
Goldhaber model [47]. The momentum correlation term between two neutrons in a

projectile A can be written as
(ml). 13012)) = 15(oj_2 ~2ofi), (3.5.1)
where 0' [H and 0'" are the momentum widths of a fragment (A-2) and a neutron,

respectively. It is easy to see that if the two neutrons are not correlated, then

(13011) . 13012)) = o, and % = J5 . In Fig. 3.5.3, the bottom graph plotted the ratio

II

between 0.”: and 0'” for all the targets used in the experiment. The dashed line is J2 .

As shown in the figure, the data points are very much lying on the dashed line except the

abnormal point for Al. This may indicate that the two neutrons in 6H6 are uncorrelated.

89

4 Summary

The kinematically complete measurement of the 6He dissociation made it possible
for us to study the 6He nucleus in a variety of perspectives. At first, the 2-n removal
cross sections for the six targets were determined with the n-4He coincidence data. The
efficiency of the detection system was taken into consideration by scaling our data to a
measured cross section on Si [17] at a similar energy. Our measured cross sections were
consistent with the two theoretical calculations by Warner et al. [30] and Ferreira et
al.[37]. For example, for U, 62,. = (1.87 i 0.24) b vs.1.68 b from ref. [30]; for C, 62,, =
(0.36 i- 005) b vs. 0.34 b from ref. [30] and 0.46 b from ref. [37]. The measured cross
sections were also adjusted for the neutron multiplicity based on the theory by Barranco
et al. [40,41]. The adjusted cross sections are somewhat smaller than the unadjusted ones

except for C and Al.

The coulomb cross sections were separated from the nuclear cross sections by two
methods, method 1 (extrapolation) and method 2 (fitting). The coulomb cross sections
from method 1 are larger than those from method 2. Except for U and Pb, the results of
method 2 are in better agreement with the calculation [37]. For U, Method 1 gives
occulomb = (1.06—£0.24) b; method 2 gives occulomb = (0.92i0.24) b . So on average, for U,

the coulomb cross section contributes about 50% to the total cross section.

Neutron and 4He momentum distributions were reported for the six targets. We
chose the parallel momentum distributions over the transverse momentum distributions

because the neutron and 4He transverse momentum distributions were shown to be

90

significantly affected by the coulomb deflection and the solid-angle acceptance of the
detection system. A Monte-Carlo simulation shows that the parallel momentum
distribution is hardly altered by the acceptance of the system. The parallel momentum
distributions were fitted with Gaussian functions. The width 0",, = (26.9i2.2) MeV/c for
C is a little bit smaller than the result by Kobayashi et al. [9] who reported a width of 32
MeV/c for a transverse momentum distribution at a beam energy of 0.8 GeV/u. It was
found that the widths of the neutron and 4He parallel distributions increase as the size of
the target decreases. This may indicate a shift of the reaction mechanism from
dominating coulomb breakup to dominating nuclear breakup. The measured width of the

4He parallel distribution, 0",, = (40.2i2.3) MeV/c, yields a rrns radius of

1
<r2>2 =2.95:L'O.l7 fin for 6He, which is consistent with the results determined by

Tanihata et al. from the 6He interaction cross sections [39,44].

The experiment was designed to measure 2-n coincidence events, in which all the
three fragments from the 6H6 breakup were detected. The kinematically complete
measurement of the breakup made it possible for us to construct the decay energy
distribution. By using the equivalent photon method, the decay energy spectrum for the
U target was fitted with a Breit-Wigner function folded with the response function of the
detection system. The fitting yields a Breit—Wigner shape dipole strength function
dB(El)/dEd with Ed = 1.9 MeV and F = 1.5 MeV. The location of the strength function
agrees with the predictions of several three-body models [24,28,45]. However, the width
of our dipole strength function appears to be narrower than those predicted in the models.

This may be the result of our system’s low sensitivity at high decay energies (> 3MeV).

91

Although our experimental result as well as the models [25,28,45] agree on the
enhancement of the dipole excitation between Ex = 2.5 MeV and 3.0 MeV. Whether it is

a soft dipole mode (SDM) is inconclusive based upon the shape of the strength function.

We looked for the post-breakup coulomb acceleration [10] in the 6He breakup.
First, from the 1n—4He coincidence events, we found that the neutron average energy is
significantly less than the 6He per-nucleon beam energy for the high Z targets, which
indicates that the breakups occur when the 6He projectile is close to the target nucleus.
The energy difference decreases with the decrease of the target charge, which is due to
the weakening of the coulomb field of the target nucleus. Then, from the velocity
difference spectra, the 4He fragment on average was found to travel faster the neutrons.
This finding supports the post-breakup coulomb acceleration. The average velocity shift
for the U target, (AV) = (0.0216i0.0045) c, leads to a resonance with a much shorter
mean lifetime than that inferred from the measured width of the dipole strength function.
So the post-breakup acceleration suggests that 6He does not break up through a resonance
state. The concentration of the dipole strength function is just a resemblance of a

resonance state.

To see if the two valence neutrons of 6He are correlated, we plotted the
distribution of the relative angle of the two neutrons in the rest frame of the 6He
projectile. Compared to the two extreme models—the dineutron model [4] and the direct
breakup model [10]—the experimental data lean toward a structure without much

correlation. We also found that the forward peaking of the relative angle distributions is

92

more prominent for heavy targets than for light targets, which may suggest the
dominance of the sequential decay of the 6He through the 5He for light targets [16].
Besides the neutron relative angle distributions, we also looked for the neutron
correlation in the 6He nucleus from the widths of the neutron and 4He momentum
distributions. The fact that, on average, the ratio between the width of the 4He
momentum distribution and that of the neutron momentum distribution is close toJ2,

strongly supports that the valence neutrons are not strongly correlated in the 6He nucleus.

93

PART II

Neutron Cross-talk in a Multiple-detector System

5.1 Introduction

A high-efficiency, position-sensitive, multi-detector system is the ideal apparatus
for studying neutrons in the final states of nuclear reactions. Usually such detection
systems are arrays of a number of neutron detectors [48—50]. In order to reduce dead
space and to be able to measure small-angle coincidences, detectors are put as close to
each other as possible. One major concern with these systems is cross-talk between the
detectors. Cross-talk happens when a neutron which gives a signal in one detector is
scattered into another detector where it again gives a signal. Thus one neutron appears to
be two. Unfortunately, neutron cross-talk inevitably distorts the measurement. The ratio
of cross-talk events to real two-neutron events varies with neutron energy and with
detector configuration, and it could be very significant on some occasions [49-52]. So, it
is very important to understand the effects cross-talk might have before such a detection
system is used in experiments, and an effective method is needed to identify cross-talk

CVCIIIS.

So far, only a few experiments have been reported on the study of cross-talk [49-
52]. Cross-talk probabilities and effects in their specific detection systems were
discussed. In this thesis, we present a method used to distinguish between cross-talk

events and real two-neutron events in the energy region up to ~ 25 MeV.

94

A pair of “Neutron Walls”, shown in Fig. 2.2.2, were built at the National
Superconducting Cyclotron Laboratory (NSCL) for experiments in which two neutrons
are produced in the final state. Most of the cross-talk events should be identified and

rejected in order for a reliable experimental conclusion to be achieved.

5.2 Cross-talk in the neutron walls

5.2.] C ross-talk types

In this paper, cross-talk events are classified into two categories as illustrated in

Fig. 5.2.1.

(a) Cross-talk between the two walls, where a neutron makes one signal in the

front wall and one signal in the back wall.

(b) Cross-talk within one wall, where a neutron makes two signals in different
cells of the same wall. We anticipate that most of the cross-talk events within one wall
happen in neighboring cells, because a neutron has to scatter at a large angle in order to
reach distant cells, and the cross section for neutron scattering decreases significantly

with increasing angle.

5.2.2 C ross-talk eflects

Cross-talk affects a two-neutron experiment in two ways.

(a) It causes overestimation of neutron coincidences. Because cross-talk events

95

    

Back Wall

Front Wall

Figure 5.2. 1 The two types of cross-talk in the neutron walls. Type (a) cross-talk
makes one signal in the front wall and another in the back wall. Type (b) cross-talk
makes both signals in either one of the two walls.

96

are really one-neutron events, the number of neutron coincidences is enhanced by cross-

talk events if these events are not identified as cross-talk events.

(b) The cross—talk within one wall distorts the small-angle correlation (Refer to the
n-n relative momentum distribution in [10]). Since a neutron cross-talk event within one
wall most probably happens in neighboring cells, the event looks like two neutrons
emitted from the source with a small relative angle. If cross-talk events are not identified,

the small—angle correlation is falsely enhanced.

Obviously, we have to reject as many cross-talk events as possible to avoid these

negative effects.

5 .3 Cross-talk identification

5.3.1 Neutron detection in liquid scintillator

It is useful to look at the main interactions between neutrons and scintillator

materials before we introduce cross-talk identification.

Since the composition of the scintillator is hydrogen and carbon, neutrons usually
interact with scintillator through the six processes listed in Table 5.3.1. Because #4 and

#6 have no neutrons in the final states, they make no contribution to cross-talk.

Neutrons are detected with the scintillation light caused by energy loss of charged
particles—protons, carbon nuclei and 0t particles — which are produced in #s 1, 2, 3 and

In Fig. 5.3.1, the light response curves for these charged particles are plotted, based on

97

 

 

 

 

 

 

 

Interactions OR (24 MeV)
1 n+p—>n+p 0.406b
2 n+C—>n+C 0.900b
3 n + C —> n’ + C + y(4.44MeV) 0.104 b
4 n + C -—> He + Be-5.71MeV 0.048 b
5 n + C —> n + 30t-7.26MeV 0.210 b
6 n + C —) p + B-12.59MeV 0.100 b

 

 

 

 

 

Table 5.3. 1 The interactions between neutrons and the nuclei in liquid scintillators —
protons and carbon. OR is the reaction cross section. The data are from the code by Cecil
et al. [9]

98

 

 
      

 

 

 

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:5 _ _
5 - _
o — l l 1 i J l l I I ‘ I _
0 10 20 30 40

Energy (MeV)

Figure 5.3. 1 The light response for electrons, protons, alphas and carbon nuclei in liquid
scintillators. l—MeVee is equal to the light produced by a l-MeV electron. The data are
from Verbinski et al. [8].

99

the data from Verbinski et al. [53]. Although #2, n—IZC elastic scattering, has the largest
cross section, it hardly contributes to neutron detection because of the very low light
response for carbon nuclei. Similarly, #3 gives little contribution to cross-talk effects
when the y—rays escape the scintillator undetected. Even if a y-ray produced in #3 is
detected, it can be ruled out by n-y discrimination. Process #5, which has a reaction
threshold of 7.86 MeV, produces low-energy a-particles. Because of the low light output

of these particles, #5 does not play an important role in neutron detection below 25 MeV.

In conclusion, among those processes with neutrons in the final states, n—p
scattering is dominant for neutron detection if En S 25 MeV. Therefore, n-p scattering is

also the primary source of cross-talk.

5.3.2 2-body kinematics

Since n-p elastic scattering is the major contributor to cross-talk, the well—known
2-body kinematics, illustrated in Fig. 5.3.2, becomes our basis for neutron cross—talk
identification. In this figure, n is the incident neutron, n’ is the scattered neutron, p is the
recoil proton, and 9 represents the neutron’s scattering angle. If we assume mn = mp,

energy and momentum conservation result in the following equations:
Enlen'Ep (5.1)

En’ = En >< c0829 (5.2)

100

 

 

(XIIYI'ZI)

    
  

(xZIYZ'ZZ)

Front Wall

Back Wall

Figure 5.3. 2 An example of cross-talk between the front wall and the back wall. The
neutron makes one signal in a cell of the front wall and another one in a cell of the
back wall. The position of each scattering is expressed by (x,y,z). The scattering in
the front wall follows the 2-body kinematics given by eqs. 1 and 2 in the text.

101

The above equations exhibit the correlation between neutron energy, proton energy and

the scattering angle. If En and l3,p are known, En’ and cose can be determined.

In the next three sections, we show how the 2-body kinematics engenders three

signatures of cross-talk.

5.3.3 ( C OS t9)c-( COS 6)," = 0 (signature #1 ofcross-talk)

Figure 5.3.2 shows a typical cross-talk event between the front wall and the back wall.
There are two scatterings detected in this case. For the first scattering, we measure by
TOF the incoming neutron’s energy — En, the light output of the recoil proton — LP, and
the position of the scattering — (x1,y1,zl). These coordinates are defined in such a way
that the x and y axes, vertical and horizontal, respectively, to the cells, are in the plane of
a wall, and the z axis points from the neutron source to the walls. The neutron source
also serves as the origin of the coordinates. If a neutron is detected in a certain cell, y] is
given by the position of the cell’s center, x1 is given by the time difference of the signals
at the ends of the cell, and z] is the distance between the source and the front wall. The
recoil proton’s energy Ep can be extracted from the light output in the NE-2l3 scintillator
by using its light response function. The response function for charged particles was
determined by fitting the light yield data of Verbinski et al. [53] with an empirical

expression of the form:

L = a-(1 — exp(-b-E°)) + d-E + f (5.3)

102

The light output L is in the unit MeVee (the light produced by an electron of 1
MeV), and E is in MeV. E denotes the energy of charged particles. The parameters — a,
b, c, d, f — which give the best fit for protons, alpha particles and carbon nuclei, are
listed in Table 5.3.2. After En and Ep are determined, we can calculate the scattered
neutron’s energy by energy conservation, En’ = En - Ep. Then eq. (5.2) is used to obtain

the value of COSO. We call it the “calculated” COSG, (COSG)C.

(cose). = (E..' / E.)"2 (5.4)

For the second scattering, we determine its position — (xz,y2,zz). From the
position in the front wall, u1 = (x1,y1,zl) and the position in the back wall, u; = (xz,y2,22),

we can obtain the “real” value of COSG. We call it the “measured” COSG, (COSG)m,

“21 = ‘12— U1 —> (cose)m = 111°1121 / lull luzrl (5-5)

If the event is a cross-talk event, (COSG)c should equal (COSO)m, i.e., (COSG)C—
(COSG)m should be zero. Due to the uncertainty in measuring all the quantities, e.g.,
energies and positions, the (COSG)c-(COSG)m distribution function is not a 5-function at
(COSG)c-(COSG)m = 0, but a peak with a width. The spread of the peak is related to the

energy resolution and the position resolution of the detection system.

Unless cross—talk events are identified, we cannot tell cross-talk events from real
2-n events in which two neutrons from the source are detected. Shown in Fig. 5.3.3 is a

real 2-n event between the front wall and the back wall. If we assume that this is a cross

103

 

 

 

 

 

 

Particles a b c d f
p -5.6375 0.115 0.838 0.7875 8 0.015
0t(<5 MeV) -6.1643 —0.001 2.2 0.01585 0.0
oc(>5 MeV) —5.2688 0.0872 1.22 0.543 0.0
C 0.0 0.0 0.0 0.017 0.0

 

 

 

 

 

 

Table 5.3. 2 The best parameters of the light response function L=ax(1—exp(—b><E°)) +
d><E + f for protons, alpha particles and carbon nuclei.

 

(XIIYI'zll

  
 
 
 
 
   

 

(sza-zzl

 

Front Wall

 

 

Back Wall

Figure 5.3. 3 An example of a real 2-n event between the front wall and the back
wall. If we assume this is a cross-talk event, 0 should be the neutron’s scattering angle
according to 2—body kinematics. However, the positions of the two scatterings give 0’.
Unlike cross-talk events, the two angles are not correlated for real 2—n events.

105

talk event, we expect 0, which is calculated on the basis of 2-body kinematics, to be the
neutron’s scattering angle. However, the positions of the two interactions give 0’. The
two angles are different because they are not correlated by 2-body kinematics. Since the
cosine of 0 gives (COSG)c and the cosine of 0’ gives (COSG)m, (COSE))c-(COSG)m is not
equal to 0. So, for real 2-n events, (COS€))c-(COSG)m won’t form a peak at zero. Instead,
(COSG)c-(COSG)m should be distributed over the range allowed by the geometry of the

neutron walls.

5.3.4 ATc-AT", = 0 (signature #2 ofcross-talk)

In part (3), we established the first signature of cross-talk in terms of (€080);-
(COSB)m. Similarly, in this part, we will establish the second signature of cross-talk from
another aspect of the 2-body kinematics of n-p scattering. Referring to the example of
cross-talk in Fig. 5.3.2, we calculate the scattered neutron’s energy En’ from the incident
neutron energy En and the recoil proton energy Ep with eq. 5.1. From En’, we calculate the
velocity of the scattered neutron vn’. L12 is the flight path of the scattered neutron
between 111 = (x1,y1,z|) in the front wall and u; = (xz,y2,zz) in the back wall. If it is a
cross-talk event, determination of vn’ and L12 gives the flight time of the scattered
neutron. We call it the “calculated” AT, ATC. The following is the logic flow leading to

ATC:

106

 

En,Ep—> En’ —>vn’
} =5 ATc= L12/vn’ (5.6)

111, U2 —>L12=lu1-u2I

On the other hand, the actual time difference can be measured by taking the
difference between the TOF of the first scattering, (TOF)1 , and that of the second

scattering, (T OF)2. We call it the “measured” AT, ATm.
ATrln = (TOF); - (TOF)] (5.7)

For neutron cross-talk events, ATc should be equal to ATm. The ATc-ATm
distribution function peaks at zero, but again, due to uncertainties of measurements, the
peak has a finite width. Since the two scatterings in a real 2-n event are not correlated by
2-body kinematics, ATc does not represent the time difference between them. Hence ATC-

ATm tends to be random for real 2-n coincidences.

5.3.5 Ep ’_<E,, ’( signature #3 0f cross-talk)

In a cross—talk event, the energy Ep’ of the recoil proton in the back wall should be
less than or equal to the energy En’ of the neutron coming from the first scattering in the
front wall. In a real 2—n event, that is not necessarily true because the two scatterings
involve two different neutrons from the source. Ep’ could be larger than En’. So, Ep’ S En’

becomes the third signature of cross-talk.

107

We have introduced the three signatures of cross—talk between the front wall and
the back wall. Cross-talk within one wall has all three signatures, too. But the first

signature, (COSG)c-(COSG)m=0, is not used because the geometric configuration of the

cells in one wall destroys our ability to determine (COSG)m, as illustrated in Fig. 5.3.4.

5.3.6 Monte-Carlo Simulation

In order to check the signatures of cross-talk, a Monte-Carlo code has been written
based on the code developed by R. A. Cecil et al. [54]. Our modifications of the code are

listed below:

a. Implementation of measured neutron differential cross sections for n-p and n-C
elastic scattering. The data were retrieved from the National Nuclear Data Center
(NNDC). The energy dependence of the angular distributions was parameterized.
Parameter interpolation is used in the code to get the differential cross section for

continuous energy values.

b. Consideration of a neutron’s reaction in the Pyrex glass cell. The Pyrex is
composed of oxygen, silicon, boron, sodium and aluminum, and more than 80% of the
material is oxygen and silicon. In order to simplify the simulation, B and A1 are treated as
O and Si respectively. Since the atomic mass number of Na is between those of O and Si,
half Na is treated as O and half is treated as Si. All data, including total cross sections
with O and Si and differential cross sections for elastic scattering with O and Si, are

obtained from the NNDC.

108

 

/7 (XZ‘YZ'ZZ)

@— _' __ , ,
(xi-Yi-zl)

 

 

 

n, I

11 source I

Neutron Wall

Figure 5.3. 4 Side view of two neutrons detected in neighboring cells. Because it is
impossible to determine the exact positions where the neutrons scattered, 0 can vary from
almost 0° to 180°.

109

c. Input of the geometric configuration of the detection system. In the original

code only one detector was treated. The modified code deals with 50 detectors.

d. Fitting of light response function. Parameters for different charged particles are

in Table 5.3.2.

A study of neutron cross-talk was conducted with the code to simulate its effect
on a measurement of the two neutrons from 11Li breakup. 11Li has two loosely bound
halo neutrons. When llLi goes through a strong Coulomb field [10], it may absorb a
virtual photon with an energy greater than the two-neutron separation energy of 11Li, and
hence break up into two neutrons and a 9Li. The difference between the energy of the
photon and the two-neutron separation energy is referred to as the decay energy. The two
neutrons and 9Li are assumed to share the decay energy according to the momentum

distribution in 3-body phase space.

In the code, the two neutrons are traced as they go through the neutron walls. If
both neutrons are detected, we have a real 2-neutron event. If only one of the neutrons is
detected, but in two different cells, we have a cross-talk event. This simulation makes it
possible for us to make a direct comparison between real coincidence events and cross-
talk events. Furthermore, it can show the reliability of our method to identify cross-talk
events from real 2-n events. The llLi beam energy we used in the code is 25 MeV/u. We
chose 1.0 MeV as the 11Li decay energy. The neutron walls are set at zero degrees
relative to the beamline and perpendicular to it. The first wall is 5 meters from the

source. The second wall is 1 meter behind the first one. The results of the simulation are

110

shown in Table 5.3.3 and Fig. 5.3.5. Table 5.3.3 gives the number of real 2-n events and
cross—talk events detected by the neutron walls when one million 11Li breakups occur.
The events are categorized into the events between the two walls, the events within the
front wall and the events within the back wall. In Fig. 5.3.5, Plot (a) gives (COSG)C-
(COSG)m distributions for the 2-neutron coincidence events between the two walls. The
solid histogram is for all the 2-n events, both real and apparent, whereas the dashed
histogram is for the real 2-n coincidences only. Their difference is the distribution for
cross-talk events. The cross-talk events form a peak at zero, as we expected. Plot (b)
gives ATc-ATm distributions for the 2-n events between the two walls and plot (0) gives
ATc-ATm distributions for the 2-n events within one wall. As in plot (a), distributions for
all the 2-n coincidence events and for the real 2-n coincidence events are plotted. Again,

the peaks around zero are the result of cross-talk.

The spread of the peaks for the cross-talk events is due to the uncertainty of the
measurements. The uncertainty parameters used in the code are: time resolution(0',) = 0.4
ns, position resolution(op) = 5 cm, light collection uncertainty(ol) = 10% for a light
output of 1.0 MeVee and the attenuation length in the NE-2l3 = 160 cm. Among the
parameters, light collection uncertainty is due to the statistical fluctuation in the amount
of light collected by the phototubes. It is proportional to l/LUZ, where L, the light
produced by charged particles, such as protons, alpha particles and carbon nuclei, is in
units of MeVee. The asymmetry of the peaks in the AT c-AT m distributions for cross-talk

events is due to neutron multiple scattering. Sometimes neutron scattering with C or H,

111

Between Two Walls Between Two Walls Within One Wall

 

 

 

 

 

 

 

 

 

 

 

 

   

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(case).—(coso)_ nr,—Ar.. (nu) AL—AT. (m)

Figure 5.3. 5 The results of a Monte—Carlo simulation in which two neutrons from llLi
breakup are detected by the neutron walls. Given by the solid histograms, “total”
represents all the two-neutron events detected by the walls. Given by the dashed
histograms, “real coin” represents the real two—neutron coincidences. G1, G2 are the gates
used to reject the cross-talk events. (a) (COSO)c-(COSG)m distribution for the events
between the two walls. (b) ATC-ATm distribution for the events between the two walls.
(0) ATc—ATm distribution for the events within either the front wall or the back wall.

112

otal 2-n events
events

events

otal 2-n events
events

events

otal 2-n events

events

events

 

Table 5.3. 3 Number of 2-n events detected by the neutron walls when one million 11Li
breakups were simulated.

113

especially with C, generates too little light to be detected. However the deflected neutron
may generate enough light to be detected in the next scattering in the scintillator.
Although multiple scattering can make (C080)m either larger or smaller, multiple
scattering always increases the neutron flight path, and hence can only increase ATm.
That is why the (COSE))c-(COSG)m peak is symmetrical while the ATc-ATm is asymmetric,

with a tail on the negative side.

The results of the simulation clearly show us the differences between cross—talk
events and real 2-n events. Based on these differences, as well as EP’SED’, cross-talk

identification can be achieved.

5.3.7 Steps for neutron cross-talk identification

From the signatures described in sections 5.3-5.5, we found that cross-talk events
form a peak at zero in both the (COS0)c-(COSO)m distribution and the ATc-ATm
distribution, and they have the property that EP’SED’. Therefore, we can reject cross-talk
events by setting gates around zero on the two distributions and by requiring EP'SEn’. The
setting of the gate should be determined by the spread of the distribution of the cross-talk
events. For convenience of explanation, we denote G as the gate on (COS0)c—(COS0)m
and G2 as that on ATc-ATm, as indicated in Fig. 5.3.5. C3 is the third condition that
EP’SEn’. From the result of the 11Li breakup simulation, we can see that there are some

real 2—n events mixed with cross—talk events in the cross-talk region. When we reject

cross-talk events, we cannot avoid losing some real 2-n coincidence events. In choosing

114

choosing gates, the goal, of course, is to reject most of the cross-talk events and keep
most of the real 2-n events. It is important to realize that a 2-n event is considered a
cross-talk event only if it is found in both of the gates G1, G2 and it satisfies C3. For real
2—n events the three conditions are not correlated. Even so, some real 2—n events may
satisfy all three conditions. For events within the front wall or within the back wall, only

G2 and C3 are used (refer to section 5.5).

Here are the three steps to tell if an event between the walls is a cross-talk event

after G1, G2 are chosen and C3 is considered.
(3) Calculate (COSG)c—(COSG)m. Is it within G1?
(b) Calculate ATc—ATm. Is it within G2?
(0) Calculate En’ and Ep’. Does it satisfy C3?

Only if the answer is “yes” for all the three steps, is the event identified as a

cross—talk event. For 2-n events within one wall, only the last two steps are used.

In the simulation for 1‘Li breakup, the method was used to identify the cross-talk
events. G1 was set from -0.2 to 0.2 (Fig. 5.3.5). G2 was set from -12 ns to 2 ns. The
results of the simulation for 2-n events between the two walls are listed in table 5.3.4. In
this particular simulation, we had 27,390 2-n events, of which 20,985 were real 2-n
events and 6,405 were cross-talk events. There were 7,340 events satisfying G1, G2 and
C3, of which 5,013 were cross-talk events and 2,327 real events. By taking the 7,340

events out as cross-talk events, we rejected 78.3% of the cross—talk events and at the same

115

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Real events 20,985
Cross-talk events 6,405
Total no. of events 27,390
Real events

in G1 10,995
in G2 3,981
satisfy C3 10,931
in G1 and in G2 2,746
in G1 and in G2 and satisfy C3 2,327
retained real events 18,658
Cross-talk events

in GI 5,904
in G2 5,474
satisfy C3 6,251
in G1 and in G2 5,118
in G1 and in G2 and satisfy C3 5,013
retained cross-talk events 1,392
% of identified cross-talk 78.3%
Loss of real events 11.1%
Cross-talk percentage of total 2-n events (before) 23.4%
Cross-talk percentage of total 2-n events (after) 6.9%

 

 

 

Table 5.3. 4 Results of the simulation of 11Li breakup for 2-n events between the two
walls. G1 and G2 are the gates set on (COS(¥))c—(COSG)m and ATc-ATm distributions,
respectively, shown in Fig. 5.3.5. C3 is the condition that EP’SEn’, explained in section
5 .5. In experiments, all the 2-n events which fall in G1, G2 and satisfy C3 are rejected as
cross-talk events.

116

time lost only 11.1% of the real 2-n events. This reduced the cross-talk impurity from
23.4% to 6.9%. Using G2 and C3, we also identified the cross-talk events within one
wall. G2 was set from -10 us to 2 ns. Following the same procedure used for 2-n events
between the two walls, we rejected 79.6% of the cross—talk events and lost 26.8% of the
real 2-n events. The cross-talk impurity was reduced from 22.9% to 7.7%. Because only
two conditions can be used for 2—n events within one wall, we lose more real events in

this case than we do in the case for 2-n events between the two walls.

Since cross-talk identification depends on the three gates, the success of the
method depends on how the gates are set. The gates depend on the spread of the
(COSE))c-(COSG)m and ATc-ATm distributions for cross-talk events. The spread is going
to be different for different detection systems. For any system, there will always be the
need for a software trade-off between size and purity of the event set. The higher the
purity demanded, the greater the number of good events sacrificed. The choice is made

by the experimenter.

5.4 Experiment

5.4.1 Setup
A test experiment was performed at the NSCL using the reaction:
7Li + p —+ n + 7Be - 1.64 MeV (5.8)
In this reaction, only one high-energy neutron is produced. Therefore, all the 2-n events

detected by the neutron walls were cross-talk events. The purpose of the experiment was

117

to check if our simulation code gives the right prediction, i.e. to see if the (COSG)C-
(C080)m and ATc-ATm distributions for cross-talk events obtained from the experiment
agree with those simulated by our computer codes. The experimental setup is shown in
Fig. 5.4.1. The neutron walls were set at 35° relative to the beamline. Concrete blocks
were placed between the downstream beam pipes and the neutron walls to shield the
walls from neutrons produced by target-scattered protons striking the pipes. Neutrons
were produced by bombarding a 0.5-mm 7Li target with 29.8—MeV protons extracted from
the K1200 cyclotron. Forty of the 50 glass cells were used in the experiment, but only 20
cells were analyzed due to problems with the pulse-shape-discrimination circuitry for the
other 20 cells. Of the 20 working cells, there were 8 cells in the front wall, from no. 5 to
no. 12, counting from the bottom. The other 12 cells were in the back wall from no. 9 to

no. 20.

5.4.2 Data Analysis

Fig. 5.4.2 shows the neutron TOF spectrum for cell no. 7 in the front wall. The
mean time of the two signals at the ends of the cell gives the start. The downscaled
cyclotron radio frequency time gives the stop. Neutrons under the sharp peaks are from
the 7Li(p,n) reaction which goes to either the ground state or the first excited state of 7Be.
The two states have an energy difference of only 0.43 MeV. The resolution of the system

is not able to distinguish between the two states. The energy of the neutrons under the

118

 

, ' Neutron Walls

29.8 MeV ./ ‘
protons - a
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100,390” 10.0

7L1 target

Beam Dump

Figure 5.4. 1 Layout of the 7Li(p,n) experiment. The front wall was placed 5 meters
from the target, 35° relative to the beamline. The second wall was 1 meter behind the
first one. The shaded area was a stock of concrete blocks

119

 

80 I l I I I I l l l I I I l I I l I I I I f

 

 

 

 

~ 26.5 MeV -
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0 M I l l I I l I l l l I l l l I I I _

0 50 100 150 200 250

TOF (ns)

Figure 5.4. 2 Time-of-flight spectrum for neutrons detected in cell #7 in the 7Li(p,n)
experiment. The signal of cell #7 gave the start and the downscaled cyclotron radio
frequency signal gave the stop. The sharp peaks are from neutrons produced in the
reactions leading to either the ground state or the first excited state of 7Be.

120

peaks can be determined from their reaction angles by 2-body kinematics. The energy
loss of the protons in the target was 0.4 MeV. Using an average of 0.2 MeV, the energy
of the neutrons under the sharp peaks detected in the front neutron wall ranges from 25.4
MeV to 27.3 MeV, depending on where the neutrons strike the wall, i.e., on the reaction
angle. The neutrons outside the sharp peaks in Fig. 5.4.2 are predominantly from the

reaction
7Li + p —> n + 3He + 4He - 3.23 MeV (5.9)

The 3-body final state makes the En spectrum a continuum. The energies of these
neutrons were measured by TOF. Simulations were carried out only for the neutrons
under the sharp peaks because their differential cross-sections were well measured and

those neutrons follow simple 2-body kinematics.
Here is how we treat each cross-talk event.

(a) Check for neutron pulses by n-y discrimination [32]. Reject any y-ray or

cosmic ray events.

(b) Determine the neutron scattering angle 0 by the positions of the two

scatterings. From the two positions, (COSO)m is determined.

(0) Determine the 7Li(p,n) reaction angle by the position of the first scattering.

From the reaction angle, the incident neutron energy 13n is calculated.

((1) Determine Ep, the energy of the recoil proton in the first scattering, using the

geometric mean of the pulse heights from the phototubes at the ends of the cell. PH, and

121

 

 

PH, denote the pulse heights read out at the left and right ends of the cell, and PHg
denotes the geometric mean. Due to the light attenuation in the NE-213 scintillator, PH,
and PH, are dependent upon the location of the interaction in the cell: PH, cc Ioexp(-x/7t)
and PH, cc Ioexp(-(L-x)/?t), where L, is the light intensity, x is the distance light travels
from where it is produced to the left end of the cell, L is the length of the cell, 7t is the

light attenuation length in such the scintillator. PHg is given by
PHg = (PH, ><1>H,)”2 cc I.exp(—u27.) (5.10)

Since L and )V are constants, PHg is proportional to the light produced in the
scintillator, and is independent of the location of the interaction in the cell. In order to
determine the light production of protons in terms of MeVee, each cell was calibrated
with the 2.38-MeV Compton edge of a 228Th source and the 4.2-MeV Compton edge of a
Pu—Be source. After the light output of each proton is determined, we use eq. 5.3 to

extract the proton energy Ep.
(e) Calculate (COSG)c from eq. 5.4 with En and Ep obtained from (c) and (d).

(1) Determine ATc from eq. 5.6 with En, EI) and the positions of the two

scatterin gs.

(g) ATm, the time difference between the scatterings, was measured in our
experiment. In some experiments, (TOF)1 and (TOF)2, the TOFs of the first scattering
and the second scattering, respectively, are measured. Then ATm is obtained by

subtracting (TOF)2 from (TOF)] (eq. 5.7).

122

Following the procedure from (a) to (g), we get (COSG)c—(COSG)m and ATc-ATm

for each 2-n event.

5.4.3 Results
In Fig. 5.4.3, the (COSB)c-(COSG)m and ATc-ATm distributions for those neutrons

under the sharp peaks in Fig. 5.4.2 are plotted with the open symbols. The histograms are
the results of our simulation. All the histograms are normalized according to the areas
covered by the data points. Our simulation results are in good agreement with the
experimental data. The data points in plot (a) are not exactly centered at zero, as the
histogram is. The shift of 0.025 may be due to some error in the measurement of the
proton energy. Using eqs. 1 and 2, we found that a systematic overestimation of 0.65
MeV in Ep could cause the 0.025 shift in the (COSG)c-(COSG)m distribution. Two
possible sources of this overestimate are an error of a few percent in the light response

function [53] or in the proton beam energy. Otherwise, all the measured features of the

cross-talk agree with the features in the simulation.

Fig. 5.4.4 shows that the distributions for all the neutron cross-talk events, those
initiated by the 2-body reaction (eq. 5.8 and the sharp peaks in Fig. 5.4.2) and those
initiated by 3-body reaction (eq. 5.9 and the continuum neutrons in Fig. 5.4.2), are similar

but somewhat broader than those for the 2-body reaction alone.

123

 

b—l

Between Two Walls Between Two Walls AI Cross—talk
so .. . . roo

 

 

 

   

 

 

 

 

 

..I-...I ...l lllll
_ (a)
150— —
N .
2 5- 5- .0.
g Q Q _
E
o E E I
U u u
50— —
‘ _ ..I. I
— —0.5 0.0 0.6 1.0 —30 —80 —10 0 10 20 80 :10 —20 —10 0 10 20 30
(ocean—(cone). AT.—A'l'. AT,-AT

Figure 5.4. 3 Cross-talk distributions for the neutrons under the sharp peaks in Fig. 5.4.3 from
the 7Li(p,n) experiment. The experimental data are given by open symbols. The histograms
are the results of our simulation. (a) (COSI‘))c-(COS(9)m distribution for the cross-talk events
between the two walls. (b) ATc-ATm distribution for the same events in (a). (c) ATc-ATm
distribution for all the cross-talk events.

124

500

400

2’; 300

O

\

E

8 200
100

I
f"
c

Figure 5.4. 4

Between Two Walls

 

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0

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O 0

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2" lllllljllllllellllJllll

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-0.6 0.0 0.6
(COBOL-(€080).

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COUNTS/0.5m

Between Two Walls

 

2150'

200

150

100

VI.

r
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d

(b)

o

6’

q;
0
o

80

9

0
0
0
9
8
0

e°'”

-20 -1o 0
org-41'. (ns)

—

11.11 '1 ll

 

108080

COUNTS/0.6m

300

200

04
-30 -20 --10 0

All Cross—talk

 

r

P

t

 

IIU'IUUI'IUIIIIUIU'IY'VTIUI

.1
Q .
Q) .
o d
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O -t
0 o _,
0 cl
0 ..
o q

9 o
C 0 —;
O 0 .,
° 1

D
10 80 30

(a)

 

51,—“. (m)

Cross-talk distributions for all the neutrons from the 7Li(p,n)

experiment—{hose from the 2-body reaction (eq. 5.8) and those from the 3-body reaction
(eq. 5.9). (a) (COSG)¢—(COSG)m distribution for the cross-talk events between the two

walls. (b) ATc-ATm distribution for the same events in (a). (c) ATc-ATm distribution for

all the cross-talk events.

125

 

5.5 Summary

A method has been introduced to identify the cross-talk events in multi-detector
systems in the energy region up to 25 MeV. In this method, three signatures of cross-

talk, (COSO)c-(COSG)m=O, ATc-ATm=0 and Ep’SEn’, were established using the n-p elastic

scattering kinematics. The three signatures were then studied by a Monte-Carlo
simulation. Following the identification procedure presented in the paper, we rejected
79% of the neutron cross-talk events in a simulated llLi breakup experiment. The cross-

talk effect was significantly reduced.

A 7Li(p,n) experiment was performed to check our simulation code. The
(COSG)¢-(COSG)m and ATc-ATm distributions from Monte-Carlo simulation were
compared with experimental data. The consistency between the experimental data and
the simulation results proves that neutron cross-talk identification can be achieved in 2-n

coincidence experiments.

Our method is based on the 2-body kinematics. In principle, it can be applied to
identify neutron cross-talk in any organic multi-detector system. How well it works

depends on the specific configuration and the neutron energy.

126

 

APPENDICES

Appendix A: Calibration of Fragment Detectors

A.1. Neutron Walls

For a 6He dissociation event detected in the experiment, the momenta of the
neutrons and the 4He had to be accurately measured. To determine a neutron’s
momentum, we have to know the velocity and the direction of the neutron. The velocity
of a neutron was determined by dividing the travel distance, which is from the target to
where it was detected in a cell of a neutron wall, by the time of flight (TOF) of the
neutron. The direction of the neutron was determined from the position of the neutron on
the wall and the position of the target. The latter was fixed and easily measured before

the experiment.

A.1.l. Neutron TOF

A neutron is detected through the light generated in the interaction between the
neutron and the scintillator material—Carbon and Hydrogen. The light is collected by
both PMTs at the ends of one cell. The time signal is picked up from the anode of a
PMT. In the experiment, the time difference between each PMT triggered by a neutron,
and the scintillator bar triggered by a 4He fragment was measured. Let TL be the time
difference between the left PMT (viewing from the target) and the scintillator bar, TR be
the time difference between the right PMT and the Scintillator bar. x is the distance from

the detection spot to the left PMT. Then

TL =1+AT0F+c,, (A.1)
V

127

where v is the velocity of light in the scintillator, ATOF is the time difference between
the cell and the scintillator bar, c1 is the constant of the electronic devices. Likewise,

TR = £35 + ATOF + c, , (A.2)
V

where l is the length of the cell. As shown in eqs. Al and A2, TL and TR are position
dependent. On the other hand, if eq. A2 is added to eq. A. 1 , the equation becomes

gl%§l=-2L+AT0F+-C‘—:c—2=ATOF+C, (A.3)
V

which is position independent because x is eliminated from the equation. In the
experiment, time calibration was conducted with the "y rays which were produced when
the primary beam 180 stopped in the scintillator bars. The 18O beam was used because it
was the most intense beam in the experiment. Almost all the 180 particles stopped in bar

#9. What we are interested in are those 'y rays which, produced in bar #9, were detected

TL + TR

 

in the neutron walls later. When the spectrum is plotted for the coincidence

events, a 7 peak can be observed as shown in Fig. A. 1. The 7 peak corresponds the time
for a y ray to travel from bar #9 to the front neutron wall. The distance between the bar
and the center of the front wall is 332 cm, which gives ATOF =11.1ns. Therefore, the 7

peak becomes the reference time. The ATOF of any event was determined relative to the
peak.

For a neutron coincidence event, ATOF is not the final TOF we are interested in
because it only measures the difference between the time for the neutron to reach the

neutron walls and the time for the fragment to reach the scintillator array. We are only

128

20

Yield (counts)

0
0

 

.1. 1.1.1.11 ..1

 

‘y-ray

 

 

 

I l
1000 1500 2000

TOF (ns)

Figure A. 1 The time of flight (TOF) calibration. The y rays, produced in scintillator
bar #9 by a 18O beam, were detected in the front neutron wall. The flight time for a y ray
between the bar and the front neutron wall is 11.1 ns.

129

interested in the absolute time of flight for the neutron, i.e. the neutron TOF from the
target to the detection spot in the neuron walls—-T0F,l from which neutron energy can be
determined. The relation between TOF,, and ATOF is ATOF = TOF,, —TOFf, where
TOF] is the fragment TOF from the target to the scintillator array. The neutron TOF can

be calculated with

TOF,, = ATOF + TOF, . (A.4)

In order to find TOFf, we have to know the velocity of the 4He fragment and its flight
distance. The velocity of the 4He was determined from the energy measured by the
scintillator array in an event—by-event base. Because the 4He fragment was deflected by
the magnet used in the experiment, it seems that the flight distance depends on the
trajectory of the fragment. It is possible to use the mapping result to find the trajectory of
each 4He, then the flight distance. However, the flight distance from the target to the
scintillator array for the 4He fragment in the experiment was found to be pretty much
independent of the trajectory. The 4He particles, with energies from 15 MeV/u to 30
MeV/u and entering the magnet at different positions, were sent through the magnet in a
program written to track the trajectories of the charged particles. The flight paths,
averaging 180.38 cm, range from 176 cm to 185 cm. If we use the average flight path for
all the 4He in the experiments, its contribution to the error of the neutron TOF is expected

to be less than 1 ns.

Al.2 Neutron Position

130

When a neutron wall was placed in the N4 vault, every cell’s position in the wall
was fixed. The position of a cell was represented by the center of the cell. The position
of a neutron in a cell is measured by taking the difference between TL and TR (referring to
eqs. Al and A2):

TL-TR=2—:+%+cl—cz=2—:+c (A.5)

So, TL — TR is proportional to x. Shown in Fig. A2 is a TL — TR spectrum for a cell of the
neutron walls. The data were collected with cosmic rays showering every cell evenly.
The middle point of the spectrum corresponds to the physical center of the cell. The two
shoulders correspond to the two ends of the cell. The length of the cell is divided by the
channel number between the half height of the shoulders to obtain the conversion

factor—from channel number to length.

A.2. Scintillator Bar Detectors
A2. 1. Energy calibration

Both 6He beam and 4He fragment stopped in the scintillator bars. For each
charged particle detected, light was collected by the two PMTs at the ends of a bar. The
geometric mean of the two signals was used to determine the energy of the particle (refer
to eq. (5.10). However, the geometric mean is not proportional to the energy of charged
particles but the intensity of the light output. Fox et al. measured the response of plastic

detectors for a wide range of incident particles and energies [55]. The response function is

131

 

 

 

 

 

1- I I I I I I I I I I I I I I I I -
4000 — _
A __ -—
3 3000 _
= _
= " -1
8 ' '1
v _ -
"U 1
-- 2000 — I , —
.2 Left end right end .
>1 i
1000 — _
O -. I I I l l I 1 l J l I I I
900 1000 1100 1200

TL - TR (channel)

Figure A. 2 The position distribution of cell #1 of the front neutron wall. The two edges
give the calibration points for the position of the cell.

132

“E (1+ R)2d—E

L:SoE—SokBojOE/a—LdEdE—Sok—BOI; ————dx—dE—dE (A.6)
1—kB— 2 ° 2+kB(1+R)——
dx dx

whereR=ln[%)/ln(%0%). The fixed parameters are E—particle energy,

dE 4m . . . .
E—energy loss, a =—‘—nucleon rest mass, and I—ronrzatron potential of the
0

scintillator(z 0048 keV for plastic scintillator). The free parameters are S—gain factor
of the device, kB—quenching factor, and To—the electron kinetic energy cutoff. The
three free parameters determined in the paper were used in the response function to
convert fragment energy (in unit of MeV) to light output (in unit of MeVee) and vice
verse. The scintillator bars were calibrated with two 4He beams at 100 MeV and 80
MeV, and the 4.44-MeV 'y ray from a Pb-Be source available at the NSCL. The two 4He
beams were chosen in such a way that most of the 4He fragments in the experiment fell
into the energy range given by the two beams. After losing energy in the Si detectors, the
energies of two 4He beams were reduced to 96.01 MeV and 75.3 MeV, respectively. The
light outputs for the three calibration sources are 49.5 MeVee, 35.2 MeVee and 2.38
MeVee respectively. Fig. A.3 shows the light outputs of the three light sources versus
the measured geometric means for bar #1. The slope gives the conversion factor. When
a 4He fragment detected, its geometric mean is converted into light output. Then, from
eq. (5.10), the energy of the 4He is determined.

With the field of the magnet set at the maximum, the 96.01 MeV 4He could only

reach bar #10, not the bars from bar #11 to #16. The field of the magnet was reduced for

133

 

I I I I I I T 7 I I I I I I l I I I I I I I

Channel

I I I I l l J | l l l I I I l l l I I l l

 

 

 

o I l I l l I I I I l I I l I l I I I l l I I I l l I
O 10 20 30 40 50

 

Light Output (MeVee)

Figure A. 3 The energy calibration of scintillator bar #1. The three calibration points in
the graph are from 2.61 MeV 'y ray of a Pb-Be source, 80 MeV and 100 MeV 4He beams,
respectively.

134

the beam to reach the bars from bar #1 to bar #9. Calibration was done for the 10 bars
with the three calibration sources. In order to calibrate the six bars from bar 11 to bar 16,
a 10 MeV/u 6Li beam was chosen to inter-calibrate the scintillator bars. The gains of the
the six bars were matched to that of bar #1. To calculate the light output of fragment in
these bars, the geometric mean is first scaled to that of bar 1, then the calibration

parameters of bar 1 are used for the conversion.

A.2.2. Inter-bar time calibration

The neutron TOF is measured from the time difference between a cell, where a
neutron is detected and a scintillator bar, where a fragment is detected. Since the time
signals of the 16 scintillator bars were processed by difference channels of electronics, the
TOF must be corrected for the time variance between the channels. The inter-bar time
calibration was conducted by using a 60C0 source. The source was placed at the same
position where the Si strip detectors were mounted. Because 60Co emits two Y rays at a
time—1.33 MeV and 1.17 MeV, Coincidence between the neutron walls and the
individual scintillator bars can be produced. Since the flight time from the source to the
bars is almost the same, the difference between the peak positions measures the time

variance of the electronics.

A.3. Si Strip Detectors
Fig. 2.7 shows a sketch of the target and the Si strip detectors in the experiment.
The two Si strip detectors were placed behind the target to detect charged particles. Each

detector consists of 16 horizontal strips and 16 vertical strips. In principle, when a

135

charged particle penetrates a strip detector, a signal is picked up by one horizontal strip
and one vertical strip. The location of the horizontal strip gives the y position of the
particle, thereafter called “y strip”, and the location of the vertical strip gives the x
position of the particle, thereafter called “x strip”. The direction of a charged particle is
then determined from the measured x and y coordinates. One problem with the strip
detectors is that there is cross talk between the neighboring strips. A cross-talk here
means that the pulse of electrons generated by a charged particle striking one strip would
induce smaller pulses in the neighboring strips. So, the strip that yields the maximum
signal was used to determine direction and energy loss of the particle. The amplitude of
signals in the cross talk strips was much less than the stricken strip. Another problem was
that no. 8 x strip of detector 2 did not work. The cross-talk of the no. 8 with no. 7 and no.
9 x strips was used to determine if there was a charged particle striking no. 8 strip. If
there is a particle striking no. 8 strip, a small cross-talk pulse can be found in no.7 and
no. 8 strips. A gate is set on the these pulses from no. 7 and no. 9 strips. If an event is
found in the gate of the no. 7 strip and in the gate of the no. 8 strip at the same time, the

no. 8 x strip must be stricken by a particle.

Energy signals were read out for all the 64 strips of the two detectors. The y strips
were used to measure the AE of the fragments in the experiment. To calibrate the AE of

the strips, two 4He beams at 20 MeV/u and 25 MeV/u, and two 9Li beams at the same

energies were sent to the Si strip detectors. The energy losses of the beams in the
detectors are 4.73 MeV, 3.91 MeV, 10.64 MeV and 8.78 MeV, respectively. In order to

ensure that all the strips were stricken by the calibration beams, the last quadrupole in the

136

 

N4 vault was turned off so that the defocused beam can cover all the strips vertically. A
steering dipole magnet in the beamline was adjusted to sweep the strip detectors
horizontally. In this way, calibration on every y strip was conducted. The calibration for

the no. 1 y strip of detector #1 is shown in Fig. A4

137

 

 

 

 

_ I I l I I I I I I T I I l 1 I I I .i

10 — —

A i I
>

O — _

g - _

33 8 _ _

a _

'4 .

gt - -

g ' _

tr: 6 — —

4 r —

r l | l 1 1 l l l I I I l J 1 | l | l _

200 300 400 500

Channel

Figure A. 4 The energy calibration of strip #1 of Si detector #1. The four data points are
from 20 MeV/u and 25 MeV/u 4He, 20 MeV/u and 25 MeV/u 9Li beams, respectively.

138

Appendix B: Electronics and Data Acquisition

B.1. Neutron Wall Electronics

All the information about a detected neutron is contained in the two electronic
signals from the two PMTs at the ends of a cell. One signal is a positive pulse extracted
from the last dynode and the other signal is a negative pulse from the anode. The
schematics of the electronics for the neutron walls are shown in Fig. A5. The dynode
signal is inverted to a negative signal before it is sent into a constant fraction
discriminator(CFD). The threshold of the CFD was set at 1 MeVee. The CFD generates
a logic signal for the signals with pulse height greater than the threshold. The logic signal
is split into three. (1) One is put into a T ime—to-FERA converter (TFC) as an individual
start. All the TFCs are stopped by the delayed OR logic between the fragment master
signal and the neutron wall master signal. The output of each TFC is then digitized by a
FERA (Fast Encoding and Readout ADC). Only those channels corresponding to the
fired PMTs are read out. The measured time from the PMTs is used to obtain neutron’s
TOF and position. (2) One is sent to a scaler. (3) The third one is send to form a logic
OR with the outputs of the other CFDs. The logic OR creates a gate signal for the FERAs
and a trigger signal for the trigger logic to control the data acquisition system. The anode
signal is put into the NSCL PSD circuit. There are four outputs from the circuit---”Fast”,

“Total”, “Attenuated Fast” and “Attenuated Total”, described in the n-y discrimination

section. “Total” and “Attenuated Total” were measured by FERAs, whereas “Fast” and

“Attenuated Fast” were measured with ADC’s due to the limited

139

 

PMT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure B. 1 Schematics of the neutron wall electronics.

140

 

veto stop
' dynode inverting constant time-to—digital
= transformer > fraction > converter
, discriminator
.anode It
other PMTs
ll
OR
trigger
cable delay gate
110 ns generator
V v v
Qtotal >
NSCL active Qfast = charge-to-
splitter/PSD Qtotal_att _ digital
circuit Qfast_att V converter
>

 

 

‘— clear

 

number of FERAs available in the lab. “Attenuated Total” is also used to determine the
energy of the recoil proton involved in neutron detection. The energy of the recoil proton

is needed to perform cross-talk identification (refer to Part II of the thesis).

B.2. Fragment Detector Electronics

The two signals from a PMT on a scintillator bar was handled the same way as
those from a PMT on a scintillator cell of the neutron walls except that there is no n-y
discrimination circuit. It is not necessary for a n-y discrimination because the light
produced by the fragments are much greater than those produced by 'y rays. The anode
signal was directly processed by an ADC.

The schematics of the electronics for the Si strip detectors are shown in Fig. A6.
The signals from horizontal and vertical strips were sent to a preamplifier built for the
S800 spectrometer at the NSCL. As shown in the figure, the horizontal signals are only
processed by the quad shapers for their pulse height. The pulse height was measured by 21
Philip ADC. The vertical signals were put to a quad shaper made at MSU. The slow

output of the quad shaper was used for the pulse height measurement, and the fast output

was sent to a CFD for timing.

B.3. Trigger Logic
B.3.1. Fragment Trigger
The fragment trigger logic is shown in Fig. A7 The scintillator master signal is

created by the OR of the CFDs for the 16 scintillator bars. The OR signal is used for

141

 

 

 

 

Horizontal strips

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x32
__> ssoo >~ Quad fast _, Wash.U -mLp Philips ADC
Preamp. shaper Shaper
Vertical strips
x32
8800 MSU Quad 510‘”- . .
- . Preamp. . shaper > Philips ADC
Fast
Lecroy CFD

Figure B. 2 Schematics for the Si strip detector electronics.

142

QDGG

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

scintillator veto QDC gates
flaw TDC start (Scint. Bars)
+\ I Wait for start of the event
" ’\/\/\,
/ W —— ADC gates
NIM (Si, PPACs)
Sealer live QDGG
Individual 330 ns
TDC “OP 0 x b To NW latch
To NW
trigger QDGG
NW dead m Veto scint live
time latch ——% x ‘
3
400 ns . NW fast
in clear Clear
NIM ve . QDCs, TDCs
NW fast clear <
End of event
I ADCs
(NIM out) C 63’
200 ns
TDC stop
Si Master
..h
_>
. S
caler
+
_>
QDGG
__ . ' x Si bit
NIM

 

 

 

 

 

 

Figure B. 3 The fragment trigger logic. The scintillator trigger logic is on the top. The
Si trigger is in the box on the bottom.

143

master trigger, which will be described later. It is also used to make the scintillator
master live signal after an AND operation with a computer not busy signal (1W ). The
master live signal is used for the following logic: (1) It is processed by a quad delayed
gate generate(QDGG) to produce a gate for the QDCs of the scintillator bars. (2) It
creates a gate for the Si detectors. (3) It starts the TDCs for the scintillator bars. The
TDCs are stopped by individual PMTs on the bars. (4) It is delayed 330 ms to latch the
neutron walls so that the neutron walls won’t be disturbed by an event coming shortly
after the previous event. We used 330 us to ensure enough time is left for the neutrons,
produced with the charged fragment, to reach and fire the neutron walls. (5) The OR
logic between the master live, the neutron wall dead time signal and the delayed clear
signal is used to veto scintillator live so it is also not disturbed when an event is
processed. (6) If the computer is still doing nothing after 400 ns, the master live clears all
the electronic modules (QDC, TDC, etc.) and wait for the next event to come.

The Si master signal is produced by the OR of the 32 vertical strips. After
delayed 200 ns, it serves as the TDC stop. The TDC is started by the neutron wall master
signal. The time difference was supposed to measure the neutron TOF. Due to poor time
signals, the Si master signal was not used for the measurement. It is sent to a Bit Register
(BR) to represent a Si single event. Being a passive bit, the Si master was not used to

trigger the data acquisition. Si data were read out whenever a scintillator bar was fired.

B.3.2. Master Trigger Logic
The logic of the master trigger for the experiment is very similar to the one

described in [56]. In an experiment like this, we measure three types of events. The first

type is neutron wall singles events in which only the neutron walls are fired. The second
type is fragment singles events in which only the scintillator array is fired. The third type
is coincidence events in which both the neutron walls and the scintillator array are fired
within 250 ns. The coincidence period is chosen so that the slowest neutrons can reach
the neutron walls. The three types of events are represented by three bit—bits l, 2 and 3
in the Bit Register. So computer starts reading data whenever a logic signal for one of the
three types triggers the data acquisition system. Because the number of singles events
overwhelms that of coincidence events, the singles events were downscaled by 500. If a
singles event does not pass the downscaler, a fast clear signal is generated to clear all the
electronic modules. By doing so, the dead time of the electronics was greatly reduced.
Other than the three bits for the three types of events, each scintillator bar uses one bit in
the Bit Register so that when a fragment is detected, a computer is directed to read out

the data from the scintillator bar, which detects the fragment.

145

Appendix C: Cross-talk Simualtion Programs

I have written a group of simulation programs for the cross-talk in the neutron
walls. All the programs are located under the directory:
USER_LOAN 2: [NEUTRON.EFF]
in the computer network at the National Superconducting Cyclotron Laboratory (NSCL).

The names of the programs and what they do are given below.

 

WALLGPN_LI7.FOR Calculate the (cos0)c-(c080)m and (AT)c-(AT),..l distributions
of the cross-talk events between the two walls.
The neutrons are from the 7Li(p, n) reaction. (Fig.

 

WALLGTOF_LI7.FOR Calculate the (AT)c-(AT)m distribution of the cross-talk
events between the two neutron walls and within one wall.
The neutrons are from the 7Li(p, n) reaction.

 

WALLGNN_LIl 1.FOR Calculate the (cos(9),~,-(cos(9)1m and (AT),,-(AT)m distributions
of the cross-talk events between the two walls. The neutrons
are from the 11Li breakup: llLi —> 9Li + n + n.

The simulation uses the 3-body phase space model.

 

 

WALLGTOF_L111.FOR Calculate the (AT),.,-(AT)m distribution of cross-talk events
between the two neutron walls and within one wall. The
neutrons are from the 11Li breakup: 11Li —-) 9Li + n + n.
The simulation uses the 3-body phase space model.

 

 

All the subroutines used in the four programs are stored in a program called
WALLSUB.FOR. To run any one of the four main programs, one has to use a command
file and an input file. The input file name is the same for all the programs. It is called
WALLGS.INP. The command files has the same names as those of the four main
programs except that the extension of the command files is COM, e.g.
WALLGNN_L111.COM. To run program WALLGNN_LIl 1.FOR, one has to modify

WALLGS.INP according to his or her own specifications (beam energy, wall

146

 

 

configuration, etc.), then run WALLGNN_L111.COM. The input parameters one may
want to change are listed below,

1. The positions of the two walls (inches)

2. The threshold for the cells (MeVee)

3. The average decay energy in the MU simulations (MeV).

4. Beam energy (MeV)

5. Time of Flight resolution (ns)

6. Fragment energy resolution (%)

7. Attenuation length in the scintillator (inches)

 

8. The gates for cross-talk identification. (Refer to Fig. 5.3.5)

These input parameters can be easily located in the file WALLGS.INP because
they are labeled. The outputs of the programs are the simulation results shown in Fig.
5.3.5 and Fig. 5.4.3. The programs can be adapted to do cross-talk simulations for any
neutron source and for any neutron detector configuration. Sally Gaff at the NSCL has
successfully adapted the programs for her thesis experiment. I would like to say, Good

Luck, to anyone who likes to explore the programs.

147

Bibliography

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[3] T. Kobayashi et al., Physics Review Letters 60 (1988) 2599
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[5] I. Tanihata et al., Nuclear Physics A478 (1988) 795C

[6] I. Tanihata et al., Nuclear Physics A522 (1991) 275C

[7] T. Kobayashi et al., Physics Letters B232 (1989) 51

[8] T. Kobayashi et al., Proc. lst Int. Conf. on Radioactive Nuclear Beam (1989) 325
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[10] D. Sackett et al., Physics Review C48 ( 1993) 118

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150

 

 

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