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HIGH-ENERGY GAMMA RAYS IN HEAVY-ION COLLISIONS

BY

Anna Rosa Lampis

A DISSERTATION

Submitted to
Michigan State University
in partial fu1fillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics

1988

ABSTRACT

HIGH-ENERGY GAMMA RAYS IN HEAVY-ION COLLISIONS

By

Anna Rosa Lampis

The production of high-energy gamma rays (BY) 20 MeV) in

intermediate-energy heavy-ion collisions was studied in the following
reactions: N + C, N + Zn and N + Pb for beam energies of E/A=20, 30 and
150 MeV. The double differential cross sections are exponentially
decreasing with energy, and the value of the inverse slope is only
weakly dependent on the target mass and ranges between 8 and 1A HeV for
beam energies between 20 and 110 MeV. The angular distributions are
slightly forward peaked and can be associated with an isotropic emission
in a frame moving with velocity close to the nucleon-nucleon center of

mass velocity.

2

The coincidence between light fragments (1H, H, 3H) and high-
energy gamma-rays in the reaction N 4- Zn at E/A=AO MeV was studied to
investigate the impact-parameter dependence of the high-energy gamma-ray
production. Energy spectra and angular distributions of protons in
coincidence with gamma rays were found to be very similar to those of

inclusive measurements. The ratio of the coincidence cross-section to

the product of the singles cross sections as a function of both proton

and gama-ray energy and angle was found to be fairly constant with an

-1
average value of 0.6 barn . A comparison between the charged-particle

multiplicity associated with the emission of a gamma-ray and the
charged-particle multiplicity associated with the emission of a charged-
particle does not indicate any substantial difference in the impact
parameter dependence of the two processes.

with two Monte Carlo codes we simulated the gamma-ray production
respectively as a product of first chance n-p collision and as a product
of secondary collisions. The ratios calculated with the first model
decrease slowly with energy, showing an anticorrelation in the energy of
the two particles as a consequence of the limited energy available in
the interaction. Such a limitation is removed in the second model which
offers a better agreement with the experimental results and suggests

that gamma-ray emission might not be limited to first n-p collision.

To my mother's courage and

and my husband's love

iv

ACKNOWLEDGEMENTS

I wish to»thank Prof. John Stevenson, my research advisor, for his
guidance and support during the last two years of my graduate career.
The helpful suggestions and patience at the weekly meetings to discuss
the status of my research are gratefully acknowledged.

Many thanks go to Prof. Walter Benenson for providing critical
coments on the content of this thesis and to Prof. George Bertsch for
the many helpful discussion on the results of the coincidence
experiment.

To Dr. Robin Smith I am indebted for answering my endless questions
about experimental physics. His friendship made long hours of data
analysis not only bearable but pleasant.

Appreciation is extended to Dr. Dan Fox for taking care of the
electronics set-up of the charged-particle detectors for the coincidence
experiment and to Ken Wilson for his work on the analysis of the charged
particle detector calibration data.

The help provided by Dr. John Winfield on the road to understanding
and modifying pieces of the data analysis software was greatly
appreciated.

It is with deep gratitude that I wish to thank my husband, Jon

Slaughter, for it is his love and understanding that sustained me during

the difficult moments of this enterprise. His critical coments and
carefu1 reading of the thesis were most welcomed and appreciated.

Many hearty thanks go to my office-mates Wen Tsae Chou and Mary
Wilson, to Silvana Angius and Aldo Bonasera. Their friendship made long
hours of work more pleasant and their help solved many practical
problems.

Last but surely not least, I would like to thank my parents, for
their constant love and support were never diminished by the distance.

A special thanks goes to my mother: her beliefs in the value of higher

education and self-discipline were instrumental in my education.

vi

TABLE OF CONTENTS

Page

LIST OF TABLES ................................................. x
LIST OF FIGURES ................................................ xi
INTRODUCTION
A. Motivation ................................................. 1
B. Thesis organization ........................................ 2
CHAPTER I
HIGH-ENERGY GAMMA RAYS
A. Experimental set-up ........................................ A

1. High-energy gamma-ray detectors ............................ A
B. Electronics ................................................ 6
C. Calibration ................................................ 7
D. Data reduction ............................................. 11
E. Results .................................................... 21
CHAPTER II
HIGH-ENERGY GAMMA RAYS: DATA COMPARISON AND THEORY
A. Experimental comparison .................................... A9
B. Theoretical models ......................................... 52

vii

1. Bremsstrahlung ............................................. 52

1a. nucleus-nucleus bremsstrahlung ........................... 5A

1b. nucleon-nucleus bremsstrahlung ........................... 5A

1c. nucleon-nucleon bremsstrahlung ........................... 55
2. Thermal emission ........................................... 67
CHAPTER III

HIGH ENERGY GAMMA RAYS - CHARGED PARTICLE COINCIDENCE

A. Experimental set-up ........................................ 73
1. AE-E detectors ............................................. 76
2. High-energy ganma ray detectors ............................ 76

B. Electronics ................................................ 76

C. Charged particle detector calibration ...................... 82

D. Data reduction ............................................. 90

E. Results .................................................... 9A
1. Ratios ..................................................... 9A
2. Multiplicity ............................................... 105

CHAPTER IV

INTERPRETATION OF THE COINCIDENCE RESULTS

A. Impact parameter dependence ................................ 118
B. n-p bremsstrahlung model ................................... 131
C. Thermal model .............................................. 1A2
D. Correlated and uncorrelated coincidences ................... 152

viii

SUMMARY AND CONCLUSIONS ........................................ 161

LIST OF REFERENCES ............................................. 164

ix

TABLE

1-1

1-2

1-3

111-1

III—2

III-3

III-A

III-5
III-6

IV-l

LIST OF TABLES

2

d o

 

Calibration-correction factors for
Y

Parameters from the best fit to the high energy ganma

ray data for EY)35 MeV ...................................

Total cross sections at 90° for gamma rays energies

above 20 MeV .............................................

Plastic scintillator properties ..........................

Lower and upper energy limits fer charged particles

detected in the AE-E telescopes ..........................

Angular position, distance and solid angle covered for

each charged particle detector ...........................

Comparison of R(6p) values for the out-of-plane and the

in-plane phoswich at 6=A0° ...............................
Source velocities ........................................

Multiplicities: Y - c.p. and c.p. - c.p ..................

Values for the ratio obtained with the assumptions of
equations IV-S, IV-11 and IV-13 as compared to the

experimental results .....................................

d0 d8 0000000000000000

PAGE

1A

32

A8
78

80

92

101
10A
109

127

FIGURE

I-1

I-2b
1-3
I-A
1—5
1-6

I-7

LIST OF FIGURES

PAGE
High-energy gamma-ray detector ........................... 5
Electronic circuit for a gamma-ray detector element ....... 8
Master trigger circuit .................................... 9
Gamma-ray detector efficiency ............................. 12
Gamma-ray detector response function ...................... 13
Gamma-ray detector energy resolution ...................... 15
Compton scattering, photoelectric effect and pair
production for CsI ........................................ 17

Energy-range correlation for electrons in lucite (C,H,O,). 18

Double-differential cross section N + C at E/A=AO MeV ..... 22
Double-differential cross section N + C at E/A=3O MeV ..... 23
Double-differential cross section N + C at E/A=20 MeV ..... 2A

Double-differential cross section N + Zn at E/AzAO MeV.... 25

Double-differential cross section + Zn at E/A=3O MeV.... 26

22

Double-differential cross section + Zn at E/A=20 MeV.... 27
Double-differential cross section N + Pb at E/AzAO MeV.... 28
Double-differential cross section N + Pb at E/A=30 MeV.... 29

Double-differential cross section N + Pb at E/A=20 MeV.... 30

xi

I-20

I-21

I-22

I-23

I-2A

I—25

I-26

I-27

I-28

II-l

II-2

II-3

Rapidity plot fer Pb, Zn and C at E/AzAO MeV ..............

Rapidity plot for Pb, Zn and C at E/A=3O MeV ..............

Rapidity plot for Pb, Zn and C at E/A=20 MeV ..............

N + C at E/A=AO MeV/n.

N + C at E/A=3O MeV/n.
20, A0 and 60 MeV .........................................

N + C at E/A=20 MeV/n.

20, A0

N + Zn
20, A0

N + Zn
20, A0

N + Zn
20, A0

N + Pb
20, A0

N + Pb
20, A0

N + Pb
20, A0

at E/AzAO MeV/n.
and 60 MeV .............................

at E/A:3O MeV/n.

Angular distribution for EY above
20, A0 and 60 MeV .........................................

Angular distribution for E

Y above

Angular distribution for EY above
and 60 MeV .........................................

Angular

Angular

distribution

distribution

for EY above

for F:Y above

and 60 MeV .........................................

at E/A=20 MeV/n.

Angular

distribution

for EY above

and 60 MeV .........................................

at E/A:AO MeV/n.

Angular

distribution

for EY above

and 60 MeV .......................... . ..............

at E/A=30 MeV/n.

Angular

distribution

for EY above

and 60 MeV .................................... .....

at E/A=20 MeV/n.

Angular

distribution

for EY above

and 60 MeV .........................................

2
do /(dE d0) at 90° for Ar + Au at E/A=30 MeV:
and ours (after calibration corrections) ..................

Kwato et al.

2
do /(dE d0) at 90°: our (after calibration corrections)
N + Zn at E/A=20 MeV and Gossett et a1. F + Ni at E/A=19
MeV .......................................................

Remington et al. theoretical results and our experimental
results for N + C and E/A=20, 30 and A0 Mev (before
calibration correction) ....... ...... ......................

35
36
37

38

39

A0

A1

A2

A3

AA

A5

A6

51

53

57

II-A

II-5

II-6

II-7

II-8

II-9

II-lO

II-ll

II-12

II-13

III-l
III-2
III-3
III-A

III-5

Number of gama rays emitted as a function of time for

the reaction N + Pb at E/A 30 MeV. The arrow indicates

the time at which the colliding nuclei have completely

fused ..................................................... 58

Angular distribution for N + C at E/A=AO MeV: Remington
et al. calculations and our data (before calibration
correction) .............. . ................................ 6O

Angular distribution for N + Pb at E/AzAO MeV: Remington
et al. and our data (before calibration correction) ....... 61

BUU calculation of the photon yield as a function of time
for C + C at E/A=AO MeV ................................... 6A

BUU impact-parameter dependence of the gamma-ray yield.... 65

2
Experimental do /(dE do) and BUU calculations. From top
to bottom: C + C at E/A=8A MeV [Gr 86] and our N + C
(before calibration corrections) at E/AzAO, 30 and 20 MeV. 66

BUU angular distributions as compared to our data (before
calibration corrections) for N + C at E/A=AO MeV and

photon energies of A0 (circles), 60 (diamonds) and 80
(squares) MeV .................................... . ........ 68

2
Experimental do /(dE d0) and BUU calculations. From top
to bottom: C + C at E/A=8A MeV [Gr 86] and our N + C
before calibration corrections) at E/A=A0, 30 and 20 MeV.. 69

BUU angular distributions as compared to our data (before
calibration corrections) for N + C at E/AzAO MeV and photon
energies of A0 (circles), 60 (diamonds) and 80 (squares)

MeV .............. . ............................ . ........... 70

Neuhauser et al. theoretical calculations compared to our
C + Pb (befbre calibration corrections) at E/A:AO MeV and

to Grosse et al. C + U at E/A=8A MeV [Gr 86] .............. 72
Aluminum vacuum chamber ................................... 7A
Experimental set-up for the coincidence experiment ........ 75
Charged particle AE-E telescope ........................... 77
Time gates for A8 and E signal.. .......................... 79
Efficiency versus gamma-ray energy for Pb converter ....... 81

xiii

III-6

III-7

III-8a
III-8b
III-9a
III-9b
III-10
III-11
III-12

III-13

III-1A

III-15

III-16

III-l7

III-18

III-19

III-20

III-21
III-22

IV-l

Logic master gate. ....... . ................................ 83
Electronic circuit for a charged particle detector ........ 8A
Isotope befbre the "gamma-neutron line" subtraction ....... 86
Isotope after the "gamma-neutron line" subtraction ........ 87

E versus channel number for a charged particle detector... 88
AE versus channel number for a charged particle detector.. 88

Energy rescaling diagram for a charged particle detector.. 89

Charged-particle detector: normal position ................ 91
Charged-particle detector: closer and farther ............. 93
Gamma ray singles at 60° and gamma rays at 60° in coinci-
dence with protons at 30° or at 70° ....................... 95
Proton singles at 30° and protons at 30° in coincidence

with gamma rays at 60° .................................... 96
Energy-integrated angular-distributions: proton singles

and protons in coincidence with gamma rays at 60° ......... 98
Ratio versus GP for ganma rays at 60° ..................... 99
Ratio versus 0p for gamma rays at 120° .................... 100
Ratio versus Ep for protons at: 30, A0, 60 and 70° ........ 103

Ratio versus EY for Ep) 30, A0, 50 or 60 MeV in a reference

frame moving with velocity equal to B=0.1A ................ 106

Multiplicity of charged particles in coincidence with
gamma rays at 60° (Y-cp) .................... . ............. 108

Charged particle-charged particle multiplicity (cp-cp).... 115
Comparison of the Y-cp and cp-cp multiplicities ........... 117
Gama-ray spectra from reference [Hi 87]:

a) coincidences with slow heavy fragments

b) coincidences with fast projectile like fragments
c) no coincidence with charged particles ......... . ....... 119

xiv

IV-2

IV-3

IV-A

IV-5

IV-6

IV-7

IV-8

IV-9

IV-lO

IV-ll

IV-12

IV-13

IV-lA

IV-15

IV-16

IV-l7

IV-18

IV-19

Overlap between the Zn nucleus (radius R,) and the N

nucleus (radius R,)........... ....... . .................... 122
RZ=1(GZ=1) versus 02:1 for 02.=1=60° ...................... 129
RZ=1(92=1) versus 62:1 for 02.=1=120° ..................... 130

Proton spectra at 30 and 70°: experimental and n-p model.. 133

Proton energy-integrated angular distribution:
experimental and n-p model results ........................ 13A

Gamma-ray spectra at 60 and 120°: experimental and n-p
model results ............................................. 13S

Gamma-ray energy-integrated angular distributions:
experimental and n-p model results..... ...... . ............ 136

Ratio versus ED for 30< 0P< 70° in the n-p model .......... 138
Ratio versus EY for Ep) 30 MeV in a reference frame moving
with velocity equal to B=0.1A (the n-p model)........ ..... 139

Ratio versus GP for gamma rays at 60° in the n-p model.... 1A0
Ratio versus GP for gamma rays at 120° in the n-p model... 1A1

Proton spectra at 30 and 70°: experimental and thermal
model ..................................................... 1A3

Proton energy—integrated angular distribution:
experimental and thermal model results .................... 1AA

Gamma-ray spectra at 60 and 120°: experimental and
thermal model results ..................................... 1A5

Gamma-ray energy-integrated angular distributions:

experimental and thermal model results .................... 1A7
Ratio versus Ep for 30 < 0P< 70° in the thermal model ..... 1A8
Ratio versus EY for Ep) 20 in the lab (thermal model) ..... 1A9

Ratio versus 9p for ganma rays at 60° in the thermal

XV

model .................................................... 150

IV-20 Ratio versus GP for ganma rays at 120° in the thermal

model ..................................................... 151
IV-21 Comparison between the experimental and the n-p model

results fOr the determination of the mean proton

multiplicity m ........................... ......... ........ 155
IV-22 Ratio versus Ep in the n-p and in the thermal model after

the corrections for the uncorrelated coincidences ......... 157
IV-23 Ratio versus EY in the n-p and in the thermal model after

the corrections for the uncorrelated coincidences ......... 158
IV-2A Ratio versus 9p for ganma rays at 60° in the n-p and in

the thermal model after the corrections for the

uncorrelated coincidences ................................. 159
IV-25 Ratio versus 6p for gamma rays at 120° in the n-p and in

the thermal model after the corrections for the
uncorrelated coincidences ................. . ............... 160

xvi

INTRODUCTION

A. MOTIVATION

In 1982 Budiansky et al.[Bu 82] studied at Berkeley, A0-500 MeV
gama rays emitted in 2 GeV/nucl. collisions of Ne and Ar with Ca and Pb
targets. The production of gama rays by nucleus-nucleus bremmstrahlung
was suggested to explain the deviation of the experimental spectra from
the spectra expected by adding the contributions of the decays of

particles like u., n and A.
High-energy gamma rays (EY> 20 MeV) in intermediate energy heavy

ion reactions were observed for the first time in 198A by two
independent experimental groups. Grosse et al. [Gr 85] at 051 observed
large yields of single gamma rays while studying neutral pion production
with a lead-glass detector. Beard et al. [Be 86] at MSU were puzzled by
the large number of positrons and electrons present in a charged pion
experiment until they found that the leptonic background was associated
with the pair conversion of gamma rays in the collimator of the pion
spectrometer .

From a theoretical view point, in heavy ion physics, gamma rays
were first suggested by Eisberg et al. [Ei 60] in 1960 as a tool to
distinguish between compound nucleus reactions and direct interactions.
The gama-ray spectrum was expected to be sensitive to the time delay
between the cessation of the current associated with the incident
particle and the initiation of the current associated with the product

particle. Theoretical predictions were made although only for photons

2
the wavelength of which is large compared to the nuclear radii and hence
for energies lower than the ones of interest here.

.1. I. Kapusta [Na 77], in an article published in 1977, used the
fireball model [We 76] to study the nucleus-nucleus bremsstrahlung
mechanism for the production of high-energy gamma rays with energies
below 10 Mev. In the same paper he suggested studying gamma rays in the
energy range between 10 and 1A0 MeV.

In 1985 D. Vasak et al. [Va 85] proposed a nucleus-nucleus
bremsstrahlung model for gamma rays above 10 MeV. Such a mechanism, if
found to reproduce the experimental data, would be able to supply
information about the dynamics of the collision and about physical
quantities such as the deceleration time and the compressibility of
nuclear matter.

The aim of this thesis is to contribute to the determination of the
characteristics of the high-energy gamma-ray yield and to try, through
the analysis of a coincidence experiment between photons and protons, to

obtain informtion about the high-energy gamma-ray production mechanism.

8. THESIS ORGANIZATION.

Chapter I contains inclusive double differential cross sections,
angular distributions and rapidity plots for high-energy gamma rays
emitted in the nine reactions: N + Pb, Zn and C at E/A=20, 30 and A0
MeV. Details of the experimental setup, detector calibration,

electronics and data reduction are also included.

3

Chapter II contains a comparison with experimental results obtained
by other groups and a brief outline of the theories proposed to
interpret the experimental results.

In chapter III is a description of the experimental setup, elec-
tronics, data reduction and detector calibration for a coincidence
experiment between high-energy gamm rays and protons in the reaction N
+ Zn at E/A=A0 MeV. The results include a qualitative comparison
between inclusive proton spectra and exclusive spectra of protons in
coincidence with high-energy gamma rays. The same comparison is also
presented for ganma-ray spectra. The ratio of the gamma ray - proton
coincidence cross section to the product of the single proton and gamma

ray cross sections is studied as a function of proton angle, gamma-ray

angle (only 60" and 120°), gamma-ray energy and proton energy.
Multiplicity histograms for protons and protons in coincidence with
gamma rays are also included in this chapter.

In chapter IV the results of the coincidence experiment are
discussed and compared with the results of a Monte Carlo calculation
based on a n-p bremsstrahlung model and on a thermal model.

A summry and conclusions end this thesis.

CHAPTER I
HIGH-ENERGY GAMMA RAYS

A. EXPERIMENTAL SET-UP
After a short test run produced promising results [Be 86] a more
comprehensive experiment investigating the target, angle and energy

dependence of the high-energy gama-ray emission was performed at the

1

A
National Superconducting Cyclotron Laboratory. It employed a N beam

2 2 2
and three targets: C(3A.8 mg/cm ), Zn(33.7 mg/cm ), and Pb(62.8 mg/cm ).
The energies used were E/A=20, 30 and A0 MeV.

Two high-energy gamma-ray detectors were positioned 50 cm from the

target. The first detector (D1) was used for the most forward angles:

30, 60 and 90°. The second detector (D2) collected data at 90, 120 and
150°. Comparison of the data collected at 90° allowed a check of the

relative efficiency of the two detectors.
1. High-energy gamma-ray detectors

An active CsI converter (10.2 x 10.2 x 0.3 cm for detector 1 and
10.2 x 11.A x 0.6 cm for detector 2) was followed by a stack of eight
Cherenkov elements. The Cherenkov elements (Bicron BC-A80) were made of

lucite (C,H.0,) with a wave shifter for better and more uniform light

collection. The first element was 1.27 cm, the second was 2.5A cm and
the rest were 5.08 cm thick. All the elements had the same surface

dimensions of 22.9 x 22.9 cm. The stack (Figure I-1) was enclosed with

 

(INVERTER
L I 0111' BOX

Figure I-1 High-energy gamma-ray detector.

anticoincidence shields: the sides and the top were made of plastic
scintillator while the front was a plastic Cherenkov detector able to
withstand higher rates of charged particles than the scintillator
material. Since the surface of the crystal was not smooth enough to
allow total internal reflection, each converter crystal was enclosed in
a fiberglass-aluminum box painted white to allow the light to undergo
many reflections before being collected by the two photomultiplier tubes
at the top and the bottom of the box.

The top and the bottom of each Cherenkov element extended
vertically to form light guides to converge the light towards the
respective photomultiplier tube (5.0A cm Hamamatsu R329). The front
shield also had two photomultiplier tubes attached to the top and the
bottom through light guides. The remaining shields had only one
phototube.

One 5.08 cm graphite absorber was positioned between the target and
the front shield of each detector to absorb most of the charged
particles produced in the reaction to reduce singles rates in the
converter and in the anticoincidence shields. Protons with energies up
to 100 MeV were completely stopped by the absorber reducing the rate by
991.

B. ELECTRONICS

The master trigger for each gamma—ray detector consisted of an
"and" of six signals: the two phototube signals from the converter and
the two phototube signals each from the first and the second Cherenkov

elements. When the conditions for the master trigger were satisfied and

the computer signal "not busy" was also present, the pulse height and
the time information was recorded for each photomultiplier tube using
LeCroy 22A9 charge integrating ADC and LeCroy 2228 TDC's.

The timing of the master gate with respect to the cyclotron RF was
also recorded.

The electronic circuit for a gamma-ray detector element is shown in
Figure I-2a. This basic circuit was repeated 2A times for each

detector. The master trigger circuit is shown in Figure I-2b

C. CALIBRATION

A complete analysis of the calibration results is beyond the aim of
this thesis and it will be discussed elsewhere [St 88]. What follows is
a brief description of the experimental technique used to calibrate the
gamma-ray detectors and an explanation of how the experimental results
presented here were accordingly corrected.

The calibration of a gamma-ray detector was performed with the
photon-tagging spectrometer of the University of Illinois. An electron
beam generated bremsstrahlung photons by interacting with a 25 um. Al
foil. The electron-beam energies used were: 99, 77, 56 and 35 MeV.
These beams provided tagged photons of 7A-82 Mev, 53-61 MeV, 37-A3 MeV,
and 17-23 Mev respectively. While the primary electron beam was
deviated into a beam dump, the electron that generated the
bremsstrahlung was bent through 180 degrees and detected in an array of
32 scintillator elements. By knowing which scintillator fired, the

bremsstrahlung energy could be determined within about 200 Kev.

lflGH
VOLTAGE

 

 

 

33:” 11/750 l

 

 

CFD ,l MASTERJ

 

 

 

 

 

 

 

 

 

 

 

 

SCALER

Figure I-2a Electronic circuit for a gamma-ray detector element.

GATE

 

; BIT REGISTER I

7‘ TDC START

 

AM)
DELAY I

GATE

 

3

 

 

COMPUTER NOT BUSY ——

__ CKIUP

S CKIDNjL:

'6 CK? URL.

:1 CKZ 0N '

g CONV UP?
CONV DN

N

8

ES

2."

E:

 

MASTER
GATE

:2}

 

 

—-> TDC COMMON STOP

 

AND
I DELAY

GATE
AND
DELAY

 

 

GATE

GATE
AND 00C STROBE
DELAY

BIT REGISTER
STROBE

> COMPUTER START

 

> BIT REGISTER 2

 

AND
DELAY

 

 

Figure I-2b Master trigger circuit.

10

The only difference between the gamma-ray detector calibrated at
the University of Illinois and the ones used in the experiment described

here is in the type of converter used: BaF, in the first case and C31 in

the last. This difference is expected to affect only the detector
efficiency determined by the pair production cross section in the
converter. The absolute efficiency of the detector was measured by
comparing it with the efficiency of a large cylindrical (30 cm diameter
X 36 cm. length ) NaI detector, provided by the University of Illinois,
and assumed to be 1001 efficient. We defined X as the ratio between the
number of gamma detector - tag counter coincidences and the total number
of times the tag counter fired. The ratio 2: can also be written as the

product of the detector efficiency e and the efficiency of the

det

spectrometer 2 (equation I-1 ).

spec

NY-ta
I-l {=TJ—‘5

e

tag det spec

Measuring L for both the large NaI and the Cherenkov telescope it was
possible to determine the efficiency of our detector relative to the NaI

(equation I-2).

I-2 2:cherenkov _ Echerenkov

= e
LNaI ENaI cherenkov

since eNaIis assumed to be equal to 1

II

The spectrometer efficiency Espec was found to be electron-beam

energy dependent varying from about 301 for the 35 MeV beam to 60$ for
the 99 Mev beam. It was, therefore, necessary to make a comparison with
the NaI detector at each beam energy. In Figure I-3 the Cherenkov
detector efficiency, as a function of photon energy, is compared to the
efficiency calculated with the pair production cross section and with
the Stanford electron—ganma shower code EGSA [Ne 85] . Both calculations
are in reasonable agreement with the measured efficiency.

In Figure I-A the response function of the gamma-ray detector is
presented both for the case in which the light generated by the pair in
the converter is and is not taken in account to calculate the total
gamma-ray energy. The addition of the energy loss in the converter
yields a good agreement between the calculated and the bremsstrahlung
photon energy. Since in the experiment described here the energy loss
in the converter was not considered, all the energy spectra had to be
corrected to account for it. The corrected spectra were found to be
still exponential with an unchanged slope but the magnitude of the yield
was found to increase by a factor ranging from 2.0 at A0 MeV to 2.5 at
20 MeV. All the results presented in this chapter have been corrected
using the multiplicative factors presented in Table I-1.

The energy resolution of the detector with and without the
contribution of the energy loss in the converter is presented in Figure

1.5.

D. DATA REDUCTION

12

 

 

 

 

 

4O ’- T T T T l I I T I T I Tj T jiT I T T l .1
C 1:3 Calibration Data 3
g: 30; — EGS4 Calculation __j
Z P ___ Original Eff. Calculations .
o I i
L'.‘
.2 "_ .3
o 20. _
E - .
[fl - a
10 —- .3
O r 1 A l 1 I 1 L 1 L LL 1 l J L J l 4 1 J_ l l l l d
O 20 4O 60 80 100
E7(MeV)
Figure 1-3 Gamma-ray detector efficiency.

13

 

 

 

 

100 r T . T T T f T I T T T T I T T T T I 1 j—T/T/
)- I / 1
if; . D No Converter .
0’ 80 .— 0 Converter [,6 —:
E L , / D -
v '- / 1
r~ _ ‘,’ 3
Ed 60 F. ,o’ ._..
c: , / .
m - /, 1:1 .
3 A ’ ‘
_ ‘3, d
40 — / __
:3 ~ ‘I/ d
o _ , D q
l-J _ / / -+
8 ’ o ’ -
20 _ /, C] q
0 h / l l l l l l L l l l l l l l l l l l l l L d

O 20 4O 60 80

E7 (MeV)
Figure I-A Gamma-ray detector response function.

1A

2
TABLE I-1 Calibration-correction factors for —d-9— .
d0 dEY
E/A 20 Mev 30 MeV A0 MeV

l5

 

 

 

 

120 F T T l I I I I I I I I T 1 I I 1 1 I I I I T I

100; D No Converter _;
I O Converter 2
in? 80 f" —:
v .- -
_ D _
:5: EH3 :_ C] _:
L11 : [:1 D 4
4O :- 0 O —:‘
C o .
20 :— —:
O .- 1 1 l l I l l l l l l l l l I l l l 1 l 1 l l :

O 20 4O 60 80 100

E7(MeV)

Figure 1-5 Gamma-ray detector energy resolution.

16

The gamna-ray transmission e'm‘, due to the attenuation in the

absorber, is 0.8A18 for 20 MeV gamma rays and 0.8569 for gamma rays
above 60 MeV. The average value of 0.8525 was used to correct the
experimental cross-sections.

The CsI efficiency in converting a gamma ray into a positron-
electron pair, which was incorporated in the cross-section calculations,
varies from 12 to 25$ for gamma rays in the 20-120 MeV range [Be 86].
In this range both Compton scattering and photoelectric effect are
negligible (Figure I-6).

The comparatively larger area of the Cherenkov elements with
respect to the converter dimensions allows for multiple scattering of
the electrons and positrons. The response of each single Cherenkov
element was equalized using cosmic muons passing through the detector in
straight lines from front to back. This condition was achieved by
requiring a signal to be present both in the converter and in a plastic
scintillator located after the last Cherenkov element.

The light generated by each component of the pair in each element
is proportional to the distance the particle traveled in the element.
Using energy-range (Figure I-7) relations it was possible to reconstruct
the gamma-ray energy as the sum of the energy of the electron-positron

pair.

8
1-3 EY : {1:0 (light)1 A51

The quantity (light)l is the average of the Cherenkov light collected by

the two opposite photomultiplier tubes of the detector element 1 divided

17

(£31

‘ Tl ITIT lT—TT ITTI rTTrTIIW
1° 1' 1 I l 1 l

 

 

 

103 SOLID -> TOTAL DOTDASH -> PHOTO
DISHES -> PAIR DOTS -> COMPTON
A
a 103
C) __________________
"J 1 fl
0 1° ’2’
\ .....
E3 100 .............................................
(U
\
{310-1 \
b °\.
10‘2 ‘ ..............
10—3 Lil—LllilllllilliltLllLLlllllL
25 50 75 100 125 150
ENERGY

Figure I-6 Compton scattering, photoelectric effect and pair
production for CsI

RANGE (cm)

Figure

50

30

20

10

I-7

18

 

 

 

 

 

 

 

 

b T T T T I' T— T T T T r T T T I T T T T j
>- -1
r- ‘1
P -
l—n —
)- -4
)- -I
—- —1
- J
.- c-I
' 1

.1
L a
)- d
-— —1
" L 4 L L 1 1 1 I 1 1 4 1 I L 1 1 1 'I

50 100 150 200
A81 130(LAEOI)

Energy-range correlation for electrons in lucite (C,H,O,).

19

by the amount of light characteristic of an electron passing through

that element. AEl is the energy related to an increment in range equal
to the difference between the detector thickness up to element 1 (x1)
and the detector thickness up to element 1-1 (xl_1) as shown in Figure

I-7. As an example, (see Table I-2) if a gamma ray of 78 MeV is
transformed into an electron of 56 Mev (which stops at the back of the
fifth detector) and in a positron of 22 MeV (which stops at the back of
the third detector) the expression in equation I-3, in an ideal case,

becomes:

I-A Eyz {2 x [2.89+5.78+13.35] + 1 x [15.60+18.08]} MeV: 78 MeV

since both the electron and the positron will travel through the first
three elements but the electron will also travel through the fourth and
the fifth elements.

The on-line triggering conditions for the acceptance of a gamma-ray
event were the presence of a signal in the converter and in the first
two Cherenkov elements. In the off-line analysis more restrictive
conditions were added to reduce the cosmic muon contamination of the
gamma-ray spectra. Since a ganIna ray would not create a signal in the
front plastic shield while a charged muon would, a condition rejecting
all the events leaving a signal in the front plastic was applied during
data analysis. Likewise, all the events passing through the top and the
side shields were eliminated. When all these conditions were applied,
the muon rate of about 30 counts per minute decreased to about 0.3

counts per minute. This information was obtained by applying the muon

20

TABLE 1-2 Energy loss of an electron going through the elements of the

gamma-ray detector.

Element # Thickness Efront Eback AE
(cm) (MeV) (MeV) (MeV)
' """ . """"""" I; """""" LL; """"" I"
2 2.5A 2.89 8.67 5.78
3 5.08 8.67 22.02 13.35
A 5.08 22.02 37.62 15.60
5 5.08 37.62 55.70 18.08
6 5.08 55.70 76.68 20.98
7 5.08 76.68 100.9 2A.22
8 5.08 100.9 129.0 28.15

21

rejection conditions to a muon run, in which the same triggering
conditions as for a gamma-ray run where required, and observing the
residual muon rate.

The flux of charged particles produced in the reaction could create
a coincidence between a charged particle and a gamma ray with a
subsequent elimination of the event. We measured this effect
(accidentals) by looking at the adjacent RF bursts. The worst
accidental rate we observed was for the lead target at A0 Mev when it
reached the value of A.1$. On average the accidental rate was 1.81 for
D1 and 0.61 for D2.

Gamma rays produced by neutron capture were found to have an energy
lower than 20 MeV and therefore did not represent a problem in the

analysis of the data.
E . RESULTS

The double differential cross-sections taken at 30, 60, 90, 120 and
150° for the three systems and for the three energies under study are
shown in Figures I-8 to I-16. The spectra are exponentially decreasing
with energy, and two components can easily be discriminated. The first,

fer EY< 20 MeV, is dominated by statistical gamma rays and is much
steeper than the second. When parameterized with a function of the form

ae'E/T‘ it gives an approximately constant value for the inverse slope

parameter 1, of about 2 MeV. The second portion of the spectra, BY) 35

MeV, can be parameterized in terms of an isotropic emission from a

10°

dza'Y/dfl dE (mb/sr MeV)
"i

10"

Figure I-8

22

N + C at E/A=4O MeV

 

T T T I T T T T I I 7 T TT I I T T ‘T I l
a 30° (x 10) + 90° (1: 10)
:1 60° (1: 10') a 120° (1 10°)
0 150°

T T I T T T ‘ T T T I T T T l T T T

 

 

 

Double-differential cross section N + C at E/AzAO MeV.

10°

dam/d0 dE (mb/sr MeV)
'5.

10“

Figure I-9

23

N + C at E/A=30 MeV

 

 

T T T T I 1 T I I T r I T I T 1 I—TT'
' (x 10L) .

 

 

a 30° + 90° (1: 10‘)
. n 60" (1 10°) 0 120° (1 10”) .
__ 0 150° -‘
I! .
" Q
. “a .1
’09 .
'_ S” ...I...I. O '1
+ ".fllnfll E $_
- ++ Ix‘l‘ '
"" Baa +*+****¢**¢¢ a. :1- T—
” O 88383...- id
.0 .lllu' I
P O... I m I I! m d
__ 000.......‘. .
I q
I- . I I I ! I
~ I 1 I l l l l L l l l L l L l l L l l
0 20 4O 80 80
E7 (MeV)
Double-differential cross section N + C at E/Az30 MeV.

2A

N + c at E/A=20 MeV

 

 

 

 

T T T T I T T l T TiT T T TIT T T T
f; 1010 '__ .1. 30° (2 10 + 90° (1: 10‘) _
g r n 60" (x 10‘) 0 120° (1: 10°) 1
h ' a, 0 150° j
U! - Age
\ 5 . T‘s 3
no 10 '—" ”i ‘Q. .. fl
. o a
E - M!“ u 000...... . _,
Ed ‘- 4'}. ”nun-“x I E -1
'U L. *++ + x“xx'l ! I 1+
+
C: 100 T Baa *‘l'u'A'n-t in I I I I I A
Old 1" a . .‘13 1
\ O 3838833 I 1
F " 53.. I 7
nab ' 0 ° Imum'l'mu: m 1'1
'U r .0... ‘
10-5 —' 0......... T —4
- ‘ n {.1
p l l J L l l L l LLL L l l L J 1 J ,J l
O 20 40 60 80

Figure I-10 Double-differential cross section N + C at E/A:20 MeV.

H

O
p
N

H I—
O 0
IF 0

d201/ d0 dE (mb/sr MeV)
52,

10-4

Figure 1-11

25

N + Zn at E/A=4O MeV

 

 

 

 

T T T r I T T T T I T T T T T T T T T r T T
' a. 30° (1 10°) + 90° (1 10‘) 1
_ :1 60° (1: 10") a 120° (1: 1oz) .

O
._ g“ 0 150 __
" Q1. .
" ’.. -4
O
L i“. m.........“ . ..
I”, I ll
. ++++ ”lung: 3:; a: x x E E I fl
' ++ !
_ + **++ ! I i I I _
a **+¢
838 ***¢ + I. I.
-— t g g .—
83 1 I I f
h- . u d
0...... D m m m m N

.- ”....... . T m d
_— I a ll" 1 .—
. i I

J l l l l l l l l J l l l I l L l l L L l L l l

20 4O 60 80 100
E7 (MeV)

Double-differential cross section N + Zn at E/Azuo MeV.

26

N + Zn at E/A=30 MeV

 

 

 

 

1012 r T T r I T T T T T fl T T T T T T
g : '1‘ 30° (x 10L) + 90° (1 10‘) .
§ ; :1 60" (x 10‘) a 120° (1 1o”) .
h 10" ~ g.“ 0 150° —
#- fl '4
< - figi. .
'0 _ ”x” ...’.000.. . . .
3104+— "u. -""!!2 "‘
F' ++ "xflgx‘ I 2.
g ' + *++ n u! l l I ‘

.4.
'U 100 g 85333 2:231, ! 1 __
\ __ .0 3883...... I i «
Nb _, ’0... ”I'm I I I III m a
“U -4 P .90........ o m E
10 "-_’ .. ' fl . ' 1 I ‘
-L l l L l L i 1 JL I l 1 L L I l l I lid
0 20 4O 60 80
E, (MeV)

Figure 1-12 Double-differential cross section N + Zn at; E/Az30 MeV.

27

N + Zn at E/A=20 MeV

 

 

 

 

1012 T T T T T T T T T T T T TT T r T
g ' '1' 30" (x 10L) + 90° (1: 10‘)
§ 2 n 60" (x 10’) a 120° (x 10‘) _
B __ .—
h 10 a“ A
m r- *4.
\ - 9,. _
To ‘! .0. s
a ... i ....
V 104 —- "fl ' '12! T} —
L- ”! ..
53 -m I Hi i.
c .. a +++ 4". I l! I ‘
'U 0 Bee *+¢¢.*. . __
\ 1° _ aa ’ i! I 1
F- _ II... I 3! ‘
Nb InflammmIll I ‘
15 - “HP ID m g s
10" —— T 9 T __
l l I l l l l 1 l l l l l l l l l l l ‘
0 20 40 60 80
E1 (MeV)

Figure 1-13 Double-differential cross section N + Zn at E/A=20 MeV.

dzU1/dfl dE (mb/sr MeV)

p

O
H
N

p.
O
O

p
O
fi

5..
O
O

28

N + Pb at E/A=40 MeV

 

 

 

 

I T j T T I T T T T I T T 1_T T T T
; .9 30° (1: 10') + 90° (1: 10‘) ‘
_ :1 60" (x 10") a 120° (1: 10‘) _‘
—- 0 150° —
F .1. -
. "99.... o. q
. '0 can .
__ “an - - . a . ° 1 1 l

”l": 2 I f
- +++ fine.» I ‘ ' ‘ ' I 4
. +4. I
.. a ++++*+N¢¢M¢¢¢ ¢ * * I! T I I;
_ Bases . ‘ - I 1 I i
- -'.Ilmn. I I E
_ o
_ ..000¢. ”. “mum!” fit
..

:— a o o a . . g g!

L I I I I l I I I I l L I I I T I I I I I

20 40 60 80 100

E7 (MeV)

Figure I-1U Double-differential cross section N + Pb at E/A:NO MeV.

dam/d0 dE (mb/sr MeV)

1012

29

N + Pb at E/A=30 MeV

 

 

j T

T 1 T T T T T T T T T T T
+ 90° (1: 10‘)
11 60° (x 10‘) 0 120° (1: 10’)

 

 

Figure I-15 Double-differential cross section N + Pb at E/A=3O MeV.

0 150° -—
‘ .
i“ I
+++ lung, “1 l .
*4- I l g .

sea ++..,.!.. I 1 I I
888 a 1111i: 1 z 1 I f
0 all- .
O... ..--."Uflm I I i I ..
0., u .

00¢0¢¢¢¢.. ..! g g
a I I ! d
l I I I l I I 1 l I l I I I l I IIIIIT
20 40 60 80

E7 (MeV)

dam/cm dE (mb/sr MeV)

H
O
O

H
O
p

H
O
O

10-4

1o-8

30

N + Pb at E/A=20 MeV

 

 

 

 

T I T T r T T r T T T T r T d

a. 30° (x 10") + 90° (2 10‘) fi

1: 60° (1: 10") a 120° (1: 102) 1

a.“ 0 150° ‘

Q; ‘

“ 0'0.... a. -

a... 1! ”may 1! g —

++ + "flli"“'! I 1

+*++ I

Essa *+ ..“ ‘ 1‘ I I —u

as 1 1! .

0.. as... I'm an I I f I:

O. m “In 0 ‘

0 ....... m ¥~

II.!! ‘

I lift Iq

I l I I I I l I I I I J J I I I q

20 40 so 30
E7 (MeV)

Figure 1-16 Double-differential cross section N + Pb at E/A=2O MeV.

31

-E/I2

recoiling source with an exponential function b The values of the

inverse slope parameter 1, are reported in Table I-3.

The cross-section (equation 1-5) was calculated at different angles

as function of B, the source velocity/c.

2 2
do _ do E
I-S dBdO source - dfidfi lab -§I:gurce

 

2

2 2
Esource = / E labsin 9 + Y (E

2

case-8813b)

lab

'The value of B, fOr each system and for each energy, corresponding
to the frame in which the emission is nearly isotropic, is reported in
Table I-3. The source velocity values are fairly close to the nucleon-
nucleon system velocities. Both source velocities and slope parameters
appear to be nearly independent of the target chosen and increase with
increasing energy.

The alternate method of making rapidity plots, to test the idea of
isotropic emission and to obtain information about the source velocity,
was also employed. In general, the rapidity y of a particle of energy E
and momentum p moving along a direction characterized by an angle 9, is

defined as in equation 1-6.

32
TABLE 1-3 Parameters from the best fit to the high-energy gamma-ray

data for EY>35 MeV.

exp n-n nucleus-
nucleus
Pb 20 10.0 0.08 0.104 0.013
Pb 30 12.0 0.11 0.127 0.016
Pb NO 1u.2 0.10 0.145 0.019
Zn 20 8.3 0.05 0.10“ 0.037
Zn 30 ' 11.8 0.11 0.127 0.045
Zn “0 13.7 0.10 0.145 0.052
C 20 7.7 0 08 0.10” 0.111
C 30 11.1 0.10 0.127 0.135
C 40 13.3 0.12 0.145 0.156

33

l(1+Bcos 9

-_1_ £421-; J__a+3
I‘6 y ‘ 2 1"( a - pg) ' 2 1“( fi') ‘ 1- Boos 9)

1 21

In the laboratory frame a particle with velocity B" has an
associate rapidity y". In a frame moving with velocity 8 with respect
to the lab frame, the same particle will have velocity 8' and rapidity
y'. The relation between the three velocities B, B', and B" is shown in

equation (I-7)

" e + 3'

1'7 B 1 + 33'

Equation I-8 shows the additive propriety of the rapidity.

 

 

 

 

 

1 B + 8'
_1 1+8 __1__ 1+88'
1'8 y"‘ 2 1“(1 - 3) ‘ 2 1“( 1 3 + 3' >
- 1 + 88'
- (1+B)(1+B') _1_l1+8 __1_ LL_3_'
y"' 21" n((1. B)(1 - B')) ‘ "(1 - 3 ) * 2 1"(1 - 3')
y"= y + y'

If a frame where the emission is isotropic exists, the plots will
be symmetric and the abscissa of the center of synmetry will represents

the rapidity of the source (equation 1-9).

311

1 1+8
{—31

In order to take advantage of the general properties of the
rapidity we used the experimental cross-section data to generate

invariant cross-section (equation I-10) versus energy plots.

The curve for each angle was fitted with a function of the form

y:Ae'Bx. The intersection between three constant values of the

invariant cross section and each of the fitted curves defined energy
values on the abscissa. For each of the three invariant cross-section

values, the rapidity (equation I-6) was plotted against the quantity p_

= Esine. Figures I-17 through I-19 show the rapidity plots for the
three systems and the three energies under consideration. The curved
line connecting the five data points is obtained with a cubic spline
fit. The rapidity for a nucleon-nucleon system is also indicated. The
general features of the plots are consistent with the idea of the
existence of an emitting source moving with a velocity close to the
nucleon-nucleon center of mass velocity.

In Figures I-20 through I-28 the angular distributions fOr N+Pb, Zn
and C at 20, 30 and 110 MeV/n are shown for three different lower energy
cuts on the gamma-ray energy at 20, 110 and 60 MeV. The angular

distributions are all slightly forward peaked. At '40 MeV/n the angular

35

E /A=40 MeV

 

200

-
d
.1
.1

——1

l T7
150
100

50

 

 

 

 

T T T T 1 T T1 T T I T I T T T T
150 Ya Zn
A
Q 100
ms 50 %k
I L I I I I I I I I I I I I I I I I I
fit: T T 1 T l T T T T | T T T T T 1 T T

TTTT TTTTITTTTITTTTITTTT TTTTITTTTITTTTITTTT

150

100

50

 

TTITTTTITTTTI

 

 

IIIIIIIIII IIIIlIlIIlIIIlIlIII IIIIIIIIIIIIIIIII

 

 

Rapidity

Figure 1-17 Rapidity plot for Pb, Zn and C at E/A=uo MeV.

an IILIIIIII

36

 

E/A=30 MeV

150

d
‘

 

 

 

 

 

 

 

 

 

 

 

 

E T Tl ]T T T T[T rT T:

1255— Yu Pb i
100'?“ -§

75E- \ j
50%- /\-§o j

g 1 1 1 1 71 1’ 1 1 *1 1 1 1 1' 1* 1 1 1_§

1005;' 9, -E

g 76;?- \ i
"113' 50E— %\ —
25 E— -;

mz~ 5H-11'111111111‘1111f
ET T T T I T j I E

100’;‘ ?, “3

75;— —:

25 3" z:::iE::::::::——’._f— "“‘-]f.__. -1

o I I I I I I I I I I I L I I I I

|
N

I
g...
0
H
N

Rapidity

Figure 1-18 Rapidity plot for Pb, Zn and C at E/Az30 MeV.

37

 

E/A=20 MeV
150 1 1 1 1 I 1 1 1

125
100
75
50

 

 

 

--
-
‘D
-
d.

125
100
75
50
25

 

llTTT'TTTTITTTTITTTTITTTT TlTT'TTTTITTTTITTTTITTTT'T

 

IIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIII

 

Eysinfi

 

 

 

 

 

 

 

 

 

 

 

" -:
: I :
' I I I I I I I I I I I I I I I I -
: T T T T l T l l T l T T T T T T T =
D d
125 g- Y C .5
: I. =
u
100 :— __
75 :— l1 -.—':
- q
- d
: A 4 A :
25 5" é: ' : —:
D d

l) : I I I I I I I I I I I I I I I I I
-2 -1 0 1 2

Rapidity

Figure I-19 Rapidity plot for Pb, Zn and C at E/Az20 MeV.

38

N + C E/A=4O MeV

 

ET r T T I T T T T I T T T T I T _‘
__ x E7>20 MeV
10"]. =_ 0 E1>40 MeV _-
E n E7>60 MeV
A " a
‘6 L X x .1
\ —2 _ x __
g 10 g X x i
\a’ : ° 0 I
.. o .
c:: 10
'U 10"”3 :r 1:1 :1 o f“;
\:L E U 0 S
I: - n .
13 r -
10'"4 :— ‘2-
E 3
10—5 I I I I I I I I I I I I I I I I I

 

 

 

0 50 100 150 '
6°

Figure I-20 N + C at E/A:M0 MeV. Angular distribution for E
NO and 60 MeV.

Y above 20,

39

N + C E/A= 30 MeV

 

 

 

 

: I 1 fI I I T I I I I I I I Tl I:
. __ X E 7>20 MeV
10.1 1:— 0 E:>4O MeV __5
5 D E7>60 MeV E
A " ‘
L1 _ -
m _ -
\ —2 u.— x X X —
.D 10 § x 3
a I x 3
v P "
c. ' ° ‘
g 10-3 :5— ° ° 0 1
I 0 I
tgr~ : [J 1
“U ~ 1: ‘
1:1 1:1

10-4 g,- D “'5‘

10-5 I I I I I I I I I I I I I I j I

O ”50 100 150

69C)

Figure I-21 N + C at E/A:30 MeV. Angular distribution for EY above 20,
40 and 60 MeV.

"O

N + C E/A=20 MeV

 

#- I I I I I I I r I l I I I I I I I:
'_‘ x E7>20 MeV
10-1 :— 0 E1>40 MeV .
o E7>60 MeV
”a C 1
Q " d
-2 __- ._
.53 10 E x 5
E : x :
- )( .
V "' X '
.. X ..
C‘.
'U 10":3 .'-Z_ ":
\z~ 5 5
b - ° 0 ‘
13 r 0 o o ‘
10"4 E‘ “'5
: [3 Cl [3 Cl C] :
10—5 I I I I I I I I I I I I I LJ I I

 

 

 

O 50 100 150
‘60

Figure 1-22 N + C at E/Az20 MeV. Angular distribution for EY above 20,
NO and 60 MeV.

1H

N + Zn E/A=40 MeV

 

 

 

 

:TTI I l I I I I I I I I I I I I d
r X E1>20 MeV ..
100 :— 0 E7>4O MeV —.-:
o E,>60 MeV
A I- -
I-l .
m _1 F

\ 10 E" x x _€
,0 : X :
a 5 x x 3
v .. 4
c 1.0—2 r- 0 O 0 .1
\?~ I o n I
b L- D D D -
Pd 10"3 :- "a
E :
L- d
10_4 =— -r_.
El I I I I I I I I I J I I I I‘I I:

O 50 100 150

60

Figure I—23 N 4- Zn at E/AleO MeV. Angular distribution for FY above
20, A0 and 60 MeV.

142

N + Zn E/A=30 MeV

 

 

 

 

: I I I I I T I I l I I I T I I T
. X E1>20 MeV _
100 E" 0 E7>40 MeV —:
o E,>60 MeV g
A +- -
I—u .. ..
m —1
\ 10 :7" -_E
.0 E x x I
E : X x :
v . x ..
C 10'"2 5— 1
'd : <> 5
: 0 o 0 -
\?~ _ d
b *- ° .
.... D
1’ 1° 3 re:— a n "2'
E D n E
10'"4 :— '1
I1] I I L I I I I I I L I I I I I :
0 50 100 150

60
Figure I-2N N + Zn at E/Az30 MeV. Angular distribution for EY above
20, NO and 60 MeV.

”3

N + Zn E/A=20 MeV

 

 

 

 

:I I I I [1 T I I I I I I I l'rI-J
_. X E7>20 MeV .
1(,0 _.____ o E7>40 MeV .—
o E,>60 MeV 32
”I: Z I
m 1
\ 10_ 5" ‘2‘;
.0 E :
I x I
\E/ L- X X ..
)(
C 10—2 5" —:-.
"U E :
‘\\\ _ :
F I-
b b o 0 o d
U 10‘3 r o *2
5 a
.- 0 C] U D a
10—4 :2— -a
:I I I I I I I I I I I I I LI'I I:
0 50 100 150

60
Figure 1-25 N + Zn at E/A=2O MeV. Angular distribution for EY above
20, HO and 60 MeV.

1M

N + Pb E/A=4O MeV

 

C I I I I l I I Ij I I I I I If r:

. X E7>20 MeV a

E U E7>60 MeV f

”I? " d
00 1 -' X x I
\ 10" 5" x x ":1
JD 5 X 5
i3, : ° o :
C. 1.0—2 r- 0 0 o -.1
"U D n
E : D D D :
U 10""3 :— ‘1
C -

10—4 5—
: I I I I l I I I #1 I I L I I I 1 "‘

 

 

 

O

50 100 150 ‘
£?C)

Figure I-26 N + Pb at E/AzllO MeV. Angular distribution for FY above
20, NO and 60 MeV.

“5

N + Pb E/A=30 MeV

 

IIIIIIITTIIIIII_II
I- -I

 

 

 

‘ x E,>zo MeV I
100 FT— 0 E1>4O MeV .5
E El E7>60 MeV f
”I: I 2
VJ

\ 10"1 a— x '1
n s x x a
a ‘ L' x 1
v ,. -I
_g __ __
g 10 E o i
\ E o o :
b5 r- 0 1
_. u n I
U 10"3 :r' 1
: D o 3
10"4 :— —:
:I L I I I I I I I I I I I I I I i:

0 50 100 150

é’C)

Figure I-27 N + Pb at E/A=3O MeV. Angular distribution for E2Y above
20, NO and 60 MeV.

“6

N +. Pb E/A=20 MeV

 

 

 

 

:I I I I I I I I I I T I I I I I I:
.. X E7>20 MeV ..
100 E. 0 E7>40 MeV __:
o E,>so MeV g
z“\ — 4
LI _. d
m

‘\\\~ :1()--11 ET' --5
n a s
8 t x X :
\.—/ _ )< )< )< d
(I: 10""2 =-' "E
g s
e~ : 3
b - o d
’U 10"3 :— 0 ° 0 “-3
5 ° 5
: a .
4 _ D 0 q
10- .'._' D -—-;‘
: IIII I 9 I I I I LI I I I I L:

0

50 100 150
_ 6°

Figure 1-28 N + Pb at E/A=2O MeV. Angular distribution for EY above
20, MO and 60 MeV.

147

distributions integrated for EY> 20 MeV give for the ratio

o(30°)/o(150°): 2.35 for Pb, 2.28 for Zn and 3.113 for C. Similar
behavior is found for all targets and beam energies. The total cross-

sections at 90° for gamma-ray energies above 20 Mev are shown in Table

I-li.

”8

TABLE I-A Total cross sections at 90° for gamma-ray energies above

20 MeV.
Target Cross section (mb)
20 MeV/n 3O MeV/n A0 MeV/n
Pb O 11 0.36 0 6“
Zn 0.10 0.21 O.A3

CHAPTER II
HIGH-ENERGY GAMMA RAYS: DATA COMPARISON AND THEORY

A . EXPERIMENTAL COMPARISON

The main characteristics of the ganuna-ray spectra emerging from the
experiment described in Chapter I are the exponential decrease of the
double-differential cross section with energy and a nearly isotropic
angular distribution in a frame moving with velocity close to the
nucleon-nucleon center of mass velocity. These general features are in
agreement with most of the results obtained by other experimental
groups.

Grosse et al. [Gr 86] studied high-energy gamma rays, at the CERN

I

2
syncrocyclotron, using a C beam of 1&8, 60, 7‘4 and 81! MeV/nucl. on
targets from C to U. For constant values of the invariant photon cross
section, they plotted the rapidity (equation I-3) against the transverse

energy E : EYsine. The symmetry around the half rapidity line, not

12 1

2
only for symmetric systems such as C + C but also for very asymmetric

12 23!
systems such as C + U , led this group to introduce the idea of

"equal participants". In this picture, gamma rays, are assumed to be
produced in a source formed from equally many participant nucleons out
of the target and the projectile. The observed value of the source
velocity could, on the other hand, be used as an argument to support the
idea of direct n-p bremsstrahlung as the mechanism responsible for the

gama-ray production .

49

50

Kwato et al. [Kw 86] conducted two experiments: one at Grenoble at

h

0
the Sara facility using an Ar beam on an Au target at EI/A=3O MeV and

.6
one at Caen at the Ganil facility using a Kr beam on C, Ag, and Au

targets at mam MeV. Great care was devoted to the determination of
the angular distribution and especially to its departure from a
perfectly isotropic one in a frame moving with velocity close to the
nucleon-nucleon center of mass velocity. A dipolar component was found
in the nu MeV/nucl. data and its amplitude was found to vary little in
the wide mass range under study, with a mean value of 2H1.

During a later experiment our group collected data on the reaction

h

0
Ar 4- Au .. Y + X at E/A=3O MeV. Figure II-1 shows a comparison at 90°
between our data and the Kwato et al. data. Within error bars the two

double-differential cross-sections agree both in slope and magnitude.

#0 15

R. Hingmann et al. [Hi 86] studied the reaction Ar + .Gd at
E/A=uu Mev at GANIL. The main aim of this experiment was to analyze the
gama-ray emission process as a function of impact parameter. Besides
observing the coincidence between ganIna rays and reaction products, the
result of which will be discussed in chapter IV, inclusive spectra at
90° and 116° were also measured. The exponential decrease of the
spectra and the fairly constant angular distribution are in agreement
with the above mentioned experiments.

Completely different results were obtained by N. Alamanos et al.

[Al 86] who made inclusive measurements of high-energy gamma rays

1

5
produced in the reaction N + Ni . Y + X with a 35 MeV/nucl. beam at
the NSCL. The slopes of the exponential spectra are independent of the

laboratory angle and the angular distribution in the laboratory is not

51

Ar + Au E/A=30 MeV

IerTIIIIIIIIIIIIIYIVI

I—b
O
O

 

0 our data
+ Kwato et al.

3W

H
o.
H

EHD°

dzoy/dQ dE (Inb/sr MeV)
23 a
I I
00 N
f
g
A?
fig.

 

l
is
F—-+—I

 

 

 

10
10—5
10-6Lllllnnlnlllllll.lli..
20 30 4o 50 60
E7(MeV)

2
Figure II-1 do /(dE d0) at 90° for Ar + Au at E/A=3O MeV: Kwato et al.
and ours (after calibration corrections).

52

forward peaked but has a predominant dipolar-like behavior with a
maximum at 90°.
Very recently C. Gossett et al. [Cu 87] studied the gamma-ray

production resulting from bombarding Al, Ni, Mo and Ta targets with a 19

‘I

9
MeV/nucl. F beam at Berkeley. Although most of the features agree with
the general trend, the magnitudes of the cross sections are larger than

the ones we obtained for similar systems. Figure II-2 shows that the

l
spectrum taken at 90° for the reaction F + Ni at E/A=19 Mev is a

1‘0 6

5
factor of 3 larger than our data for the reaction N 4- Zn at E/A=20

MeV at the same angle.
B. THEORETICAL MODELS

The explanation of the existence of a reaction product not present
in the entrance channel of a reaction is not a simple theoretical task.
Several reaction mechanisms have been suggested in the last few years to

interpret the experimental high-energy gamma-ray spectra.
1. Bremsstrahlung

When charged particles pass through matter they are scattered and
lose energy mainly by collisions with the atomic electrons since nuclear
collisions are much less likely to happen. Energy loss is also possible
by emission of electromagnetic radiation. When a charged particle
passes through a nuclear field, its velocity changes which gives rise to

acceleration and, from Maxwell's equations, to electromagnetic

53

 

I

I I I I I I I I I I F
0 ‘LF + “Ni at 19 MeV/n

 

A
% 10° 0
E + 1‘N + “Zn at. 20 MeV/n
L. 10-1 +0
II) +00
\ +
'0 1.0-2 Iii-Du
i3, *. Do
-3 *‘HDDD
[:1 10 t. 0 n
'U giiin D D
c _4 i D D
'U 10 ii of
\ ii g D D
b 10"5 of I
”'13 [in 0
10-6 I I I P L I I I I I I I L I I I I I I
0 20 40 60 80
E7 (MeV)

2
Figure II-2 do /(dE d0) at 90°: our N + Zn at E/Az20 MeV (after
calibration corrections) and Gossett et al. F + Ni at
E/Az19 MeV.

514

radiation. The emitted radiation is often called bremsstrahlung
(braking radiation).

In a heavy ion collision, bremsstrahlung radiation can arise from
mechanisms involving different degrees of collectivity: nucleus-nucleus,
nucleon-nucleus, or nucleon-nucleon collisions. Below isla short
description of the models used for the different processes. Their

ability to reproduce the experimental results is also discussed.
1a. Nucleus-nucleus bremsstrahlung.

This component of the bremsstrahlung is associated with the
collective behavior of the nucleons in the first stage of the reaction.
For symetric systems, the angular distribution in the center of mass
frame has a quadrupolar nature with a characteristic minimum at 90° [Va
81%]. In asynmetric systems the same behavior is still predicted for
collisions where the projectile and target have the same A/Z ratio [Ni

85]. A look at the angular distribution obtained for the symmetric

1

2
system C + C [Cr 86] and for the nearly symmetric system

1

“N + C [St
86] clearly rules out the nucleus-nucleus bremsstrahlung as the main
mechanism in the gamma-ray production.

Ko et al. [Ko 86], in a study done with the intranuclear cascade
model (INC) [Be 81], suggested the possibility of observing this
collective process in the photon range between 10 and 30 MeV for heavy
nuclei with A>u0. Experiments in search of this component have

recently been performed and they are currently under analysis.

1b. Nucleon-nucleus

55

The nucleon-nucleus bremsstrahlung contribution to the gamma-ray
yield has been studied by Bauer et al. [Ba 85] in the framework of the
time dependent Hartree-Fock (TDHF) theory and found to be at least an
order of magnitude too small to explain the data.

K. Nakayama and G. F. Bersch [Na 86] used the infinite matter
approximation to study the contribution of the bremsstrahlung from a
potential field compared to the contribution of the collisional process

and found it to be negligible.

1c. Nucleon-nucleon bremsstrahlung

In the nucleon-nucleon bremsstrahlung the dipolar proton-neutron
bremsstrahlung is the predominant component and the quadrupolar proton-
proton bremsstrahlung is several orders of magnitude smaller [Ni 85].

Remington et al. [Re 87a] used the Boltzmann master equation (BME)
[Bl 81] to follow the intranuclear nucleon-nucleon collision process.
Boltzmann-like coupled, first-order differential equations are used to
describe the rate of change of the nucleon occupation probability as a
function of energy above the bottom of the nuclear well. The Fermi
motion of both the target and the projectile are considered and
superimposed on the projectile momentum to obtain gamma-ray energies
above the kinematical limit given by the projectile energy. The Fermi
motion is also expected to flatten the dipolar angular distribution so
as to reproduce the nearly isotropic experimental results. The neutron-
proton bremsstrahlung is added to the BME as a perturbation and the

elementary reaction process is represented by equation II-2.

2
dN a e-B 603

= 2 zk=1 “ “ - ‘ ‘
d1:‘.Ydi'2Y(21)lEIY 1-q-B1-q-B

 

II-2

Where a =8 7%? is the fine structure constant, 81 and B are the

f

A A A

initial and final proton velocities, Ei’ cf. and q are the unit vectors

representing the two directions of polarization and the direction of

B Y
propagation of the gamma ray. P = f f is a quantum correction
fac BiYi

 

related to the available final state phase space [Na 86]. The (1 + X)
factor for X = 0 reduces equation II-2 to a semiclassical result and for
X = 1 gives a crude correction for meson exchange effects [Br 73]. The
value X = 1 is chosen for the nucleus-nucleus calculations since the
simpler proton-nucleus data of Edgington and Rose [Eg 66] are reproduced
with it. Since the BME follows the intranuclear cascade only in energy
space, no angular distribution is directly available. The cross section

at 90° can, however, be obtained by dividing the differential cross

section 3; in the nucleon-nucleon center of mass by An and neglecting

 

the transformation factor Y z 1 between the center of mass and

laboratory frame. Figure II-3 shows a comparison between the

1'. 1§ 2°

theoretical predictions for N + ”C and N + 7Pb at E/A=20, 30 and
”0 MeV and the experimental results. Not included in the figure are the
calibration correction factors of 2.5, 2.2 and 2.0 for beam energies of
20, 30 and 140 MeV/nucl. respectively. Figure II-A shows the gamma-ray

production as a mnction of time. The gamma-ray production seems to be

57

 

I l I
o 0 IIONIsV/nuclcon
‘ A 30 II II

    
   
 
 

—- (3 2c) M II
(Stevenson
-4 \ st al.)
10 '— \1I~ +12c "
t \s
In
% -
2
3
g 10"— s _
I K \
I
«N: :sk P- I:—
[m
1:

3
L
I

 

 

x 10"?—

— Classical x 2

 

 

 

’- ‘ ---O.usntum x 10.:
x 10'2 I
10-10 1 l 1 1 l
0 4O 80 120 0 4O 80 120
E,(MoV)

Figure II-3 Remington et al. theoretical results and our experimental
results for N + C at E/A:20, 30 and NO MeV (before
calibration).

58

 

 

 
  
 

10" ' T ' T r I
“N + 208Pb
‘g 30 MeV/nucleon
VI -5 --I
S; 1° IE,- 10 MeV
53
z; 10" ’- "\, ".
.. ‘. E, - 40 MeV
z ‘. (x 10‘)
v 10" - ‘- "*
.u . I
a 1
a a
‘5 10-3 1— "I'. E7- 80 MeV -
‘ (x 102)
10-9 1 I I I l. I

 

 

 

O 2 4 6
Time (In units of 10'22 see)

Figure II-A Number of‘ gamma rays emitted as a function of time for the
reaction N + Pb at E/A:3O MeV. The arrow indicates the
time at which the colliding nuclei have completely fused.

S9

strongly related to the initial stage of the collision and the most
energetic gamma rays appear to be produced mainly in the first
collisions.

In a second study, Remington et al. [Re 87b] defined an "acceptance
window" A6, for injection of nucleons into the nuclear well. The
uncertainty of the injection angle is then folded with equation II-1.
Figures II-5 and II-6 show the angular distributions obtained within
this picture and their comparison with the experimental values (before
calibration). The dashed curves show the contribution of the first
collision and the solid curves represent the sum of the first collision
contribution and the secondary collision component assumed to be
isotropic in the nucleon-nucleon center of mass.

Two recent dynamical studies of the neutron-proton bremsstrahlung
done by Bauer et a1. follow the collision both in coordinate and in
momentum space. In the first [Ba 86], the elementary photon production
cross section is represented by the non-relativistic expression
(equation II-3) obtained by considering the collision of a particle of

charge e and mass m with a fixed sphere of radius R.

2 2

do cR
11-3 ._._ele_m=-——[23

dE dflY 121! BY

2

2
f +3Bisin 9

Y]

where a = :c and R = radius of a sphere. The value R z / 3 fm fits

 

the data of Edginton and Rose. 81 and Bf are the initial and final

velocities of the proton in the n-p center of mass. The impact

parameter dependent double differential cross section is expressed as

60

 

J

I IIIII

4o MeV/u L 14N +120

--L
c?
(A)
I
I
I
l
i
O
l
C
1'
O!
I
I
I I IIIIIII

 

 

 

  
 
 
 

[’1
.'
LI I IIIIII

dfly( mb/ MeV sr)
1
1

'5:

I I I IIIIII ‘

\

E

Y
1
H”;
1—1

/

/
/
7‘8 I
I
“L. . f.....|

2

d o/d
I I IIIIIII

60 120 ' 180
eY (deg)

Figure II-S Angular distribution for N + C at E/AzuO MeV: Remington et

al. calculations and our data (before calibration
correction).

 

 

 

--A
“.3
c:)‘\l

61

 

_L
O
L
lllllll
1:)
C3
_?,_
(D
S
C:

l l ”HUI

l

11y3

BI
I
I

\

I
10’
I

I
I
I1

0 I Illlllll l lll\lllll ‘
Y \
‘ I
I
I
I
I
_ . I
I.
g /
l

dfly(mb/MeVsr)

 

/
I
I
l

._
l3

 

10-5

2
d ME
6 ’Y
[I

.__——
I
17 1 1 111111, 41 1 1 11111

 

l
60 120 180
67 (deg)

Figure II-6 Angular distribution for N + Pb at E/AzuO MeV: Remington et
al. and our data (before calibration correction).

 

II-u

62

2 2
d N(b) d0 E 1 d oelem (k,,k,)

as d = £n_p °°11 u: 2' 0 ds' d
Y QY QY

X [1-f(r,k,,t)][1-f(r,k.,t)].

The single particle distribution function fi=f(ri,pi,t) is a Wigner

function, representing the phase-space density, and its time evolution

is governed by the Boltzman-Uehling-Uhlembeck equation

II-S

where

3f, u , , do
-——— + v-vrr, - vru . v r, = -—— , d k, d k,d0 v.,
at p (21) do

 

x a’<k1+ k,- k,- k.) [r,r,(1-r,)(1-r.) - r,r.(1-r.)(1-f.>]

U(o)= - 218 MeV p/po + 161 MeV (p/p.)“/’.

Integration of equation 11-1 over impact parameter gives the total yield

in the nucleon-nucleon center of mass.

II-6

eff

2

2
d o d N(b)

: Zflbdb

dEY dflY dEY d0Y

 

63

From the dynamical nature of this model it is possible to extract

information on the time the ganma rays are emitted. Figure II-7 shows

‘

12 2
the photon yield as a fUnction of time for the C + C system at E/A=fl0
MeV.

In the interval between t,=15 fm/c, when the two nuclei start
touching each other, and t2: 33 fm/o when maximum overlap takes place,

about 90% of the gamma rays are emitted. It is clear that in this
model, high-energy gamma rays can be regarded as probes of the momentum
and energy of the nucleons in the early stages of a heavy ion reaction.
Figure II-8 shows the impact parameter dependence of the gamma-ray
yield. A comparison with the result obtained with a simple geometrical
overlap of two circles is also shown. Overall this geometrical
approximation reproduces reasonable well the BUU calculated impact-
parameter dependence of the high-energy gamma-ray production.

The calculated double differential cross sections reproduce well
the general behavior of the experimental results (before calibration)
as shown in Figure II-9. However, the magnitude of the yield is too
large, and the gap between the prediction and the experimental results
becomes greater with decreasing beam energy. While, after the
calibration corrections, the ”0 MeV data is well reproduced the 20 MeV
data is still overestimated. The general behavior of the differential
cross-section angular distribution is well reproduced (after calibration
correction) for 40 Mev gamma rays, but for higher gamma-ray energies the
predicted angular distribution is more forward peaked then the

experimental one.

150

HH
ON
00‘

0'0
O

vv'v

Yield [arb.units]
N a
U. 0'

O

Figure II-7 BUU

 

AA‘AA

 

 

A A ‘ k- A

 

AAA

 

 

t [fm/c]

calculation of the photon yield as a function of time
for C + C at E/Azuo MeV.

50 so

65

 

 

 

 

 

 

 

1.5

 
  

 

 

 

1.0

 

 

Figure II-8 BUU impact-parameter dependence of the gamma-ray yield.

66

 

103 vrrv1vMflnvvrvrv7

 

 

  
 

da/dfldE [nb-MeV'1-sr'1]

 

 

10‘1
I
1
lO‘zfl- 1
» +¢+ 0«
10-3 e“--‘-'-~~~WL—n¢

 

40 60 50 100
E, [MeV]

2
Figure II-9 Experimental do /(dE d9) and BUU calculations. From top
to bottom: C + C at E/Az84 MeV [Gr 86] and our N + C
at NO, 30 and 20 MeV/n (before calibration corrections).

67

In the second dynamical study, Bauer et al. [Ba 87] used a
relativistic expression including the radiative corrections to the
mesons w and 0 exchange in the elementary process. Figure II-10 and II-
12 show the comparison between theoretical and experimental results
(before calibration) both for the double differential and for the

angular distribution.

2. Thermal emission

The exponential behavior of the gamma-ray spectra and the
possibility of finding a reference frame in which the emission is
isotropic could, on the other hand, be interpreted as a signature of a
thermal process. In this picture gamma rays are produced during
nucleon-nucleon collisions in a "fireball" or hot zone formed by part of
the target and part of the projectile nucleons. Since the total
available energy, in this case, is the sum of the hot zone nucleon
energies, the high gamma-ray energies (50 - 100 MeV) can easily be
obtained.

Bonasera et al. [Bo 87b] reduce the mass and the total energy of
the fireball, obtained from geometrical considerations, to take in
account the limitations in the number of collisions imposed by the Pauli
principle. The decay rate is calculated with the Heisskopf theory.
While the slopes of the gamma-ray spectra are well reproduced, the total
yield is overestimated, even after calibration corrections, by at least
a factor of 3.

Nifenecker et al. [Ni 85] used a Boltzmann gas of temperature T to

represent the fireball. The velocities of the colliding nucleons obey

68

 

V V V l T r V V " V V ' v I V V V

o
0 0

.1.-

‘3)
N

-l

 

da/dEdn [nb-MeV"~sr'1]
3;

 

p
O
O

 

l 0.5 0 -0.5 -1

case“...

Figure II-1O BUU angular distributions as compared to our data (before
calibration corrections) for N + C at E/AzuO MeV and
photon energies of HO (circles), 60 (diamonds) and 80

(squares) MeV.

69

 

 

100
715
T. 10 5A
> :
03 I
z ..
.D 1 ._
5 ,0
.o
[‘5' I°<> "
% 01 —
\ '
O :
'0 c
0.01 .5.-
0.001

 

 

 

 

 

40 so so 100
E1 [MeV]

2
Figure II-11 Experimental do /(dE d0) and BUU calculations. From top
to bottom: C + C at E/Az8u Mev [Gr 86] and our N + C
(before calibration corrections) at E/A:40, 30 and 20 MeV.

7O

 

100

dO/dEdQ [nb - MeV"-sr"]

 

'- -

l I ll
1 o -1
coselab

Figure II-12 BUU angular distributions as compared to our data (before
calibration corrections) for N + C at E/Azuo Mev and
photon energies of 40 (circles), 60 (diamonds) and 80
(squares) MeV.

 

 

 

71

Maxwell distributions, and the emitted radiation is incoherent because
of the lack of correlation between nucleons in the fireball. The n-p

bremsstrahlung emission is studied in the soft-photon approximation and

only the portion of the spectrum ‘ZC + C at E/A=8u Mev below 50 Mev can
be reproduced well using thermal emission as the main mechanism.

D. Neuhauser and S. E. Koonin [Ne 87] substituted the exact quantal
nucleon-nucleon bremsstrahlung cross section in place of the classical
soft-photon approximation. This substitution appears to modify

substantially the theoretical spectrum especially at high energies.

‘l

q
Good agreement is found for the reactions N + Pb at E/A=u0 MeV (before

1

2
calibration) and C + U at E/Az8h MeV (Figure II-13).

10'
10°
10"
|o°2 .
1:
‘1”
> 10'3
§
a
3 lo"
1. ‘3
1: =5 102
[0| _
10°
10"
10'2

72

 

T I r I T

o) N + Pb
40 MeV/A

 

 

\
\
\
\
\
\
\
l l l l 1
T f l l I
b) C + U
\ I ' e4 MeV/A
\\
\
\
\
\
\
\
\
\
\
\\ .
\\ I
\
\
\
\
\
\
\
\
1 1 1 - 1 1 >
so ICC 150
k (MeV)

Figure II-13 Neuhauser et al. theoretical calculations compared to our
C + Pb (before calibration corrections) at E/A=MO MeV and

to Grosse et al. C + U at E/Az84 MeV [Gr 86].

CHAPTER III
HIGH-ENERGY GAMMA RAY-CHARGED PARTICLE COINCIDENCE
A. EXPERIMENTAL SET-UP

In order to shed some light on the high energy gamma-ray production
mechanism we performed an experiment at the National Superconducting
Cyclotron Laboratory to study the coincidence between high-energy gauma
rays and light (2:1) charged particles (c.p.) emitted in the reaction:

1”" + Zn -> Y + c.p. + X at E/A=HO Mev

Where X is any other reaction product.

On one side of the beam, sixteen charged particle telescopes were
placed outside a small aluminum vacuum chamber (Figure 111-1) and viewed
the target through three thin (0.25“ am) kapton windows. Fourteen of
the telescopes were grouped in pairs and covered the angular range
between 30° and 120°, one was positioned at 130°, and the last one was
at 9=u0° and ¢=90° out of the plane. The total solid angle covered was
250 msr.

0n the other side of the beam two high-energy gamma-ray telescopes
were positioned, outside the chamber, at 60° and 120° each covering a
solid angle of 125 msr. The vacuum chamber wall facing the high-energy
gamma-ray detectors was 0.95 cm thick. The transmission coefficient for
10 Mev gamma rays is 0.9“23 and 0.9413 for 60 Mev gamma rays. The

experimental set-up is shown in Figure III-2. The experiment ran for

‘l

1. 2
ten days with about 20 enA of E/A=uo MeV N on a 30 mg/cm Zn target.

73

71$

TARGET LADDER HOLE

-
BEN - -

APP

KAPTON WINDOWS

 

 

 

 

 

Figure III-1 Aluminium vacuum chamber.

 

75

GAMMA - RAY TELESCOPES
D1 (60 °) 02 (120 °)
3 BEAM VACUUM CHAMBER

% \
PH1 (30°)

PH2 (40°) PHB (130°)
PH3 (60°) 1 PH7 (120°)
PH4 (70°) PH6 (90°)
PH5 (80°)

 

 

 

 

 

CHARGED-PARTICLE DETECTORS

Figure III-2 Experimental set-up for the coincidence experiment.

76

1. AE-E detectors.

The charged particle AE-E telescopes (Figure III-3) were plastic
scintillators, often called "phoswichs" (phosphorous sandwich). They
consisted of a fast scintillating plastic (Bicron BC-A12) 1.6 mm thick
for AE measurements followed by a tapered 127 mm slow scintillating
plastic (Bicron BC-AAA) for E measurements. The properties of the
plastic scintillator material are reported in Table 111-1.

A single photomultiplier tube (Amperex 2202), viewing the detector
through the end of the E detector, could provide a AE and an E signal by
applying a narrow time gate for the 60 ns short component and a broad
gate for the 260 ns component (Figure III-A). Protons, deuterons and
tritons could easily be separated. The energy range of particles
detected in the telescopes is summarized in Table III-2. The different
low and high energy limit for each detector is due to the different
amount of target, kapton window and air crossed by charged particles

detected at different angles.

2. High-energy gamma-ray detector

The high energy gamma-ray detectors used in this experiment were
essentially the same ones used in the singles experiment described in
chapter I. The only difference was the type of converter used. He
replaced the active CsI converters with two equal 12.? x 12.7 x 0.35 cm

passive Pb converters characterized by higher efficiency (Figure III-5).

B. ELECTRONICS

 

77

 

 

 

 

 

 

 

 

 

 

msu-a7.244
V .630m
.36cm ‘
\
4.36cm AE E PMT
I 5.63 cm
_.: l2.7cm __. .
O.l5cm

Figure III-3 Charged particle AE-E telescope.

78

Table 111-1 Plastic scintillator properties.

Fast plastic Slow plastic
(BC-A12) (BC-AAA)
Rise time (ns) 1.0 19.
Decay time (ns) 3.3 179.7
Pulse width (FWHM ns) “.2 171.9
Wavelength of maximum A34 u28

emission(nm)

79

53 MeV/nucleon 1: Signal

2C! ICXD ZIXD 3CK)
I I I I

AE E

Figure III-A Time gates for AF and E signal.

80
Table 111-2 Lower and upper energy limits for charged particle

detected in the AE-E telescopes.

DET p d t
L(MeV) H(MeV) L(MeV) H(MeV) L(MeV) 11(MeV)

PH1 14.5 135 19.7 182 23.5 218
PH2 14.5 135 19.7 182 23.5 218
PH3 19.5 135 19.7 182 23.5 218
PH“ 13.9 139 18.7 182 22.3 218
PHS 1A.1 134 18.9 182 22.7 218
PH6 1A.5 135 19.7 182 23.3 218
PH7 19.5 135 19.5 182 23.3 218
PH8U 14.1 139 19.1 182 22.7 218

PH8D 15.5 135 21.1 182 2u.9 218

81

 

 

 

 

80 I if I I l I j I I l I T r T I I T I j
5‘ 60— _
G - .
Q) ~ a
0'4
C) ' .
.H __ _+
‘43 _
1» 4°? .
8\° . .
20_ Pb __
r d
L .
o L l l l I L 1 l I I l I l l I l L l 1 d
O 50 100 150 200

E7 (MeV)

Figure III-5 Efficiency versus gamma—ray energy for Pb converter.

82

The electronics set-up allowed the simultaneous collection of four

different types of events:

1) Gamma-ray singles taken by either one of the two gamma detectors.

2) Gamma ray-charged particle coincidence between either Cherenkov
detector and any of the phoswich detectors.

3) Sealed down charged particle singles and two-fold coincidences.

A) All charged particle three fold and higher coincidences.

The scale-down factor was different for different positions in
order to obtain comparable count rates: it was 1000 for the first four
most forward angles (30-70°), 500 for the next two (80 and 90°) and 200
for the last two (120 and 130°).

Figure III-6 is a drawing of the logic master gate. The electronic
circuit for a charged particle detector is shown in Figure III-7, and
the circuit used for each high-energy ganma-ray telescope was the same

as the one shown in chapter I in Figure I-2a.

C. CHARGED PARTICLE DETECTOR CALIBRATION

The energy scale of the 2:1 isotopes in the AE-E spectra was

calibrated using a deuteron beam at E/A=53 MeV on a 19.31 mg/cm2 Au
target. Three calibration points were obtained using the elastic
scattering peak and the two peaks produced by degrading the elastically
scattered deuterons using Al absorbers 11 and 18 mm thick.

Before the calibration points could be used to define an energy
scale it was necessary to correct the AE-E spectra by the so called

"gamma-neutron line subtraction". For each charged particle event the

83

’ CKI up
cx1 0N
cxz UP
cxz 0N

conv UP

_ CONV DN

CKI UP
CKI DN
CK2 up
cxz DN
CONV UP
_ CONV DN

PHI UP
PHI DN
PH2 UP

PH8 DN

     
 
 

QNCLES

DETECTOR I

SINGLES

    

Y-

 

DETECTOR 2

 

PHI UP
PHI DN
PH2 UP

PH8 DN

PHI UP
PHI DN
PH2 UP
PH2 DN

PH3 UP
PH3 DN
PH4 UP
PH4 DN

PHS UP
PHS DN
PH6 UP
PH6 DN

PH7 UP
PH7 DN
PH8 UP
PH8 0N

IAOOO

    

DUOOO

Figure III-6 Logic master gate.

811

 

SCALER
SCALE-001m
0R
’ SCALE
DOWN
x4
SCALER 1113.351:
AE SCALER {“0153 ’3 3
UN: )3 ‘
AMP
PMT ‘CFD m SCALER

 

 

 

 

 

 

‘ 5911111211 XIG
E 10c '
5109

Y Y SNGLES
-

BIT
REG

 

 

Figure III-7 Electronic circuit for a charged particle detector.

85

AE signal is always contaminated by part of the E signal causing the AE
signal to increase with increasing energy. The data from neutron and
ganma-ray events can be used to correct for the false rise due to the
nature of the interaction of these uncharged particles in the detector.
The interaction probability of neutrons and gamma rays in the AE portion
is small, because it is thin, but the interaction probability of these
particles in the E portion is not small. Thus, for these reactions,
light only comes from the E portion of the detector and the AE signal is
entirely due to contamination from the E signal. The AE-E spectrum for
neutrons and gamma rays is a line beginning at the origin (the "gums-
neutron line) which represents the false rise in AF as a function of E.
The corrected charged-particle spectra were found by taking a point by
point difference between the AE of each charged particle event and the
ordinate of a point in the "ganma-neutron line" having the same value of
E. Figures III-8a and III-8b show a AE-E spectrum before and after the
subtraction respectively.

Shown in Figures III-9a and III-9b are plots of energy versus
channel number for one of the charged particle detectors. Plots are
shown both for AF and the E part of the detector. The calibration was
done both fer the gamma ray-charged particle coincidence and the charged
particle single trigger configuration since a difference in the timing
of the two produced a slight difference in the AE-E spectra.

Since the plots of energy versus channel number vary from detector
to detector and we desired to have a unique energy scale for all
detectors, we employed the following simple rescaling process. In
Figure III-10, line (a) represents an arbitrary reference line while

line (b) represents a phoswich calibration line obtained by fitting the

86

 

120 —

100 -

80r-

      

60 — ., ..
. .
.- <}— 7 — neutron line

 

 

o 1 L 1 1 1 1

 

 

O 20 4O 60 80 100 1 20

Figure III-8a Isotope lines before "gamma-neutron line" subtraction.

87

 

 
    
     
 
      

 

 

1 20 — .I.‘ .- I
'I
V
100 I- ,.
.._.‘...:'. .I: ‘
, . ..
:0‘.‘ .‘ ‘
‘ " ‘.'.' o. -. '.
. A I. 7 e. ' .
\ 6 ' ,.. "‘ o ' .
.a ’, "'3'.
l '\ \ ’1 t '
.
80 I ’
.:v \ I
.5
_ .l- .
:1 a. ,- . .
. _ | ‘ , . I . _ . ' _ .
' ,.:’--\_.'.‘.: ~ _. -- ‘~ _ . . _ ~' . ‘ . u. .\ .
- . '-~c . . ' » -- - - .
' 'o'o-u ' .. '
I y.‘ . ."p'I ' ' _ . . U D ‘ .. . .. . . ' -' ‘ ' o .I .-
. .:1-'\" 7,; v" -.'.' 2.0. . . v .. . ‘ . . .
60 '"I-‘M '1-1 . ' ‘ q -‘ n.‘v ~ J ' .
v n" - ’ ‘ 0‘ " 2‘20' -‘-‘o - I'
- .:.. ’ UV.» -" I , -
... 04";3'”... \‘.f..f,“ 0:, . '. '1
g " “.. .
«1.1.19.5. ~; ~
.- ..... - ;. 3." "
. ,‘ ‘-.'-.--' .4. .
- u 9 o
. o l.- . ' \ '
t" a s :- \ o .
o. 'O . J '
. I '0 ~
1 1 ’. "._"1._..".' _ . .
\ ".:'._. . .-
-.:. an u.. . .-. ., .:. gnifhkfli\m'
" . .. . . .- -. - ' ' '1" ‘ -., . - ‘."‘ JQ'l‘. ‘11J‘u'.“‘n"'
» ‘. - ’. . - , - - -.-. -':-. rj-gc-q-‘uwz
1' "“ 53".”3-4
°. 00 a. - ..'-
.J‘. '0’“... - "
04'" *1 v -
. Jan -‘."'- -
ho _"..' . .
17“”5 ' 1
20 . .

O 20 4O 60 80 100

120

Figure III-8b Isotope lines after "gamma-neutron line" subraction.

 

88

 

 

 

 

 

150 IIrT IIII I1II IIIT II—II IITI IIII IIII IIII I—ITI IIII IIII

E I I I I I g I I I I I _

125 :_ PHI E 050? cps - PHI E 0201' CC? ’3

A 100E» x j x —5
:> i E E
m 755— x —: x .1
2 : : 1
v c : 1
m 5°"? x ‘5 x ‘2
I- -I 1

25 E- —; ~--:

0 LLLLIlLlllLLllLlilllJllJlljJ:lulllllJllJIILLuliLllllll
0 25 50 75 100 125 25 50 75 100 125 150

channel #

Figure III-9a E versus channel number for a charged particle detector.

 

8 IIIlIIIIIIrIIIIIIIlIIfi‘lIIII

: E:IIIIIIIT‘IIITIIIIIIIIIIIIIjjIE

5? PHI AE DEUT cps ‘3‘ PHI AE DEUT ace 1

b ~ +

A 4E- x -E x '_3
> I: 1 :
Q) 3% _: _§
[1:] 2E:— X ""3 X “'3
1% -~f —a
llllllllijlllllllllul‘ll jLllllllLlLLlLLlelllllljll

 

 

 

 

5 10152025305 1015202530
channel #

Figure III-9b 05 versus channel number for a charged particle detector.

89

 

 

 

 

 

 

MSU-87—245
E A
Ell = ml. Ch" + E0
1 (b). (a).
P(Ch",E") '
EusE' QICh ,E|)
E
/° I
E'=m'ch'
II I .
0 ch ch ch

Figure III-10 Energy rescaling diagram for a charged particle detector.

90
data points of plots similar to Figure III-9. Points P and Q have the

same energy but different channel number. Equating the two energies:

III-1 E'zE" => m'ch': m"ch" + 5,

the new value of ch' is ch':m"ch"/m'+E./m'. The value of m' defines the

energy scale.
The kinetic energy of each charged particle was obtained by adding
together the contributions, rescaled using the calibration data, of the

fast AE component and the slow E: component.

D. DATA REDUCTION

The major contamination in the high energy gamma-ray spectrum is
due to cosmic muons. To reduce this background to a minimum it was
required that there be: no signal out of the discriminator for the
front, side and top anticoincidence shields. More restrictive
conditions additionally required the pulse height in the detector
shields be below a minimum value.

All 16 charged particle detectors were originally designed to be
positioned 143.2 cm away from the target so that, at that distance, both
the front and the back faces subtended the same solid angle (Figure III-
11). In the coincidence experiment, some of the detectors were
positioned at much smaller distances (Table 111-3) creating problems
with particles escaping from the sides (Figure III-12). Since the E
portion of the signal for the escaping particles is smaller than the one

obtained for a completely contained particle, the point representing the

91

TARGET

43.2 cm

PHOSWICH
(normal posi’rion)

Figure III-11 Charged-particle detector: normal position.

 

92
Table III-3. Angular position, distance and solid angle covered for

each charged particle detector.

DETECTOR ANGLE 0 (°) SOLID ANGLE(msr) DISTANCE FROM
TARGET(cm)

PH1U 31.3 5.150 61.03

PH1D 31.3 5.150 61.03

PH2U “2.3 5.116 61.24

PHZD “2.3 5.116 61.2“

PH3U 61.0 15.962 30.67

PH3D 61.0 15.962 34.67

PHHU 72.6 20.653 30.u8

PHHD 72.6 20.653 30.48

PHSU 81.5 20.350 30.71

PHSD 81.5 20.350 30.71

PH6U 91.0 21.110 30.15

PH6D 91.0 21.110 30.15

PH7U 122.0 22.800 29.00

PH7D 122.0 22.800 29.00

PH8U 131.9 22.250. 29.36

PH8D 40.0 “.200 67.56

TARGET

 

Region where

por’ricles punch PHOSWICH
OUT The Slde (1,00 close)

Region where

por’ricles punch
in The side PHOSWICH

_ (+00 dis’roni)

/ \

E“igure III-12 Charged-particle detector: closer and farther.

 

 

 

911

particle in 08-5 plot, is shifted to the left of the correct isotope
line. The overall effect is that the covered solid angle is then
determined by the back face of the detector. Other detectors sat
farther away, allowing a particle to enter from the side and miss the AE
portion of the detector (Figure III-12). These events look like neutron
events since the AE signal will always be a fraction of the 15: signal as
explained above and will therefore be rejected in the analysis. One of
the charged particle detectors at 80° failed before the calibration and
the data from it were never included in the results.

Gates were drawn on the 08-8 plots to separate particles with
different mass and charge. Separate sets of gates were drawn for
charged particle singles and for charged particles in coincidence with
high-energy ganma rays because of the spectral difference caused by the
different electronic timing. The coincidence between a ganma ray and a
charged particle was defined by drawing a gate on a two dimensional time

plot of the first Cherenkov element versus each phoswich.

E . RESULTS

1 . Ratios.

A comparison of the spectra for high-energy gamma-ray singles at
60° and for high-energy ganma rays at 60° in coincidence with protons at
30° or at 70° did not show any strong features (Figure III-13). The
comparison of the spectra for proton singles at 30° and protons at 30°
in coincidence with ganlna rays at 60° (Figure III-1n) also failed to

1I'lodicate any marked difference in the coincidence data. The energy

# COUNTS

95

HIGH—ENERGY GAMMA RAYS 0,=60°

 

  
 

D SINGLES

V Ifi r I I r I I I I T I I r I T I I r T I I 'I I I I d
-—.i

8335 x comc ep=3O° 1
<> COINC ep=70° .

 

 

E7 (MeV)

dence with protons at 30° or at 70°.

Xx

x .

a a g i i i mmmmmmmmm —:
§§ EH mmmm 3

i IN @003 J

§§i {1; fl 0‘

if I
1.1.12.1.L1.1.1...nlln..l.d
40 60 80 100 120

E7igure III-13 Gamma ray singles at 60° and gamma rays at 60° in coinci-

96

PROTONS Bur-30°

IITIIIIIIII‘IIYIIleIIIIII

 

I I

x COINC a,=eo°
<> SINGLES

III I IIIIIIII

# COUNTS
H
O
N
I IIIIIIII
N
196
196
196
HH
1-)(-'|
1961
1 1111111' 1 1LLLla 1 11111111 J 1L111111 1 11111111 1 1

H
O
H
j I I IIIIII
F——%&4
F—fid

 

 

 

100 l l l L 1 l I l l 1 l L J_ l L 1 l I l l l 1 l 1 1 L
40 60 80 100 120
Ep(MeV)

E7igure III-1N Proton singles at 30° and protons at 30° in coincidence
with gamma rays at 60°.

97
integrated angular distributions for the two sets of events also showed
the same overall behavior as a function of angle (Figure III-15). This
comparisons are only qualitative since the solid angles used are the
ones determined by the frontal 08 surface while for phoswichs at a
distance smaller than 113.2 cm, because of the scattering out of the
particles, the physical solid angle can be up to 25% smaller. A more
careful examination of the data seemed to be necessary to uncover small
differences. To do so we studied the ratio of the coincidence cross
section to the product of the singles cross-sections. The energy

integrated angular distribution of the ratio defined in equation III-2

2

 

0
Y d 0
III-2 R(e )= —L— where o = —— .
p 0Y 0p YP dflYde
d0 d0
0 = ""—"""" O :
Y C! ' do
07 p p

is shown in Figure III-16 for coincidence with Detector 1 (at 60°) and
in Figure III-17 for coincidence with Detector 2 (at 120°). The energy
range is 20-128 MeV for gamma rays and 30-135 MeV protOns. The
uncertainties are assumed to be statistical in origin and they are

calculated using the quadrature method. For both gamma-ray detectors

_1
the ratio is fairly constant with a mean value of 0.6 barn .

The values of the ratio R(9p) obtained for the out-of-plane

phoswich at 0:90°,9=lIO° are compared in Table III-ii to the values
obtained for the corresponding in plane phoswich at ¢=0°,e=u0°. While

for coincidences with D2(120°) the two values agree within error bars in

104

103

# COUNTS / (MeVatmsr)

98

AN GULAR DISTRIBUTION

 

rTTYTIrTTlIIIIIrYVUIUVrIIUYV
X
X
0 X x
O
D X
0 o x
0 x
D U 0 X
0
. 0
Xp—smgles D o

0 p—Dl coinc
D p—DZ coinc

lLllllJllilllLlJllLlllllJlllL

25 50 75 100 125 150

®p

Figure III-15 Energy-integrated angular-distributions: proton singles

and protons in coincidence with gamma rays at 60°.

f—b H
N 01
0| 0

H
O
O

—1
(rm/0pm., (barn)

g: c:

3 8’:

F’
a:
GI

(IOU

99

 

ITIITIYIIITTI‘IIIIllTWrrlTIj

9.,=60°

IIIIIITUIIIIIIIIIITTI1IIIIII

 

lllllllkllllllllLlllllLllllll

¢1L41LL11LL1LL1LL1L11llLllLiLlL

 

 

25 50 75 100 125

6p

Figure III-16 Ratio versus Op for gamma rays at 60°.

150

100

 

H
0"
O

WITTIITIrlTIITT—TjITIFI{IIIII

[KIT

2"
to
on

9,=120°

!‘
<3
<3

—1
O'p7/ 01,3607 (barn)

0

6'1

(125

RH
96
I—X—i
illLllllllllllll111111111111

O

U!

C
IIfirrTIrIlIUIIIITIIIITIII

 

 

0.00 LllJLlllllllllllllllJllllLLll
25 50 75 100 125 150

9p

Figure III-17 Ratio versus Op for gamma rays at 120°.

 

101

Table III-14. Comparison of R(8p) values for the out-of-plane and

the in-plane phoswich at 9=NO°.

0+

e=u0°, ¢=0° 0.61 i 0.02 0.6a

e=u0°, ¢=9oo 0.51 1 0.03 0.57 1 0.05

102
the case of coincidences with D1(60°) the difference between the two is
approximately two standard deviations.

To study the proton energy dependence, the ratio R(Ep) was defined

 

do
III-14 R(E ) = where o : ——
o o E Y d dB 0 ’
p Y 9(9) p 0Y pdp

2
o-—d—°— o-L
‘ deE Y‘ d '
p p p 0‘!

Figure III-18 shows the ratio R calculated at four angles: 30, 110,

1

60 and 70°. Again R is basically constant with a value of 0.6 barn' .
The ratio at back angles could not be calculated because of inadequate
statistics.

To study the gama-ray energy dependence of the ratio we used a
thermal source parameterization of the proton spectra both for the
singles and for the coincidence case. The proton source velocities are
listed in Table 111-5. The ratio as a function of gamma ray energy was
studied in the laboratory frame for proton energies integrated above
four different lower values. The lower values of‘ the proton energy
corresponded to energies of 30, 110, SO and 60 MeV in a source frame

moving with velocity 8:0.1u2c. The ratio RUBY), as function of gamma-

ray energy is

103

 

1.50 IIIIIIIIIIIIIWTTIIIIIII

.

1111

ITIIITIIIITI—I—IIIIIIIIIIYI

1135

1130

6p=30° ap=40° 1L
0f75

xx *1} XXI)?

11111111111L1U11111l111L

Immuliwlmul

IIIIIIIITTIIIIIITIIIIIIIIIII

 

 

 

 

 

v.4
|
A
E x
0.50 >I<
CU
Q 0.25 . -
Q4 0.00 11l1LL1l1111llJJllllllllljllllIJlllllllllllllllllllLl:
b E E E
>)(< 1.25 _— 1 ":
b?‘ : j :
1.00 E— _ o I -—: __ o '4:
\Q E 0p—60 j zap—7o 5
A 0.75 :- X I '_:
b E X x j X x :
0.50 :— it % J. —_j * * _.
0.25 ;— -E —I
E 1 :

Llllllllllllljllllllllll 11"

—

 

0.00 LlllllllIllllLllllllllllL

Ep (MeV)

Figure III-18 Ratio versus Ep for protons at: 30, ”0, 60 and 70°.

mu

Table III-5. Proton source velocities.

B=v/c -
proton singles 0.1HS
proton in coincidence with D1 0.140

proton in coincidence with D2 0.135

105

 

( 01pm.) .1. I
111-5 R ) = where o = ----- *,
EY op oY(EY) Yp dQYdEYde sz 2p
2
o - _C.l_°_ , - ALI .
- , _
Y dQYdEY p de Epz Ep

I
and Ep 2 30, 40, 50 or 60 MeV.

The results are shown in Figure III-19. Within experimental errors
no gamma-ray energy dependence is seen in the value of the ratio for
energies above 25 MeV. For energies around 20 MeV, where gamma rays are
strongly associated with the giant dipole resonance, the value of the

ratio R(EY) is smaller which indicates a less likely coincidence.

2. Multiplicity.

A specific parameter was constructed to count how many phoswichs
registered a charged particle in each event. The value of this
parameter defined the event multiplicity for our experimental geometry.
Because the phoswich 5UP was not calibrated, and phoswich 8DN was out of
plane, the total number of detectors used in determining the
multiplicity was 111. The total solid angle covered was 2211 msr. The
gamma ray - charged particle multiplicity parameter was incremented if

the following conditions were satisfied for a given phoswich:

-1
ayp/ayémp (barn)

Figure III-19 Ratio versus E

3.0
2.5
2.0
1.5
1.0
0.5
0.0
2.5
2.0
1.5
1.0
0.5
0.0

106

 

TIITTIIIIITIITTIIIITIIIIT

Ep> 30 MeV

x *

IrTIIIIWIIIIIIII11lIlIIlfiII

11i1LL1111111111111111lL1

IITTIIHI‘I’V‘TIIIIIIllllI—I

Ep> 40 MeV

x*:]r

111 1111l1111l111111111l1

 

 

 

 

x x X
x in ’1‘ x ,I{ {K
hLLlllJJlllllllllllllLlll[11111111111111111llllLLllllll
: 3 3
t— “; 1
5. . _=
; Ep> 50 MeV ‘i Ep> 60 MeV g
:— 11. ‘1 1
E ’1‘ 111 1 5
:_ x * >1< )1, + j x in 11‘ {K _:
:x : x :
: 1111111111111111111111111:111111111'1111111L111 llL’éL‘

 

 

 

25 50 75100125

25 50 75100125

E7 (MeV)

Y

for Ep) 30,

H0, 50 or 60 MeV in a

reference frame moving with velocity equal to 3:0.1u.

107
1) On a 2-dimensional TDC plot of the phoswich versus the first element
of the gamma-ray detector positioned at 60°, the event under
consideration was inside the proper coincidence gate.
2) The gamma ray had an energy equal to or greater than 20 MeV.
3) The charged particle was a 2:1 isotope.
H) The 2:1 isotope had an energy equal to or greater than 30 MeV.

An event with a gamma ray of energy equal to or above 20 MeV but
with no 2:1 isotope satisfying the above conditions was counted as
multiplicity 0. The ganma - charged particle multiplicity H histogram
is shown in Figure III-20. The number of counts and the uncertainties
(purely statistical errors) are listed in Table III-6.

Because of the complexity of the master gate, the charged particle
- charged particle multiplicity was by far more difficult to obtain than
the previous multiplicity. All the charged particle events with
multiplicity less than three were scaled down by various factors
depending upon the detector position. The number of counts in the
multiplicity-one bin was the result of the sum over all detectors of the

number of events with multiplicity one for each phoswich, PHk’

multiplied by the appropriate scale-down factor nk. The total

multiplicity-one datum can then be written as

111 111

III-u E=1 #counts PHk= E=1 #counts recorded PHK . nk

An event was accepted in any given phoswich if it represented a 2:1
isotope with energy above or equal to 30 MeV, had correct timing and no

other 2:1 isotope was registered in the other phoswichs.

108

‘y—c.p. MULTIPLICITY

 

 

 

 

 

 

 

 

 

 

109 ~— '—
" E, > 20 MeV

106 _ Ez_,1 > 30 MeV __
E53 _ 4
z
D _ a
8 3
=14: 10 ~—

10°

0 1 2

M

Figure III-20 Multiplicity of charged particles in coincidence with
gamma rays at 60° (Y-op).

109

Table III-6. Multiplicities: Y - c.p. and c.p. - c.p.

Y - c p c.p - c p
M:0 177913 f 691 M:1 u2792u6u0 t 2071u
n:1 8689 i 93 M:2 705639“ f 3046

(frontal solid angle)

7085198 1 3057

(back solid angle)

I +

M:2 63 f 8 M=3 97927 167

1+

M u 682

12

110
In calculating the uncertainty, we have to consider two sources of

error. The first originates from the nature of the scale-down factor:
a count f0r PHk is not recorded until the real number of counts reaches
an integer multiple of nk. The correct number of counts in phoswich PH

k

is, therefore, between

III-5 (# counts recorded PHk - nk)
and
III-6 (# counts recorded PHk + 1) - nk.

To make this error symmetric we can rewrite it as

n
1 + k
III-7 [(# counts recorded PHk + —5— ) . nk .1—5—]

The second uncertainty is purely statistical and for phoswich PHk is

just [# counts PHkl1/2. The uncertainty for Pfi(, obtained with the

quadrature method, is then

III-8 A(#counts PHK)=

 

” 2
{I k]2 + / [#counts recorded PH + 0.5).“ ] }1/2
2 k k

111

and the multiplicity-one datum can be written as:

111
“1‘9 E111 connts recorded PHk+ —g- ] . "k 1
1‘4 n
$111715]?! + H counts recorded PHk+ 0,5] . nk11/2'

The multiplicity-two analysis was complicated by the fact that the
coincidence of the two 2:1 isotopes was scaled down by a factor
consisting of a combination of the scale-down factors of the two

detectors under consideration. If PHi and PH represent two phoswichs,

J

and n their respective scale-

1 .1

down factors, the total number of coincidences for the pair would be:

not part of the same "or" group, and n

# coinc. PHi PHJrecorded
III-10 # coinc. PHi PH = 1

J + -1—
nJ n.n

11

 

 

_1_
“1

For phoswichs in the same "or" group the number of coincidences is

simply :

# coinc. PHi PHJrecorded
III-11 # coinc. PHi PH :

J _1_

In considering coincidences between a phoswich, PHk’ and any other

phoswich the solid angle available to detect the second charged particle

112
is reduced to the solid angle covered by the remaining 13 detectors. In
order to be able to directly compare the Y-c.p. with c.p.-c.p.
coincidence counts, we normalized the c.p.-c.p. data to the same solid
angle as for the Y-c.p. data by multiplying the the number of
114
coincidences, I: #coinc. PHkPHI, by the factor in equation III-12. Auk
1:;
is the solid angle covered by phoswich PHk.

111
§ A0
:1 1

i=1AQl - Aok.

 

The total multiplicity-two datum is then the sum of 182 contributions

and can be written as

 

111
1H 1H §_,A9J
III-13 z [2 # coinc. PHkPHl [ u ‘ )]
k:1 l:1 §_1Ao - 50k
l=k - J

Both the statistical error and the error introduced by the scale-
down factors are considered in the determination of the total
uncertainty for the multiplicity-two datum given by equation III-1L1.

The compound scale-down factor for the pair of phoswichs PHk and PHlis

indicated as sokl .

113

 

1a
111 {HAoj 111
111-1“ {2 [ u ' ] 2 [# coinc.PHkPleecorded + 0.5] - sc
k:1 § A0 - A0 1:1
:1 J k l=k

kl}

111
1a A0 1n
:1

45 J ] §=1W3°k1>2 A +

“‘1 §=1°91 ' Auk l:k

[[# coinc.PHkPleecorded + 0.5] . sckl]1/2}.

+
[‘1

 

The physical solid angle, for phoswichs positioned at distances closer
than 113.2 cm., is somewhat smaller than the solid angle determined by
the front of the detector and bigger than the one determined by the back
of it. In Table Iv-6 are reported both the upper and the lower limit of
the multiplicity calculated for the two cases.

Multiplicity three and above were not scaled down and thus were
obtained in the same fashion as in the gamma - charged particle
multiplicity, incrementing the multiplicity parameter when the time,
isotope and energy requirements were met. The uncertainty for
multiplicities equal to or above three is simply the statistical error.

The recorded multiplicity-three datum is the sum of all different
three-fOld combinations of the 1“ phoswichs
u

u u

1
E PH PH PHi'

III-15 _, k J

Hm...

j 1
k k

1
J

The needed multiplicity-three datum is given, though, by the left-hand

side of equation III-16.

11H

.1:
t

u u H

1
E PH PH 9H1)

III-16 :1 R J

1 1
fi 1 PHkPHJPHi = 3 [§
1

gm;
II II

Lam—b

J 1
k k

1
k

H-H-Hri—b
u u V

”BL:-

A further correction is necessary to take in account the smaller solid
angle available in the c.p.-c.p. case then in the Y-c.p. case. For the

coincidence PH PH PH the correct factor would be

 

k J 1
1a 11
A A0
III-17 “E‘1 0k u§=k i with 1:1 and Jzk.
é=1A°1 ‘ A01 1=kA°1 ' ““1

but since the detailed angular information is lost the mean correction

factor used was:

1” 13
III-18 -T§-'-T§-.

Following the same kind of reasoning the correction factor fkn~ the

recorded multiplicity-four datum was:

14 13 12
13 12 11

 

III-19 u

The'charged particle - charged particle multiplicity M, is shown in
Figure III-21. The number of counts and the uncertainties are listed in

Table III-6.

115

c.p.— c.p. MULTIPLICITY

 

 

 

 

 

 

 

 

 

 

109 -— —
_ E,,,,1 > 30 MeV -
10° -— "
m an
9.. 1-
Z
::) _ .
8 3
=11: 10 —
10°

 

 

 

 

M

Figure III-21 Charged particle-charged particle multiplicity (cp-cp).

116
Figure III-22 shows a comparison of the rescaled multiplicities.
The ratio between the gamma - charged particle multiplicity M:1 (a 2:1
charged particle in coincidence with a gamma ray) and the charged

particle - charged particle multiplicity M:2 (a 2:1 charged particle in
coincidence with a 2:1 charged particle) is 1.103 t 0.012 using frontal

solid angles and 1.098 t 0.012 using back solid angles. Because of the
small number of counts in the Y-c.p. M:2 bin and the large uncertainty
in the c.p.-c.p. M:3 bin, due to the lack of a precise solid angle
correction, a comparison between these two multiplicities can not be

made quantitatively.

117

 

 

 

 

 

 

 

 

 

 

 

 

109 ~— -‘
" —— 7—C.p. MULT. ‘
- —— c.p.—c.p. MULTA
6 __ _
m 10 E, > 20 MeV
E _ Ez=1 > 30 Mev .4
D - ..
8 3
:11: 10 —
L ..
10O

 

 

Figure III-22 Comparison of the Y-cp and cp-cp multiplicities.

CHAPTER IV
INTERPRETATION OF THE COINCIDENCE RESULTS
A. IMPACT-PARAMETER DEPENDENCE

Hingmann et al. [Hi 87] performed at GANIL the first exclusive

high-energy gauma-ray experiment observing the products of the reaction

‘00 1

Ar + MGd at E/A:’-11-1 MeV. Gama rays at 90° fulfilling the following
conditions were examined:
(a) coincidences with slow heavy fragments (central collisions)
(b) coincidences with fast projectile-like fragments (peripheral
collisions).
(o) no coincidences with charged particles (grazing collisions)

The gamma-ray spectra obtained in the three cases are shown in
Figure IV-1. Keeping in mind that the conditions under study probably
contain some overlap, a comparison of spectra (a) and (b) shows a larger
yield of gamma rays associated with more central collisions. The
difference in the slope parameter could be simply related to the poor
statistics in the high-energy portion of spectrum (b). The dashed lines
in Figure IV-1 are the results of a nucleon-nucleon bremsstrahlung
calculation.

Herrmann et al. [He 87] studied high-energy ganma rays produced in

92 92
the reaction Mo + Mo at the incident beam energy of 19.5 MeV/nucl.

at the UNILAC at 681. Gamma rays were observed in the angular range

between 90 and 170° in coincidence with binary fragments of charge 2>10

118

119

 

E031. 30 MeV .—

l

E,=1/.:2 MeV ‘1’

o \
L

  
  
   

1

1 “w -1'

 

 

 

I r T

‘1

 

 

 

 

E, (MeV)

Figure IV-1 Gamma-ray spectra from reference [Hi 87]:
(a) coincidences with slow heavy fragments
(b) coincidences with fast projectile like fragments
(o) no coincidence with charged particles

120

detected in the forward hemisphere. The gamua-ray yield was studied as
a function of the total kinetic-energy loss in the collision (TKEL).
Increasing TKEL was found to be associated with an increase in the
gamma-ray yield and with a flatter spectral slope. Their interpretation
associated the gamma-ray production to a statistical emission from the
excited fragments rather then to a nucleon-nucleon bremmstrahlung
process.

To test further the impact parameter dependence of the gamma-ray
emission we studied the charged particle (2:1) multiplicity associated
with gamma-ray production (Figure III-19) and compared it with the
charged-particle (2:1) multiplicity associated with charged-particle
production (Figure III-20). If gamma rays are produced mainly in
central collisions, the average charged-particle multiplicity associated
with the emission of a gamma ray is expected to be higher than the
charged-particle multiplicity associated with the emission of other
particles such as 2:1 isotopes. A comparison of the two (Figure III-21
and Table III-6) shows only a small enhancement (21101) of the charged-
particle (2:1) production when a gamma ray is also produced. 0n the
limited basis of this result, since higher multiplicities results are
not available, high-energy gamma-ray emission appears to have an impact-
parameter dependence similar to that of the light 2:1 charged-particle
production. A fundamental difference between the two measurements needs
to be pointed out: while in the gamma ray case the coincidences are
detected on the opposite side of the beam in the charged particle -
charged particle case both particles are detected on the the same side
of the beam. The p-p, p-d and d-d coincidence results of D. Fox et a1.

[F0 87] for C + Ag at E/Azl10 MeV do not show much difference between

121
coincidences of particle detected on the same or on the opposite side of
the beam and suggests a similar behavior for coincidences of 2:1
particles.

In chapter II we saw that recent calculations [Ba 86] predict the
impact-parameter dependence of the gamma-ray yield to be proportional to
the overlap area of the colliding nuclei. We calculated the value of
the ratio R using this geometrical approximation.

The overlap area, A(b), of the projectile and the target nucleus is

/3

1
calculated assuming the nuclei to be spheres with radii R: 1.2 A fm

(Figure IV—2). In our specific case, R, is the radius of the zinc
nucleus, R2 is the radius of the nitrogen nucleus, and b is the impact

parameter.

The ordinate of the two intersection points is indicated by y,, and

its value is fOund by solving the system formed by the equations of the
two circles representing the two nuclei (equation 111-1). The resulting

expression for ya is given in equation IV-2.

IV-1 x + y = R,

IV-Z yo:

122

/\y -

 

 

v ” /. .
A2 A‘“ < <6 y y°

 

Figure IV-2 Overlap between the Zn nucleus (radius R,) and the N

nucleus (radius R,) .

123

For b 2 (R, - R,) the shaded overlap area A,(b), a section of the
circle of radius R,, is given by equation IV-3. The shaded overlap area
A,(b), a section of the circle of radius R,, is given by equation IV-u.
The total overlap area is A(b) : A,(b) + A,(b). For b S (R, - R,,) the

overlap area is simply the area of the smallest circle namely A(b) :

 

 

 

11R,.
R.
2 2
IV-3 A1(b) = 2 / R, - y dy :
Yo
2 2
R, arccos l" - y, R, / 1 - [1°]
R1 R1
R2
2 2
IV-“ Az(b) = 2 / R2 - ( b - y ) dy =
b ' Yo

 

2

 

2 _ b ’ Yo
R; arccos R,,-1° - R2(b'Yo) 1’ 1' I R J
z 2

The coincidence to singles ratio can be calculated by assuming that
the proton and gamma-ray cross sections are both proportional to A(b) .

The ratio R assuming the following proportionality:

12H

 

 

IV-S oY « A(b), 0D x A(b) and oYp a A(b)A(b)
is then given by equation IV-6.
R,+ R2
22
6 0 [A(b)] d b
IV- R = =
R1+ R2 2 2
I A(b) d b J
0
R,+ R, R.- R2
22 222
[A,(b) + A,(b)] d b + I [uR,] d b
R,- R1 0
R1* R2 2 R1‘ R1 2 2 z
I [ A,(b) + A,(b)] d b + I nR, d b ]
R,- R2 0

The integration was performed numerically.
We also considered an impact parameter dependence proportional to
the overlap volume of the two nuclei. The ordinate of the two

intersection points is indicated with 2,, and its value is found by

solving the system formed by the equations of the two spheres
representing the two nuclei (equation IV-7). The resulting expression

for z, is given in equation IV-8.

IV-7

2 2 2 2
x + y + (z - b) = R2.

125

2 2 2
R,- R,+ b
111-8 2,: ——
2b

For b 2 (R, - R,) the shaded overlap volume V,(b), a section of the
sphere of radius R,, is given by the integral in equation IV-9 and the
shaded overlap volume V,(b), a section of the sphere of radius R, is

given by the integral in equation IV-10. The total overlap volume is

V(b) = V,(b) + V,(b).

For b S (R, - R,) the overlap volume is simply the volume of the

smallest sphere namely V(b) : —l3‘— 11R,.

211 arcos(z,/R,) R, ,
d0 I sine d0 r dr :

IV-9 V1(b) = I
0 zo/cose

0

3 2 3
-%—[ 2R,- 320R, 4- 2,]

2n arccos(b-z.)/R, R, ,
do I sine d6 r dr :

IV-10 V,(b) = I
0 (b-z,)/cose

0

%[ 2R:- 3(b-zo)R: + (ID-2031'

Under the assumptions shown in equation IV-11, the ratio R then is

given by equation IV-12.

126

IV-11 CY a V(b), op K V(b) and °Yp ¢ V(b)V(b)

R,+ R,
[V(b)] d b

 

V(b) dab]:

IV-12 R

IR,+ R,

0

R,+ R, R1' R2

[V,(b) + v,(b)]2 dab + I [-%—1R: ]2 dzb
0

R,- R,
R,+ R, 2
[ I [V,(b) + V,(b)] d b +

IR1' R2 u 3 z 2
R,- R,

-§-1R, d b]
0

We also calculated the ratio with the following assumptions:

 

IV-13 0Y « A(b), op « V(b) and °Yp ¢ V(b)A(b)
The ratio R then becomes:
R,+ R,
2
[V(b)A(b)] d b
IV"” R = R,+ R, , R,+ R, ,
I V(b) d b A(b) d b]

0 0

Table IV-1 is a list of the results obtained under the different

assumptions made. The values of the ratio obtained with the different

127

TABLE IV-1. Values for the ratio obtained with the assumptions of
equations IV-S, IV-11 and IV-13 as compared to the

experimental result.

AREA VOLUME AREA + VOLUME EXP.

(barn)' (barn)- (barn)- (barn)-

RATIO 0.903 1.001 0.948 0.6

128

assumptions are not very different from each other, but they

overestimate the experimental results by at least 501.

While the assumption oY ¢ A(b) is based upon theoretical
calculations [Ba 86], the assumption 0pc: A(b) is somehow ad hoc . In

order to establish if the above calculations fail to reproduce the
experimental result because of a poor parametrization of the proton

cross-section we calculated, the ratio R in equation IV-15 as a

2:1

function of the 2:1 isotope angle.

o2:1 Z'=1(ep)
z‘=1 °z=1<92=1)

 

-1 R =
IV 5 p(6p) 0

Figure IV-3 and NJ show R2:1 for 92.=1: 60° and ez.=1= 120°

respectively. The value of Rz_1 is constant over the angular range

1

studied and the mean value is fairly close to the value of 0.6 barn-
f0und in the gamma ray-charged particle case. The experimental value is
again overestimated by at least 50%. This result, since an estimated

half of the 2:1 isotope data is represented by protons, seems to
indicate that the suggested parametrization is not indeed a very good

approximation. Energy constraints in the emission of the second
particle could cause a reduction in the number of coincidences observed
which would in this case be a function of the fragment energy. No such
energy dependence is, though, observed experimentally at least in the Y-

c.p. case.

_,(be1r'n)_1

*WTZ—

1

1 Z=I/%72

0,:

Figure IV-3 RZ:1(eZ:1) versus 9

150

125

100

075

050

025

000

129

 

 

TITIIIITIIIIII[ITITIIIIII'ITT

r d
1- 4
1— -1
1- -4
~— —-1
P 6 -—60° ‘
1— ‘ _ -d
. 2-1 .
'- -1
—— —
£- —1
F- -1
” ‘1
b i d
— —1
b u:
I— -l
1- -1
1— c1
1- 4
- 4
.- .1
1111111111111111111111L111111

 

 

25

50

2:1

for 0

'75
62:1
Z.:1=60°.

100

125

150

130

 

 

 

 

 

H I r
l 1.50 r- r I I I I I I I l I I I I I I r I I T I I I I I I I -I
A _ 4
E “ :
G3 1135 :f' -_ o _:
v I" d
5N I i
F ——1
11 : I I .
b: _ .
b 0.50 :— -:
\\\\ _ I, .
1—1 _ -
H - :
3* (IEKS :— { -j
11 . E .
bN 0 00 L 1 1 1 I L 1 1 1 I 1 1 1 L I 1 1 J 1 I 1 1 L 1 I 1 1 1 1 ..
' 25 50 75 100 125 150
62:1
FiSUre 1v-u R2:1(92:1) versus 02:1 for 92.:1z120°.

131

B. n-p BREMSSTRAHLUNG MODEL.

We wrote a Monte Carlo code to simulate the gamma-ray emission by a
n-p bremsstrahlung process since this is one of the mechanisms proposed
to explain the inclusive gamma-ray data. We used the code to study the
ratio of the coincidence cross section to the product of the singles
cross sections as a function of the gamma-ray and proton angle and
energy. What follows is a brief description of the model, the results
obtained with it and their comparison with the experimental results.
The inputs of the program are: the number of n-p collisions to be
studied and the experimental beam energy.

The three components of the proton and neutron momenta are randomly

chosen to be inside a cube of side 2*pfermicentered around zero in such

a way that the magnitude of each momentum is smaller than the Fermi
momentum. The additional velocity associated with one of the particles
being part of the beam (either the proton or the neutron) is added to
obtain the total momentum of each particle. After a collision, in the
center of mass of the n-p system, one of the hadronic directions is
chosen randomly (isotropic scattering) and the direction of the second
hadron is such that the total momentum is conserved. The gamma-ray
kinetic energy is randomly picked to be between 0 and the maximum
kinetic energy available in the center of mss. The gamma-ray emission
probability, based on equation II-2, is then calculated. If a gamma ray
is emitted, half of its energy is subtracted from both the neutron and

the proton energy. In the lab frame the transformed momenta of the

132

neutron and proton are checked for Pauli blocking. If the momentum of
the particle coming from the beam lies inside the projectile Fermi
sphere or if the momentum of the target particle lies inside a non
moving Fermi sphere, the event, even if it produced a gamma ray, is
rejected. The Fermi energy is then subtracted from the energy of both
particles. The outputs of the program are the direction, 9 and 41, and
the energy for both the proton and the gamma ray (if produced).

The first concern was to see if, with the n-p model, we could
reproduce the correct angular distribution and energy dependence of both
gamma rays and proton singles. The exponential decrease with energy and
the slope of the proton spectra are well reproduced by the model as
shown in Figure IV-S. While the agreement for the angles between 30 and
90° is fairly good, for larger angles, the model underpredicts the
experimental results (Figure IV-6). The poor agreement at back angles
is attributed to target fragments which are not included in the model.

The exponential decrease with energy and the slope of the gamma-ray
spectra at 60 and 120° are well reproduced by the model as shown in
Figure IV-7. The ganIna-ray energy-integrated (20 - 128 MeV) angular
distribution obtained with the model is compared in Figure IV-8 to the
angular distribution obtained in the experiment described in Chapter'I.
'The two data points from the inclusive data of the coincidence
experiment are also shown. It is clear that the dipolar character of
the gamma-ray emission probability of equation II-3 dominates the
angular distribution obtained with the model and while the agreement for
the middle angles is reasonably good the forward and backward angles are

underpredicted by #01.

133

 

8
10 IITIIIIIIIIITIIIIIIleI—I

7 , x 30° PROTON n-p
1° “ 0 70° PROTON n—p T
0 30° PROTON exp

+ 70° PROTON exp

 

#COUNTS

 

 

 

 

100 1*1 l l I l l I I 1 l 1 I l 1 l 1 l k 10L 1 l l l
40 60 80 100 120

E1) (MeV)

Figure IV-S Proton spectra at 30 and 70°: experimental and n-p model.

13H

 

 

 

P I I I I T I I I I I rI I I I I I I Ifi I I I I I .-
106 k . ‘2
E 0 p Singles exp 5
5 . X p singles n-p *
10 ¥j<x> ‘?
t X xox 5
I X x .
(I) x
94 104 r‘ ° x%<
Z xox
8 ~'- ’“x .
(g) 10:3 X x x: o
:14: X
2 X X x
10 x

101‘1111111111J1111111111L117
25 50 75 100 125 150

Q!)

Figure IV-6 Proton energy-integrated angular distribution: experimental
and n-p model results.

135

 

 

 

7

10 j I I I Ijfij I T I I I I I I I I I IiI I I I fi r—I
x 60° GAMMA n—p 3
106 — 0 60° GAMMA exp ‘3
,, :1 120° GAMMA n-p g
105 o " x ,, + 120° GAMMA exp —-.:
09°99, * " H i
O N _
U) 4 0%... x a: x —-
E“ 10 “ 0o x 5
‘0. x x -
E; 3 B °°°°°onun I: x I
O 10 B B m an! _E
+ a Q fix!!! ”iii 2
O +++ B E ii :

:11: 102 +2, 8 ,, ififia
+++*H¢** I m m it
1 *¢¢.,. “1 m .1
10 iiggi @ Q a
if in 3
100 1 I 1 1 I 1 1 1 1 1 l 1 L l 1 l i 1 I grit L 1T1 AL

20 40 60 80 100 120

E, (MeV)

Figure IV-7 Gamma-ray spectra at 60 and 120°: experimental and n-p
model results.

136

 

 

 

 

E X singles n—p 3
C 0 singles sing. exp. :
- 0 singles coinc. eXp. .
104 :— —5
: x 1
U) I x x l
E ' x :
D - ° 0 o x -
O
i 103 E— D 0 O "'5
I n :
102 L l l l 1 1 l l l 1 l L 1 1 1 1 L
0 50 100 150
(H)?

Figure IV—8 Gamma-ray energy-integrated angular distributions:
experimental and n-p model results.

136

 

105 I I I j I j 1 I

... f I I I T I I r I
E X singles n—p :
i 0 singles sing. exp. :
- 0 singles coinc. exp. .
104 :— 1
C x x :
U) I x ..
D - ° 0 x 4

0
O

O .—
25: 103 E— U 0 :
: 2
: n j

102 L 1 L l 1 1 l 1 1 1 1 1 1 1 1 1 1

 

 

 

Figure IV-8 Gamma-ray energy-integrated angular distributions:
experimental and n-p model results.

137
Our next step was to calculate the ratio of the coincidence to the
product of the singles cross-sections and study it as a function of
proton and gamma-ray angle and energy. In the calculations we used the

impact parameter distribution, N(b), suggested in reference [Ba 85]

Iv-15 N(b) « A(b)

where A(b) is the overlap area between the two nuclei and ogeo is the

geometrical cross section. The ratio R is then

[A(b)A(b)21Ib db n

 

1v-16 R = , ,
[]A(b)2ub db ] “Y np

where an,nY and np are the number, divided by the number of collisions

studied, of gama ray - proton coincidences, gamma rays and protons

respectively. From Table IV-1 the ratio can be rewritten as

Figures IV-9 through IV-12 show the n-p model results. While the
experimental results do not show any appreciable variation with any of
the physical quantities studied, the ratios obtained with the n-p model
decrease fairly rapidly both when studied as a function of gamma-ray

energy and when studied as a function of proton energy. The value of

138

 

21)

 

 

 

bI III I rt I I I I I I I I I I I III I_I II I flar‘
T - 30° <9p< 70°
7:? F
1.5 — -
3.. — 07 = 60°
«5 _
I'D "' -1
v _ fl
0.1.0 - ~-+
b - x ,
*%‘ r x
b : x x
\Q 05 —- x x Z i
Px _ I X i
b » i ,
_ i f A.
‘ - i ii} -*
0.0 1 111111 111 1 1 111 111J1 1 lxlx %L
20 4O 60 80 100 120 140
Ep (MeV)

Figure IV-9 Ratio versus Ep for 30 < 0? < 70° in the n-p model.

139

 

 

 

 

2.0 I I I I I I I fl I I 1 r I , _T_.
F I I I I '7
7 . 30° <9p< 70° .
7:? 5 H ‘
l. _— _.
a - 9, = 60° .
63 p
,Q r .
v L- 4
‘1. 1.0 *“ a,
b ~ .
2x: _
?\ F A
Q ~ .
g: 05 i“ x X _J
” x
b _ x
’ z X .X «
F" I i i a
00 1 L 1 l L 1 1 1 1 1 1 1 1 1 1 IX lilfix€1 *—-1~)(—‘
20 40 60 80 100
E37 (MeV)

Figure IV-IO Ratio versus E for Ep> 30 MeV in a reference frame

Y
moving with velocity equal to 8:0.1M (n-p model).

2.0
T
A
g: 1.5
L4
(U
,o
v
o. 1.0
b
>)(<
pt
b
\‘3, 0.5
?\
b
0.0

Figure IV-11

140

 

 

 

 

I I I I I I I I I fir I I I I—I I I I I I I I I I—I I f
I— —<
9 —‘ 60° I
r- 1
y-
F- «I
_ i
r— -4
'- i
r- X 4
’ x
I- 4
_ ""1
- I I: x <
b- i <4
P
r- «I
1 1 L 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I * I I I J

25 50 75 100 125 150

6p

Ratio versus 0p for gamma rays at 60° in the n-p model.

1N1

 

 

 

 

20 __ V '7 I I I I I 1 I I I I 1 I I I I rrI 1 I 1 I I I T 4

H .- : 0 —4

I t 07 120 ‘

A

:2 1.5 >—- .1

I... — .

(U P '4

.o I ,

v __ 7‘

D. 1.0 — _.

b F -.
2X: _
?~ _

b _ x x 4

\9, 0.5 —- x ..

?~ — x .

b : x i q

P1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1% I

0.0 [+441 .

25 50 75 100 125 150
6P

Figure IV-12 Ratio versus Op for gamma rays at 120° in the n-p model.

1142
the ratio studied as a function of proton angle decreases with
increasing angle, and for a given proton angle the ratio is higher for
D1(60°) than for D2(120°). It seems natural to associate the decreasing
behavior of the ratios to the energy constraints implicit to the n-p
model. We wondered if our experimental results were not an indication

of a more collective process.

D . THERMAL MODEL

In order to mimic a process in which ganma rays are not produced in
the first n-p collisions but are instead produced in a later stage of
the reaction when the initial energy constrictions have been removed by
multiple scatterings, we modify our previous model so that the energies
of the proton and neutron are randomly picked from an exponential

distribution y=AeIEVT

where A is a constant and T is a parameter often
called "temperature". The inputs of the program are: the number of
collisions to be studied, the value of the parameter T and the velocity
8 of the moving thermal source.

As before, we first tested the ability of the model to reproduce
qualitatively the features of the singles spectra. Different values of
B and T were employed to see how the value of these parameters affected
the magnitude and the slope of both gamma-ray and proton spectra. The
values 8:0.10 and T=16 MeV were found to reproduce well the slope and
the angular distribution for protons as shown in Figures IV-13 and IV-

1‘4. However, a value of T higher than 16 MeV is needed to reproduce

better the gamma-ray spectra slope as shown in Figure IV-15. The

1143

 

1,05 HT....,....,....,TW,,,,
x 30° PROTON th.

107 — 0 70° PROTON th. —*

106 —x D 30° PROTON exp _
" x x + 70° PROTON exp

#COUNTS

 

+

100 1 1 1 1 1 1 1 1 1 1 1 1 1 L4 1 1 1 1 1 1 I 1 1 l

 

 

 

40 60 80 100 120

ED (MeV)

Figure IV-13 Proton spectra at 30 and 70°: experimental and thermal
model results.

11411

 

 

.‘TIIIITTTIIIIIIrIIfiIIfIrTITrII‘
106 g-
: 0 p singles exp.
5 t X p singles th.
10 E x o
-x x
U) : x x x x x0" x x
E" 104 ’6xxo)<
z XOX x X
:2 . x x x
O 103 Xxox
g) >Px)(x
102

101 111111111i1111L111111111I111L_
25 50 75 100 125 150

('91:

Figure IV-M Proton energy-integrated angular distribution:
experimental and thermal model results.

1N5

 

a

10 I I I I I T I r I I I I I I I I T I I I I I I—
7 x 60° GAMMA th.

10 _ ,5“ X 60° GAMMA exp. _

106 __,, " a 120° GAMMA th. __

'1' 120° GAMMA exp.

#COUNTS

L
TIQI
J

 

 

 

 

 

125
137 (MeV)

Figure IV-15 Gamma-ray spectra at 60 and 120°: experimental and thermal
model results.

1116
obtained gamma-ray angular distribution is in good agreement with the
experimental results as shown in Figure IV-16.

The best value Of the parameter 8, 0.10, is smaller than the
experimental value 0.1“ which we found by transforming both the singles
proton spectra and the spectra Of protons in coincidence with gamma rays
in a frame were the distribution is isotropic. The high value of T
needed to fit the proton spectra could be justified since it represents
the "temperature" of the proton source at a very early stage. Further
interactions of the protons with matter after the first stage, should
make the exponential slope steeper and might reproduce the lower
experimental values of T.

With these limitations in mind, we went ahead and calculated the
ratios. Figure IV-17 shows the ratio calculated as a function of proton
energy for protons emitted in a solid angle equivalent to the sum of the
solid angles covered by the four most forward charged particles
detectors. The low probability of producing an energetic gama ray
(both the neutron and the proton have to be picked from the high-energy
tail of the exponential spectra) increased dramatically the number of
collisions needed to obtain adequate statistics to calculate a ratio as
a function of ganma-ray energy. Due to the enormous amount of computer
time needed, we were not able to obtain enough counts to establish the
behavior of the ratio as a function of gamma-ray energy for proton
energies above 30 Mev in the moving frame as in the experimental result.
Figure IV-18 shows the ratio as a function of gamma-ray energy for
proton energies above 20 MeV in the laboratory. In Figure IV-19 and IV-
20 the ratio is studied as a function of proton angle for gamma rays

detected at 60° (D1) and for gamma rays detected at 120° (D2). The

1117

 

 

 

 

105 r- I I I I I I I I I I I I I I I I I :
E x singles th. 5
: 0 singles sing. exp. :
. 0 singles coinc. exp. 1
10‘4 :— .1
m 5 x x :
:2 - ° . 0 3
O
L=é 103 E— D 0 0 _:
_ n 1
102 1 1 1 1 J 1 1 1 1 1 1 1 1 1 J 1 1
0 50 100 150
(”)7

Figure IV-16 Gamma-ray energy-integrated angular distributions:
experimental and thermal model results.

148

 

 

 

 

 

20 _ I I I r I I I I I I I I I I I T I I I—j
- I
T : J
A
C. 1.5 — I I
L. >— 4
(U ~ 1 1 I A
a : x x x X x x X $ ,
0.. 1.0 *— X i I .
b r i
2* ‘- .4
P‘ e
Q ~ 4
9.. 0.5 '_ __d
?\ t l
b - .
00 L 1 1 4 I 1 1 1 I 1 1 1 1 1 1 1 1 1 1_,:
20 40 60 80 100

Ep (MeV)

Figure IV—17 Ratio versus Ep for 30 < OP< 70° in the thermal model.

1149

 

2.0 _ I I I I I I I I I I I I I I T:
T — -
A F A
C} 1.5 — _q
fa ’ I .
,Q t x i i I ‘
v X i I "
_ x x x A
e _.. L
b » .
:x: ..
?~ _
b _ -
\\EL ()55 r“ .4
a.
b

 

0.0kl l 1 1 11 I 1 1 11

 

 

20 4O 60
13, (MeV)

Figure IV-18 Ratio versus EY for Ep) 20 MeV in the lab (thermal model).

150

 

 

 

 

20 _‘ I I I I I I I I I I I I‘T I I I f1 I I I I—r TI I I 4
Fr ’ £97 3:; 63()0 1
A ' -1
£3 1.5 -- _l
L4 - l
CU » -
fl : " " x —
{L 1.0 — ‘ x i ~
b — x J
'* — 1
t? *' i ‘
,‘\ +- 1
EL 0.5 *- __
P~ _ I
b — l
0.0 J l L l I l l l 1 l l l l l J J l l l J l l 1 L11 1 1 l
25 50 75 100 125 -150
69K)

Figure IV-19 Ratio versus Op for gamma rays at 60° in the thermal model

151

 

2.0

 

 

 

_r I I—F‘I I I I I I I I I I I I I I I I Ij I I I I I I— d
T r 67 = 1200 I
A " d
c: 1.5 — $ _
L. r q
o I i I i
Q I x 4
V r- q
o. 1.0 r— ‘ x _l
b ~ 1 _
x; .- -4
A _ 3‘ d
\b I q
a 0.5 —- l
A b .1
t3 " 4
0.0 1 1 1 1 l 1 1 1 1 l 1 l l 1 L1 1 1 1 l 1 L 1 l 1 1 1 14
25 50 75 100 125 150

Figure IV-20 Ratio versus Op

model.

6p

for gamma rays at 120° in the thermal

152
features of these two angular distributions are due to the strong
correlation between the directions of the ganma ray and the proton in in

the denominator (1 - q-Bf) of the equation II-2 used to represent the

gamma-ray emissionprobability. If 9,¢ and 6',¢' are used to indicate
respectively the ganma ray direction and the proton direction, then the

denominator can be rewritten as

IV-18 1 + B[sinesin6'cos(¢-¢') + cosecose']

After averaging over 4» and ¢'(this was done with the results of the

simulations to improve the statistics) it becomes

IV-19 1 + Boosecose' or for 9=60° 1 + 0.87Bcose'

9:120° 1 - 0.87Bcose'

The monotonic increase of the function case in the 0,11 range explains
qualitatively the behavior of the angular distributions in Figures IV—19
and 20.

The different behavior of the angular distributions obtained with
the n-p simulation is probably due the smaller amount of energy

available in the collision and to the presence of Pauli blocking.

C. CORRELATED AND UNCORRELATED COINCIDENCE

A fundamental problem in any coincidence experiment lies in being

able to distinguish between coincidences of particles produced in the

153
same event and the so called "accidental coincidences" of particles
produced in separate events but detected within the same experimental
time-acceptance window. In our coincidence experiment the "accidental"
rate was determined by measuring the number of coincidences in adjacent
cyclotron rf bursts and it was found to be about 201 of the total
coincidence rate.

To connect the results of the two Monte Carlo simulation to the
experimental results in the following we will call a "correlated
coincidence" the coincidence between a gamma ray and the proton that
produced it and an "uncorrelated coincidence" the coincidence between a.
gamma ray and one of the protons produced in the same reaction but not
responsible for the photon emission.

While is extremely unlikely that two gamm rays might be produced
in the same reaction since the cross section is of the order of 1 mbarn,
the production of more than one proton should be investigated. No
experimental results regarding the proton multiplicity for beam energies
close to no MeV/n, are presently available. Lacking a direct
experimental result, we used the following procedure in the attempt to
estimate the mean proton multiplicity. With our n-p bremsstrahlung
simulation program we can find the number of protons emitted in the
solid angle A0 for each energy interval AE for a reaction with a beam
energy of HO MeV/n. The double differential cross-section can be

written as

d o ogeo n[AE,An)

IV‘20 dE do ‘ AB 19 N

1514

where ogeo: u[1.2-[A;;3 + Ail/3)? m2 is the geometrical cross-section,
m is the average proton multiplicity and N is the number of collisions
studied. A comparison between the cross-section in equation IV-ZO and
the experimental double differential cross-section at 90° allows the
determination of m (Figure IV-21). The ratio of the experimental cross
section to the cross section in equation IV-18 gives a value of m equal
to 3.55. The same procedure applied to the thermal model results gave a
value fer m of 3.10.

As a second method to estimate the mean proton multiplicity we

considered that the proton cross-section op can be written as

IV-21 op ogeo

We parametrized our experimental proton double differential cross

section at 90° with a function of the form Ae'BE where A and B are

parameters and E is the energy. Integrating this function between 0 and

infinity and multiplying it by An gives a rough value of op The value

of m obtained with this method was “.8.

From the above estimates, approximately three fourths of our
experimental coincidences would be due to uncorrelated coincidences.
For an uncorrelated coincidence, the probability of observing a gamma
ray in coincidence with a proton is simply the product between the
probability of observing a gama ray and the probability of observing a

proton as in equation IV-22

155

 

 

 

 

2
A 10 I I I I I I I I I l' I I I T rfi I I I I I I I a
:3 X 90° p singles (n—p) 3
2 1 0 90° p singles (exp) i
h 10 5.
fl ’0 :
. '1
,0 O 0.......‘ a
a 10 x OCO¢ *5
Eda. C x '1 “nun“ 1
I
'0 10‘1 .:.— x 3 fl §§§ ii *5
\ I 1 1
Nb 10‘2 .— f ~—
~o f
: 3‘
10-3 1 1 1 1 l 1 1 1 1 1 1 1 1 1 I J 1 1 1 1 1 L 1 L d
30 4O 50 60 7O 80
Ep (MeV)

Figure TWJM Comparison between the experimental and the n-p model
results for the determination of the mean proton
multiplicity m.

IV-22 P=PP or -—lp——-1

The ratio of the coincidence cross section to the product of the singles
cross sections, if multiplied by the geometrical cross section,
represents the ratio of probabilities as in equation 111-22. If we add
the contribution of the uncorrelated coincidences to the results of the
n-p bremsstrahlung (equation Ill-23) or to the results of the thermal
simulation (equation IV-Zu) the obtained quantities can be directly

compared to the experimental results.

geo

 

IV-le R 0 1 4-K;
0
geo

Figures IV-22 through IV-25 show how the addition of the uncorrelated-
coincidence contribution changes the results obtained with the two
models. Both sets of results are now very close to the experimental
values, but the ratios obtained with the n-p bremsstrahlung are still
characterized by a small slope while the ratios obtained with thermal
model are flatter, much like the experimental results. A higher mean
proton multiplicity would decrease the slope of the n-p results but

would also increase the absolute value of the ratios.

157

 

 

2.0 ITjIIFITWIIIIIIIIIIIIITIITIII

: -4

_ .4

151- n-p ;

-I - .4

| " 4

,—.\ 1.C) :— .1:

L4 : )( x )( j

- ””""xxx x _

pgg CLES b ,‘ x "" x Iii‘ X ><zx x a

\_4/ - 1

Q4 P111111l11|1111|1_141 1111111114

b ; I

% C :

\\\\ : :

g - .

1.C) :" x d

b P x X .4
b X

()15 :- ._9

00-1111111l11111111111111111111 4

 

 

 

p—b
4;
O

20 4O 60 80 100 120

E

I)

Figure IV-22 Ratio versus Ep in the n-p and in the thermal model after

the corrections for the uncorrelated coincidences.

2.0
1.5
I
A 1.0
C.‘
L...
CU 0.5
,0
v
CL
b
*A
b 1.5
\
CL
?‘ LO
b
0.5
0.0

Figure IV-23

158

 

 

 

 

 

’- I T T I I I j I T I I I r I I I f I I

_ r1——I) -
I :
:- ‘3'
C -(
I— -1
)1. X X ——4
t x x " x " R x x x x x x x«
I. 1 1 1 1 1 1 1 1 1 1 1 l 1 1 1 1 1 1 a
I th :
Z 1
C ..
:— A
: x X a: x 3: :x X :
x x X X X X x x *4
t... _.
I- —1
- 4
b 1 1 l 1 I L 1 1 1 l 1 1 1 1 1 L 1 1 1‘

20 4O 60 80 100

Ratio versus EY in the n-p and in the thermal model after

the corrections for the uncorrelated coincidences.

159

 

 

 

 

 

2.0 _ I f V I I T I W I I T I I I I I I _,
E n— 1
1.5 :- P _:
1 : 1
I - 1
A 1.0 :— .1
C1 : 1
LI - x x .
(U 0.5 f- X x x x x x _;
Q _ i
v - .1
D.‘ b l 1 1 1 1 l l 1 1 1 1 l 1 1 1 1 l A
b - .
>X< - 4
?\ ;_ tll _:
b 1.5 : 1
\ - 3
Q 10 P —7
b ' : :
I I x " >* " x >< I
0.5 [— x j
00 r- l 1 1 1 L I l 1 1 l l l 1 1 1 1 l 'l

50 100 150

(H)

I)

Figure 1v-2u Ratio versus 9p for gamma rays at 60° in the n-p and in

the thermal model after the corrections for the
uncorrelated coincidences.

160

 

 

 

 

 

20 .- I I I I j I I I I I I I T I fiT
I n... 1
1.5 _— p j
.. I I
I >- .,
A 1.0 r f
E : :
r- -(
CU 0.5 f“ x X " " x x :1: X j
,0 _ 4
v L d
0.. '- ;1 1 1 1 l I #1 1 1 1 1 1 1 1 L ‘4
b '- -<
3‘; 2 th I
— —J
b 1.5 _ .
\ _ .
S: 10 P ‘
' _ fl
b : x i
I x x " " x x x :
0.5 :- f
- 4

0.0 A 1 1 l 1 1 1 1 #1 l 1 l 1 L 1 1

50 100 150

D

Figure IV-25 Ratio versus 9p for gama rays at 120° in the n-p and in

the thermal model after the corrections for the
uncorrelated coincidences.

SUMMARY AND CONCLUSIONS

The energy spectra of the high-energy gamma rays produced in the
reactions N + C, Zn and Pb at 20, 30 and #0 MeV/n decrease exponentially
with energy. The double differential cross sections were parametrized
for EY>35 MeV with a function of the form A55”. The value of the
parameter 1 is almost independent of the target used and ranges from 8
to 14 Mev for beam energies between 20 and HO MeV/n.

The angular distributions are all slightly forward peaked. The
ratio o(30°)/o(150°) at 1&0 MeV/n is equal to 2.35 for Pb, 2.28 for Zn
and 3.114 for C. An isotropic emission from a moving source was
considered and the gamma-ray emission was found to be nearly isotropic
in a frame moving with velocity close to the nucleon-nucleon center of
mass velocity.

The total cross section at 90° slowly increases with target mass
and beam energy from 0.02 mb for N + C at 20 MeV/n to 0.6“ mb for N + Pb
at 1&0 MeV/n.

The theories proposed to explain the origin of the photons in this
energy range, such as first collision n-p bremsstrahlung and statistical
emission, all do a reasonably good Job in reproducing the experimental
features. In order to provide a testing ground for these theories we
studied the coincidences between high-energy gamma rays and light
charged particles (2:1) in the reaction N + Zn at no MeV/n.

A qualitative comparison between inclusive proton spectra and
exclusive spectra of protons in coincidence with gamma rays did not show
any marked difference. The same kind of result was obtained by

comparing the ganma-ray singles spectrum with the spectra of gamma rays

161

162

in coincidence with protons at several proton angles. He then studied
the ratio of the gama ray - proton cross section to the product of the
proton and gamma-ray cross sections as a function of proton angle,
gamma-ray angle (only 60° and 120°), gamma-ray energy and proton energy.
The value of the ratio was found to be independent of all of the above
variables, within the experimental uncertainty, with an approximate
value of 0.6 barn-1. Multiplying this value by the geometrical cross
sectixni, ogeo=1.86 barn, produces a value of 1.12. The ratios are then
Just 121 above the value of 1 characteristic of coincidence probability
of independent events.

Two Monte Carlo codes were written to simulate the gamma-ray
production as a product of first chance n-p collision and as a product
of secondary collisions respectively. To connect the simulation results
to the experimental results we investigated the possibility of
"uncorrelated coincidences", i.e. coincidences between a gamma ray and
one of the protons produced in the same reaction but not responsible for
the photon emission. We estimated the mean proton multiplicity at 110
MeV to be about 11 per collision. With the assumption that 3/14 of the
experimental coincidences are "uncorrelated" we were able to obtain
simulation results suitable fOr comparison with the experimental data.

The most striking characteristic of the ratios obtained with the
first collision model is a slow decrease in energy. This behaviour is
expected to be a consequence of the limited amount of energy available
in the system. A lower value of the mean proton multiplicity would make
this effect more visible and a coincidence experiment using light
systems might help to completely rule out first chance collision as the

main mechanism in the gama-ray production.

163

While the results obtained with the second model appear to be in
overall better agreement with the experimental results, it should also
be pointed out that, due to the enormous amount of computer time needed,
the conditions applied to obtain them are different from the ones used
both in the analysis of the experimental results and in the first chance
simulation.

The charged-particle multiplicity associated with the emission of a
ganma ray and the charged-particle multiplicity associated with the
emission of a charged particle were studied to obtain information about
the impact-parameter dependence of the gamma-ray production. The gamma
- charged particle multiplicity M:1 (a 2:1 charged particle in
coincidence with a gamma ray) was found to be only 101 higher than the
charged particle multiplicity M:2 (a 2:1 particle in coincidence with a
2:1 charged particle). Higher multiplicities could not be compared due
both to an insufficient statistics in the gamma - charged particle
multiplicity and to a large uncertainty in the higher orders of the
charged particle-charged particle multiplicity. On the limited basis of
the multiplicity result, the gamma ray and the light charged particle
production appear to share a very similar impact parameter dependence.
A similar experiment where the gamma-ray detector can be substituted
with a phoswich and the scale down factors are removed could provide a
nnre precise comparison of the two multiplicities and extend it to

higher orders.

[Al 86]

[Ba 86a]

[Ba 86b]

[Ba 87]

[Be 81]

[Be 85a]

[Be 85b]
[Be 87]

[Bl 81]
[Bo 87]
[Bo 87]
[Br 73]
[Bu 82]

[Cs 8“]

[Es 66]
[£1 60]

LIST 0? REFERENCES
A
N. Alamanos, P. Braun-Munzinger, R. F. Freifelder, P. Paul, J.
Stachel, T.C. Awes, R. L. Ferguson, F. E. Obenshain, F.
Plasil, and G. R. Young, Phys. Lett. 173 B, 392 (1986).
B

W. Bauer, W. Cassing, U. Mosel, and M. Tohyama, Nucl. Phys.
Afl, 159 (1986).

W. Bauer, G. F. Bertsch, W. Cassing, and U. Mosel, Phys. Rev C
35, 2127 (1986).

W. Bauer, T. S. Biro, W. Cassing, U. Mosel, K. Niita, A. L.
De Pauli, G. F. Bertsch preprint.

G. F. Bertsch and J. Cugnon, Phys. Rev. C 23, 251A (1981).

K. Beard, W. Benenson, C. Block, E. Kashy, J. Stevenson, D. J.
Morrissey, J. van der Plicht, B. Sherrill, and J. S.
Winfield, Phys. Rev. C 32, 1111 (1985).

K. Beard Ph. D. thesis, unpublished.

12. Bertholet, M. Kwato NJock, M. Maurel, E. Monnard, H.
Nifenecker, P. Perrin, J. A. Pinston, F. Schussler, D.
Barneoud, submitted to Nuc. Phys.

Blann, Phys. Rev. C g;, 205 (1981).

A. Bonasera, L.Csernai, and B. Schurmann, preprint (1987).

A. Bonasera, M. di Toro and C. Gregoire, preprint.

V. R. Brown and J. Franklin, Phys. Rev. C 8, 1706 (1973).

M.E% Budiansky, S. P. Ahlen, G. Tarle', and P. B. Price,
Phys. Rev. Lett. fig, 361 (1982).

G
L. Csernai, Magyar Fizikai Folyoirat fig, 231 (1989).
E
J. A. Edgington and B. Rose, Nucl. Phys 89, 523 (1966).

R. M. Eisberg, D. R. Yennie and D. H. Wilkinson, Nucl. Phys.
_1_8_, 338 (1960).

169

[F0 87]

[Gr 89]
[Gr 86]

[Gu 87]

[He 87]

[Hi 87]

[Ka 77]
[Kw 86]
[Ko 85]

[Ni 85]

[Na 86]
[Ne 85]

[Ne 87]

[Re 87a]

[Re 87b]

165

D. Fox, D. A. Cebra, Z. M. Koenig, P. Ugorowski, and G. D.
Westfall, Phys. Rev. C 33, 1590 (1987).

G
E. Grosse LBL-16281.
E. Grosse, P.Grimm, H. Heckwolf, W. F. J. Mueller, H. Noll,
A. Oskarson, H.Stelzer, and W. Roesch, Europhysics Lett. g, 9
(1986).
C. Gossett, Fourth Gull Lake Nuclear Physics Conference.

H
N. Herrmann, R. Bock, H. Emling, R. Freifelder, A. Gobbi, E.
Grosse, K. D. Hildenbrand, R. Kulessa, T. Matulewicz, F. Rami,
R. 5. Simon, H. Stelzer, J. Wessels, P. R. Maurenzig, A. Olmi,
A. A. Stefanini, W. Kuhn, V. Metag, R. Novotny, M. Gnirs, D.
Pelte, P. Braun-Munzinger, L. G. Moretto, GSI preprint.
R. Hingmann, W. Kuhn, V. Metag, R. Muhlahans, R. Novotny, A.
Ruckelshausen, W. Cssing, B. Haas, J. P. Vivien, A. Boullay,
H. Delagrange, H. Doubre, C. Gregoire, Y. Schutz, Phys. Rev.
Lett. 3, 759 (1987).

K
J. I. Kapusta, Phys. Rev C 15, 1580 (1977).
M. Kwato Njock, Phys. Lett. 175B, 125 (1986).

C. M. Ko, G. Bertsch, and J. Aichelin, Phys. Rev. C31, 2329
(1985).

H. Nifenecker and J. P. Bondorf, Nucl. Phys. A ”42, 478
(1985).

K. Nakayama and G. F. Bertsch, Phys. Rev. Gigi, 2190 (1986).

W. R. Nelson, Hideo Hirayama, and D. W. 0. Rogers, SLAC-265
UC-32 (1985).

D. Neuhauser and S. E. Koonin, Nucl. Phys. A 562, 163 (1987).
R

A. Remington, M. Blann, G. F. Bertsch, Phys. Rev. C 32, 1720
(1987).

A. Remington, M. Blann, G. F. Bertsch preprint.
S

166
[St 86] J. Stevenson, K. B. Beard, W. Benenson, J. Clayton, F. Kaskyu
A. Lampis, D. J. Morrissey, M. Samuel, R. J. Smith, C. L. Tam,
and J. S. Winfield. Phys. Rew. Lett. 57, 555 (1986).
[St 88] Stevenson et al., in preparation.
V

[Va 85] D. Vasak, Berndt Muller and Walter Greiner,J. Phys. G: Nucl.
Phys. 11. 1309 (1985).

H
[We 76] G. D. Westfall, J. Gosset, P.J. Johansen, A. M. Poskanzer, W.

G. Meyer, H. H. Gutbrod, A. Sandoval, and R.Stock, Phys. Rev.
Lett. 31, 1202 (1976).