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This is to certify that the
dissertation entitled
"Evolut ion of Fission-Like React ions in
Median Energy Heavy Ion Collisions”
presented by

J aeyong Yee

has been accepted towards fulfillment
of the requirements for

Ph. D . degree in Physics

 
   

Major professor

Date January 3, 1996

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

LIBRARY
Michigan State
Unlverslty

 

 

 

PLACE Ii RETURN BOXto romovothio ohookoflfl'om your rooord.
TO AVOID FINES mum on or bdoro dot. duo.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU is An Nflrmotivo Action/Equal Opportunity Institution
WW1

EVOLUTION OF FISSION LIKE REACTIONS
IN MEDIUM ENERGY HEAVY ION
COLLISIONS

By

J aeyong Yee

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1995

ABSTRACT

EVOLUTION OF FISSION LIKE REACTIONS

IN MEDIUM ENERGY HEAVY ION COLLISIONS

By

J aeyong Yee

MSU 41r Array has been completed with the addition of multiwire proportional
counters (MWPC) . Bragg curve counters (BCC) have been successfully run in the
standalone mode. These detectors combined with other components of the Array
enabled the measurement of intermediate mass fragment (IMF : 3 3 Z 2 18) as
well as light charged particles in coincidence with fissionlike fragments in a 41r ge-
ometry, over a wide energy range (E4,em = 15 — 115 AMeV) for the reaction 4'°Ar
+ 232Th. The exclusive folding angle distribution data provide direct evidence
that fissionlike processes following incomplete-fusion are still an appreciable exit
channel for beam energies as high as 115 AMeV. Three distinct sources of IMF
emission are identified by the azimuthal angular correlation function among two
fissionlike fragments and an IMF. Respective contributions of the three emission
modes to the IMF multiplicity with the beam energy are estimated. Prefission
emission gains dominance in this energy range while the evaporation from the fis-
sionlike fragments decreases to the point that its importance becomes comparable

to that of simultaneous ternary breakup.

To Grandma

ii

ACKNOWLEDGEMENTS

Paying respect cannot be done by mimicking the way in which one has not
grown. Although I’ve learned quite a few things in this culture, my sincere thanks

and respect can only be expressed in my way. I will call him
Gary D. Westfall, The Teacher.

Without his continuous support and encouragement, I’m sure to have left this
institute, only to lose my self—confidence. Sometimes I thought his patience would

surpass mine toward myself. I am in debt to him.

Professor W. Benenson is thanked for his service during most of my stay as an
associate director. He continued to support me even during my not so satisfactory
years. Professor J. Kovacs made it possible for me to start all this by accepting
me into this department. Professors W. Benenson, P. Danielewicz, J. Kovacs, S.
Mahanti, and W. Repko are thanked for their guidance as guidance committee
members. Professor W. Repko is acknowledged for his agreement to join the

committee in response to my almost unreasonable last minute request.

“Skip” Vander Molen is appreciated for all his yelling and I regret I had to
call him up so many times in the middle of the night. D. Swan and J. Yurkon are
thanked for their endurance of our detector lab take-over for over a year. They

were also most helpful.

The best atmosphere I enjoyed was when W. Ken Wilson and R. Lacey were
both around. They initiated my research and made it enjoyable. I wish I had had

longer overlap with them. That could have most likely made my life here even

iii

easier and happier. E. Gualtieri is one of the unfortunate souls who had no choice
but to take the worst of me for so long time. I appreciate all the discussions we
had. 3. Hannuschke is thanked for his willingness to answer and talk in a very

pleasant way.

Lily and Hyunju are two of the most negatively benefited people by all this.
I find no means to make it up for them. All I can do is to write here that I love

them most.

iv

Contents

Abstract .................................. i
Acknowledgments ............................ iii

1 Introduction 1
1.1 Physics Justification ......................... 1
1.2 Organization of This Thesis . . . . . . . . . . I .......... 6

2 Experiments 7
2.1 Introduction .............................. 7
2.1.1 Experimental Design ..................... 7

2.1.2 MSU 4x Array ........................ 7

2.2 MWPC ................................ 9
2.2.1 Construction ......................... 9

2.2.2 Signal Processing ....................... 11

2.2.3 Coordinate Determination .................. 11

2.2.4 Time Analysis ......................... 18

2.2.5 Efficiency . ........................... 22

2.2.6 Particle Identification ..................... 22

2.3 Phoswich Detectors .......................... 24
2.3.1 Signals ............................. 24
2.3.2 Particle Identification ..................... 24

2.4 Bragg Curve Counters ........................ 29
2.4.1 Construction ......................... 29
2.4.2 EZ Mode ........................... 32
2.4.3 Ion Chamber Mode ...................... 32

Folding Angle Analysis 35

3.1 Introduction .............................. 35
3.1.1 Motivation ........................... 35
3.1.2 Background .......................... 36
3.1.3 Present Work ......................... 37

3.2 Experimental Description ...................... 37

3.3 Definitions ............................... 38
3.3.1 Folding Angle ......................... 38
3.3.2 Linear Momentum Transfer ................. 39

3.4 Analysis ................................ 41
3.4.1 Inclusive Fission Fragment Folding Angle .......... 41
3.4.2 Out-of-plane Distribution .................. 41

vi

3.4.3 IMF Emission Angle and Event Selection .......... 47

3.4.4 Two Cases of Linear Momentum Transfer ......... 49
3.4.5 Fissionlike Process Cross Section .............. 49

3.5 Conclusion ............................... 53
4 IMF Emission in Fissionlike Collisions 59
4.1 Introduction .............................. 59
4.1.1 Motivation ........................... 59

4. 1.2 Background ........ - ......... . ......... 60

4.1.3 Present Work ......................... 61

4.2 Correlation Method .......................... 61
4.2.1 High Order Azimuthal Correlation Method ......... 61
4.2.2 Third Order Azimuthal Correlation Method ........ 61
4.2.3 Definitions ........................... 62
4.2.4 Interpretation of $3 ...................... 63

4.3 Event Selection ............................ 65
4.3.1 Description .......................... 65
4.3.2 Folding Angle and Impact Parameter ............ 67
4.3.3 Additional Condition ..................... 68

4.4 Analysis ................................ 70
4.4.1 C(z/Ja) Distribution ...................... 70

vii

4.4.2 Signature of Neck Emission ................. 71

4.4.3 Comparison of Data and Simulation ............. 74
4.5 Conclusion ............................... 76
4.5.1 IMF Emission Mechanism .................. 76

4.5.2 Multiplicity of IMF from Each Emission Mechanism . . . . 80

4.5.3 Summary ........................... 80

5 Conclusion 84

viii

List of Figures

1.1

1.2

1.3

2.1

2.2

2.3

2.4

2.5

Relative probability of evaporation (E), binary fission (F) and
cracking (C) as a function of excitation energy of the 131Xe nu-

cleus ..................................

In-plane angular correlation of fission fragments for the system “Ar

+ 232Th at 31, 35, 39, and 44 MeV/u . ...............

Fission fragment folding angle distributions measured in coinci-

dence with Be, C, O, and Ne fragments. ........ r ......

(a) A single module that consists of MSU 4x Array. (b) Side view
of MSU 41r Array ............................

Exploded view of the layers making up an MWPC. ........

(a) Anode signal output from preamp. (b) Cathode signal output

from preamp. .............................
Cathode signal of one end vs. the other end. ............

Position spectra using a mask that covers a hexagonal type MWPC
except for the holes at each corner and lower character ‘h’ in the

center. .................................

ix

10

12

13

2.6

(a) Cathode coordinate system (z', y'). (b) Module coordinate sys-

tem (:c,y,z). (c) The orientation of the unit vectors of module

coordinate system in lab. frame. (d) r = R + x .......... 16
2.7 Angular distribution of MWPC events ............... 17
2.8 (a) Velocity spectra of the particles detected in MWPC. (b) Recoil

velocity of the compound nucleus ................... 19
2.9 (a) Ideal case of tap. (b) Wrapping—around occurred. (c) The RF

time signal is clipped on both sides. ................ 20
2.10 Efficiency of MWPC relative to BCC as a function of charge number

of nucleus detected is shown in the case of 35 MeV/ nucleon ‘OAr

beam. ................................. 23
2.11 BCC E signal in E2 mode vs. MWPC pulse height. ....... 25
2.12 MWPC pulse height vs. folding angle of the events that either one

of the two particles doesn’t leave signal in the BCC ......... 26
2.13 Folding angle distribution of (Cl) inclusive data, (x) IMF—

contaminated data, (0) IMF-suppressed data ............ 27
2.14 Fast output vs. slow output ...................... 28
2.15 Particle identification template that assigns charge, mass and en-

ergy values to a particle projected onto a certain point. ...... 30
2.16 Schematic diagram of BCC. ..................... 31
2.17 Typical spectra of BCC with the pid gates superimposed ...... 33

2.18 Typical 2-dimensional plot of BCC E vs fast plastic. ....... 34

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

3.10

3.11

3.12

3.13

4.1

Distribution of angles that fission axis makes with beam direction. 40

Inclusive fission fragment folding angle distributions for Ar + Th
reactions from 15 to 115 AMeV .................... 42

Contour plot of ¢II vs. 9!! for the reaction of Ar + Th at Em", =
15 - 115 AMeV. ........................... 44

Fission fragment azimuthal distributions for Ar + Th reaction from

15 to 115 AMeV gated on low LMT. ................ 45

Fission fragment azimuthal distributions for Ar + Th reaction from

15 to 115 AMeV gated on high LMT. ............... 46

Width of gaussian distributions used to fit the data vs. beam en-

IMF gated folding angles ....................... 50

Average and most probable LMT values in terms of beam momentum. 51

LMT per projectile nucleon. ..................... 52
Calculated excitation energy using the hybrid model. ....... 54
Calculated number of prefission emission nucleons .......... 55
Estimated size of compound nucleus after prefission emission of
nucleons. ............................... 56
Cross sections for fissionlike processes compared with model pre-

diction .................................. 57

Demonstration of $3 values with various combination of three az-

imuthal separation angles. ...................... 64

xi

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

Azimuthal correlation function C(ng). ...............

Contour plot of IMF rapidity in the center of mass frame (ycm) and

folding angle (0”). ..........................
Azimuthal correlation function (C (1%)) vs. 21.3. ..........

IMF energy distributions for the reaction ‘°Ar + 232Th at Em", =
35 A MeV ................................

Azimuthal correlation function distributions for the reaction ”Ar

+ 232T}; at Em", = 15 - 115 A MeV .................

Excitation energy of the reaction “Ar + 232Th with varying beam

energy. ................................

Relative cross sections of three IMF emission modes in fissionlike

reaction of 40Ar + 232Th at Em". 15 — 115 A MeV. ........

Mean number of IMF associated with each IMF emission mode. .

xii

72

75

77

78

81

82

Chapter 1

Introduction

1.1 Physics Justification

In medium energy heavy ion collisions (Bum a: 10 ~ 100 AMeV), when the
beam energy is well above the Coulomb barrier, it is known that a hot (T Z 3
MeV) compound nucleus can be formed [Soye89]. It is of great interest how this
hot nucleus decays. Identifying and understanding specific decay modes would
provide important insight into nuclear reaction dynamics and ultimately help to
characterize the nuclear equation of state. One of the attempts to predict the
decay modes and their relative cross section is from the statistical approach. An
example is given in Fig. 1.1 that was obtained by microcanonical calculation. It

is seen that there are possibly three mechanisms competing, evaporation, binary

fission, and cracking.

When a compound nucleus decays through fission, one of the techniques that
can best describe the mechanism is angular correlations, namely the folding angle
technique. Over the past several years, exhaustive studies of inclusive fragment-
fragment folding angle distributions have been performed, and the results from

these studies have provided a wealth of insights into linear momentum transfer

1

 

       

 

     

 

 

 

-100

s - -

E “ "

.9

m 50-

.2 L

:9- -

2 '— /
0’- ; 43/4-" . 1 1 1
O 200 400 600 800 1000 1200

E’lMeVl

Figure 1.1: Relative probability of evaporation (E), binary fission (F) and crack-
ing (C) as a function of excitation energy of the 131X e nucleus ( microcanonical

calculation from [Zhen87] )

and energy dissipation in heavy ion collisions (see Fig. 1.2 ). Intuitively, one
would expect to get the highest energy dissipation for the most central collisions.
At low energies (E S 10 AMeV), the reaction is indeed dominated by the fusion
process or strongly damped collisions. With increasing beam energy, a quite large
number of fast particles having almost the beam velocity can be observed which
are very likely emitted during the early stages of the collision. The consequence
will be a decrease of the available linear momentum in the entrance channel for
fusion. Complete fusion processes will then be strongly reduced, and the so called
incomplete fusion or massive transfer process will take place. This process is
observed to dominate complete fusion at energies as low as Em," z 15 A MeV.
It was suggested that fission following the incomplete fusion may not be observed

for E5“... > 40 AMeV with the folding angle technique [Conj85].

Another aspect to consider is the enhancement of non-equilibrium processes
in the early state of the collision. With increasing beam energy, this effect would
result in an enhanced number of emitted particles. This enhancement may affect
the folding angle distribution, that contains only fissionlike fragments, so that
position of the peak located at smaller 0” values would shift. An example of such

an effect is shown in Fig. 1.3 .

Now, we have two motivations to investigate more closely the fissionlike reac-
tion. The first is to map out one of the three competing decay modes which is
the fissioning of the hot compound nucleus in medium energy heavy ion collisions.
The fate of fissionlike reactions with increasing beam energy is not firmly estab-
lished. Secondly, it becomes more necessary to take IMF emission into account

with increasing beam energy when we study fissionlike reaction, because IMFs

70° “Aanh ' '

«human, tau.)

N
O
O
f

100 ..

 

31mm: . L :1 .

 

35HlV/U L L i 4

39mm: L

 

 

1 r I 1 1 . n 4 I .i__i___l.__L—_f
“WV/U so 90 100 no 120 130 11.0 150 160 no so 6"!)

Figure 1.2: In-plane angular correlation of fission fragments for the system 40Ar
+ 232Th at 31, 35, 39, and 44 MeV/u . Curves are drawn to guide the eye.
The vertical lines at each energy correspond to 0” = 170° and 110° ( LMT of
about 0.8 and 7 GeV/c respectively ); the arrows indicate the locations of the full
momentum transfer. From [Conj85] .

 

T I I

 

 

 

I I I I
I INCLUSIVE
’3‘. '03.? .0 0 Be
. : I. a C
3 i A. A O
‘5 ’ o, o N.
,_, .
3 I02:-
o .
cg E
ch“ '
D b
\ I
3'0 E' ‘
H u-
s :
a P
3 .
b( '0»—
U I o
59“,.3126
I
' 1 -l l l L L 7
IZO I40 ISO ISO
9“ (deg)

Figure 1.3: Fission fragment folding angle distributions measured in coincidence
with Be, C, O, and Ne fragments detected at 011m: = -51° ( open points )
and 0”" = +126° ( filled points ). Solid lines through points are to guide
the eye. Upper solid line represents the inclusive folding angle distribution; its
normalization is arbitrary. From [Faty87] .

play a more important role in the decay of hot nucleus with increasing beam en-
ergy. The effect of IMF production is not a well addressed subject partly because
of the difficulty in the exclusive measurement of fissionlike fragments and IMFs

at the same time, for which our detector system is designed.

1.2 Organization of This Thesis

This thesis is made of mainly three parts. In Chapter 2, I review the MSU
41r Array concerning previously existing components and describe the multiwire
proportional counters (MWPC) in detail. The techniques used to extract time
and position information are given explicitly. Classification of detected particles

along with bragg curve counters (BCC) is demonstrated.

In Chapter 3, I employ a folding angle technique to track the fissionlike reac-
tions in central collisions. In-plane and out-of-plane folding angle distributions are
presented. IMF emission along with linear momentum transfer (LMT) is studied.
Cross sections for the reaction are obtained and compared with the hybrid model

calculations.

In Chapter 4, azimuthal correlation functions are introduced to analyze the fis-
sionlike reaction events. Three distinct modes of IMF emission in central collision
fissionlike reaction are identified. Their respective contributions to the relative
cross sections with beam energy are estimated and presented in terms of average

number of IMF emission from each mode.

In Chapter 5, I summarize the results and give conclusions.

Chapter 2

Experiments

2.1 Introduction

2.1.1 Experimental Design

The experiment was proposed to investigate the disappearance of fusion and the
onset of multifragmentation. To probe fusion, folding angle is one of the interesting
observables, which requires detecting fissionlike fragments [Conj85]. Study of the
onset of multifragmentation requires the detection of IMFs within the same setup.
These requirements call for a detection system with wide dynamic range as well

as excellent spatial coverage.

2.1.2 MSU 41r Array

The completed MSU 4x Array is an ideal detection system for this purpose. It
consists of the main ball phoswiches[Cebr90], forward array phoswiches[WilsQl],
Bragg curve counters(BCC) in ion chamber mode [Li93] and E2 mode[Gual95a],
and multiwire proportional counters(MWPC). Individual modules(subarrays)
each have all the components (see Fig. 2.1 (a) ) in the concept of logarithmic

detection[West85], except for the forward array. A cross sectional view of the

7

FOOT/£0. “71C SCINYILLM’W

 

 

 

 

 

 

 

(b)

 

lSZS ~20

 

 

zmcm). Amen“). Wen“) :BCC, Phoswich
9(Ncnga). “New name

 

 

 

Figure 2.1: (a) A single module that consists of MSU 41r Array. (b) Side view of
MSU 41r Array, that shows the arrangement of each component.

fully assembled array is shown in Fig. 2.1 (b).

2.2 MWPC

Low pressure multiwire proportional counters(LP-MWPCs) have been con-
structed as part of MSU 4x Array[West85]. There are two main purposes of
this detector subarray. First, it enables us to detect fission fragments with 1 °
angular resolution. Secondly, due to its fast response time, we now have proper
triggering signal to use Bragg Curve Counter (BCC) as standalone EZ detec-
tors. Altogether, the MSU 4n- Array makes the optimum detection system for the

studies that require wide dynamic range of particles as well as spatial acceptance.

2.2.1 Construction

Previously, the MSU 47r Array consisted of an inner layer of BCCs in front of a
layer of plastic phoswich detectors. In the present configuration, the MWPCs are

mounted in front of the BCC, forming the innermost layer of the Array.

The frame of the MWPC is made of 6 layers of G10 fiberglass with kapton
foils (0.3 mil) forming front and rear pressure windows. The anode forms the
center layer and consists of a plane of 12 mm diameter gold—plated tungsten wires
spaced 1 mm apart. This layer is between two cathode planes which are made of
stretched polypropylene foils. A layer of aluminum is evaporated on the surface of
the foil, and is divided into 5 mm wide strips connected by a 1 mm wide strip of
resistive (1 k9) nichrome. (See Fig. 2.2 .) The thickness of the layer of evaporated
Al, as well as the thickness of the nichrome layer is 1 RA. Originally, a thinner

nichrome strip was to be used. However problem related to the strength of the

 

Figure 2.2: Exploded view of the layers making up an MWPC. Charges are col-
lected at the end of each nichrome strip.

10

strip developed. Any minor stress on the foil caused the strip to crack and the
resistance to increase significantly. Because of this, the width of the Al strip
had to be narrowed to 1 mm in the region where the nichrome strip crosses, so
that thicker nichrome strip can be used while maintaining same resistance. Even
with these measures taken, the phenomena of rising resistance still remains as a

concern, but the problem is greatly lessened.

2.2.2 Signal Processing

With an operating condition of 5 torr isobutane gas and +510 V anode bias,
we get two types of signals each from the anode and cathode. Anode signals
originate from electron avalanche and are intrinsically much faster than cathode
signals [Bres79]. We use the anode signal to set up the triggering condition, while
the cathode signal is used to give position information. The preamp was designed
with two goals in mind. (See Fig. 2.3 .) The plateau area in the cathode output
corresponds to the charge collected at the end of the nichrome strip. If we plot
the amount of collected charge of one end vs. the other end, we get Fig. 2.4 .
The radiating lines of this fan-like picture represent each aluminum strip, hinting
that the position along the line that traverses aluminum strips can be determined.
Details are discussed in the next section. An example of the use of the cathode
signal to reconstruct the image of a mask in front of an MWPC is presented in

Fig. 2.5 .

2.2.3 Coordinate Determination

To identify the position of particles in the lab frame where they go into the
MWPC, we use 3 different coordinate systems. In addition to these frames, there

11

 

 

 

 

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z —2oog—-

.29 :

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a -400r - .
fl :PLLl-lLllllllllll:
a -500

 

-1O 0 10 20

time ( ns')

TTVTIIIUTI ‘
d

d

I

d

4

‘

1

1

L1 l l l 1 111L141 l4 1 l

0 1 2 3
time-(#8)

 

A_

VIIIUUUI'IUV'UUIUIIUIE
a q
u

 

lllllllllll

fl

 

 

 

pulse height ( mV )

Figure 2.3: (a) Anode signal output from preamp. (b) Cathode signal output
from preamp. Note that the time interval to be integrated is order of magnitude
bigger than the case of phoswich ( ~ 100ns ).

12

.3

. .1. .
; .- - ‘.
-£;,¢.f¢

”taunt-4.

 

Figure 2.4: Cathode signal of one end vs. the other end.

 

s
O.
.
sf: .
.‘
o
o
.
o
o o
o
o
o o
. o o I.’
\
O. .
o
o
0
~

Figure 2.5: Position spectra using a mask that covers a. hexagonal type MWPC
except for the holes at each corner and lower character ‘h’ in the center.

14

are 3 distinct types of detector modules, which makes the conversion parameters

between the coordinate systems vary.
0 Cathode Coordinate System (x',y')

—- This is the natural coordinate system following cathode orientation. Capital
A to F mean the charge collected at the end of nichrome wire on the corresponding

side. (See Fig. 2.6 (a) ) The coordinates are given as follows;

For hexagon type,

. D—A
. C—F
y — (C+F)'d"

For pentagon type,

:r' = — (Ff—A.) - (81 + 82) + 82 (2-2)
3" = - (3%) -(s: +32) + as.

0 Module Coordinate System (x,y,z)

— :r,y axes lie in the same plane defined by .r', y'. But the unit vectors are

defined a, a. = 6,9 = 8,2 = R. (See Fig. 2.6 (b),(c) )'

 

1: _ ..sin(.0+a)_ 231.110! (2.3)
srn0 s1n0
__ . cos(0+a) . sin0+sinaocos(0+a))
y _ I sin0 +y ( sin9-sin(9+a) '

15

 

X

Figure 2.6: (a) Cathode coordinate system (x', y'). (b) Module coordinate system
(z,y,z). (c) The orientation of the unit vectors of module coordinate system in

lab. frame. (d) r = R + x

16

300

 

 

 

 

0 50 100 150
Blah (0)

Figure 2.7: Angular distribution of MWPC events.

17

 

hex pent(6 — 10) pent(2l — 25)
60° 72° 72°
or 0 72° 36°

 

%

 

 

 

 

 

 

 

0 Ball Coordinate System (r, 0, d; X,Y, Z)

— Same as laboratory frame. It has the origin at target position, and Z is the
beam direction. R is pointing the center of each module, that is the origin of the

module coordinate system. (See Fig. 2.6 (c),(d) )

tan9 __ R’sin29+r2cos’9+2Ra'sin9-cose+y2i 24
- R’cos’6+zzsin29-2stine-cose (°)

 

(RsinO-I-zcose) -sin<I>+ycos<I>
(Rsin9+zcosO)-cos<I>-ysin<l>'

 

tan¢ =

Data are shown in F ig. 2.7 with identified 0 and d value of each event. Space
that each module occupies is clearly demonstrated divided by the walliarea around
the module. Target frame shadowing traverses near 0 z 90° and one of the rod
holding the frame is shown near 43 z 240°. Forward modules even show the

cathode strips quite well.

2.2.4 Time Analysis

In the normal setup of the MSU 41r Array, the relative time of flight of each particle
with respect to the triggering signal gets recorded for the case of phoswich and
MWPC. The time difference between the cyclotron radio frequency (RF) and the
triggering signal is also recorded. But, this information was never used to obtain

the velocity of a particle directly, partly because we can get the energy values

18

400

 

 

 

 

 

 

.-T....T....l.
: (a)V
A 3001
2 i o
E 200}
O
100;-
g C
H 0:
><i
>‘. 3007
4" C
.8 b
O 200?
H .
(1) .
:> 100:-
O: ..l.mr.l .....
0 5 100 150

 

 

0
9 (°)
ff
Figure 2.8: (a) Velocity spectra of the particles detected in MWPC. The line is

from the Viola’s empirical formular. See text for details. (b) Recoil velocity of

the compound nucleus. Data are from the reaction ”Ar + 232Th at E5”... = 35
A MeV

19

 

 

 

 

 

 

 

 

 

a)
10:3 g- 1
102 r 1 —l-IL :
101 r 1 .
A O 4 i - .
10 . . -
:3 3 b)
:3 1° F 1
2
El 10 I I M
:3 101 r i
8 100 a . -
10:3 r C) [v
I
102 r : —-h—h—+—
101 r 1
100 bl . l L r .
1000

RF time (channel)

Figure 2.9: (a) Ideal case of tap. (b) Wrapping-around occurred. (c) The RF
time signal is clipped on both sides. The shaded bar on the RF time line is the
spread of triggering particle

20

from the pulse height in the case of phoswich detectors, which is very difficult for

MWPCs. So, we devised a method to obtain the velocity using time information.

It involves three kind of time signals, thpc, tap, and tphowgch, as well as
the energy values of the particles corresponding to tphomch. With this reference
to the phoswich, the absolute time of flight for the particle recorded in MWPC
can be obtained. In Fig. 2.8 , we show the results. The validity of this method is
checked in Fig. 2.8 (a) with Viola systematics[Vi0183], that should match the value
at 9” z 180°. (For 01;, see [Viol89].) Because Viola’s empirical formula predicts
the kinetic energy of the fission fragment as a function of the charge and mass
of the fissioning nucleus in the frame of the fissioning nucleus, the velocity of the
fission fragment obtained from peripheral collision is expected to be comparable
to that calculated by the formula. Unless a transformation is performed using
recoil velocity, the velocity of the fission fragment from a central collision will
have slightly higher value than the calculation. Such a trend can be seen in
Fig. 2.8 (a) . Recoil velocity data in Fig. 2.8 (b) also shows the agreement with
the expected values, since it should go to near zero at 0,, z 180°, which indicates

the most peripheral collision.

One thing to give particular attention to is the RF time signal relative to the
triggering particle. The typical spread in velocity spectra is 1 cm/ns, and the
distance between the target and the MWPC is about 15 cm. Thus the typical
time spread of the triggering particle is 15 as, which is same order of magnitude
of RF interval. Hence, wrapping-around of t 3; may occur as the beam energy
changes. Clipping on both sides in tap may occur as the RF interval gets shorter

than time spread of triggering particle. In Fig. 2.9 , we show those cases from

21

data. In the case of (b) and (c), the time analysis is inevitably more erratic than

in (a).
2.2.5 Eficiency

In this experiment, MWPCs are used to detect fissionlike particles. So the de-
tection efficiency is tuned to high Z particles. Although the efficiency relative to
the BCC is near 100 % for the particles with Z Z 10, the MWPCs still have the
capability to detect lighter IMFs with reduced eficiencies. (See Fig. 2.10 .) The

response shows little dependency on the beam energy over the range studied.

We were unable to measure the absolute efficiency as a function of Z.

2.2.6 Particle Identification

A measurement of the fission fragment folding angle is meaningful only when the
two observed particles, whose velocity vectors make that angle, are both fissionlike
fragments. Because we know that the MWPCs we use are quite efficient for IMF 3
too, we have to identify those events in which either of the signals from MWPCs
is generated by an IMF. For the case when a particle leaves a signal in both the
MWPC and the backing BCC, we can plot the E signal from the BCC vs. pulse
height of the corresponding MWPC as in Fig. 2.11 . From the BCC particle
identification, we identify the peaked region on the left as IMFs, while the bottom
region with small E values are recognized as fissionlike fragments. When a particle
is stopped before it reaches BCC, we plot the pulse height vs. folding angle. (See
Fig. 2.12 .) Unlike the inclusive case in which we don’t care whether there is a
coincident signal in BCC, the IMFs reveal themselves in the bottom left region.

The right region represent valid target fission events.

22

 

150

'_I

 

 

 

_ I I I I I .
125E— .;
MNP- .gulllllllll—

A . "
g\° : I :
:75.— ‘j
‘6‘ : I ..
50';- . .2.
25E— 1 .{
ELI I I I I I I L3.
2 4 6 8

10 12 14 16 18
Z

Figure 2.10: Efficiency of MWPC relative to BCC as a function of charge number
of nucleus detected is shown in the case of 35 MeV / nucleon °°Ar beam.

23

Combining those two methods, the IMF contamination can be removed in the

folding angle plot as seen in Fig. 2.13 .

2.3 Phoswich Detectors

2.3.1 Signals

A phoswich detector produces composite signal of fast and slow components, that
depends on the charge and deposited energy of the incoming particles[Wilk52].
Although the charge resolution is not as good as Si detectors, the flexibility of
fabrication both in size and shape, and thus possible greater stopping power,
make the phoswich the choice of closed packed arrays such as MSU 4x Array. By
gating the fast and slow components separately and integrating the charge within

the gate, we get bands of isotope lines shown in Fig. 2.14 .

2.3.2 Particle Identification

The light output as a function of deposited energy from the plastic scintillator is
not linear, but rather a complicated function of charge, mass and energy of the
incoming particle [Becc76]. The response function for MSU 4w Array phoswiches

was found to be[Cebr90]

1.4
A“ . 20.8
(fast output) or E0'5

(slow output) oc (2.5)

where E is the incident energy of the particle with charge Z and mass A. Using
an energy—loss program such as DONNA[Meye81], E, Z and A values are mapped

out onto a 2—dimensional space as shown in Fig. 2.14 . (See Fig. 2.15 .) By

24

 

 

 

 

 

O 500 ‘ 10004 .1500
ph(a.u.)

Figure 2.11: BCC E signal in EZ mode vs. MWPC pulse height. There are two
distinct groups in the left and bottom regions.

25

 

 

 

 

Figure 2.12: MWPC pulse height vs. folding angle of the events that either one
of the two particles doesn’t leave signal in the BCC.

26

 

10000 I ' I I I l I I I I i I I

 

count(a.u.)

 

 

 

Figure 2.13: Folding angle distribution of (U) inclusive data, (x) IMF —
contaminated data, (0) IMF—suppressed data.

27

Fast Plastic (channel)

300

250

200

150

100

50

 

IIIIIIIIUTIITI'IFII

   

 

 

I

 

  

-'IIIIllIIIlILIIlIIIIlIIII

50 100 150 200 250

Slow Plastic (channel)

Figure 2.14: Fast output vs. slow output.

28

 

300

transforming and overlaying Fig. 2.14 onto Fig. 2.15 and finding the best fit, we

assign each particle the charge, mass and incident energy.

2.4 Bragg Curve Counters

When a charged particle traverses a volume of gas, it loses energy as it interacts
with the gas atoms along the way. Generally, the rate of energy loss increases log-
arithmically and then increases dramatically just before the particle stops within
the gas. After that it falls down sharply. The term Bragg curve refers to this en-
ergy loss function, and the peak at the end is called the Bragg peak. The height
of the Bragg peak is proportional to the charge of the particle. The total energy
loss can be obtained by integrating the Bragg curve [Gruh82].

2.4.1 Construction

The gas chamber is made of 010 fiberglass. On the inside surface, there are field
shaping strips connected by 1.55 M52 resistors, producing a radial electric field
along the path from the entrance kapton window (900 pg/cmz) to the aluminized
surface on the face of the backing phoswich fast plastic Which serves as the anode.
The entrance window frame does dual duty as the cathode and pressure window.
A grounded Frisch grid 1 cm from the anode surface prevents the induced image
charge from being collected in the anode. (See Fig. 2.16 ) It was operated with
125 torr CgFo gas at +150 V anode voltage and -500 V of cathode bias.

29

 

500

400

300

 

 

200

 

 

 

 

Fast Plastic (channel)

100

 

 

 

 

Slow Plastic (channel)

Figure 2.15: Particle identification template that assigns charge, mass and energy
values to a particle projected onto a certain point.

30

 

 

 

 

 

 

   

‘ .

Frisch Grid

(3st 633 at 125 TO" ,.

 

 

 

 

 

 

 

Figure 2.16: Schematic diagram of BCC.

31

l
I
l
' Anna.
I

   

 

Pro-amp
Hold Shaping Grld
~ ~ ~
Q
~
Q
~
Q
Q
.__, ~ ~
~ Q
- - — - -
. .I-
B» chaln = +150V

2.4.2 EZ Mode

When a particle stops inside the gas volume, a Bragg peak is produced, and we
get both charge and energy information for that particle by measuring the peak
height and integrated signal, respectively. Gate lines were drawn by matching the
punch-out point with calculations. ELOSS[Zieg85] was used to calculated energy
loss and map out energy values. Typical spectra with gate lines superimposed are

shown in Fig. 2.17 .

2.4.3 Ion Chamber Mode

When a particle punches into the fast plastic and stops there such that it doesn’t
produce Bragg peak in the gas, we are in much the same situation as in the
phoswich. The integrated E signal from BCC vs. fast plastic signal is shown in

Fig. 2.18 . The response functions are found to be

1.4
20.8 . ADA
(BCC E) o: 3“,

(fast output) or (2.6)

where E is the incident energy. Previous test [Cebr91] has found that the BCC
E output is quite linear to incident energy. But, with this setup there was found
some non-linearity. The same technique is used as in phoswich to map out charge,

mass and energy values.

32

 

  
  

250 —

.—

ZPunch-out Line '
200 i

   

150

100

 

BCC E (channel)

 
  

. .5 ch-in Line

UI
G

 

 

.lLLIilllLlllLlilllli

0 100 15 200 250
BCC Z (channel)

Figure 2.17: Typical spectra of BCC with the pid gates superimposed.

33

 

120

§

so a“,

60

BCC E (channel)
r”?-

40

20

 

 

 

1 l 1 1 L l 1 l l l 1 l l l L n l 1_
20 40 60 80 .100 120
Fast Plastic (channel)

 

Figure 2.18: Typical 2-dimensional plot of BCC E vs fast plastic. BCC is used
as an ion chamber.

34

Chapter 3

Folding Angle Analysis

F ission—like fragments and coincident charged particles have been measured in
a 41r geometry over a wide energy range (15 — 115 AMeV) for the reaction
”Ar + 232Th. The exclusive folding angle distribution data provide direct evidence
that fission—like processes following incomplete—fusion are still an appreciable exit

channel for beam energies as high as 115 AMeV.

3.1 Introduction

3.1.1 Motivation

Angular correlation studies of fission-like fragments produced via the bombard-
ment of highly fissile targets provide important insights into nuclear reaction dy-
namics. Over the past several years, exhaustive studies of inclusive fragment-
fragment folding angle distributions have been performed, and the results from
these studies have provided a wealth of insights on linear momentum transfer
and energy dissipation in heavy ion collisions[Bege92, Lera84, Poll84, Conj85,
Jacq84, Vi0189, Tsan84]. However as the beam energy increases, the inclusive

fragment-fragment folding angle alone cannot effectively describe the reaction be-

35

cause intermediate mass fragment (IMF) is expected to play a more important
role. Exclusive folding angle data along with wide dynamic range measurement

of light charged particles and IMFs is called for. The MSU 41r Array is the ideal

setup for this kind of measurement.

3.1.2 Background

Fragment-fragment folding angle distributions are typically characterized by two
peaks; one at small folding angles (< 180°) and the other at large folding angles
(3 180°) [Conj85, Jacq84, Vi0189, Tsan84, Leeg92, Faty85, Schw94]. The peak at
small folding angles is usually attributed to fusion-like reactions or incomplete—
fusion resulting in high linear-momentum—transfer (LMT). The other peak, located
at large folding angles, is linked to peripheral reactions or target-fission with
small LMT. One of the prominent features of folding angle distributions is the
rapid decrease of the high linear-momentum-transfer peak with increasing beam

energy[Conj85, Jacq84, Vi0189, F aty85, Schw94].

In a series of inclusive measurements, Pollacco and Conjeaud observed that
the high LMT peak in the folding angle distribution for ‘°Ar + 232Th is
strongly suppressed for beam energies Em," > 30 AMeV, and disappears for

Em,” 2 44 AMeV[Poll84, Conj85]. Many speculations pertaining to the nature
of central heavy ion collisions have been generated by these rather surprising re-
sults, and a few exclusive measurements have been performed with the explicit
intent of addressing the fate of central Ar + Th collisions for beam energies

_>_ 30 AMeV[Schw94, Jian89]. Nonetheless the detailed nature of the reaction

mechanism remains unclear.

36

3.1.3 Present Work

In this chapter, we report results from an extensive set of °°Ar + 232Th measure-
ments (Em... = 15-115 AMeV) in which we have simultaneously detected light-
charged particles, intermediate mass fragments (IMF: 3 5 Z S 18), and fission
fragments with nearly 41r coverage. We observe direct evidence for fission-like re-
actions in a beam energy range where prior inclusive measurements have pointed to
the possible disappearance of such processes. Earlier exclusive measurements for
this system have employed setups with significantly less solid angle coverage for the

simultaneous detection of fragments and light-charged particles.[Schw94,Jian89].

3.2 Experimental Description

The ‘°Ar beams [15, 25, 30, 35, 40, 45, 55, 75, and 115 AMeV] used in this ex-
periment were provided by the K1200 cyclotron at the National Superconducting
Cyclotron Laboratory (NSCL). The beam intensity was approximately 100 elec-
trical pA and the thickness of the Th target was 1.0 mg/cm’. Charged reaction
products were detected with the fully configured MSU 4r Array[West85]. The
MSU 41r Array consists of a main ball of 170 phoswich detectors (arranged in 20
hexagonal and 10 pentagonal subarrays) covering angles from 23° to 157° and a
forward array of 45 phoswich detectors covering angles from 7° to 18°. Thirty
multiwire proportional counters (MWPCs) were installed in front of 55 Bragg
curve counters (BCCs) which in turn were installed in front of the hexagonal and
pentagonal phoswich sub-arrays. The MWPCs and BCCs were operated with 5
torr of isobutane gas and 125 torr of CgFg gas respectively. In addition to pro-

viding Z and E signals for fragments stopped in their active volume, the BCCs

37

provided AE signals for charged fragments (Z _>_ 2) that stopped in the fast plastic
scintillator of the main ball. Fission-like fragments were detected in the MWPCs
with an angular resolution of z 1°. Time signals obtained from these MWPCs al-
lowed the determination of the fragment velocities. The 41r Array provided clear Z
identification for charges of Z = 1 through 18. Low energy thresholds for the main
ball were 17 AMeV, 2 AMeV, and 4 AMeV for fragments of Z=l,3, and 12 re-
spectively. The low energy threshold for the forward array was z 17 AMeV. Data

were taken with a minimum bias MWPC trigger (one or more charged fragments
detected in the MWPCs).

The efficiency of MWPCs relative to BCCs rises from 25% for Z = 3 to 100%
for Z 2 10. Consequently, it was necessary to apply offline gates to separate
the fission-like fragments from the IMFs. The fragments which stopped in the
B003, provided two distinct groups which were identified and assigned to IMFs
and fission fragments. Low energy fragments which triggered the MWPCs but
left no signal in the B008 were separated by the pulse height difference.

3.3 Definitions

3.3.1 Folding Angle

Folding angle (0”) is defined as the angle between two velocity vectors, in this
analysis, two fissionlike fragments’ velocity vectors. In the Cartesian coordinate
system where beam direction is same as z direction, the cosine of the folding angle

can be calculated from polar and azimuthal angles of two velocity vectors.
c030” = c030 - 0030’ + sinfl - sinfl’ - cos(¢ — 45’). (3.1)

38

0" can have values between 0° and 180°, inclusively.

The out of plane angle (05”) is defined as the angle between the two planes
that are defined by the beam direction and each of the two fissionlike fragment
vectors. (0,, = 0° is taken such that three vectors mentioned above are all in
the same plane with beam direction in the middle. When the fissionlike reaction

results in this configuration, we call it a perfectly coplanar event.

The fission axis is defined as the line defined by joining the tips of the two
fissionlike fragment velocity vectors. Given in Fig. 3.1 is the distribution of the
angle that the fission axis makes with the beam direction. Note that the distribu-
tion for central collision peaks near 0,.“ z 90° . That suggests that those events

are from symmetric fission.

3.3.2 Linear Momentum Transfer

When a nucleus of charge Z and mass A fissions, it releases, in the mean, a value
of kinetic energy < Ex > in the frame of fissioning nucleus. According to Viola’s

empirical formula [Vi0185],

2

< Ex > = (0.1189 a: 0.001) Z + 7.3(:L-1.5)MeV. (3.2)

AI/s

When the projectile has mass M, and energy 5),, thus momentum p0, the average
linear momentum transfer < p > is given by the formula that is a function of
folding angle (0”) and the angle of one of the fission fragment to the velocity of
fissioning nucleus (01) [Leeg92].

1/2

<p>_
p.

M< Ex >
ME».

81119},
[233.11%91] - 01) + 2.9111201 — sinMHP/T

 

 

(3.3)

 

 

39

 

1000

500 f

 

 

200

count (a.u.)

2000

‘Tf

v v

V I '

1000

 

 

 

0 50
9re1(deg)

Figure 3.1: Distribution of angles that fission axis makes with beam direction. 0
is for inclusive data. 0 is for peripheral collision. O is for central collision.

40

The velocity of fissioning nucleus is roughly the same as the beam direction when

compound nucleus is formed, but not so in peripheral collision.

3.4 Analysis

3.4.1 Inclusive Fission fiagment Folding Angle

Folding-angle (0") distributions for Ar + Th are shown in Fig. 3.2 for E5“... = 15,
25, 30, 35, 45, 55, 75, and 115 AMeV. Events are selected when there are two and
only two fission—like fragments (Z > 18) detected in the MWPCs, irrespective
of the existence of coincident IMFs or light charged particles. Folding angles
were determined [event by event] from the directional unit vectors (1') of these
two fission-like fragments: 91 f = arccos(f1 ~f3). The angle between the two
planes defined by the beam axis and the unit vector of each fragment, <0”, was
allowed to vary between -90° and 90° for these distributions. The double peaked
structure which is characteristic of folding angle distributions is clearly visible
in Fig. 3.2 for beam energies S 45 AMeV. The high and low LMT peaks are
located at approximately 110° and 165°, respectively. The energy dependence of
these distributions are similar to those previously reported for comparable beam
energies[P01184, Conj85, Schw94]. They corroborate the previous observation that
the high LMT peak essentially disappears for Em," z 50 AMeV.

3.4.2 Out-of-plane Distribution

In Fig. 3.3 , 4311 vs. 9,, is plotted. At low beam energy, two peaks in those contour
plots are identified corresponding two peaks in 0” distribution of Fig. 3.2 . These

contours are symmetric for ct" = 0°, which means that the fissionlike fragments

41

 

 

 

 

da/dafi ( mb/deg )

 

0 w l
50 100 15050 100 150
0,,(deg)

   

Figure 3.2: Inclusive fission fragment folding angle distributions for Ar + Th
reactions from 15 to 115 AMeV.

42

have mostly the same masses. For the high LMT peak, the height decreases while
the width stays as beam energy increases, as far as we can identify that peak.
We can say quantitatively that the width of ¢ff increases as the beam energy

increases. The low LMT peaks show little change.

To quantify these results, we plot Fig. 3.4 and Fig. 3.5 . Note the difference in
the scale between figures. The open circles in Fig. 3.4 represent the distributions
gated on the low LMT peak, 0” > 135°. The solid squares in Fig. 3.5 represent
distributions gated on the high LMT peak, 85° 5 0,; S 135°. Distributions
are shown for several beam energies as indicated in the figure. The widths of the
gaussian curves used to fit these distributions are shown in Fig. 3.6 with the same

symbolic convention as that of the previous two figures.

A striking feature of this figure is the beam energy dependence of the widths of
the 41, I distributions for high LMT. In contrast to the widths for the low LMT at"
distributions (z 30°), these widths show a monotonic increase (from 25° to 70°)
with increasing beam energy. Because target fission with low LMT is essentially
a binary process, one can conclude that the high LMT reaction mechanism be-
comes increasingly difi'erent from a binary one as the beam energy increases. We
attribute this trend to a growth in the importance of multi fragment final states
[not necessarily simultaneous multifragmentation] with increasing beam energy.
It appears that the suppression of the high LMT peak with increasing beam en-
ergy (cf. Fig. 3.2 ) is not only associated with a decrease in the cross section
for fission—like processes that follow incomplete-fusion but also with a change in
reaction mechanism from an essentially binary one to non-binary one. Therefore,

proper selection of multi fragment final states could lead to selective enhancement

43

 

 

 

   

 

 

   

-50}
*j t A i 1 a
50 _- C) 30 AMBV
A O i- g P'"’)’K« .90
DD E A

q) -50 l-
3 ~.

33 50;. e) 45 AMeV
‘S~ ;
—50i

A A A. l A A l A l A I A
v v I T v V v I V’ v

1
4
4
q
4
1
4
.1
q

   

 

 

 

(I).
-50;-

'....I.-.LI.-. ....IY1..-I...‘

50 100 150 50 100 150

6,,(deg)

Figure 3.3: Contour plot of 43;, vs. 0” for the reaction of Ar + Th at E5“... =
15 — 115 A MeV.

44

 

100

i a) 15 urev b) 25 new i

50 cs g

A i :9 59°. ’
00 o: r

Q) . c) 30 AMeV d) 36 AMeV :

“U ; .

.0 . . e

O ’ .37 (11". 7‘: J

v . e) 46 AMeV t) 66 AMeV ,

L 1

3.1 » .

‘9~ 50 L ‘9 <0 .

"U i 39 gs I

b 0 -‘ = ,

'U C a) 76 AMeV h) 116 “IN .

60} s .. I

i .99 a 1

 

 

-60 0 50 -50 O 60

9511(d93)

Figure 3.4: Fission fragment azimuthal distributions for Ar + Th reaction from
15 to 115 AMeV gated on low LMT. Linear scale.

45

 

h) 115 mov

 

-60 0 50 -50 0 60

¢fl(deg)

Figure 3.5: Fission fragment azimuthal distributions for Ar + Th reaction from 15
to 115 AMeV gated on high LMT. Same as Fig. 3.4 , but gated on high LMT. Even
though it decreases substantially with beam energy, the high LMT distribution

maintains its gaussian shape.

46

of the high LMT peak in the of, distributions.

3.4.3 IMF Emission Angle and Event Selection

In Fig. 3.7 , we compare folding angle distributions for fission-like fragments emit-
ted in multi fragment events. The left column of the figure (Fig. 3.7 (a)-(d) )
shows distributions gated on one or more IMFs at forward angles (90.0 < 15°).
The middle column (Fig. 3.7 (e) - (h) ) shows distributions gated by the detection
of one or more IMFs at backward angles (0M, > 68°). The right column (Fig. 3.7
(i) - (l) ) shows distributions gated on the top 10% of the total-transversekinetic-
energy impact parameter filter. The four rows in Fig. 3.7 (from top to bottom)
show results for E5“... = 35, 45, 75, and 115 AMeV, respectively. It should be
noted here that the cross sections reported in the figure are not corrected for the
detection efficiency of the IMFs. In contrast to the double peaked folding angle
distributions shown in Fig. 3.2 , the distributions shown in Fig. 3.7 are charac-
terized by a single peak which can be linked to either high or low LMT. The
distributions gated on forward IMF 3 show peaks which are clearly associated with
low LMT, while the distributions gated on backward IMFs or small impact pa-
rameters show the expected peaks for high LMT. As the beam energy increases,
the high LMT peak can only be identified when the fission-like fragments are
measured along with other particles. This fact is evident when one compares
Fig. 3.7 to Fig. 3.2 . It is noteworthy that the high LMT peak is well-separated
from the low LMT peak even at Em," = 115 AMeV, which provides the direct
evidence that the fission—like processes persist up to this beam energy. Moreover,
the gating condition requires these events to be non-binary. We conclude that the

fission-like process which follows incomplete—fusion is a well-defined exit channel

47

 

width(deg)

 

 

 

 

Figure 3.6: Width of gaussian distributions used to fit the data in Fig. 3.4 and
Fig. 3.5 vs. beam energy. The symbols follow the same convention. Straight lines
are to guide the eye.

48

 

for the entire beam energy range of our measurements and that it changes its char-
acteristics from an essentially binary mechanism [at low energy] to one involving

more than two fragments.

3.4.4 Two Cases of Linear Momentum Transfer

Folding angles can be translated into LMT event by event[Leeg92]. We have
extracted average LMT values, < p > / 11mm, considering both target-fission
as well as fusion—fission. They are estimated to be 86, 70, 62, 54, 41, 32, 23,
and 16% fer Figs. la-lh, respectively. A maximum of 151 d: 11 MeV/c per
projectile nucleon is observed for Em,” z 30 AMeV, which' agrees with previous
data[Viol89, Tsan84]. The methods used in Fig. 3.7 to identify and enhance the
high LMT peak make it possible for us to extract the most probable LMT as
well for the entire energy range measured. A maximum of 172 :1: 11 MeV/c per
projectile nucleon is obtained for Em", z 30 AMeV. (See Fig. 3.8 and Fig. 3.9
). In spite of the difference between the average and most probable LMT values
for 30 AMeV, one is still led to the conclusion that there is a limit to the amount
of linear momentum that can be transferred from the projectile to the fission—like
fragments. This limitation is apparently due to the fact that, with increasing
beam energy, a significant fraction of the available momentum is carried away by
particles other than fission—like fragments. This is the case identified in the right

two columns of Fig. 3.7 .

3.4.5 Fissionlike Process Cross Section

In order to gain insight on the evolution of the reaction mechanism, we have
performed a simple two stage model calculation [Harp7l, Desb87a, Cerr89]. In
49

 

A9" 9? A9“ 98

A9!" 9L

 

A9” 911

 
 

I”

Figure 3.7: Fission fragment folding angle distributions for Ar + Th reactions
gated on IMFs at forward angles (left column), IMFs at large angles (center
column), and central collision impact parameter obtained by the total transverse
kinetic energy. Solid lines are gaussian fits to guide the eye.

50

 

 

Ir,
1

100

rTI

 

 

 

g3 BOE' ii Eb d
a 60" .D ""5 I’
a e U 2
do 40" OI:I 1
\ : .0 U :
Q-I L _1
20: 0 :
0:. l I . LIEUJO d

 

5 10 50 100
Ebem ( AMeV )

Figure 3.8: Average and most probable LMT values in terms of beam momentum.
Cl is for pm. 0 is for < p >. O is for previously published data [Vi0189, Tsan84]

51

 

 

 

 

g 200i "'I ‘ ‘ FTI'”!

T.) I CIIEIUUD I
:3 150 “' a .0 ‘
fl 2 ° [:1 2
Q : ~ :
> 100 1" .. '2'
Q) I. ..
2 : o 1
V 50 r '1
"2* . .
<0. 0 {IIIJ . I I ILIUI :
D. 5 10 50 100

E/A ( MeV/n )

Figure 3.9: LMT per projectile nucleon. Symbols follow the same convention as
in Fig. 3.8 .

52

 

this model the nucleons of a projectile are trapped inside the potential well of the
target, and the resulting system undergoes pre—equilibrium emission of particles
and then expands isentropically. Extracted percolation parameters then determine
whether the system eventually experiences multifragmentation or fissions. This
hybrid model can calculate the excitation energy of the compound nucleus and
it is plotted in Fig. 3.10 . It also calculates the number of prefission emission
nucleons, which is plotted in Fig. 3.11 . That enables us to estimate the size of

compound nucleus after prefission emission of nucleons. (See Fig. 3.12 .)

In Fig. 3.13 , the fission-like process cross section from the data is plotted
along with the calculation. Both show that there is a substantial decrease in the
cross section for fission-like reactions as the beam energy increases, but the model
under-predicts the cross section in the high energy range where the non-binary

fission takes over the reaction mechanism.

3.5 Conclusion

In conclusion, we have performed an extensive set of exclusive folding angle mea-
surements. We see a monotonic decrease (86 ‘70 to 16 %) in momentum transfer
of the projectile to the fission-like fragments with increasing beam energy. This
trend is consistent with the notion that as the beam energy increases more violent
collisions occur and large number of particles are ejected each carrying a fraction
of the available linear momentum. Apparently the occurrence of pure binary fis-
sion seems to be less likely with increasing beam energy and a different reaction
mechanism leading to multi body final states takes over. Our exclusive measure-

ment makes it possible to observe fission-like reactions even at Em”, z 115

53

 

10 YYrTl'YUV'VVrrliYY'l'IFYII'U'f
h

~ 1

8: C1-
; : 1‘:
<0 6? Cl ‘
2 L I? i
<1: .
v a

4- a —
*
La

 

 

 

O 1.1.1....l.u111.1.1....11...:
0 20 40 60 80 100120

Ebeam ( AMGV)

Figure 3.10: Calculated excitation energy using the hybrid model mentioned in
the text.

54

 

30_
25:
20’

15:

mass #

10'

 

 

 

 

O .
0 20 40 60 80 100120
Ebem ( AMeV )

Figure 3.11: Calculated number of prefission emission nucleons. O is for proton
and D is for neutron.

55

 

 

:SOO TY'IIrI 'I'lIU UUIIFIVIIYIIIFI'T
P d
D ‘

 

 

 

 

280}- {
It 260}
II)
I!)
m D
S 240_-
220} _:
200 PIII‘IHL‘I‘l‘4l11111.,,llu‘l:

0 20 40 60 80 100120
Einc ( MeV/n )

Figure 3.12: Estimated size of compound nucleus after prefission emission of nu-
cleons.

56

 

104

A 103

.o

E 102

V

b 101
00

 

 

20 40 00 so 100 120
Ebeam ( AMeV )

Figure 3.13: Comparison of the extracted fission-like process cross sections for Ar
+ Th data (solid circles) with the predictions of the model (open circles). Lines
are drawn to guide the eye.

57

 

 

AMeV, and provide direct evidence for the persistence of these reactions albeit in

non-binary form over the energy range we studied.

58

Chapter 4

IMF Emission in Fissionlike
Collisions

Intermediate mass fragments (IMF:3 S Z S 18) in coincidence with fissionlike
fragments were measured in the reaction ”Ar + 23“Th at Em", = 15 - 115 A
MeV. Three distinct sources of IMF emission are identified by the azimuthal an-
gular correlation function among two fissionlike fragments and an IMF. Respective
contributions of the three emission modes to the IMF multiplicity with the beam
energy are estimated. Prefission emission gains dominance in this energy range
while the evaporation from the fissionlike fragments decreases to the point that

its importance becomes comparable as that of simultaneous ternary breakup.

4.1 Introduction

4.1.1 Motivation

As a transient state between pure binary fission and multifragmentation, fission-
like reactions tend to produce one or two IMFs (intermediate mass fragments)
[Klot87, Troc89, Hano93]. To study more closely the evolution of the fissionlike

reaction with beam energy, it is necessary that the IMF emission mechanism be

59

 

examined beyond observing the increase of mean number of IMFs accompanying
the fissionlike fragments [Yee95]. By identifying the IMF emission mechanisms, if
there are more than one, and estimating the relative contribution of those mech-
anisms to the IMF production, one can then have a more complete description of

the fissionlike reaction mechanism.

4.1.2 Background

At low energy (5 10 A MeV), Boger et.al. identified three distinct modes of IMF
formation [Boge90]. Those are the two—body breakup of fission or evaporationlike
character, IMF ejection from the composite nucleus followed by sequential fission
and a simultaneous ternary breakup. Although they mentioned the IMF ejection
from fission fragments after their formation and acceleration, the relative cross
section was not given for that channel. The fact that the data were only for one

energy leaves the question of evolution unanswered.

In a series of experiments geared toward folding angle measurement, the Viola
group successfully showed the existence of IMF emission from the neck region of a
fissioning nucleus [Faty87, Fiel92], which is similar to alpha—accompanied ternary

fission. [Siwe93]. This result also lacks the varying incident energy.

Trockel et.al. used correlation method to demonstrate that their data showed

the sequential nature of multifragrnent emission [Troc87]. They looked at
f.f(fission fragment)-f.f., IMF—HR(heavy residue) and IMF-IMF correlations.

IMF-f.f.-f.f. correlation would be the natural next step.

60

4.1.3 Present Work

With MSU 411' Array described in Chapter 2, we have the ability to detect fis-
sionlike fragments and IMFs simultaneously with near 41r geometric coverage. We
ran experiments by bombarding 40Ar to 232Th targets from 15 A MeV to 115 A
MeV. The thickness of the target was 1 mg/cm’. Beam current was maintained
near 100 electrical pA. With this setup, we present the energy dependence of the
relative cross section of each IMF emission mechanism, which has not been done
in this energy range. To introduce one combining variable of fissionlike fragments

and the accompanying IMF, the azimuthal angular correlation method has been

adopted.

4.2 Correlation Method

4.2.1 High Order Azimuthal Correlation Method

Stemming from interferometry studies, arbitrary order azimuthal angular corre-
lation functions have been used as an alternative way to study multifragrnent
collective flow [Wang91, Jian92]. More recently, the same method has been ap-
plied to show the disappearance of collective flow at the balance energy, without

referring to the reaction plane [Lace93, Laur94, Buta95].

4.2.2 Third Order Azimuthal Correlation Method

In this analysis, we are interested in the fissionlike reaction where there is one or
more IMFs involved. In particular, the relation between individual IMF and two
fissionlike fragments is of importance. IMF-IMF correlation is of little concern

because such an event is quite rare in this energy range and more importantly

61

because the emission pattern of IMF with respect to the fissionlike fragments is
what we are trying to establish. Therefore, the third order azimuthal correlation

function involving two fissionlike fragments and one IMF is the suitable choice.
4.2.3 Definitions

Let’s consider general case where the event size is M. For w—th order azimuthal
correlation, i.e. the azimuthal correlation of to particles out of M fragments, a
variable 7,12,, is introduced, which is the geometric mean of k pairwise azimuthal

separations(¢,-j) between the fragments.

I: l/k l
d)“, = (11¢gj) ,k = §w(w — 1). (4.1)

One thing to remember is the possible multiplets of size w for an event in which M
fragments are detected, which is M! / (M - w)!w!. Appropriate weighting should

always be done by this factor.

The correlation function is defined as a ratio of two 1b,, distributions.

YWM cor)
I’M“; uncor) °

 

C(11)...) = (4-2)

Y(z/2,,; car) is the observed 11),, distribution, while I’M“; uncor) is from the mixed
and randomly chosen events.

For the purpose of this analysis, we choose as = 3. Then, the variable $3 can

be written in more explicit form.

$3 = (¢f1'f2 ' ¢f1-1 ° ¢f2-1)l/3 v (4'3)

where f,, I mean the fissionlike fragment and IMF, respectively. In this kind of

selection scheme, the weighting factor should be always the same for any triplet

62

because two of the triplet elements are fixed with fissionlike fragments and there
is only one degree of freedom in terms of choosing IMF. For completeness, let’s

write down the correlation function for w = 3 case.

Y(¢’3; 00")

CW3) Y(z[)3; uncor).

 

(4.4)

4.2.4 Interpretation of @123

From the definition, the values that 1123 can have are between 0° and 120°, inclu-
sively. However, they are not evenly probable. Because we focus our interest on
fissionlike events, «#1,- 12 makes a normal distribution around 180° with a width
that depends on the incident energy and impact parameter [Yee95]. Therefore,
the azimuthal IMF emission angle with respect to either of fissionlike fragment is
the determining factor of 1123. In Fig. 4.1 , the above two points are demonstrated
at the same time. Take the azimuthal angle of one of the fissionlike fragments as
0°. Then, the angle of the other fragment will be 180° — a, where a has been
shown to form a normal distribution around 0°. Varying 431, the azimuthal angle
of IMF, from 0° to 360°, the corresponding 11:; values are plotted. Regardless of
the values of a, the distributions maintain similar form, demonstrating the m as
the determining factor. Note that $3 is very sensitive for 43; close to either one
of fissionlike fragments’ azimuthal angle, while its value changes little for wide
range of 431 when the IMF is emitted farther from both of the fissionlike frag-
ments. In fact, if 10° bins are made for $3, ¢f,_f, = ¢f,_1 = «1%-; = 120° and

¢h-h = 180°, 435-1 = ¢f,-1 = 90° make the same bins.

63

_- .mn

 

 

¢1(°)

 

 

 
 
   
 

o 50 100050 100
¢3(°)

    

Figure 4.1: Demonstration of 11);; values with various combination of three az-
imuthal separation angles. The distribution maintains similar form from coplanar
fissionlike events(a = 0°) to much less probable out-of-plane events(a = 60°).
Also, note the sensitive and less sensitive range of $3.

64

Let’s plot the correlation function C(tbg) for particular cases as a function of
113. There are three such cases. First is when d); is independent of the fissionlike
fragment emission angle. As expected, in Fig. 4.2 (a), there’s no correlation (C( 1113)
= 1 for all 1,123). The second case is when the IMF is emitted so that its velocity
vector forms a cone shape distribution around either one of fissionlike fragment.
Fig. 4.2 (b) shows the correlation function in such a case where there is a strong
correlation for 1&3 < 80° while there is strong anticorrelation for 2123 > 90°. For
$3 < 30°, it is not plotted because such an event is rather an exception and the
lack of statistics gives erratic and misleading results. The third case is when IMF
is emitted with similar azimuthal separations from the fissionlike fragments. From
the reason explained in the previous paragraph, C(¢3) has sharp correlation at
the biggest bin of $3, as shown in Fig. 4.2 (c). All these combined with certain
weighting factor, we expect that the azimuthal correlation function from data

would look like Fig. 4.2 (d).

4.3 Event Selection

4.3.1 Description

By examining the IMF emission pattern, we try to explain the evolution of fis-
sionlike reaction in medium energy heavy ion reactions. We analyze events with
two fissionlike fragments and one or more IMFs. As described in Chapter 2, we
select fissionlike fragments requiring that their charges are greater than that of
projectile, in this case 18. MWPC and BCC work cooperatively to accomplish
this task. We restrict the range of IMFs to be 3 5 Z S 18, which is well within

the capacity of the detection system. Now that we know that the desired event

65

 

 

 

CW3)

 

 

 

 

 

 

50 100 ’50‘ A A 106
1/13(deg

Figure 4.2: Azimuthal correlation function C(zbg). (a), (b) and (c) each repre-
sents particular mode of IMF emission while ((1) shows the combined correlation
function with arbitrary chosen weighting factor.

66

can be selected properly, we have to think of the way to classify these events
by centrality. This is important because the azimuthal correlation function we
are considering will not be able to distinguish peripheral collision from sequential
ternary breakup. In the former case, the IMF is essentially a projectile particle.
In the latter case, the IMF is ejected from composite system prior to scission. We
use two observables simultaneously to accomplish this task. Those are the folding
angle between the two fissionlike fragments and the rapidity of the IMF in the

center of mass frame. In the next two sections, we will describe the details.

4.3.2 Folding Angle and Impact Parameter

In Chapter 3, folding angle is discussed in detail. Simply put, it is an angle between
two directional vectors of two fissionlike fragments. This variable is known to be
related to linear momentum transfer [Viol89], but it can also be used as a reaction
filter [Tsan89]. Comparing the usual impact parameter selection variables such
as charged particle multiplicity and midrapidity charge, it can be shown that the
events associated with smaller folding angle range are from central collisions, while
the events associated with larger folding angle range are from peripheral collisions.
This conforms to the fact that the folding angle is inversely proportional to the
amount of linear momentum transferred. It is not hard to imagine that in the
central collision most of the linear momentum carried by the projectile would be
transferred to the composite system, while in peripheral collision it is expected

that the projectilelike particle still carries most of the original linear momentum.

67

 

‘_ -

4.3.3 Additional Condition

It is shown in Chapter 3 that the IMF polar angle is an efficient tool for centrality
cut in the fissionlike reaction. It is well demonstrated that the proper use of the
IMF polar angle can reveal the high linear momentum transfer peak buried under
the tail of dominant low linear momentum transfer peak, especially as the beam
energy increases. To minimize this contamination by peripheral collision, that will
surely confuse the relative cross section of IMF emission mode in central collisions,
we put an additional condition of IMF rapidity in the center of mass frame in
conjunction with folding angle distribution. This variable can be regarded as an
extension of IMF polar angle in the laboratory frame. The peripheral collision
peak has a tail with comparable intensity to that of the central collision peak (see

Fig. 4.3 ). Efficiency mismatch for IMF detection among the different components

of the detection system results in the three distinct peaks near 0;, z 100°. These
components should form a single peak. If we use only a 1 dimensional cut on
folding, the peripheral collision tail will always be selected also. Considering that

the situation worsens with beam energy, it is essential to use a 2 dimensional
condition to select events we analyze. As a summary, the detection system is

fully capable of collecting data for fissionlike reaction with coincident IMF. We

have two centrality variables, folding angle and rapidity of IMF in center of mass

frame, that can separate two fission mechanisms that are obviously different but

expected to show very similar results in azimuthal correlation functions in certain

C3388.

68

 

 

 

4O Ivrvlertltrvrlrv
q
d

20:-

 

ycm(X 100)
S
I

-10} i

_20W111

O 50 00150
9ft deg)

 

 

 

Figure 4.3: Contour plot of IMF rapidity in the center of mass frame (ycm) and
folding angle (0”). The peaks near 9,, = 100° are related to central collision
while the strong peak near 0,; = 160° is from peripheral collision. Note the tail
of this strong peak smears into 0” z 100° region. Data are from the reaction

“Ar + 232Th at Em", = 45 A MeV.

69

4.4 Analysis

4.4.1 C(1/i3) Distribution

The azimuthal correlation function technique has been applied to fissionlike re-
actions with coincident IMF, to exploit the evolution of that reaction mechanism
with beam energy. From the correlation function, we deduce the IMF emission
pattern asociated with fissionlike reactions. Relative cross sections in term of
IMF multiplicity are obtained for each emission pattern. In Fig. 4.4 , the az-
imuthal correlation functions (C ( ¢3)) as a function of $3 are presented for central
and peripheral collisions. When a projectile just touches the-target and the target
fissions, we do not expect any azimuthal correlation. Azimuthal separations be-
tween IMF, projectilelike particle, and the fissionlike fragments are uncorrelated.
On the other hand, the central collisions show a structure in the distribution that
is changing its intensity with beam energy. This structure matches the one we

predicted in Fig. 4.2 (d) . There we considered three distinct IMF emission modes

whose combining effect would result in the prediction.

Now that we can say that those three modes may well be the candidates for
what happens in the fissionlike reaction, let’s consider each one more closely. Ear-
liest in the time line, before the compound nucleus breaks into two comparable size
fragments, fissionlike fragments, an IMF could be ejected first. This process may
be called a sequential ternary break-up. In this case, the IMF has no information
about the breakup angle of fissionlike fragment. Hence, the azimuthal correla-
tion should have flat value of 1, i.e. no correlation (see Fig. 4.2 (a) ). During
the scission stage, an IMF may be produced simultaneously with two fissionlike

fragments. That we will call a simultaneous ternary breakup. Because the IMF is

70

 

 

driven out mainly by the Coulomb force exerted by two fissionlike fragments that
move almost back to back in the frame of fissioning nucleus, the resultant Coulomb
force directs the IMF along the near perpendicular direction to the fission line. If
this happens it is expected that we see a strong correlation for $3 2 110°, while
for smaller $3, there would be a strong anticorrelation (see Fig. 4.2 (c) ). After
the breakup of compound nucleus, the fully accelerated fissionlike fragment may
still emit an IMF. In the frame of fissioning nucleus, the emitted IMF’s velocity
distribution forms a cone around the fissionlike fragment’s velocity vector. Broad
strong correlations are expected for 1&3 < 80°, while for $3 values, with which
simultaneously ternary breakup shows strong correlation, there is strong anticor-
relation. Lacking any of those emission mode, it is not possible to reproduce the
data with any combination of weighting factor. Simultaneous ternary breakup
and emission from fully accelerated fissionlike fragment are obviously necessary
from Fig. 4.4 . Not so obvious is that sequential ternary fission is also necessary to
make the distribution’s intensity comparable to data. To summarize, we proposed
three distinct modes of IMF emission in fissionlike reaction. The proposition is
plausible because data and the prediction using only those emission modes show

a qualitative match.

4.4.2 Signature of Neck Emission

It has been known that at low energy (Em... < 10A MeV), there exists ternary
fission involving or emission [Sowi86, Vand73]. A recent study investigated such an
emission for the same system as ours (“Ar + 23"I’h) but at lower energy (Emm z
9 A MeV) [Siwe93]. They found that it is necessary to introduce near scission

emission of 0: particles in addition to the prefission emission and the emission

71

 

 

 

b) 25 AMeV?
9%
/ .

2117f. . ”a.

 

’ l
p .

 

I %4 v v I r #0
(p c) 30 AMeV 3:

  
 

 

 

CW3)

 

A A
v T f

h) 115 AMeV?

   
 

l
1

 

 

 

 

Figure 4.4: Azimuthal correlation function ( C($3) ) vs. $3. Open squares (C1) are
for central collisions, and closed circles (o) are for peripheral collisions. C($3) = 1
means no correlation. $3 < 30° region is not plotted because of the lack of
statistics. Such a case does not have different meaning from C ($3) 2 50° so that
dropping that region does not affect the argument. Data are from the reaction
°°Ar + ”2Tb at Eben", = 15 - 115 A MeV.

72

 

from fully accelerated fragments to explain the energy distribution of detected 0
particles. The component in the or energy distribution from near scission emission
is located between those of the other two emission modes. Prefission a’s always
have bigger energy values than near scission emission a’s. They also observed
that the near scission emission is from necklike structure so that the (1 particles
are emitted preferentially in the direction perpendicular to the fission axis. Those
are two of the prominent signatures of near scission emission a’s from necklike

structures.

Near scission emission (NSE) of IMFs from necklike structures is much less
frequently observed than that of a. It has been reported such an event was
observed for the system formed in high linear momentum transfer reaction [Fie192].
High linear momentum transfer is one of the two centrality cut criteria we used
and it loosely selects central collision events. They identified neck emission using
the energy and emission angle criteria mentioned above. They observed unusually

low energy components near the emitting direction perpendicular to fission axis.

Lower energies and preferred perpendicular emission angle to the fission axis
are now established as the signatures of IMF emission from necklike structure at
near scission stage. With Fig. 4.5 we check if we observe such a signature. Recall
that the smaller $3 values get, the closer the IMF emission angle is to either of
fissionlike fragment velocity vectors. As $3 approaches its maximum value 120°,
IMF emission angle is nearly perpendicular to the fission axis. The former cases
are Fig. 4.5 (a) and (b), and the latter are Fig. 4.5 (c) and (d) . Notice the
emerging shoulder in lower energy range in IMF energy distribution as $3 gets

larger. We attribute that shoulder to the signature of neck emission. The fact

73

 

that it emerges only when $3 values become large and that it emerges on the
smaller energy value side satisfies the conditions previously established. Another
thing to note is that perpendicular directional emission alone cannot ensure the
neck emission. The high energy component does not change intensity very much
with $3, hinting that sequential ternary fission is dominant in this beam energy.
Because such emission should be isotropic, it will also populate the direction near
perpendicular to the fission axis with stronger intensity than that of neck emission.
But as shown in Fig. 4.2 (a) and (c), the behavior in correlation function will be
very different between the two cases. Here, we verified that we indeed observed

near scission emission of IMF from necklike structures.

4.4.3 Comparison of Data and Simulation

We now established three components that make the azimuthal correlation func-
tion distribution in central collision. With these, we tried to simulate the experi-
mental data. The simulation is semi-empirical in that the experimental distribu-
tion in space for the fissionlike fragments is used to sample the events. Sequential
ternary breakup is simple. The IMF emission angle is taken isotropically around
the fissioning nucleus. In the case of simultaneous ternary breakup, the IMF emis-
sion direction is randomly chosen from a normal distribution around the line that
is equally distant from the fissionlike fragment vectors in the fissioning nucleus
frame. When an IMF is emitted from a fully accelerated fission fragment, its
velocity vector, viewed from fissioning nucleus frame, forms a cone shape around
fissionlike fragment velocity vector. We pick the direction randomly from the
normal distribution around the fissionlike fragment velocity. Now we have two

free parameters. Those are the widths of the two normal distributions mentioned

74

 

 

 

401<a>

N
O
. I .

 

.Count(a.u.)
3 2
o
v

 

 

 

 

20 - *- -
O r . . 1 .4 r r l i r r 1 Mr 1 m r 1
O 50 100 O 50 100
Eimf(Mev)

Figure 4.5: IMF energy distributions for the reaction ‘°Ar + 232Th at Em,” = 35
A MeV for different ranges in $3 values. $3 = 30° ~ 60°,60° ~ 80°,80° ~ 100°,
and 100° ~ 120°, for (a), (b), (c), and ((1), respectively.

75

above. There are two more parameters. Because we need relative contribution
from each of three emission modes, when two of the modes in the sampling are
set, the other one is determined. By varying these parameters, we find the best
fit. The result is presented in Fig. 4.6 . This simple simulation is quite successful
in reproducing experimental result throughout the energy range observed. The
result is not very sensitive to the first two parameters determining the width of
normal distribution. What governs the shape of the correlation function is the
relative frequency of sampling. Two things can be said. The three IMF emission
modes can explain what’s happening in the fissionlike reaction when it produces
coincident IMF. Over the energy range we present, there is no need to introduce
another major emission mode. What’s changing is relative probability of each

emission mode, not the emission mechanism itself.

4.5 Conclusion

4.5.1 IMF Emission Mechanism

We showed that the three IMF emission modes could explain the data throughout
the energy range studied. The only change is how each mode is weighted. This
may be understood considering the change in excitation energy. We established

the absence of saturation in energy deposition [Gua195b].

The excitation energy increases with beam energy without saturation in this
beam energy range (see Fig. 4.7 ) . A qualitative deduction can be followed for
the relative cross section of each IMF emission mode. As the excitation energy
increases, a hotter compound nucleus would form. Such a nucleus is more likely to

emit small fragments at the earlier stage than less excited nucleus. Consequently,

76

 

 

 

 

2? m + . I
t 3 ‘1’ s 1
1:. .............. . ...... l— .............. .. ..... _.

l I I; U '

O ’ l . : c j - I * j 4 c : : %
go i 30 AMeV (E s 35 AMeV:
2 _ Q o «T Q. .J
’ [D . If m i
,
. :: fl

1.. .............. ing- ........... -.'....'.:
’ ‘ I 41 g .
°° :: :

$~ O f j e f j t ‘ : l L + - - j -
V .I .
U » 45 AMeV 1: 55 AMev.
2, 1r '3
* 9‘- "570 j
1?. ......... :6 ....... .1 ....... ‘. ....... .1
... I: ... .

 

N O
1

,

q_

,

.

.

__

 

 

 

 

Figure 4.6: Azimuthal correlation function distributions for the reaction °°Ar +
232Th at Eben,” = 15 - 115 A MeV. Only central collisions are considered. Open
squares ( D ) are experimental data. Closed circles ( s ) are from simulation.

77

 

 

<e'> [AMeV]
L I O
i E
——s3——

GISNUSUIGQQO

Cl.

1I'UUTU'YIT'1TI'YIUUUIIUITI'TTTU'I'UUIUVWU

l n

so 150 L 120
EmlAMeV]

 

 

 

...
g-
3;
s.

Figure 4.7: Excitation energy of the reaction °°Ar + 232Th with varying beam
energy. For the model calculation, see Refs. [Cerr89, Desb87a, Gua195b, Harp71].

78

 

it is expected that the sequential ternary breakup mode would gain its importance

as beam energy increases.

On the contrary, emission from fully accelerated fissionlike fragment would
be less probable as the excitation energy gets larger. More excitation energy
would be carried away before the breakup occurs, and the size and excitation
energy available to the fissioning nucleus would be smaller and less. Hence we
expect smaller and less excited fissionlike fragment as the excitation energy gets
larger. Smaller sized fissionlike fragments have been observed with increasing
beam energy for the same system [Conj85]. Near scission emission from necklike
structure would also gain its share. Because of the smaller size of the fissionlike
fragments, there would be less chance that the neck emitting IMF be reabsorbed

before it is driven away by the resultant Coulomb force of two fissionlike fragments.

In Fig. 4.8 the relative cross sections of those three IMF emission modes are
presented in percentage. At the lowest energy, sequential ternary breakup and
emission from fully accelerated fissionlike fragments occur at about the same rate,
consuming all the cross section. Simultaneous ternary fission exists, but during
only a few percent of time it actually happens. As beam energy increases, and also
as the excitation increases at the same time sequential ternary breakup gradually
takes up around 80 % of the cross section and flattens out at about Em," = 45 A
MeV. Meanwhile, the emission mode from fully accelerated fissionlike fragments
decreases down to around 10 % at E5“... z 45 A MeV and continues to do so
although much less rapidly. Simultaneous ternary breakup cross section increases
its share through the beam energy range we studied. At Em", z 75 A MeV, this

mode becomes almost as probable as the emission of IMF from fully accelerated

79

 

fissionlike fragments and surpasses that mode at EM", :5 115 A MeV reducing
nearly 10 % of the cross section. Those observation agrees well with qualitative

predictions deduced from excitation energy data.

4.5.2 Multiplicity of IMF from Each Emission Mechanism

To give more physical meaning to the ratio in Fig. 4.8 , we plot the mean number
of IMF s as a function of incident energy (see Fig. 4.9 ). Note the projectilelike
particles in peripheral collision do not count here. Because the overall mean
number of IMF 3 changes smoothly, the distribution does not show a significant
difference from that of Fig. 4.8 . However, we expect this distribution to be
different from that of a particle emission mode. Siwek-Wilezynska et. al. [Siwe93]
reported a result for a particle emission in the same reaction as ours at Em", z
9 AMeV. Their beam energy is just one step below our lowest energy. They
observed the prefission emission as a dominant mode while we expect that to
be less important than emission from a fully accelerated fragment (postfission
emission in their terms). Near scission emission is most rare in their case also,
but the relative cross section is much larger in the case of a in which it is about
one—third that of postfission emission. In the case of IMFs, near scission emission
at that beam energy is not certain to be observed. We were unable to find any

reference to compare to the IMF emission mode.

4.5.3 Summary

We applied the azimuthal correlation method to study the evolution of the IMF
emission mechanism in fissionlike reactions. The variable $3 is defined such that
the azimuthal separation of IMF emission from either of fissionlike fragment is

80

 

 

100 r 1 T I l I T U I l I

Ratio(%)
8

 

 

 

 

O 1 5O 1 ’IOOI
Ebeam ( AMGV )

Figure 4.8: Relative cross sections of three IMF emission modes in fissionlike
reaction of “’Ar + 232Th at Em", 15 - 115 A MeV. Cl is for sequential ternary
breakup. o is for the emission from fully accelerated fissionlike fragment. 0 is for
simultaneous ternary breakup that near scission emission from necklike structure.

81

 

1.5 U I T r r I I T I I

 

 

 

 

Figure 4.9: Mean number of IMF associated with each IMF emission mode. Con-
vention for symbols is same as that of Fig. 4.8 .

82

represented by that variable. To avoid the confusion caused by projectile frag-
ments, we used a folding angle technique along with the rapidity of accompanying
IMF. This effectively removes the contamination from the peripheral collisions.
We try to explain the azimuthal correlation function distribution by introducing
three components of IMF emission mode. Sequential ternary breakup that occurs
before scission is one. Next in the time line is simultaneous ternary breakup that
occurs during scission. After the scission, when the fissionlike fragment are fully
accelerated, there is another mode of IMF emission from those fragments. Using
only these three mechanism, we successfully reproduce the data by simulation. As
beam energy increases, the first and third mechanism exchange their dominance
so that sequential ternary breakup prevails at higher energy range. Simultane-
ously ternary breakup starts out being insignificant but increases constantly so
that at the highest energy range it wins over the emission mode from fully ac-
celerated fissionlike fragments, although still makes up only around 10 % of the
relative cross section. Arguments employing excitation energy can predict this

result qualitatively.

83

Chapter 5

Conclusion

As a transient decay mode of hot nuclei between evaporation and multifragmen-
tation, fission evolves in itself from pure binary mechanism to one that involves
IMF emission. To study this evolution of fissionlike reaction, one has to make
exclusive measurements over a wide dynamic range from light charged particle to
fission fragments. We completed the MSU 41r Array with the addition of multi-
wire proportional counter (MWPC) as a fission fragment detector. In addition
to that, by successfully operating Bragg curve counters (BCC) in standalone E-Z
mode, we were able to lower the energy threshold of IMF measurement, at the

same time effectively detecting IMFs with near beam charge.

With this setup, we first tried to establish the existence of a fissionlike reaction
mechanism to the extent where such a mechanism had been believed negligible.
A folding angle technique is employed while we show that the coincident IMF
emission angle can serve as a reaction filter. We see a monotonic decrease in
linear momentum transfer (LMT) with beam energy. From there, we confirm the
notion that more smaller particles are ejected, with increasing beam energy, each

carrying away a fraction of the linear momentum available to fissionlike fragments.

84

 

Consequently, the occurrence of pure binary fission decreases in its frequency. Still,
we provide direct evidence for the persistence of fissionlike reactions even at E53“.

:3 115 AMeV, albeit in non-binary form.

Now that we have shown the existence of multi body fissionlike reactions, we
tried to look more closely into the source of IMF emission. By doing so, we
expect to understand in more detail the mechanism that leads into the observed
final states. The azimuthal correlation method turned out to be an excellent
way to do this because it deals with two fissionlike fragments and one coincident
IMF altogether and makes the relation into one variable. We identify two IMF
emission modes that have a more direct relation with fissionlike reaction and a
third mode. The former two are sequential ternary breakup and simultaneous
breakup of compound nucleus and the latter is the emission from fully accelerated
fissionlike fragment. We were able to reproduce the data with these three emission
mechanism over the energy range we studied. Sequential ternary breakup gains
its dominance with beam energy, while the emission from the fully accelerated
fissionlike fragment loses its importance down to the point that the continuously
increasing simultaneous ternary breakup mode surpasses that mode at the highest
energy we have. Excitation energy values over the energy range can qualitatively

explain this change in relative cross section of each IMF emission mode.

As a conclusion, we show the direct evidence of fissionlike reaction throughout
the energy range we studied. Binary breakup where the accompanying IMF, if
any, is emitted after scission decreases while ternary breakup where the accompa-
nying IMF is emitted on or before scission becomes prevailing. Sequential ternary

breakup in which the IMF is emitted before scission happens around 80 % of the

85

time, while simultaneous ternary breakup happens about 10 % of the time, at the
highest energy we measured. This result contrasts with the case at the lowest en-
ergy we measured, in which only about 50 % of the cross section is from sequential

ternary breakup, and the simultaneous ternary breakup is negligible.

 

 

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