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LIBRARY

University

This is to certify that the
dissertation entitled
NEUTRONS I N COINCI DENCE WI TH I NTERMEDI ATE MASS

FRAGMENTS AT LARGE ANGLES FROM 1"N + Ag REACTIONS AT
20 AND 35 MeV/NUCLEON

presented by

Charles Bloch

has been accepted towards fulfillment
of the requirements for

Ph.D. degreein Physms

Major professor

me HM 0?, #14:?

"(Hi-n- {wk-‘1... : - r, In . I . . 042171

 

 

MSU

LIBRARIES
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RETURNING MATERIALS:
Place in book drop to
remove this checkout from
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NEUTRONS IN COINCIDENCE WITH INTERMEDIATE MASS FRAGMENTS AT LARGE ANGLES
FROM 1"N + Ag REACTIONS AT 20 AND 35 MeV/NUCLEON

By

Charles Bloch

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

1987

ABSTRACT

NEUTRONS IN COINCIDENCE WITH INTERMEDIATE MASS FRAGMENTS AT LARGE ANGLES
FROM "‘N + Ag REACTIONS AT 20 AND 35 MeV/NUCLEON

By

Charles Bloch

The spectral shape and multiplicity of neutrons from the reac-
tion of ‘“N+Ag at E/A = 20 and 35 MeV have been measured for neutrons in
coincidence with intermediate mass nuclei emitted at 50, 70 and 90°.
The spectral shape clearly suggests two moving sources. The slower
source velocity is about 65% of the center of mass velocity for E/A=35
MeV and 80% of the center of mass velocity for E/Az20 MeV (71 and 9% of
the beam velocity, respectively). The faster source velocity is
slightly less than half of the beam velocity for each case. Knowledge
of the neutron multiplicity is necessary for models which attempt to ex-
plain the low effective temperature which has been determined from
recent measurements of excited state populations. The data are also
compared to the Harp-Miller-Bern exciton model. In addition, the
neutron decay of excited states of 7Li, “Li, 10Be, “Be, and "B has
been investigated in the same reactions. The production of these ex-

cited states is compared to that of the ground state and other states

ii

of lower excitation energy for each isotope investigated. Under the as-
sumption of a Boltzmann distribution of excited state populations, each
of these comparisons imply a nuclear temperature. Furthermore, the
feeding of the 7Li ground state from the neutron decay of the 2.255 MeV
unbound state in “Li (one of those measured) is another process that
could lead to low temperature observations in previous experiments. The
degree of feeding is compared to predictions made by a quantum statisti-
cal model to determine the total feeding from all possible channels.
The net effect of this feeding is applied to these and other recent
nuclear temperature measurements to determine if the data are consistent
with a single nuclear emission temperature characterizing the energies
of these reactions. In general, temperatures in the 2-3 MeV range are

obtained .

iii

What the hell...To my wife Amy.

iv

ACKNOWLEDGMENTS

First and foremost, I must offer my sincere thanks to my ad-
visor, Walt Benenson. From the first day we met his relaxed attitude,
patience, humor, and understanding helped me gain a perspective that was
absolutely crucial to the completion of my degree. I think it is
remarkable that from the first day I worked for Walt he gave me, a per-
fect stranger, support equal to that of my closest friends and
relatives. For that I owe him my deepest gratitude. It was that kind
of support that gave me the confidence to do what I set out to do. It
certainly made my work as easy as it could be. I also wish to thank my
other friends and relatives for all they have done for me. Thank you
Dad, Mom, Diane, Jim Miller, Dave Bonner, Tim Meert, Lorry Inglehart,
George, Jim Houthoofd, my in-laws, and of course my wife Amy.

In additjtni, I must thank many of my co-workers and professors
for their help, without which I could not have attained this goal. I'll
(unit the nature of their contributions, but let me thank Brad Sherrill,
Dave Morrissey, Mark Lowe, Ed Kashy, John Winfield, Dick Blue, Reg
Ronningen, Aaron Galonsky, MrDave, Bruce Remington, Greg Caskey, RJ, the
staff of the National Superconducting Cyclotron Laboratory, George
Bertsch, Wayne Repko, Vic P01, and Russ Wong.

Finally, let me thank my producer, my agent, members of the
academy, and all the little people who are too numerous to mention. You

know who you are, and I thank you.

TABLE OF CONTENTS

Page

LIST OF TABLES .................................................... viii

LIST OF FIGURES ................................................... ix
Chapter

I Introduction .............................................. 1

11 Experimental .............................................. 8

11.1 Equipment .......................................... 8

11.2 Electronics ........................................ 10

III Data Analysis ............................................. 17

111.1 Calibration ........................................ 17

111.2 Single Particle Inclusive Data ..................... 23

111.3 Coincident Neutron Data ............................ 28

III.3.1 Neutron/Y-ray Discrimination .............. 28

III.3.2 Neutron Time-of-flight .................... 30

III.3.3 Neutron Kinetic Energy .................... 3”

111.3.” Neutron Relative Velocity ................. 42

III.“ Errors ............................................. 55

IV Discussion ................................................ 57

IV.1 Fragment Moving Source Fits ......................... 57

IV.2 Neutron Kinetic Energy Spectra Fits ................. 59

IV.2.1 Two-source Moving Source Model - Source #1 . 59
IV.2.2 Two-source Moving Source Model - Source #2 . 63
IV.2.3 Harp—Miller-Berne Model .................... 65

IV.3 Final State Interactions ............................ 71

vi

IV.“ Sequential Decay .................................... 75

V Summary and Conclusions ................................... 83
v.1 Summary .............................................. 83

v.2 Conclusions .......................................... 87
Appendix A aBe Contamination of 7Li Spectra ..................... 93

Appendix B Calculation of relative velocity geometric
efficiencies ......................................... 105

LIST OF REFERENCES ................................................ 11H

vii

TABLE

II.l.l

III.2.l

III.2.2

III.3.1

III.3.2

III.3.3

111.3.“

III.3.5

IV.U.1

IV.4.2

IV.N.3

LIST OF TABLES

Physical characteristics of the neutron detectors.
(All dimensions given in cm) ............................

Fragment kinetic energy moving source fit parameters.
E/Az35 MeV ..............................................

Fragment kinetic energy moving source fit parameters.
E/A=2O MeV ..............................................

Associated neutron kinetic energy moving source fit
parameters. E/A=35 MeV .................................

Associated neutron kinetic energy moving source fit
parameters. E/A=20 MeV .................................

(an) (as described in the text) in percent for the
decays and beam energies listed .........................

Excited state ratios, R, and corresponding temperatures,
kT, from equation 1.1 (not corrected for sequential
decay) ..................................................

Feeding (in percent) of the ground state of A(Z,N) from
the neutron-unbound excited state of A(Z,N+1) ...........

Li isotope distributions. (Yields normalized such that
7Li yield equals 1) .....................................

Fraction of fragments in an excited state for several
Y-emitting states .......................................

Excited state ratios, R, corrected for feeding via

equation IV.11 and their corresponding temperatures, kT,
according to equation 1.1 ...............................

viii

PAGE

12

27

27

38

NO

52

52

5M

77

77

81

FIGURE

11.1.1

11.2.1

111.1.1

111.1.2

111.2.1

III.2.2

111.2.3

III.3.1

111.3.2

III.3.3

111.3.“

III.3.5

III.3.6

LIST OF FIGURES

Schematic of experimental set-up ........................
Electronics schematic ...................................

Time-of-flight spectrum for Y rays in neutron detector-1
in coincidence with 7Li fragments in any telescope,
E/A:20 MeV ..............................................

Neutron detector efficiency as a function of neutron
kinetic energy ..........................................

AE vs. E particle identification map for telescope N,
E/A= 35 MeV ..............................................

Fragment kinetic energy singles spectra with moving
source fit, E/A=35 MeV ..................................

Fragment kinetic energy singles spectra with moving
source fit, E/A=20 MeV ..................................

QDC1 vs. QDC2 for neutron detector-8, E/A=35 MeV ........

Neutron real plus accidental time-of-flight histogram
(solid) with corresponding shadow bar histogram (dots)
for neutron detector-1, E/A=35 MeV ......................

Neutron accidental time-of—flight histogram (solid) with
corresponding shadow bar histogram (dots) for neutron
detector-1, E/A=35 MeV ..................................

Neutron real time-of-flight histogram for neutron
detector—1, E/A=35 MeV ..................................

Kinetic energy histogram for neutrons at 50° in
coincidence with 7Li at 50° before and after folding in
the neutron detector efficiency .........................

Kinetic energy spectra for neutrons in coincidence with
’Li at 0:50°, ¢:0° (data points) with two-source moving
source fit (solid lines). The order of the neutron
detectors (from top to bottom) is: 20°, -30°, 50°, -70°,
70°, -90°, -110°, 120°, ~140°, and 160° in the lab. The
spectra are separated artificially by an order of

ix

PAGE

11

13

20

22

24

25

26

29

31

32

33

35

111.3.7

111.3.8

111.3.9

111.3.10

111.3.11

IV.2.1

IV.2.2

1V.4.1

A.

B.

1.

.1.

l.

1

1

magnitude each, with the 160° data at unit
normalization ...........................................

Kinetic energy spectra for neutrons in coincidence with
“B at 9:50°, ¢=0° (data points) with two-source moving
source fit (solid lines), as in Figure III.3.6 ..........

Relative velocity vs. kinetic energy for neutrons in
detector-1 in coincidence with 7Li in telescope-1 (50°),
E/A=35 MeV ..............................................

Relative velocity histograms for neutrons in detector-1
in coincidence with fragments in telescope-1 (50°),
E/A=35 MeV ..............................................

Relative velocity histogram with thermal background for
neutrons in detector-1 in coincidence with ’Li in
telescope-1 (50°), E/Az35 MeV ...........................

Relative velocity histogram minus thermal background,
for neutrons in detector-1 in coincidence with 7Li in
telescope-1 (50°), E/A=35 MeV ...........................

Neutron energy distribution from moving source model
(representative points plotted) compared to that from
Harp-Miller-Berne Model (lines) for E/A=20 MeV ..........

Neutron energy distribution from moving source model
(representative points plotted) compared to that from
Harp-Miller-Berne Model (lines) for E/A=35 MeV ..........

Feeding to the 7Li ground state via the neutron decay of
the 2.255 MeV state of °Li, as calculated by quantum
statistical model .......................................

Y rays in coincidence with fragments identified as 7Li
and 7Be from HN+C at E=112 MeV .........................

cAfl(E) for Aflz5, 9, 22 and 24 msr .......................

cn(E) for neutron in coincidence with 6Li, forward and
backward relative velocity peaks ........................

36

A3

N5

A6

A9

50

67

68

79

9A
98

108

CHAPTER 1 : INTRODUCTION

The concept of nuclear temperature has been relatively success-
ful in describing heavy ion reactions at both low (E/A<10 MeV) and high
(E/A>100 MeV) bombarding energies [Pu77, Ne82, M086, We76, Cu80]. The
question arises as to whether the concept of temperature can be applied
to intermediate energy heavy ion collisions in the course of which tem-
peratures should comparable to the binding energy of a nucleon in the
nucleus. This is the region in which a liquid-gas phase transition has
been estimated to take place [Cu83, 8e83, BoBlla]. Much of the ex-
perimental [e.g. Ch83, Cu83, Ja83, Ly83, Fi8u, Hi8ub, M084, We8u, Po85a,
SO86] and theoretical [e.g. B181, Fa82, Fr83b, 8084a, 8185, Ha86, Pa811,
Pa85] work in this energy region focussed on thermodynamic aspects.
Data in this energy range indicate that the fragment yields depend on a
power law [Ch83] with the exponent in the range predicted by the thermal
liquid drop model [F167] for condensation around a critical point.
Toward determining the validity of the temperature assumptions in this
energy region, we have investigated the reaction of ‘“N+Ag at E/A=20 and
35 MeV.

An important component of reactions of this nature has been the

observation of intermediate mass fragments (A<A<A m) at large angles

bea

in the lab (9))6 ) [Me80, We82, We8fl, W085, Fi86]. The importance

grazing

of the large lab angle is to reduce the contribution from quasi-elastic

processes [F186]. This technique has shown to be successful at biasing

2

the data toward central, high multiplicity events [Me80, W085]. There
are many inclusive measurements of the spectra of such particles [ERY71,
Ch83, Ja83, F1811, We8ll, W085, Ch86, Fi86]. Simple one step processes
would not produce such large fragments at such large angles. One model
that is fairly successful at describing the energy spectra of such frag-
ments is the moving source model [Ja83]. In that description, a set of
nucleons moving in the lab frame emit fragments thermally. The thermal
assumption means that the emission direction is isotropic in the rest
frame and that the energy dependence contains a factor of e-E/kT, where
E is fragment energy in the rest frame and kT is an emission tempera-
ture. Such spectra may contain particles from pre-equilibrium processes
and hence would not reflect the true temperature. Contributions from
such processes are forward peaked, and in order to select central colli-
sions, we have excluded the forward angles. A limited angular range of
measurements may have a greater responsibility for the success of the
moving source model than the actual physics of a thermal source [W085,
Ch86b, F186].

In order to see if the slope parameter extracted from such fits
is actually a temperature, a second technique for measuring nuclear tem-
perature was developed [M0811]. This technique relies on measuring the
distribution of nuclei in their various quantum states. If the nuclei
are from a thermalized source, their population distribution in excited
states should be Boltzmann-like (ignoring spin factors), and the tem-
perature should be the same as that predicted by the moving source
model”, 'The A=7 nuclei are particularly simple temperature probes since

they have only one bound excited state [A1814]. For two levels in

3
statistical equilibrium, the ratio, R, of the population of the excited

state to the population of the ground state is given by:

R:%fil—;xexp(lfi-§ (1.1)

where j, and J, are the spins of the ground and excited states, respec-
tively, and AE is the energy difference between the states [D078].
Recent experiments have measured the production of bound excited states
«of intermediate mass fragments emitted at large angles from reaction
1"N+Ag at E/A=20, 25, and 35 MeV [M08A, M085, 8186].

These recently reported measurements of the production of bound
excited states of 7Li and ’Be nuclei emitted at large angles from the
reaction of HN+Ag at E/A=35 MeV [Mo8u, M085, 8186] indicated a large
discrepancy between the temperature calculated from the excited state
populations (about 0.5 MeV) and the temperature extracted from the shape
of the particle kinetic energy spectra (about 12 MeV). In addition,
recent measurements of unbound state populations in similar reactions,
yielded temperatures around 5 MeV [P085a, Ch86a]. Two mechanisms fre-
quently discussed that might explain these discrepancies are final state
interactions [Bo8llb] and sequential decay [Ha86]. The present work
reports on the direct investigation of the former, and a more indirect
investigation of the latter. Both of these bases for the discrepancies
result ffiwnn the difficulty involved in directly measuring the original
ground state population. Experimentally, the accessible quantities are:
the population of the excited state, obtained by observing its as-
sociated Y ray and the total fragment production in the ground and Y-

emitting states, obtained with a silicon AE-E telescope. Dividing those

1]
two numbers gives the fraction, f, of fragments in the excited state.
The fraction is related to the temperature through the ratio, R, in the

following ways:

R f

f=m or R:-(—1'—:—ir)-.

(1.2)

A possible difficulty arises in this type of measurement in that one of
the states in the ratio has a unique property. The ground state of most
of the nuclei studied here it is unique in that it does not decay. This
makes it more susceptible to problems caused by final state interactions
and sequential decay.

If we produce an equilibrated system, it will emit fragments
with a distribution of excited states» described by equation (1.1). In
the first experiments which used this idea, the populations of the ex-
cited states were determined by observing the Y ray emitted in the
de-excitation. If the excited fragment interacts with other particles
emitted from the same reaction, it can de-excite without emitting this Y
ray. This is what is meant by "final state interactions". Boal made
one attempt to calculate the effect of this process [8084b] . In addi-
tion to several theoretical assumptions, Boal was forced to estimate the
associated neutron multiplicity since no data for this existed. The
first goal of this experiment, was to measure these multiplicities.
Previously, there have been many experiments with neutron coincidences
e.g. [11179, Ga83, H083, Hi8lla, Ca85, Ca86, De86a, De86b, H086, Re86].
But in all previous experiments, the neutrons were measured in
coincidence with one or more of the following: projectile-like frag-

ments, fission fragments, or evaporation residues. The present

5

measurement is unique in that it is the first time that neutrons have
been measured in coincidence with intermediate-mass fragments at large
angles. Considering the significance of these fragments in intermediate
energy heavy ion collisions, these measurements could be a very impor-
tant key to understanding the mechanisms involved in these reactions.
This thesis reports the associated neutron multiplicities for neutrons
in coincidence with °L1, 7L1, °L1, ’Be, ’Be, 10Be, 10B, and “B frag-
ments observed at 50°, 70°, and 90° in the lab from the reaction of
"'N+Ag at both E/A=35 MeV and E/A=20 MeV.

In addition to measuring the associated neutron multiplicities,
we were also able to observe quantitatively sequential decay of several
intermediate mass fragments using a technique developed by Kiss et al.
[K187]. These measurements are important in the attempt to resolve the
discrepancies between nuclear temperatures extracted from various types
of excited-state population measurements. Excited-state population tem-
perature measurements can be divided into two categories: those that
measure bound state populations and those that measure unbound state
populations. This distinction seems to be important since more recent
measurements of the populations of unbound states in light nuclei
[Po85a, Ch86a] systematically yield higher temperatures (11 or 5 MeV)
than do the measurements of bound state populations (temperatures from
0.5 to 1 MeV) [M081], M085, 8186] for intermediate-energy (E/A=20 to 60
MeV) heavy-ion reactions.

Attempts to reconcile the differences described above have cen-
tered on preferential feeding of the ground state by sequential decay as
discussed in Refs. M085 and Ha86. The bound state populations will, of

course, fail to reflect the initial Boltzmann distribution if there is

6

significant differential feeding of any of the observed states from par-
ticle unbound states in larger nuclei. 'This effect generally is
expected to be greatest f0r those ratios which involve the gnound state
population. We have measured the extent of feeding from sequential
decay for a system previously used in a bound state temperature measure-
ment. This was done via a measurement of the neutron decay of the 2.255
MeV excited state of 8L1 nuclei observed from the reaction of ‘“N+Ag at
E/A=20 and 35 MeV. Specifically, the feeding of the ground state of 7L1
due to the production of the 2.255 MeV state in °Li has been measured.

In order to compare 7L1 excited state production to that of the
ground state, a correction should be made for contamination of the 7Li
energy spectrum by pairs of 0 particles from the ground state decay of
'Be [8186]. For this work, the nature of the contamination and the
necessary correction are described in Appendix A. In the study of
neutron decay of unbound states and to obtain absolute quantitative in-
formation about the excited state population, it is necessary to
calculate the relative geometric efficiency of detecting the neutron
ffiwnn the particular decay. This calculation is described in detail in
Appendix B. Comparison of the production of these two unbound states to
the previously measured lower-lying excited states allows the calcula-
tion of a nuclear temperature. Furthermore, the fraction of the 7L1 and
6Li nuclei from the neutron decay of these states is significant in that
it can resolve some of the discrepancies between recent nuclear tempera-
ture measurements. In addition, neutron decay of the 7.371 MeV excited
state of ‘°Be, the 3.89 MeV excited state of “Be, and the 3.388 MeV ex—

cited state of ”B was observed. Finally, while quantitative results

7
were not obtained, it appears that the decay of the 1.69 MeV excited
state of 9Be has been observed.

The neutrons in coincidence with the intermediate mass fragments
were binned in kinetic energy spectra. These spectra were fit with a
two-source moving source model [Ja83]. This model has several benefits.
First, it provides an excellent parameterization of the data in terms of
six parameters. Two of the parameters in this model are the associated
neutron multiplicities for the two apparent neutron sources. This al-
lows us to extract inmediately one of the physical quantities we are
after, namely the associated neutron multiplicity. Second, this model
provides an analytic expression for the neutron spectra (in the non—
relativistic limit), which is easily integrated over solid angle to give
an expression for the neutron energy distribution, 3%. Putting the
moving source fit parameters into that expression produces a histogram
of the energy distribution. This histogram can be and is then readily
compared to predictions made by a Harp-Miller-Berne Exciton Model as
modified by Blann [8181]. A discussion of the physical implications of
the other moving source parameters and the exciton model comparison is
included. Finally, the sequential decay measurements are compared to
predictions made by Hahn and Stocker's Quantum Statistical Model [Ha86].
The results are used to draw conclusions about the validity of the as-

sumption of statistical equilibrium and to resolve apparent

discrepancies of recent temperature measurements.

CHAPTER II: EXPERIMENTAL
II.1 Equipment

The experimental details are similar to those described in Re86.
Neutrons and intermediate mass fragments were produced by the interac-
tion of nitrogen ions with a silver target. Beams of A90 MeV 1"N“ and
280 MeV "'N"+ ions were provided by the K500 cyclotron of the National
Superconducting Cyclotron Laboratory at Michigan State University. The
cyclotron periods were 52.370 and 68.788 ns, respectively. The target
was a self-supporting foil of natural silver, 1.8 mg/cmz thick. It was
mounted in an aluminum target ladder inside a steel 110" cylindrical
scattering chamber with domed lid and bottom. The chamber had 9"
diameter ports at 0°, 90°, 180°, and 270°. The beam entered through the
open 180° port and exited through the open 0° port. The 90° port had a
Lexan plate with high-vacuum electronic feed-throughs, while the 270°
port had a clear Lucite window. In addition, there were 5" ports.at
135° and 315°. The 135° port had a clear Lucite window. The 315° port
had a Lexan cover with feed-throughs for cooling for the detectors in
the chamber with alcohol. The target ladder had vertical positions for
A targets, and also could be rotated from outside the chamber. The beam
passed through the target and the current was measured in a shielded

Faraday cup, roughly 10 feet from the target.

9

The target was oriented with its normal at either 25° or 115°
with respect to the beam. Charged particles (2)2) were detected in four
silicon AE-E telescopes each with a 300 mm2 area. (Of course, these
detectors were also sensitive to fragments with charge 1 or 2, but these
events were rejected electronically, as described later). The silicon
detectors were located inside the scattering chamber with azimuthal
angles (with respect to the beam direction), 0, of 50°, 70°, and -90° in
a horizontal plane (polar angle 0:0), and the fourth detector was lo-
cated at 0=50°, ¢=90° (below the beam axis in a vertical plane with the
beam). The detectors were in aluminum mounts, which had provisions for
liquid cooling. Refrigerated alcohol was run through channels in the
mounts to keep the temperature at approximately -30° C throughout the
experiment. The two telescopes at 50° had AE detectors 100 pm thick,
while the other two telescopes had AE detectors 50 pm thick. The E
detector of each telescope was 1000 pm thick. The front of each tele—
scope was covered with a gold foil 3 mg/cm2 thick to reduce the number
of heavy reaction products hitting the AE detector. Rare-earth magnets
were fastened to the detector mounts above and below the AE detector to
deflect electrons. Each of the four telescopes was placed approximately
17.6 cm from the target. The solid angles of these detectors were
determined by placing a 1.5 uCi 2"‘Am source in the target ladderu 'The
AE elements of the telescopes were found to have solid angles of about
9.6 msr. For the data runs the E element of the telescopes limited the
solid angle. These were approximately 0.7 cm behind the AE elements,
which gives a telescope solid angle of 8.9 msr. With the use of these

cooled detector telescopes, isotopically-resolved inclusive energy

10
spectra were obtained for fragments which were identified as ‘Li, 7L1,
°Li, 7Be, ’Be, ‘°Be, ‘°B and “B.

Neutrons were detected in coincidence with the fragments listed
above in any of ten liquid scintillators. The scintillators were ap-
proximately 1 liter of NE213 in a sealed glass cell approximately 12.7
cm in diameter and 7.6 cm thick. These were located in the horizontal
plane at angles of 20°, 50°, 70°, 120°, 160°, -30°, -70°, -90°, -110°,
and -1A0° with respect to the beam. A schematic diagram of the detector
positions is given in Figure 11.1.1. The front of each of these detec—
tors was located 125 cm from the target, with the exception of the 20°
neutron detector, which was 200 cm from the target. The typical neutron
detector had a geometric solid angle of approximately 7.5 msr. Table
11.1.1 gives a complete list of the physical parameters of the neutron
detectors. Immediately in front of each neutron detector was a plastic
paddle (NE102A) 0.6 cm thick that was used to electronically veto events
where charged particles struck the neutron detectors.

The in-beam background of scattered neutrons was measured by
taking data.with shadow bars between the neutron detectors and the tar-
get. The shadow bars were conical sections of brass, with the same
solid angle as the neutron detectors and a length equal to half the

flight path.
11.2 Electronics
Figure 11.2.1 shows a schematic diagram outlining the basic

electronic modules used for the particle telescopes and the neutron

detectors. The pulse height of the silicon detector signals was

11

<— BEAM LINE

NEUTRON DETECTORS ‘
’ J 0
V \

’

 

 

 

 

.l '

/
SI TELESCOPES <31, \
‘ I

~ ‘3 \l.

 

\I
ATT 1 HA R —_’ ,.
SC ER NC C “35
I

 

 

 

/' BEAM DUMP

 

 

 

 

 

 

 

 

 

Figure 11.1.1 Schematic of experimental set-up

12

TABLE 11.1.1 Physical characteristics of the neutron detectors.
(All dimensions given in cm).

Det. No. Depth Radius Distance A0 (msr) 0 (Lab)

 

1 7.0 6.2” 131 7.15 50°
2 7.5 6.35 130 7.99 70°
3 7.5 6.35 130 7.49 120°
A 7.6 6.35 129 7.59 160°
5 7.0 6.29 206 2.89 20°
6 7.5 6.35 130 7.99 -140°
7 7.5 6.29 131 7.13 -110°
8 5.7 5.56 129 5.82 - 90°
9 7.6 6.35 129 7.59 — 70°
10 7.0 6.2“ 131 7.15 - 30°

00C
GATES

ADC
STROBE

TDC START
UT REGISTER

TDC
STOP
1110
STIP

3%
58
I §>>
IE5 III
a s -
2.2 SE
3 ‘1 g
2 a
. = 5
i: 2

A“
a

Figure 11.2.1 Electronics schematic

DflAY

508
SPUTT

111

digitized in analog-to-digital converters (12 bit 0rtec AD811 ADC's).
The area of the neutron detector signals (proportional to the charge)
was digitized in charge-to-digital converters (LeCroy 22A9W QDC's). The
area of the first 30 ns of the neutron detector signal (charge collected
in the first 30 ns) was also digitized to give pulse shape information
to be used in discriminating between neutrons and Y rays. In addition,
an amplified version of each of these latter two signals was also
digitized to give additional resolution for small signals. Finally, the
time information for all detectors that produced signals above threshold
in a 500 ns window was digitized by time-to-digital converters (LeCroy
2228A TDC's).

For the data aquisition, there were 111 detectors: 11 AE-E tele-
scopes and 10 neutron detectors. A valid telescope event required a
coincidence between both silicon elements. A valid neutron event re-
quired a coincidence between a signal in a neutron detector and no
signal in the plastic paddle in front of the same detector. In this way
the 28 detector elements were reduce to 111 detectors. A bit register
was set to record all the detectors in a valid event. Thus, for each
event there was a sixteen-bit bit register, a AE pulse height, an E
pulse height and a telescope time for each telescope that fired, a
charge, a delta-charge, an amplified charge, an amplified delta-charge,
and a neutron time for each neutron detector that fired. The data was
read from the CAMAC by a system which employed a Motorola 68000 [Va85] .
In conjunction with this, an LSI microprocessor read data rates (both
raw and live) from sealers, including an integrated beam current signal.
These two microprocessors filled buffers (data and scaler,

respectively), and then sent them to a VAX 750. In addition to reading

15

the data buffers from the CAMAC modules, the 68000 based system was
programed to discriminate against 252 fragments in any of the tele-
scopes and reject those events on-line. This was done prhmufily to
reduce the amount of subsequent data analysis. Once the buffers were
received by the VAX, they were written to tape at 6250 bpi and sampled
on-line via the program SARA [Sh85]. The electronics was operated in
one of three different modes: particle singles, particle-neutron
coincidences, and neutron singles. Selection of the mode was done by
pushing the appropriate buttons on a coincidence module.

In particle singles mode, only the silicon telescopes were
necessary to trigger an event. The silicon detectors were biased at the
voltages recommended by Ortec. The signal from each silicon detector
went through an LBL pulser/preamplifier toia Tenelec 241$ amplifier.
The shaped output went to an Ortec AD811 ADC (12 bit). The fast.cn1tput
went to a constant fraction discriminator. This produced a relatively
pulse-height independent timing NIM pulse. The width of this pulse was
50 ns for the AE detectors and 200 ns for the E detectors. The AE sig-
nal was delayed 30 ns relative to the E signal, as determined with the
pulsers. For a given telescope, these two signals were sent to a
coincidence module. A coincidence between both telescopes implies a
good telescope event, and resulted in a 50 ns wide NIM signal fixed in
time relative to the arrival of particles in the AE element of the tele-
scope. An OR of the four telescopes was put into an AND coincidence
unit with the computer not busy signal. The output of this coincidence
unit was the master gate for particle singles.

Neutron/Y-ray identification in the liquid scintillators was

done via a two-QDC method. This consisted of comparing the anode signal

16
from the photomultiplier integrated over two different time periods.
The different pulse shape produced by Y rays (compared to neutrons) al—
lowed us to discriminate against Y rays in our analysis. The neutron
kinetic energy was determined by measuring the time of flight, relative

to the pulse produced by the coincident intermediate mass fragment.

CHAPTER III: DATA ANALYSIS

3.1 Calibration

The energy calibration of the silicon detectors was determined
with calibrated pulsers. Pulses in 5 MeV increments for the AE detec-
tors (10 MeV increments for the E detectors) were recorded several times
throughout the experiment. A linear fit between the known signal (read
off the pulser dial) and the observed pulse height determined the
calibration. The fit was very good, and changed negligibly over the
duration of the experiment (recall that the detectors were cold; the
width of the signal increased as a result of radiation damage to the
detectors). A check of the calibration of the pulsers was made by com-
paring the energy range for a given isotope to what is expected based on
the detector thicknesses and the stopping ranges given in Ziegler
[2180]. In no case was any error discernable.

Before discussing the calibration of the TDC's, it is necessary
to understand what their value represents, and in fact it will be con-
venient to replace the measured parameter with a related pseudo-
parameter. The relatively poorly defined time structure of the K500
cyclotron beam prevented timing against the rf signal. For this reason,
meaningful time information was only obtained for coincidence events:
when two detectors fired, the time of one would determine the time of

the master gate. Then that detector's TDC would provide no new

17

18
inf0rmation. The time information would all be in the second detector's
TDC. That TDC was started by the master gate and stopped by the second
detector (actually a delayed signal from that detector). The only
coincident events considered in this experiment were fragment-neutron
coincidences. In that mode, the neutron signal time determined the
master gate time, so the neutron TDC contained no useful information (at
least for single neutron coincidences). The telescope's TDC would be
started by the master gate (neutron time plus a constant) and stopped by
a delayed telescope signal (fragment time plus a constant). Thus the
neutron TDC value minus the fragment TDC value gives the difference be-
tween the neutron time of flight and the fragment time of flight within
a constant. For any given event, the fragment time of flight independ-
ently can be calculated from the particle identification, fragment
energy, and target-to-AE-detector distance. The constant can be deter-
mined by looking at Y-ray events as their time of flight is well known.
Then the neutron time of flight is given by the neutron TDC value minus
the fragment TDC value plus the fragment time of flight minus the con-
stant. This value is a pseudo-parameter that will be used in place of
the TDC parameter. Then, to determine the neutron time of flight in any
event, we must have the neutron TDC value, the telescope TDC value, and

the fragment mass and energy. In this way, the TDC histograms can be

 

replaced by neutron time of flight histograms, which are more readily
understood. The raw TDC histogram for any telescope is difficult to in-
terpret since time runs from right to left, and the TDC start comes from
the master gate, which can be determined by any one of ten neutron
detectors, all of which have slightly different time characteristics.

Conversely, the time-of-flight pseudo parameter for a given neutron

19
detector in coincidence with fragments in any given telescope shows time
running from left to right.

The TDC's were calibrated by comparing the periodicity of the
time-of—flight histogram to the period of the cyclotron. The
time-of-flight histogram gated on Y rays (eliminating the neutron sig-
nals by pulse shape discrimination) for each neutron detector in
coincidence with a signal from any particle telescope showed six Y-ray
peaks for the E/A=35 MeV data and five for the E/A=20 MeV data. Figure
111.1.1 shows the time-of—flight histogram for Y rays in neutron
detector-1 in coincidence with ’Li fragments for the E/A:20 MeV data.
The periodic structure is due to the cyclotron periodicity, and the
large peak is due to real coincidences (the Y ray and coincident frag-
ment from the same beam pulse) and the others to accidental coincidences
(the Y ray and coincident fragment from different beam pulses). The
centroids of these peaks were measured for each case. The average num-
ber of channels between peaks for each TDC was set equal to the
cyclotron period (which is known to 5 significant figures) to obtain the
number of seconds/division for that TDC. In no case did the discrepancy
of the observed period exceed the width of the gamma peak. The TDC
calibration was 0.227 ns/channel.

The electron equivalent energy of the neutron detector pulse
heights was calibrated using three different Y sources: 22Na, ‘°Co, and
2”Pb. The neutron detectors are sensitive to the Compton electrons
produced by the Y rays from these sources. The pulse height distribu-
tion of each source showed a step function at the Compton edge. The
Compton edge for the observed Y rays was defined to be at half the maxi-

mum value of the step function. The Y rays observed were: 0.511 MeV

20

E /A=20 MeV
I ' T ' l

1000*“ -

 

 

 

 

 

7 rays / ns
p_a
O
O
I
I

 

 

 

 

 

 

 

 

 

 

   

103“”

Figure 111.1.1 Time-of-flight spectrum for Y rays in neutron detector-1
in coincidence with 'Li fragments in any telescope, E/A=20 MeV.

. . 1 I'll Mill 7
100 200 300
Time—of—Flight (ns)

 

21
and 1.27 MeV from the 22Na, 1.25 MeV (average of the 1.17 and 1.33 MeV Y
rays) from ”Co, and 2.62 MeV from the “sz. For Compton scattering,
the scattered wavelength, A', is related to the original wavelength, A,

by:
1' - 1 = 3- (1-0030) (III 1)
mo ’ °

where h/mc is 211 times the electron Compton wavelength and 0 is the
scattering angle of the Y ray. For 9=n, this gives the scattered energy

in terms of the original energy, E, as:

E, _ 0.51m:

- m. (111.2)

A linear fit between the Compton edge channel number and these scattered
energies calculated from the original energies and equation 111.2 gave
the calibration of the pulse height in electron equivalent energy. This
information was used to determine the lower cutoff of the pulse height
in electron equivalent energy, a necessary input to determine the
neutron detector efficiency.

The neutron detector efficiency was determined by the code
fHTTEFF [Ku6A]. In Ref. Re86, TOTEFF was compared to a Monte Carlo code
developed by Cecil et al. [Ce79]. Based on that comparison, the uncer-
tainty in the absolutely neutron detector efficiency is approximately
10%. Figure 111.1.2 shows a typical neutron detector efficiency as a

function of neutron kinetic energy.

22

 

C10
0

I I I

N
0'1

 

l

x 1 1 j
t

p_a
O
1 . I . .7 .

1|]

0 60 120
Energy (MeV)

E1 1 lLll, i I 1 J, I l ;I
I l J I J, l l, I I l I .l l IJ l l I I I l 1 l

 

I

Neutron Det. #1 Efficiency (%)
'61

 

 

 

I l 1 i 1
1 U 1 r
A:
j
1
_

 

 

 

 

 

 

 

 

 

 

 

Figure 111.1.2 Neutron detector efficiency as a function of neutron
kinetic energy.

23

111.2 Single Particle Inclusive Data

Charged particle inclusive data were taken with the neutron
coincidence requirement removed from the master gate. This was done for
approximately one-half to one hour every four to eight hours throughout
the duration of the experiment. All of these runs were binned into a
single AE vs. E (the signal from the front silicon detector vs. the sig-
nal from the back silicon detector) histogram for each telescope.
Figure 111.2.1 shows the AE-E histogram for telescope-A. Particle iden-
tification gates were drawn for each of the following isotopes: ‘Li,
7L1, 8L1, 7Be, ’Be, ‘°Be, ‘°B, and “B. The same singles runs were then
binned into kinetic energy spectra for each isotope in each telescope.
'Dypical spectra are shown for the E/A=35 MeV data in Figure III.2.2 and
for the E/A=20 MeV data in Figure III.2.3. The solid lines shown in
these two figures represent the moving source analysis described next.

For each isotope identified, the kinetic energy spectra were fit
by a moving source model [Ja83]. A single parameter set of normaliza-
tion, slope parameter (kT in the temperature interpretation) and source
velocity was obtained f0r all spectra of a given isotope. A Coulomb
shift [We78] was employed, where the shift was a fraction of the Coulomb
barrier between the observed fragment and the residual nucleus, trans-
formed from center of mass to lab coordinates. The fit parameters
(including the Coulomb shifts used) are given in Table 111.2.1 for the

E/A=35 MeV data and in Table III.2.2 for the E/A=20 MeV data.

29

E/A=85 MeV

 

 

 

 

 

/"\

(I)

+9

E 400

:3

>»

CD ..
5-1

0)

C1

C1)

. 200 :-
,0

s...
<6 ‘1.
v ‘4
[2:1

<

100 200
E (arb. energy units)

Figure 111.2.1 AE vs. E particle identification map for telescope A,

E/A=35 MeV.

E /A=35 MeV

 

1000

100 —\}\ 6L1 —\ “’11

10 T

 

 

dzo/dEdQ (ub/MeV/sr)

 

 

 

 

 

100 100
Kinetic Energy (MeV)

Figure III.2.2 Fragment kinetic energy singles spectra with moving
source fit, E/A=35 MeV.

100

10

h 1
\
;>
G)
:2

\10.0
,0

3 1.0

55 0.1
[:2]
"U
E

«PG 10.0

1.0

O1

26
E /A=20 MeV

 

 

 

 

 

 

 

r- .‘\~\“\ 6151 ”—4é::;;::::‘t .7141
— — 0‘
a l . l
\ 7Be _
.\» _
I 1 1 l .
108 11B
_ __ \
\ \\
1 l . l .
100 100

Kinetic Energy (MeV)

Figure 111.2.3 Fragment kinetic energy singles spectra with moving
source fit, E/A=20 MeV.

 

TABLE 111.2.1 Fragment

27

kinetic energy moving source fit parameters.

(mb)

 

 

 

Coulomb
Isotope Shift (MeV) 0
6L1 10 54.
7Li 10 92.
°L1 10 12.
7Be 13 18.
’Be 13 20.
‘°Be 13 13.
‘°B 16 1A.
“B 16 28.

TABLE III.2.2 Fragment

8(1)
9(2)
9(1)
0(1)
5(1)
2(1)
8(1)
1(1)

 

E/A:35 MeV

T (MeV) B

11.2(5) 0.075(2)
12.8(3) 0.081(1)
14.5(5) 0.070(4)
15.0(3) 0.098(3)
13.0(9) 0.083(2)
13.7(7) 0.082(1)
15.0(u) 0.092(5)
11.2(u) 0.086(u)

xz/dof
“0.9

79.2
10.9
11.6
13.0
6.1
6.8
8.5

399;
8A
91

101

107

108

108

119

110

kinetic energy moving source fit parameters.

 

 

 

Coulomb
Isotope Shift (MeV) 0 (mb)
°Li 10 32.5(1)
7L1 10 99.8(1)
“L1 10 6.1(1)
7Be 13 8.0(1)
’Be 13 12.4(1)
‘°Be 13 6.9(1)
‘°B 16 9.2(1)
“B 16 18.0(1)

 

11.0(9)

E/A:20 MeV

T (MeV) B

10.3(3) 0.067(3)
11.3(A) 0.068(2)
13.3(5) 0.058(1)
11.5(3) 0.072(3)
10.8(9) 0.066(1)
11.6(7) 0.067(1)
11.6(3) 0.071(3)

0

.069(1)

xz/dof
20.6

92.5
6.8
4.0
6.3
3.6
3.9
3.5

gggg
92
99
99
103
113
108
99
110

28

111.3 Coincident Neutron Data

111.3.1 Neutron/Y-ray Discrimination

Neutrons were distinguished from Y rays by pulse shape dis-
crimination above a threshold of approximately 200 keV electron
equivalent energy, independent of the time of flight. The pulse shape
discrimination was done with a 2-QDC method. The signal from the anode
of the neutron detector photomultiplier was split and fed into two
QDC's. Each QDC began integrating at the same point in time, but one
(QDC2) integrated the total charge (over approximately 300 ns) while the
other (QDC1) only integrated the charge collected in approximately the
first 30 ns. In Fig. 111.3.1, QDC1 versus QDC2, two distinct groups can
be seen. One group corresponds to Y rays, which deposit a greater frac-
tion of their total energy in a short time than do neutrons, the other
group. Software gates were set on the neutron groups for each neutron
detecttn‘1vith thresholds near 200 keV electron equivalent energy. The
gain on the neutron detector signals was set high to get maximum resolu-
tion at low energies, when the two groups (neutrons and Y rays) are
close together. In order to retain the events that would otherwise end
up in the overflow channel, attenuated versions of these signals where
fed into a second pair of QDC's. The final neutron spectra are a com-
bination of all events that could be identified as neutrons in either

QDC map.

‘ I-P
O
O

QDC 1 (short gate)
N
O
O

29

E /A=35 MeV

I ' l '
_ I

 

 

', a ' 1“ .
J" - 0"
‘ .0

" '('o ’u
I

O
..,o
1 .39.

. u .“I.. g n _ ‘ I

 

1 . www.c-

 

 

mid. \of—‘cu-u— . .L~ . _ L l

200 400
QDC2 (long gate)

 

Figure III.3.1 QDC1 vs. QDC2 for neutron detector-8, E/A=35 MeV.

30

III.3.2 Neutron Time-of-flight

The neutron time-of-flight was measured relative to the charged
particle signal from the front detectors of the telescopes. The time
between the nuclear event and the silicon telescope signal was estab-
lished from the distance from the target to the silicon detector, the
particle mass, and the particle energy. Figure 111.1.1 shows the total
range of time information for events in the neutron detectors in
coincidence with telescope events. This extends over nearly five
cyclotron periods (for E/A=20 MeV) or about 3A0 ns. The true
coincidences end before the end of two periods, so the first two periods
(from 0 to 105 ns for E/A=35 MeV and from 0 to 138 ns for E/A=20 MeV)
were considered the real plus the accidental coincidences. Figure
III.3.2 shows this portion of the time-of-flight spectrum for neutrons
in neutron detector-1 in coincidence with "Li fragments. This spectrum
must be corrected for indirect neutron events by the subtraction of a
scaled (by the ratio of the integrated beam currents) version of the
same histogram for data runs with shadow bars in place (shown in dots in
Figure III.3.2). The second two periods of the spectrum (from 105 to
209 ns for E/A=35 MeV and from 138 to 275 ns for E/A:20 MeV) were con-
sidered to be the accidental coincidences (shown in Figure III.3.3, with
the dots representing the shadow bar data), and subtracted from the real
plus accidental coincidences spectrum (after both were corrected for in-
direct neutrons by subtraction of the appropriate shadow bar histogram)
to yield the true real coincidences (shown in Figure 111.3.11). This
technique was used throughout the analysis, for each type of neutron

histogram.

31

 

300" _

200- -

Neutrons / ns

p_a

O

O
I
I

 

 

 

() Pn.::i::3:£;;1".l 1; l .l .3;:£3:-;tfi.z . f .; ...
20 40 60 80

Time—of—Flight (ns)
Figure III.3.2 Neutron real plus accidental time-of-flight histogram

(solid) with corresponding shadow bar histogram (dots) for neutron
detector-1, E/A=35 MeV.

32

E/A=35 MeV
50 ' I ' I ' I ' I T

 

405' -

30— 1

 

 

 

 

 

Neutrons / ns

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20 40 60 80
Time—of—Flight (ns)
Figure III.3.3 Neutron accidental time-of-flight histogram (solid) with

corresponding shadow bar histogram (dots) for neutron detector-1, E/A=35
MeV.

33

E /A=35 MeV

 

300 ' 1 ' 1 ' I ' I

1 11

 

 

N

O

O
I

100'-

Neutrons / ns

 

 

 

 

0 1 1 . 1 . 1
20 40 60 80

Time—of—Flight (ns)

Figure 111.3.“ Neutron real time-of-flight histogram for neutron
detector-1, E/A=35 MeV.

 

34

III.3.3 Neutron Kinetic Energy

The distance from the target to each neutron detector was
measured, and when combined with the neutron time-of—flight, allowed
calculation of the neutron kinetic energy on an event-by-event basis.
Figure 111.3.5 shows a neutron kinetic energy spectrum (neutron
detector-1 in coincidence with 7L1 in telescope-1) both before and after
correction for the energy dependence of the neutron detector efficiency.
The neutron detector efficiency as a function of energy was calculated
with the code TOTEFF [Ku64] and folded into the neutron data. Figure
III.3.6 shows all 10 neutron spectra with the neutron detector ef-
ficiency included. Similar kinetic energy spectra were generated for
neutrons in coincidence with each charged particle, in each telescope,
and for each neutron detector. These spectra were then fit with a
two-source moving source model [Ja83]. The double differential multi-

dzM

plicity, m, is given by:

8211 2 THE __
m : 121W eXPI-(E-Z/EiECOS(G)+Ei)/kTi]y (111.3)

where E is the neutron kinetic energy, 0 is the neutron angle in the
lab, M1 and k'1‘i are the associated neutron multiplicity and the slope
parameter (temperature), respectively for each source, and Si is the

kinetic energy per nucleon of the source, given by:

- x _1 -
Ei - 931.5 (/1-B; 1), (111.4)

35

Neutrons With 7Li at 50°

 

H
O
CO

 

 

 

H
O
N

1...;
O
H

I IIIIIIII I IIIII

h 102

E3 F: (”3%.“

‘\\\\ 1-():1 g;__ #1}.

2 100 : 1 l I 1I I E :
\\

(n 103 With

g Efficiency
1...

.4.)

:3

Q)

2:

 

 

 

100 I l I I I I I I I fl I
50 100

Energy (MeV)

Figure III.3.5 Kinetic energy histogram for neutrons at 50° in
coincidence with 7Li at 50° before and after folding in the neutron
detector efficiency.

0

36

Neutrons with 7Li at 50°

 

 

 

 

 

 

€13

... 12 -1
O .

3’. 11 -
$10 _
a 9..

1: 8 '
a 7 ‘
\ -
E5 ‘
\ 4" I
E 3" ‘
E 2 "
:1 1 -
° I

z 0 I l l

O

60 1 20
Energy (MeV)

Figure III.3.6 Kinetic energy spectra for neutrons in coincidence with
7Li at 0=50°, ¢=0° (data points) with two-source moving source fit
(solid lines). The order of the neutron detectors (from top to bottom)
is: 20°, -30°, 50°, -70°, 70°, —90°, -110°, 120°, -140°, and 160° in the
lab. The spectra are separated artificially by an order of magnitude
each, with the 160° data at unit normalization.

37

where B1 is the source velocity for each source in units of c, the speed

of light. The pre-factor of /E in equation 111.3 arises for two dif-
ferent reasons for the two different sources. For the slower source,
the temperature parameter indicates a relatively low excitation energy
per nucleon. This implies "surface emission" of the neutrons, which for
single neutron emission corresponds to a pre-factor of E [0078]. But
the associated multiplicity indicates multiple neutron emission, which

5/11

corresponds to a prefactor of E [Le59]. This has been approximated

by JE. In this case, kT is an effective temperature parameter. This is
slightly less than the temperature of the daughter nucleus after the
first neutron emission by a factor of 11/12 [Le59]. Throughout this
thesis, only the effective temperature parameter is discussed. For the

second source, the temperature parameters are much higher, and "volume

emission" is assumed. In that case, the pre-factor is /E [G078].

The neutron kinetic energy spectra fit parameters (Mi’ ”1’ and
Bi;i:1,2) are shown in Table III.3.1 for the E/A:35 MeV data and in
Table III.3.2 for the E/A:20 MeV data. The parameters are listed
separately for neutrons in coincidence with each isotope observed (‘Li,
7Li, °Li, 7Be, 9Be, ‘°Be, ‘°B, and “B) and for each position of silicon
detector (0:50°, 70°, 90°, ¢=0°, and 0:50°, 0:90°). Generally, all 10
neutron detectors were included in each fit. The exceptions were for
the 0=50°, 70°, ¢=0° detectors when the coincident fragment was ‘Li,
“’Li, 9Be, 1°Be, or ‘ ‘B. In those cases, the neutron detector that was
colinear with the fragment detector was excluded from the fitted data.
These cases were particularly sensitive to neutrons from the sequential

decay of intermediate mass fragments in particle unbound states. The

'TABLE III.3.1

38

Associated neutron kinetic energy moving source fit parameters.

 

 

 

 

E/A=35 MeV
Source #1 Source #2
IMF Angle M1 '1, 8, M2 T2 81, xz/dof #dof
‘L1 500 6.32(7) 3.07(5) 0.021(6) 2.02(6) 12.7(5) 0.096(4) 1.269 249
°Li 70° 6.54(11) 2.98(5) 0.022(2) 2 00(10) 14 0(9) 0.101(8) 0.932 194
“L1 900 6.19(16) 3.23(17) 0.020(3) 1.97(18) 16.1(10) 0.143(17) 0.762 135
°Li 50°f 6.05(7) 2.72(4) 0.016(1) 1.46(5) 11.0(5) 0.092(5) 1.142 224
7L1 50° 6.48(6) 3.07(3) 0.020(3) 1.88(3) 12.5(3) 0.099(3) 1.689 291
7L1 700 6.35(10) 2.91(6) 0.019(1) 1.97(8) 13.7(7) 0.103(6) 1.036 218
7L1 90° 6.33(14) 3 0(3) 0.020(1) 2.48(17) 19 4(10) 0 105(15) 0.814 162
7L1 50°f 5.55(5) 2.81(4) 0.015(1) 1.19(3) 9.7(9) 0.116(13) 1.463 260
°L1 50° 6.43(15) 2.80(10) 0.022(9) 2 56(13) 12 0(10) 0.084(16) 0.848 171
°Li 70o 5.7(3) 2 9(2) 0.023(4) 2.8(3) 12 8(10) 0.042(38) 0.654 89
°Li 90° 5.8(4) 2.3(3) 0.024(5) 5.0(6) 13.8(10) 0.020(36) 0.547 61
°Li 5001 5.09(15) 2.91(10) 0.015(3) 1.43(15) 12.2(9) 0 090(11) 0.810 107
’Be 50° 7.23(13) 3.02(8) 0 022(2) 2.12(11) 11.9(8) 0.101(9) 1.172 181
’Be 70° 6.9(3) 2.57(15) 0.023(9) 4.3(4) 15.8(16) 0.05(6) 0.696 103
7Be 900 7.5(6) 2.5(4) 0 01(2) 9.2(4) 23(9) 0.24(10) 0.474 38
7Be 50°f 6.17(14) 2.60(9) 0.015(2) 1.56(13) 13.5(10) 0.088(18) 0.747 135
’Be 50° 6.76(12) 2.79(9) 0.021(3) 2.29(12) 12.5(7) 0.096(7) 1.012 149
9Be 70° 6.7(3) 2.54(18) 0.019(3) 3.9(3) 19.2(10) 0.09(4) 0.543 81
’Be 90° 7.6(10) 2.2(10) 0.01(5) 2.6(8) 6.0(16) 0.13(9) 0.318 29
’Be 5001 5.10(14) 2.81(12) 0 019(3) 1 47(14) 13.4(10) 0.101(17) 0.643 122
‘°Be 50° 5 48(18) 2.88(16) 0.021(5) 2.7(2) 12.2(10) 0.076(12) 0.589 121
‘°Be 70o 6.0(4) 2.0(4) 0 021(3) 4.6(5) 10 3(10) 0.07(3) 0.443 53
‘°Be 90° 4 1(10) 3(7) 0.01(2) 6(9) 11(3) 0.1(7) 0.282 13
‘°Be 50°T 5.30(18) 2.75(14) 0.011(9) 1.27(19) 11.3(10) 0.11(3) 0.708 85

108
108
108
108

‘13
“B
1'3
“B

50° 6.64(17)
70° 6.4(3)
90o 14.1(7)
50,1 5.18(21)
50° 7.06(14)
70° 7.05(15)
90° 9(14)
5001 5.14(15)

T50° out of the

39

TABLE III.3.1

2.79(11)
2.8(3)
3.4(5)
2.38(8)

3.26(9)
2.8(2)
2(7)
2.83(12)

reaction

0.019(3)
0.028(5)
0.03(1)

0.015(3)

0.025(4)
0.022(3)
0.02(5)

0.015(4)

plane.

[Vt-=10

szN

.5(2)
.8(8)
.5(10)
.4(2)

.22(17)
.0(5)
.4(10)
.62(14)

(cont'd.)

13.6(10)
14.6(10)
13.8(10)

9.3(10)

21.0(17)
18.1(10)
10(4)

10.4(10)

0000

0000

.077(14)
.04(6)

.128(11)
.053(16)

.110(13)
.02(4)
.14(8)
.079(9)

COO-b

.257
.483
.299
.773

.081
.773
.492
.833

127
54
12
90

151
71
15

121

40

TABLE III.3.2 Associated neutron kinetic energy moving source fit parameters.

 

 

 

E/A:20 MeV
Source #1 Source #2

IMF Angle M1 T, B, M; T2 82 xz/dof #dof
°Li 50° 5.23(7) 2.54(6) 0.017(2) 0 91(5) 8 2(7) 0.089(6) 1.205 149
611 70a 5 13(10) 2.44(8) 0.017(2) 1.38(10) 9 4(10) 0.05(4) 1.167 114
°Li 90o 4.71(17) 2.1(9) 0.02(1) 1.83(17) 9.1(10) 0 034(18) 0.869 89
“Li 500+ 4.71(7) 2 25(7) 0.015(1) 0.73(6) 11.1(10) 0.052(18) 1.196 131
’11 50° 5.07(5) 2.56(4) 0 019(1) 0.91(4) 11.8(8) 0.065(10) 1.573 176
711 70° 4.75(9) 2 24(7) 0.019(1) 1.48(8) 8 5(10) 0.051(7) 1.556 125
7L1 900 4.91(12) 2.48(11) 0.021(2) 1.34(13) 11.0(10) 0.03(7) 0.818 107
711 50°1 4.28(6) 2.36(3) 0.010(1) 0 57(3) 6 3(10) 0 08(4) 1.292 144
811 50° 5.03(14) 2.51(12) 0.018(3) 1 08(17) 10 3(10) 0.07(3) 0.823 82
°Li 700 5 4(3) 2 6(2) 0.025(3) 2.1(4) 10.0(10) 0.02(4) 0.739 51
“Li 90° 5.8(4) 0.59(14) 0.027(3) 5.0(4) 4.5(8) 0.011(1) 0.559 31
°Li 50°, 4.01(18) 2.14(15) 0.009(7) 1.5(2) 9.7(10) 0.08(4) 0.773 62
7Be 50° 3 74(13) 2.92(17) 0.026(3) 0.41(17) 8.2(10) 0.000(3) 1.299 65
”Be 70° 3.8(3) 2.0(3) 0.018(5) 2.6(5) 9.8(10) 0.1(9) 0.894 37
7Be 90° 5.2(7) 4.4(8) 0.02(2) 0.20(93) 9 5(10) 0 0(9) 0.379 8
7Be 50°T 2.82(16) 2.8(3) 0.010(8) 0 01(26) 9.5(10) 0.00(3) 0.743 32
9Be 50° 4 09(15) 2.08(13) 0 022(3) 2 40(15) 7.2(10) 0.028(25) 0.993 87
“Be 700 5.3(3) 2 20(19) 0 022(3) 3.4(5) 11.1(10) 0.03(6) 0.772 54
’Be 90° 5 8(5) 2 4(6) 0.02(5) 1.9(10) 9.3(10) 0.1(8) 0.509 26
’Be 500* 3.31(14) 2.24(18) 0.020(3) 1.15(15) 6.1(10) 0.000(1) 0.775 64
‘°Be 50° 4.84(19) 2.6(2) 0.021(4) 1.5(2) 11.3(10) 0.000(1) 0.819 60
‘°Be 70o 5.4(4) 1.9(3) 0.024(4) 3.6(7) 11(2) 0.01(5) 0.663 35
‘°Be 90° 6.4(9) 3 5(8) 0.02(10) 1.1(10) 9.5(10) 0.06(73) 0.229 10
‘°Be 50°T 4.1(2) 2.5(3) 0.01(2) 0.8(9) 10.0(10) 0.10(17) 0.492 41

108
108
108
108

“B
“B
“B
“B

500 4
700 5
90° 9
50°] 4
50°
70°
90°
50°1

J=O\O\Ul

T50° out

.28(17)
.7(5)
.6(7)
.7(2)

.29(14)
.5(3)
.6(5)
.05(13)

of the

41

TABLE III.3.2

2.8(2)
1.4(2)
2.5(7)
2.5(3)

2.71(13)
2.8(2)
1.8(7)
2.5(5)

0000

.017(5)
.013(8)
.008(8)
.012(6)

.016(7)
.016(7)
.02(3)

.011(5)

reaction plane.

Cam—a

JUIOO

(cont'd.)

.2(3) 10.0(10)
.8(8) 9.7(9)
.7(9) 5.0(10)
.6(4) 9.8(10)

.97(19) 10.8(10)
.8(5) 1.7(6)
.0(10) 8.6(9)
.0(3) 9.0(10)

.14(9)
.061(57)
.1(9)
.09(6)

.12(8)
.20(3)
.13(11)
.15(5)

0000

COO—b

.793
.402
.627
.548

.054
.667
.380
.746

60
33

42

79
47
15
57

42

coincident charged particle was then the residue from such a decay. For
example, in Figure 111.3.7 (neutrons in coincidence with “B at 0=50°,
0:0°, from the E/A:35 MeV data) the prominent peak near 7 MeV in the 50°
neutron spectrum is due to such a process. The solid lines shown in
Figures III.3.6 and 111.3.7 represent the double-differential multi-
plicity as calculated by equation 111.3 using the appropriate parameters
from Table III.3.1 for each neutron detector angle. While such a line
is drawn for the colinear neutron detector, it should be remembered that
that detector was excluded when determining the fit parameters.

The errors quoted for the fit parameters are the change in that
parameter that corresponds to increasing x2 by 1, with all other
parameters optimized. For each set of fit parameters, x2 per degree cu?
freedom (xz/dof) and the number of’degrees of freedom (#dof) is given.
(The number of degrees of freedom equals the number of data points in
the set minus the number of fit parameters, which in this case is six).
Caution should be exercised in interpreting the uncertainty of these
fits. In some of the cases, the fit parameter errors are smaller than
the maximum uncertainty of the fit parameters. This is because x2 is

not a valid test for very small data sets.

111.3.4 Neutron Relative Velocity

Using a technique developed by Kiss et al. [K187] it was pos-
sible to interpret the neutron decay of certain states of various
nuclides observed in the neutron detectors that were colinear with a
silicon telescope and the target. In particular, the present work

reports on the neutron decay of the 2.255 MeV excited state of 'Li and

43

Neutrons with 11B at 50°

 

 

 

 

 

 

 

 

 

 

:5: 12 I I r

"5 11" " " ~ Ill 1:
23 ].() '— ““56 "1?. I 1“

2 9 -
8 8 1
1: 7 -
E 6 1
\

:> 5 "
(D

2 4 '-
\ 3 q
00

8 2 .
S-c

5 1 1
‘D I

:2: () I l

Energy (MeV)

Figure 111.3.7 Kinetic energy spectra for neutrons in coincidence with
“B at 0:50°, ¢=0° (data points) with two-source moving source fit
(solid lines), as in Figure III.3.6.

44
the neutron decay of the 7.456 MeV excited state of 7Li, which feed the
ground states of 7Li and ‘Li, respectively.

For neutrons in coincidence with each observed isotope, the data
were binned into two-dimensional histograms, the x-axis corresponding to
relative velocity and the y-axis corresponding to neutron energy. (The
relative velocity is defined as the neutron velocity minus the coinci-
dent fragment velocity). Figure 111.3.8 shows such a histogram for
neutrons in coincidence with 7Li from the E/A=35 MeV data. The value of
each channel of these histograms was corrected for the neutron detector
efficiency for neutrons of the appropriate kinetic energy (previously
calculated, as described at the beginning of this chapter), to create a
new two-dimensional probability histogram. Then, for each value of the
relative velocity, the histogram bins were summed over neutron kinetic
energy to give a one-dimensional histogram (with relative velocity the
remaining axis). This resulting histogram is the velocity distribution
of the neutrons shifted to the moving frame of the coincident fragment
on an event by event basis. Figure 111.3.9 shows such velocity dis-
tributions for neutrons in coincidence with various fragments from the
E/A:35 MeV data.

Neutrons from the decay of a relatively narrow discrete state
with a small excitation energy in a particular isotope give rise to a
peak in the relative velocity distribution for neutrons in coincidence
with the daughter nucleus. The histograms shown in Fig. 111.3.9 cor-
respond to the decay of the 7.456 MeV state of 7L1, the 2.255 MeV state
of °Li, the 7.371 MeV state of ‘°Be, the 3.89 MeV state of “Be, and the
3.388 MeV state of ‘2B [Aj84, Aj85]. These were observed in coincidence

with 6L1, 7L1, 9Be, 1°Be, and “B, respectively, all in the

45

E /A=85 MeV

 

I—3

O

O
I
I

)- ..
.. J
. .' J
1- . .q
50 1.. . y...
1' . ?.':',o '. ' v: . ‘3‘ "1

Syri!‘ ' . . '. 3....

£:§" tats”
)- :" “.1:- 239 '33-“ ' -1

o u . il. .

Neutron Energy (MeV)

 

 

 

 

5
Relative Velocity (cm/ns)

Figure 111.3.8 Relative velocity vs. kinetic energy for neutrons in
detector-1 in coincidence with 'L1 in telescope-1 (50°), E/A=35 MeV.

 

150 I I I 7 I I

100 5

UT
0
I
'9-
L
I
O
I

 

 

Neutrons / mm/ns / Insr

 

 

 

 

 

—5 0 5 —5 0 5 1
Relative Velocity (cm/ns)

Figure III.3.9 Relative velocity histograms for neutrons in detector-1
in coincidence with fragments in telescope-1 (50°), E/A=35 MeV.

47

ground state except the ”Be which was in the 3.3680 MeV excited state.
Also, the same type of histogram is shown for neutrons in coincidence
with ’Be. This shape corresponds to random correlations, where no nar-
row state with small excitation energy contributes significantly to the
coincidences.

1n the frame of the parent nucleus, the available kinetic
energy, T, is related to the nuclear binding energies, represented by

B(Z,N), by:
T = B(Z,N-1) - B(Z,N) + Eex(Z,N) - Eex(Z,N-1)

where Z and N represent the number of protons and neutrons, respec-
tively, in the parent nucleus, and Eéx(Z,N) is the excitation energy of
the level in the nucleus identified by Z and N. These kinetic energies
(or Q values) are 206 keV, 222 keV, 559 keV, 20 keV, and 19 keV, respec-
tively, for the decays listed [Aj84, Aj85], and correspond to relative
velocities of 0.679 cm/ns, 0.698 cm/ns, 1.092 cm/ns, 0.205 cm/ns, and
0.199 cm/ns, respectively. Broad states are not observed because the
emitted neutrons do not have a sharp relative velocity. Neutrons from
states with large excitation energies are also not observed due to a
greatly reduced efficiency (partly the inherent neutron detector ef-
ficiency but primarily the geometric efficiency due to kinematic
focusing).

In order to determine the number of neutrons from a specific
decay process, it was necessary to subtract a background spectrum of
neutrons from other processes. Since both the charged particle spectra

and the neutron spectra are easily parameterized in terms of moving

48

source fits, their inclusive velocity distributions are equally well
known. The parameters from the faster source of the neutron fit also
provided a reasonable representation of the charged particle spectra.
Using those neutron fit parameters as a representation of the charged
particle kinetic energy distribution and the two-source neutron fit
parameters as a representation of the neutron kinetic energy distribu-
tion, it was possible to calculate the relative velocity distribution
between uncorrelated charged particles and neutrons. This uncorrelated
thermal relative velocity distribution (shown in Figure III.3.10 as the
solid line) was in excellent agreement with the data from non-colinear
geometries (not shown) and was subtracted from the relative velocity
histogram (the difference is shown in Figure 111.3.11) to determine t1“;
number of fragments observed in the neutron unstable state.

The geometric efficiency of the neutron detector for observing
the decay of a particular state in a given isotope depends on the
velocity of the emitting system and the emission velocity of the
neutron. This geometric efficiency, En(E), was determined by a
Monte-Carlo calculation as a function of the parent nucleus energy both
for neutrons emitted in the direction of the moving system and for
neutrons emitted in the opposite direction. An average geometric ef-
ficiency, (En), was then obtained by weighting g1(E) by the yield of
parent fragments, Y(E), which was determined from inclusive data, in-

tegrating over energy and dividing by the total yield. That is,

IEn(E)Y(E)dE
IY(E)dE

 

<5n> = (111.5)

49

7L1 from :35 MeV/A 14N+Ag

I l I I’ I II I I I I I I I I *r I I II

11

 

125

p_a
O
O

()1

O

C)

01
O

Neutrons / Inm/ns / msr
(\3
01

Q
"J ”11¢
‘-1 II
.' .: a“

30
11 0TH“
4

. . '0.
..cs‘.é!1111l1111l1L11 urn".

2.5 0 2.5 5
Relative Velocity (cm/ns)

_<1

0‘1
II I If I l I I I I l I I I I I I I I I l I I I I I TI
I I I I 11 I, I I I I 11 I I I II I I I I I I I I I I

 

 

Figure III.3.10 Relative velocity histogram with thermal background for
neutrons in detector-1 in coincidence with 7Li in telescope-1 (50°),
E/A=35 MeV.

50

7Lifrom 35 MeV/A 14N+Ag

lIlllIIITIIIlIIIIlII

 

on
O

L-

50°

C)
O
I I I
1 l .

 

 

  

Neutrons / mm/ns / msr
m 4:-
o o
I I
I

 

 

I 1.1 NEW) 11141.1..1
—2.5lL

Relative Velocity5 (cm/5ns)

Figure III.3.11 Relative velocity histogram minus the thermal
background, for neutrons in detector-1 in coincidence with 7L1 in
telescope-1 (50°), E/A=35 MeV.

51

Appendix B gives a detailed description of the calculation of (en) for
each case, and the resulting values are listed in Table III.3.3. The
number of neutrons observed in each peak was then divided by the average
efficiency (for the 2.255 MeV state of I’Li, (en>:4(1)% for the neutrons
emitted forward in the moving system and <€n>:2.5(6)% for those emitted
backward in the moving system) to give the total number of fragments in
the particular neutron emitting state. A similar analysis of neutron
emission for each state and isotope listed above was used to determine
the number of fragments in each of those excited states. In the case of
the 7.456 MeV excited state of 71.1, the total 71.1 yield was corrected
for ‘Be contamination [B186] (about 20% of the observed 7Li yield for
E/Az35 MeV and 13% for EI/A=20 MeV, as shown in Appendix A of this
thesis). In addition, the results were corrected for the fact that this
state branches to ‘Li+n 77% of the time (and to a+t the rest of the
time) [A384].

Table 111.3.4 contains the ratio of the population of neutron
unbound excited states of various nuclei to the populations of the
ground state and any bound excited states with previously measured
populations of the same nuclei. The populations of the bound 0.478 MeV
state in “’Li and 0.9808 MeV state in ”Li were taken from Refs. 8186 and
M085 respectively. Using equation (1.1) to relate these ratios to tem-
peratures gives the values shown in Table 111.3.4. The ratio of the
populations of the second to the first excited state of “Li is beyond
the maximum allowed by their spin factors (7/3), but this is primarily
due to the large uncertainty in the excited state fraction reported in
Ref. M085. The calculated temperature of 2.8(3) MeV (from 7Li (7.456)

and “’Li (0.478)) is higher than the 0.54 MeV observed with the bound

52

TABLE III.3.3 <£n> (as described in the text) in percent for the decays

and beam energies listed.

 

Decay

 

 

 

7Li(7.456) to ‘Li(g.s.)
aLi(2.255) to ’Li(g.s.)
‘°Be(7.371) to 9Be(g.s.)
“Be(3.89) to ‘°Be(3.368)
‘28 (3.388) to “B (g.s.)

E/A=35 MeV
forward backward
4.5(11) 2.8(7)
4.2(11) 2.5(6)
2.2(6) 0.9(2)
32(10) 29(9)

34(11)

32(11)

 

E/Az20 MeV
forward backward
4.3(11) 2.6(6)
4.0(10) 2.3(6)
2.1(5) 0.8(2)
30(10) 27(9)
33(11) 30(10)

TABLE III.3.4 Excited state ratios, R, and their corresponding

temperatures, kT, from equation 1.1. (not corrected for sequential

States Compared

 

’Li(7.456) to 7Li(g.s.)
’Li(7.456) to 'Li(0.478)a
°L1(2.255) to °L1(g.s.)
'Li(2.255) to °Li(0.9808)a
‘°Be(7.371) to ‘°Be(g.s.)
12B (3.388) to 12B (3.8.)

States Compared
7Li(7.456) to ’Li(g.s.)
’Li(7.456) to 'Li(0.478)a
‘Li(2.255) to 'Li(g.s.)

‘°Be(7.371) to ‘°Be(g.s.)
123 (3.388) to ‘28 (g.s.)

decay).

E/Az35 MeV:

 

R (ratio)

 

0.05(1)
0.24(6)
0.40(8)
7.4:6.9
0.22(5)
0.334(7)

E/A:20 MeV:

 

R (ratio)

 

0.031(7)
0.36(13)
0.32(6)
0.20(5)
0.270(6)

kT (from Eq;,I.1)

 

kT

2.2(2)
2.8(3)
1.8(3)
a 0.8
2.13(15)
1.74(2)

(from Eq.

MeV
MeV
MeV
MeV
MeV
MeV

1.1)

 

1.9(1)
3.3(6)
1.5(2)
2.o7(15)
1.57(2)

aPopulation of Y-emitting states from Refs. M085 and 8186.

MeV
MeV
MeV
MeV
MeV

S3
excited state [8186]. This is qualitatively consistent with feeding ar-
guments since the present measurement does not involve the ground state
and should therefore be less susceptible to the effects of feeding ffiwnn
sequential decay. However, the temperature of 2.8(3) MeV is still some-
what lower than those based on charged-particle unbound levels reported
in Refs. P085a and Ch86a.

The feeding of the ’Li yield from the 2.255 MeV state in °LJ..is
defined as the number of 'L1 in that state (as determined above) divided
by the total number of observed 7Li (corrected for °Be contamination).
TablieIIII.3.5 gives the feedings to the ground states from the observed
neutron unbound states. In the case of the 3.89 MeV excited state of
‘ ‘Be, the observed decay was to the 3.3680 excited state of 10Be. The
quoted feeding is to the ground state of ‘°8e via this branch. The
branching ratio for the decay of the 3.89 MeV excited state to the
ground state of ‘°Be is unknown, and this feeding was not measured. The
amount of feeding of the 7Li inclusive yield from sequential decay of
the 2.255 MeV state in 'Li is 7(1) percent for the E/A=35 MeV data, a
fairly small value. Similarly, the feeding of the ’Li inclusive yield
via the same decay channel is 4(1) percent for the E/A=20 MeV data.
These feedings alone will produce only a small correction in the tem-
peratures extracted in Ref. 8186, which still gives temperatures less
that 1 MeV. However, note that these measurements are only of one decay
channel. These single values must be used in conjunctitn11nith a model
for the sequential decay to estimate the total feeding from all possible

decay channels, as discussed later in this thesis.

54

TABLE III.3.5 Feeding (in percent) of the ground state of A(Z,N) from
the neutron-unbound excited state of A(Z,N+1).

 

 

 

 

Excited State State Fed E/A=3S MeV E/A:20 MeV
’Li(7.456) ‘Li(g.s.) 3.9(8) 2.7(6)
°L1(2.255) ’Li(g.s.) 7.1(13) 4.4(9)

‘°Be(7.371) ’Be(g.s.) 14(3) 11(3)

“Be(3.89) ‘°Be(g.s.)b 1.1(1) 1.1(u)

128 (3.388) “8 (g.s.) 4.39(4) 3.66(4)

b

This is only the feeding through the ‘°8e(3.3680) state; the feeding
through the branch directly to the ground state is unknown.

55

111.4 Errors

Considerable beam time (about 1/3 of the total experiment) was
devoted to the shadow bar runs so that their statistical uncertainty
would not contribute significantly to the final data. 0n-line estimates
of the coincident neutron count rate indicated a shadow-bar-in to
shadow-bar-out ratio of ~1/4. In order to minimize the net statistical
uncertainty, this implied the beam time ratio should be the square-root
of that number, or 1/2. The net statistical uncertainty was obtained by
taking the square root of the sum of the squares of the individual un-
certainties. The systematic errors in the present data are primarily
due to uncertainties in determining the neutron detector efficiency
(310%), the geometrical efficiency for observing the decay, and the
thermal background subtracted from the relative velocity distributions.

A possible error in the geometric efficiency is that due to
misalignment of the silicon telescope and the neutron detector in the
colinear geometry. Any misalignment of the detectors will result in
overestimating the geometric efficiency, and hence underestimating the
yield from the state in question. However, due to the large target-to-
detector distance of 130 cm, it was possible to position the neutron
detectors such that their angles were known to :0.1°, which introduced a
relatively insignificant effect on the geometric efficiency. A finite-
sized beam spot and possible error in centering the beam have much
greater effect on the efficiency. In this experiment, the beam spot
diameter was approximately 3 mm, and we estimate that it was within 2 mm

of the geometric center. Therefore, the beam was contained within 3.5

56

mm of the geometric center with an average distance of less than 2 mm
from the center. Since the AE elements of the silicon detectors were
176 11111 from the target, this produced an average effective detector
misalignment of about 0.6 degrees. The geometric efficiency is quite
sensitive to this misalignment. For example, an error of 1° reduces (e)
by 1/3, which produces a 50% increase in the calculated populations.
The values and uncertainties given throughout this thesis for the
geometric efficiencies reflect the size and location of the beam spot.

The major source of error in the thermal background is not due
to uncertainty in the parameters or the calculation, but rather in that
we ignore the possibility of large angle correlations. Such correla-
tions could reduce the normalization of the background by as much as
401, which would increase the measUred value of the unbound excited
state populations. However, the model gives a good fit to the spectrum
away from the peaks.

Combining these uncertainties with the statistical errors (12 to
20%) gives the results shown in Table 111.3.4 (with total uncertainties
typically less than 30%). While the uncertainty may seem large, it does
not significantly change any of the conclusions made here. The depend-
ence of the temperature given by equation (1.1) on the ratio is very
slow in this neighborhood. For instance, increasing the ratio of the
populations of the 7.456 MeV state to the 0.478 MeV states in ’Li from
0.24 to 0.31 (a 301 increase) only increases the temperature from 2.8 to
3.1 (an 111 increase). To reflect a temperature of 5 MeV, this ratio

would have to be 0.743, more than twice as large as observed.

CHAPTER IV: DISCUSSION

IV.1 Fragment Moving Source Fits

For each isotope identified, the kinetic energy spectra from
each angle were fit by a moving source model with one single parameter
set, as described in Chapter III. This is commonly done [e.g. Aw80,
Aw81a, Aw81b, Aw82, Ch86b, Fi84, Fi86, P085a, He78, He82, We84], and it
is done here for two reasons: one, so this data would be easily com-
parable to other such measurements, and two, because it provides a
reasonable parameterization of the data. It should be stressed that
this is only a parameterization and the concept of a single moving
source with a unique temperature is not to be taken literally. A more
plausible description is that this source represents an ensemble average
of sources with a continuum of velocities and temperatures [F186,
8187b]. Chitwood et al. [Ch86b] show three models with distinct physi-
cal differences that can fit this type of data equally well over this
angular range. The fit parameters depend strongly on the model used,
with cross sections differing by as much as a factor of two [Ch86b].

The values observed here are entirely consistent with both pre-
vious measurements [11084, M085] and predictions based on similar
reactions [He84, F186, Ch86b]. As mentioned previously, the resulting

parameters are fairly independent of the isotope considered. This fact

57

58
is one of the primary motivations for a thermal model. However, any
such model could have systematic errors which affect each observed slope
identically and which would change a set of self-consistent temperatures
into a different yet still self-consistent temperatures. For example,
thermal models generally ignore rotational energy. This energy is fixed
by angular momentum conservation, and should not be treated ther-
modynamically. Secondly, the treatment of the Coulomb shift is fairly
critical. Each different way of estimating this quantity produces a
different set of self-consistent temperatures. (This correction is at
best an estimate. The magnitude is generally unknown, unless the target
residue is detected. Even then, a two body process must be assumed).
While one method will usually produce the lowest value for x’, there is
some uncertainty in the significance of that result. The dependence of
x2 on the Coulomb shift is most sensitive to the shape of the spectrum
near the peak which is due to a combination of effects including the
Coulomb barrier. However, this is also usually quite near the lower
threshold of typical silicon detectors, particularly for the heavier
fragments. There is, naturally, always a question of whether the shape
there is due to a change in the detector efficiency near its threshold.
For these reasons, the kinetic energy slope parameter is best inter-
preted as being related to the temperature but not necessarily equal to
it. (Certainly, for the same method of determining the fits and for the
same detector, a higher slope parameter implies a higher temperature).
In this data, we have inclusive spectra at only 3 angles (50°, 70°, and
90°) over a limited angular range (40° in the lab). The fits to this
data are not to determine the moving source parameters but to show con-

sistency with fits to previous measurements. Finally, it should be

59
noted that the fits to the 7Li spectra (at both E/A=20 and 35 MeV) have
the largest value for x2. This can be attributed to the contamination
of these spectra by (1 pairs from the decay of 8Be [8186]. The spectra
of (1 pairs has a different shape due to the geometric efficiency for
detecting the coincident pair (see Appendix A for a detailed

explanation).

1V.2 Neutron Kinetic Energy Spectra Fits

IV.2.1 Two-source Moving Source Model - Source #1

The spectral shape of neutrons in coincidence with intermediate
mass nuclei emitted at 50°, 70°, and 90° from the reaction of both 20
and 35 MeV/A ”N on Ag clearly suggests two moving sources. For E/A<5
MeV, neutron spectra can be parameterized as being emitted from a single
moving source [H179]. For greater bombarding energies, another process
of neutron emission, which can be characterized by a second moving
source, is observed [Ga71]. For the present data, a two-source moving
source fit provides an excellent parameterization (x2 typically less
than 1.3) in terms of the source velocities, the associated neutron mul-
tiplicities, and the slope parameters ("temperatures"). Unlike the
charged particle data, no Coulomb shift is necessary in these fits.
While two moving sources provide an accurate description, a third source
leads to ambiguous results. This was demonstrated by Holub et al.
[H086] for very similar data with three-source fits. In the present
work, the slower source source has a velocity of about 65% of the center
of mass velocity for E/A=35 MeV and 80% for E/A=20 MeV (or 7 to 91 of

the beam velocity), while the faster source has a velocity slightly less

60
than half the beam velocity for each energy (actually about 35% of the
beam velocity).

The mechanism responsible for the emission of neutrons from the
slower source is certainly better understood than for the faster source.
For sufficiently low beam energies (E/A<5 MeV) emission from this slower
source is observed exclusively [Pe77, Ey78, Ge78, H178, We78b, H179].
At those energies, the projectile and target form a compound nucleus
(for central collisions) which de-excites via neutron emission (among
other processes). The compound nucleus is sufficiently long lived for
the following to occur. First of all, no nucleons escape before the
formation, so all of the beam's energy and momentum is transferred to
the compound system. Secondly, the energy is distributed sufficiently
throughout all of the nucleons in, the system such that statistical
descriptions are accurate. To that extent, the system has thermalized
or reached equilibrium. The velocity obtained from moving source fits
of the observed neutron spectra is the center of mass velocity. The
slope parameter obtained from such fits will be related to the compound
nucleus temperature by a factor of 12/11 [Le59]. (The temperature of
the compound nucleus is before any neutron emission, and hence before
any cooling. For multiple neutron emission, the typical sampled neutron
is emitted after some cooling has occurred, and hence the slope
parameter will be reduce by some amount. To get the original tempera-
ture, the slope parameter must be multiplied by 12/11 [Le59]).

As beam energies are increased beyond 5 MeV/nucleon to the
levels studied here, this process evolves into a slightly different

process. Less than all of the nucleons combine to form the resulting

61
compound system. This process is called incomplete fusion, and the com-
pound system that is formed is referred to as the target residue. The
target residue is not unique; the number of nucleons involved will be1a.
finite distribution about some average, reflecting the variations in im-
pact parameters. Since some of the nucleons do not participate in the
incomplete fusion, some of the momentum and energy from the beam will be
"lost". The velocity of the target residue is determined by the center
of mass momentum minus the "missing momentum". Similarly, the tempera-
ture of the target residue is determined by the energy available iJi‘the
center of mass, minus that carried off by other particles. This is con-
sistent with what is observed for the slower of the two moving sources.
At each beam energy, the source velocity is somewhat less than the cen-
ter of mass velocity, indicating incomplete momentum transfer from the
beam. The lower beam energy is closer to energies at which compound
nucleus reactions are observed, and the target residue velocity observed
in that case is closer to the center of mass velocity than for the
higher beam energy. An increase in the beam energy from 280 MeV to 490
MeV would correspond to a 32% increase in the temperature based on the

simple equation applicable to a Fermi gas:
E = a T2 (IV.1)

(where E* is available excitation energy, a is the level density, and T
the temperature), but only a 20% increase is observed for typical values
found in Table III.3.1 and III.3.2. This again suggests that an in-
crease in the beam energy corresponds to a smaller fraction of that

energy being transferred to the target residue. So this source is

62
similar to the compound nucleus and can be readily understood in that
framework.

The associated neutron multiplicities observed for the target
residue source are consistent with those observed by Remington et al.
[Re86], who measured the multiplicities for neutrons in coincidence with
intermediate mass fragments (IMF's) observed at forward angles (7° to
30° in the lab) from the reaction of "‘N+“5Ho at E/A=35 MeV.
Specifically, the "target-like source" multiplicities for "high energy"
fragments from that work should be considered. The Remington data
clearly exhibit an increase with increasing lab angle. Extrapolating to
50° would result in associated multiplicities of around 10, slightly
higher than those reported here for reactions at E/A=35 MeV (typically 6
to 7). The multiplicities reported here do not show any dependence on
the lab angle of the coincident IMF. The conclusion is that this de-
pendence ends somewhere between 30° to 50°, where the maximum value is
reached. In that sense, an IMF at a large lab angle (025W) is a good
indication of a central collision. Additionally, no left-right asym-
metry (i.e. difference between the associated multiplicity for neutrons
on the same side of the beam as the coincident IMF and that for neutrons
on the opposite side of the beam as the coincident IMF) is observed.
This is consistent with what is observed for strongly damped projectile
like fragments in similar reaction [Ca85, Ca86, Re86], in contrast to
what is seen for quasi-elastic projectile-like fragments. This is
evidence that an IMF observed at a large angle is a good trigger for
central collisions. In addition, recoil effects [Ca86] are not going to

be pronounced, since the coincident IMF is only a small fraction of the

63
total mass and momentum, and is not a strong trigger for the reaction
plane or the target residue recoil.

Finally, by comparing the multiplicities from the two 0=50°
detectors (one in the plane of the neutron detectors, ¢=0°, and the
other at ¢=90° with respect to the plane determined by the neutron
detectors) we can determining the out-of—plane anisotropy,

d0 0 d0 _ 0
A2 = ammo ) / (70411-90 )] — 1. (1V.2)

For both E/A=35 MeV and E/A=20 MeV data, A2=0.2(1) for the target
residue source. This anisotropy greater than zero indicates one of the
limitations of the moving source model. The description of the neutron
kinetic energy spectra given by equation 111.3 assumes isotropic emis-
sion. The observed anisotropy indicates that there is actually a
preferred plane of emission. Actually, one would expect emission to oc-
cur preferentially in the plane perpendicular to the angular momentum
vector of the system. The observed anisotropy reflects not only the
strength of that preference (which should be determined by the magnitude
of the angular momentum relative to the emission temperature) but also

the degree to which the observed IMF determines the reaction plane.

IV.2.2 Two-source Moving Source Model - Source #2

Typically, the process that is parameterized by the faster
source is described as non-equilibrium or pre-equilibrium (PE) neutron
emission [Ga71, H179]. Pre-equilibrium neutron emission occurs in the
early stages of formation and prior to the thermalization of the target

residue. While this process has been observed for some time, it is far

64

from understood. Several distinctly different models have been sug-
gested to explain this process [0e77, Gr77, We77, 8080, 8185], each
meeting with limited success. However, the moving source parameteriza—
tion has been quite successful at describing the observed spectra.
Typically, such a moving source has a velocity parameter slightly less
than half of the beam velocity. This suggests that such emission occurs
early in the collision process, specifically, after each projectile
nucleon has undergone only a single nucleon-nucleon collision
(accounting for the velocity equal to 1/2 of the beam velocity).

In the framework of these coincidence measurements, the impor-
tance of the PE neutron source is emphasized by the similarity between
those fit parameters (given in Tables III.3.1 and III.3.2) and those for
the intermediate mass charged particle inclusive spectra (given in
Tables 111.2.1 and III.2.2). Indeed, considering the uncertainty in the
parameters due to the Coulomb shift, the parameters are similar to sug-
gest they are parameterizations of the same moving source. (However,
since this is just a model that parameterizes the data, it is not pos-
sible to conclude that the same physical process is responsible for the
emission of both these neutrons and intermediate mass charged
particles). In the discussion of the de-excitation of these inter-
mediate mass fragments via final state interactions, only the PE
neutrons (not the sequential neutrons from the target residue) can play
a role. The model assumes a single thermal source for the fragments and
the neutrons, which can then only be the PE neutron source. Secondly,
the neutrons from the target residue occur in a sequential process, and

could not all be available for final state interactions with a single

65

intermediate mass fragment (the time of emission is too long). This
process (final state interactions) is discussed later in this chapter.

The associated PE neutron multiplicities for the E/A=35 MeV data
(given in Table III.3.1) are consistent with predictions by Fields et
al. [F186] from associated proton PE multiplicities from a very similar
reaction (”S+Ag at E/A=22.5 MeV). Again, as with the neutrons emitted
from the target residue, no left-right asymmetry is observed. For the
E/A=35 MeV, Az=0.5(2) while for the E/A=20 MeV data, A2=0.4(2) for the
PE source. This anisotropy is greater than that observed for the target
residue source. Qualitatively, this is predicted by the theory of
Ericson and Strutinsky [Er58] which says that the out-of-plane
anisotropy should increase with a decrease in the moment of inertia of

the source.

IV.2.3 Harp-Miller-Berne Model

The Harp-Miller-Berne model (HMB) as modified by Blann [8181]
for heavy-ion reactions, predicts the time evolution of the system with
the Boltzmann master equation. The model considers the
target+projectile system in terms of single particle occupation prob-
ability densities for the total excitation energy available. For a
given number of initial degrees of freedom, the model lets the system
relax via either internal nucleon-nucleon scattering or particle emis-

-23 s). The model can then

sion over finite time steps (At=2.1X10
predict the observed emission after any number of time steps. In the
simplest model, the number of initial degrees of freedom, or exciton

number no, is equal to the number of projectile nucleons, Ap [8181].

66

Other descriptions suggest that no should equal Ap+3, to approximate ef-
fects due to collective degrees of freedom [8181, 8185, H086]. In
addition, empirical results from some works have suggested an energy de-
pendence for no [Aw82, H083, H086]. The exciton number is primarily
responsible for the shape of the energy distribution predicted by the
HMB model [8181]. The overall normalization is determined by the in-
tranuclear transition rates, which are fixed parameters in the model
[8181].

Since the HMB model is a phase space calculation, it only
predicts the neutron energy distribution, g—g. The prediction does not
depend on the fragment with which the neutrons are in coincidence. From
the results shown in Tables III.3.1 and III.3.2, the neutron moving
source fit parameters do not depend strongly on the coincident isotope.
For that reason, neutrons associated with a specific fragment (’Li is
chosen as it has the best statistics) will be compared directly to the
in terms of the moving

do
dEdQ

source fit parameters. Integrating that equation over sol id angle, d0,

HMB model predictions. Equation 111.3 gives

gives [H179]:

d0 M. 2/£—. E

2
58 = Z W exp[- (8+5i )/1<Ti ] x Sinka 1 ). (IV-3)
i=kT1

 

Putting the fit parameters for neutrons in coincidence with ’Li
(averaged over the 50°, 70°, and 90° in-plane fragment angles) from
Table III.3.1 (including the errors on the parameters) into the above
equation for discrete energies (E) gives the points plotted in Figures

IV.2.1. (for E/A=20 MeV) and IV.2.2 (for E/A=35 MeV). It is important

67

E /A=20 MeV

l I I

1.000 — 0.2 x 10-21 .......... -«

2.0 x 10"“1 — — — —
4.0 x 10'”1

 

 
 
   
 

_

 

0.100 1

0.010 4

 

 

 

 

  
   
 

 

T \

> ) ¢>\\

g 0.001 1- 14 Excitons ”-

v 1 1

Lil 1.000 " -

"U a) 0.2 X 10'31 ..........

\ 2.0x10"21-———

2 0.100 _ 4.0 X 10-21 —
0.010 P —

M>

0.001 1- 17 Excitons
1 1

0 20 40 60
Energy (MeV)

 

 

 

 

 

Figure IV.2.1 Neutron energy distribution from moving source model
(representative points plotted) compared to that from Harp-Miller-Berne
Model (lines) for E/A=20 MeV.

68

E/A=35 MeV

l l I

0.2 x 10-31 ..........
1'00 — 2.0x10"an ——__ '—

 

  
   

 

4.0 x 10““

 

H
O
O

 

dM / dE (MeV—1)

FD
p_a
O

 

.0
O
H

17 Excitons

 

 

l J I

O 20 4O 60
Energy (MeV)

Figure IV.2.2 Neutron energy distribution from moving source model
(representative points plotted) compared to that from Harp-Miller-Berne
Model (lines) for E/A=35 MeV.

 

69

to note that while the normalization of the moving source model is a fit
parameter, the normalization of the HMB model is absolute, as plotted.

Generally, the agreement between the moving source model and the
data is excellent (for each type of coincident IMF, for each IMF angle,
and for both beam energies). For convenience, the HMB model is compared
to the moving source model, rather than the data. (The moving source
model can easily be integrated over solid angle to obtain the energy
distmdlnltion, which is predicted by the HMB model). As stated earlier,
the most naive approach suggests that n°=Ap, while a first change from
that might be nozAp+3. Calculations based on these two choices are
shown in Figures IV.2.1 (for E/A:20 MeV) and IV.2.2 (for E/A=35 MeV).
In each figure, the HMB model predictions are shown for three time
slices in the reaction: t=0.2, 2.0, and 4.0 x 10“21 seconds after the
collision. Considering primarily the high energy end of the neutron
spectrum, the best agreement between the two models (and hence between
the HMB model and the data) occurs for n°=17 (=Ap+3) for the E/A=35 MeV
data. For the E/A=20 MeV data, it is not clear which value, no=14 or
no=fr7, is better, but these values seem to provide reasonable limits on
the exciton number. Certainly this range of variation in the exciton
number is sufficient to describe all of the data presented here.

These results contrast somewhat to those presented in Refs.
Aw82, H083, and H086. In their paper on light particle emission from
“0+"'Au reactions at 140, 215, and 310 MeV, Awes et al. report that to
describe the proton spectra, exciton numbers of 18, 25, and 30 must be
assumed for the three beam energies, respectively [Aw82]. In additflxni,
in both H083 and H086, agreement between the HMB model and the neutron

data could be obtained only with arbitrary normalizations. In addition,

70

Holub et a1. summarize what is described as an energy dependence of no.
The dependence is given as a function of (Ecm—Vc)/u, where Ecm is the
center'of mass energy, V0 is the Coulomb barrier, and u is the reduced
mass. For the present work, this value is 16 and 31 MeV/nucleon for
E/A=20 MeV and E/A=35 MeV, respectively. These results support the
statement in 8086 that for (Ecm-Vc)/u220 MeV/nucleon no is constant at
roughly Ap+3. However, based on the E/A=20 MeV data where
(Ecm-VC)/u=16, the present work does not support the observation of a
pronounced rise in no above Ap+3 for 55(Ecm-Vc)/u520 MeV/nucleon. In
the present work, no energy dependence of no is seen beyond a possible
rise from no=Ap to no=Ap+3. In both that respect and the overall nor-
malization of the HMB predictions, the HMB model appears to agree with
the data very well.

Finally, the HMB model predicts the time evolution of the sys-
tem. The predictions given by this model are entirely consistent with
the two-source moving source model and more quantitative. From Figs.
4.2.1 and 4.2.2, it can be seen that the PE component of the evaporation
occurs entirely within the first 0.2x10-21 3. 0n the other hand, it
takes 10 to 20 times as long for the target residue to reach equi-
librium. This reinforces the moving source model description of the PE:
neutron emission being very prompt, and the target residue emission
being of a compound nucleus like sequential nature (hence it occurs over

a much longer time span).

71
IV.3 Final State Interactions

One mechanism previously put forth to reconcile the low tempera—
tures reported in Refs. M084, M085, and 8186 is cooling via final state
interactions [8084b]. Fragments emitted in excited states can be de-
excited by interactions with other simultaneously emitted fragments,
which would lead to a low observed excited state population. In his es—
timate of this effect, Boal assumes the 1Li coincident fragment
multiplicity has the equivalent cross section of 20 neutrons [8084b].
Based on the neutron multiplicities reported in this thesis and light
charged particle multiplicities reported for a similar reaction [F186],
a better estimate of the effective crOSS section is possible.

In his paper on final state interactions [8084b], Boal addresses
the de-excitation of ’Li from its first excited state (0.478 MeV) via
collisions with other nuclei being emitted from the same thermal system.
These de-excitations will result in a low apparent temperature based on
observed excited state populations. In comparing the observed tempera-

11
ture, T , to the actual temperature, To, Boal writes:

*
T A“ '1 1
i .-. { #5121} /3, (1V.4)

where A is related to the spatial extent of the expanding nucleon gas,
specifically,

1.2xA1/3

l5

 

m, (1v.5)

Elm

72

u is the 7Li-n reduced mass,

 

where m is the nucleon mass, A is the equivalent number of neutrons in
the gas, and 0 is the inelastic cross section for n+"Li(0.478) for
neutrons in the 1/2 to 15 MeV region.

For 32S+Ag at E/A:22.5 MeV, Fields et al. report an associated
PE proton multiplicity of 2.0 for protons in coincidence with Li of
momentum, <PX>:820 MeV/c. (This momentum most closely resembles the
typical momentum of "Li fragments observed in the E/A=35 MeV data
presented here). Based on the similarity between that measurement and
the associated PE neutron multiplicity for neutrons in coincidence with
"Li reported here for E/A=35 MeV (1.86 given in Table III.3.1), the
charged particle multiplicities reported in F186 are probably close to
the corresponding multiplicities for this reaction. Under that assump-
tion, then, for this reaction at E/A=35 MeV the number of coincident
light fragments is 6, and the total associated PE baryon multiplicity is
10. In calculating the effect of final state interactions, Boal used
the significantly larger values of 17.6 and 28.4 for estimates of the
number of coincident fragments and the total associated baryon multi-
plicity at E/A=35 MeV [8086b].

As given in the previous chapter, at E/A=20 MeV the associated
PE neutron multiplicity is typically 1, half the typical value at E/A=35
MeV. Under the assumption that all associated PE light fragment multi-

plicities have the same dependence on beam energy, the number of

73
coincident light fragments would be 3, and the total associated PE
baryon multiplicity would be 5 for the E/A=20 MeV case.
To obtain the values of 17.6 coincident light fragments and

28.4 coincident baryons, Boal used as his estimates:

Mp + Mn 2 12.7
Md: 1.4
Mt: 1.]
M = 2.1]
a
If 0p, on, 0d, at, and 00 are the inelastic cross sections for scatter-

ing p, n, d, t, and a respectively from 7Li(0.478) then

> - x
Mpop+Mnon+Mdod+Mtot+Maoa - (Mp+Mn+Md+Mt+Ma)°n - 17.6 On (IV.7)

under the assumption 0p, 0d, 0

10f ejectiles associated with a 7Li fragment in the estimate Boal used).

t’ and 0a 2 on. (17.6 is the total number
Similarly, it seems apparent that when the number of baryons is con—

sidered,

< ..
Mpop+Mnon+Mdod+Mtot+Maoa - (Mp+Mn+2Md+3Mt-I-4Ma)on — 28.4X0n (IV.8)
(28.4 is the total number of baryons in the ejectiles associated with a

7Li fragment in the estimate Boal used). So Boal assumes that

Mpop+Mnon+Mdod+Mtot+Maoa = 20X0n (IV.9)

(i.e. A=20 where A is the effective number of coincident neutrons),

which relies on 0p, 0 t’ and 0 2 0 .

d’ 0 a n

74
Putting in numerical values gives: A2 = 2.88 A2/3 mb, which im-
plies that
11

I. _ { (2.88 mb)=n~(7/8) }1/3 A.2/9
To ' (500 mb)2

= 0.1u1 A'2/9. (IV.10)

For Boal's assumption of A:20, this gives, T« = 0.073 x To. Then for
To:8.6, T*=0.62, and for To:40, T*=2.9, both predictions made by Boal.
However, the multiplicities Boal used were estimates and we can now use
better values. For E/A:35 MeV,

M +M :LI.O

p n
Md : 0.5
Mt = 0.3
M =1.2

Cl

[F186, 8187]. Then, the number of ejectiles is 6 and the number of
baryons is 10.7. So 6$AS10.7. Suppose A=8. Then,

T*=0.141(8)-2/9

XTo=0.089XTo, which is not significantly different from
the result obtained by Boal. Furthermore, for E/A=20 MeV, the as-
sociated multiplicities are reduced by half. This implies that 3SA§5.3.
If we choose A=4, then T*=0.10><To which is still not significantly dif-
ferent. In fact, if we have only one coincident ejectile (on average)
then, T*=0.14XTo. For final state interactions to be negligible, TI/To
~ 1 which occurs when Az1.SX10-u. This shows that Boal's model of cool-
ing is very insensitive to the associated multiplicities. If the model
is correct, significant cooling must always be present. Essentially,
these associated multiplicities do not change the conclusions made in

8084b. However, as suggested in M085, Boal's model of the cooling rep-

resents a limiting case.

75

IV.4 Sequential Decay

Charged particle decay measurements in reference 8186 show that
the bound excited state populations increase slightly with increasing
beam energy. This trend is contrary to the sequential decay argument
previously put forth to explain the apparent low temperature [M085,
Ha86]. At lower beam energies, a lower temperature is expected, which
corresponds to lower populations of particle-unstable states that can
decay to ’L1 or 7Be, which will result in less feeding of the ground
state. If this feeding were the sole cause of the discrepancy between
the excited state production temperature measurements and the kinetic
energy slope parameter, its effect would be reduced at lower beam
energies, and the result would be higher observed temperatures at lower
beam energies. Nevertheless, there is certainly some feeding which oc-
curs, as evidenced by the correlated neutrons, and it is possible to
give quantitative estimates of the effects.

In order to determine the extent to which feeding from sequen-
tial decay reduces the observed fractions reported in Refs. M084, Mo85,
and 8186, we need to estimate the total feeding from the present
measurements of the feeding from a single decay channel. An attempt at
this can be made with the quantum-statistical model of Hahn and Stocker
[Ha86]. The calculation assumes an initial statistical equilibrium dis-
tribution from infinite nuclear matter which is determined by the
binding energy of the isotopes, including the excited state populations
(using all known states). Subsequently, the final isotope distributions

are calculated using all known decays and their branching ratios. The

76

model assumes the temperature, kT, the break-up density, p, and the
initial proton to neutron ratio, Z/N, for the system in equilibrium are
known. The results are relatively insensitive to the break-up density
over the range investigated (10% to 150% normal nuclear matter density,
po). The calculations reported here are all for p=po/4. At this den-
sity it is plausible to assume nuclear interactions are negligible. In
choosing the proton to neutron ratio, we assumed that the system con-
sisted of the 14 beam nucleons, plus 14 target nucleons which form a
"hot-spot". Based on the proton to neutron ratios of the constituents,
this provides 13 protons and 15 neutrons (Z/N=0.88). The source
velocity extracted from moving source fits of the inclusive particle
spectra is roughly half the beam velocity, which suggests that this pic-
ture is appropriate. The isotope diStribution is the most sensitive
test of Z/N, and Z/N=13/15 reproduces the L1 isotope distribution to
within 30 percent for E/A:35 MeV and to within 15 percent for E/A=20 MeV
(for kT=3 MeV and p/po=0.250). Table IV.4.1 compares the Li isotope
distributions calculated for three values of Z/N to the experimental
values.

For temperatures above 2 MeV and the other parameters in the
ranges specified above, the model predicts a large amount of feeding
(from 30 to 70%) to the ground states of the Li and 8e isotopes. The
feeding is significant in that the predicted fractions of excited state
populations for some low-lying particle bound states are brought close
to the observed values [M084, M085, 8186] (as shown in Table IV.4.2).
While the model does not agree with the data in every case, these and
similar calculations [Xu86] still suggest that feeding may contribute

significantly to the discrepancies in the reported temperatures. The

77

TABLE IV.4.1
(Yields normalized such that the ’Li yield equals 1).

L1 isotope distributions.

Quantum-Statistical Model Predictions

 

 

 

 

 

(with kT=3.0 MeV and p/po=0.250) Experimentala
IMF Z/N=13/15 Z/N=19/23 Z/N=54/68 E/Az35 MeV E/A=20 MeV
111 0.70 0.50 0.39 0.76(2) 0.708(9)
7Li 1.00 1.00 1.00 1.00 1.00
111 0.13 0.18 0.21 0.183(5) 0.151(2)

aExperimental values are for a fixed energy range in the lab at 50°.

TABLE IV.4.2 Fraction of fragments in an excited state for several

Y-emitting states.

Quantum-Statistical Model

 

 

 

 

 

 

bThese values from Refs. M084, M085 and 8186.

(with Z/N=13/15 and p/poz0.250) Experimentalb
State kT:2.0 kT=3.0 kT=4.0 kT=5.0 E/Az35 MeV E/Az20 MeV
‘Li(3.0) 0.04u 0.048 0.056 0.065 0.01(2) unknown
711(0.5) 0.228 0.199 0.186 0.183 0.171(24) 0.079(24)
a11(1.0) 0.271 0.269 0.262 0.255 0.051(47) unknown
’Be(0.4) 0.273 0.257 0.240 0.230 0.183(29) 0.083(22)

78
present data provides an independent check of this. Since, for each
initial parameter set, the model predicts (among other things) the num—
ber of 'Li initially in the 2.255 MeV excited state, 7L1 initially in
the 7.456 MeV excited state, 7L1 in the final distribution, and ‘L1 in
the final distribution, we can readily compare the predicted feeding
from specific branches to that observed. Figure IV.4.1 shows the
predicted feeding to the 7[.1 yield from the neutron decay of the 2.255
MeV state in °Li. (Note, these predictions are not peculiar to Hahn and
Stécker's model, as comparable results are predicted by a micro-
canonical ensemble model [Fa83]). A comparison of the feeding of 7%
observed for a single decay channel for E/A=35 Mall to the calculation
shown in Figure IV.4.1, indicates that the temperature should be about 4
MeV. Then with a temperature of 4 MeV (and the other model parameters
unchanged) the model predicts that the total feeding to the 7Li yields
from all known decays is 55 percent. That is, 55% of the observed 7L1
yield is from particle decay of other nuclei. Furthermore, the model
predicts significant feeding to the first excited state (26%). The
0.478 MeV excited state to ground state population ratio, R, can be ob-
tained from the observed excited state fraction, fex’ and the observed
fraction in any Y-emitting states, fY’ including feeding to the ground

state, F83, and to the excited state, Fex’ from the relation:

f
ex

l-f‘Y-ng

R = x (1 - Fex). (IV.11)

Then, the bound excited state fraction of 0.17110.024 from Ref. 8186
gives the ratio of the populations of the first excited state to the

ground state of 7L1 as 0.45:0.11 which (using equation 1.1) corresponds

79

 

10

 

 

 

 

 

o 1 1 1
1 2 3 4 5

Temperature (MeV)

Figure IV.4.1 Feeding to the 7L1 ground state via the neutron decay of
the 2.255 MeV state of 'L1, as calculated by the quantum statistical
model.

80
to a temperature of 4.5:;3 MeV. Note that both feedings (0.55 to the
ground state and 0.26 to the 0.478 MeV state) were used as exact (while
they clearly are not). This temperature is then consistent with that
obtained by comparing the two excited state populations. Furthermore,
the ratio of the populations of the 7.456 MeV state to the ground state
in 7L1 reported in Table III.3.1 can be corrected for feeding in a
similar manner. (The feeding to the 7.456 MeV state of 7L1 is negli-
gible at this temperature). In that case, the corrected ratio is
0.15:0.03 which corresponds to a temperature of 3.2103 MeV. Again, no
attempt was made to include errors on the feeding values. Similarly,
this procedure can be carried out for the E/A=20 MeV data. In that
case, the observed feeding from the 2.255 MeV state of °Li to the ground
state of 7Li, 4.4(9) percent, implies a temperature of around 3 MeV when
compared to the calculation shown in Figure IV.1.1. At 3 MeV, the quan-
tum statistical model predicts 311 feeding to the ’Li ground state and
16% total feeding to the 0.478 MeV excited state of 7L1. The corrected
ratios and their corresponding temperatures for both energies are shown
in Table IV.4.3. Considering that there is a large uncertainty in the
total feeding, it is reasonable to say that for E/A=35 MeV, all three
temperatures obtained from the populations of levels of 7Li and the ex-
tent of the feeding to the “’Li yield from the 2.255 MeV state in “L1
provide consistent temperatures. For the E/A=20 MeV, the observed level
of feeding indicates a temperature of about 3 MeV; the population of the
7.456 MeV state of 7Li compared to both the ground state and the 0.478
MeV state indicates a temperatures of 2.2 and 3.3 MeV, respectively. 0f
the 7Li measurements, only the population of the 0.478 MeV state of 7Li

relative to the ground state still (after

81

TABLE IV.4.3 Excited state ratios, R, corrected for feeding via

equation IV.11 and their corresponding temperatures, kT, according to

equation 1.1.

 

 

 

 

 

 

E/A=35 MeV:
States Compared R (ratio)
711(0.u78)a to ’Li(g.s.) 0.45(11)
7Li(7.456) to ’Li(g.s.) 0.15(3)
E/Az20 MeV:
States Compared R (ratio)
711(0.478)a to ’Li(g.s.) 0.1111)
7Li(7.456) to 7L1(g.s.) 0.047(12)

aPopulation of Y-emitting state from Ref. 8186.

kT (from Eq. 1.1)

+00

-3..3
3.2(3) MeV

4..5 Merv

kT (from Ego 1.1)

+0.08
—0.07

2.2(2) MeV

0.32 MeV

82
corrections for feeding) indicates a low temperature (kT<0.5 MeV).
Considering how rapidly the predicted feeding changes as a function of
temperature in this region and the large uncertainties in the correc-
tions, it is possible that this discrepancy is due to an error in

estimating the effects of the feeding.

CHAPTER V: SUMMARY AND CONCLUSIONS

V.1 Summary

Kinetic energy spectra were obtained for neutrons in coincidence
with intermediate mass fragments observed at 50°, 70°, and 90° in the
lab from the reaction of ‘“N+Ag at both E/A:35 MeV and E/A=20 MeV.
While there have been numerous previous neutron coincidence experiments
[Hi79, Ga83, H083, H184a, Ca85, Ca86, De86a, De86b, H086, Re86], these
were limited to measuring neutrons in coincidence with either
projectile-like fragments, fission fragments, or evaporation residues.
The present measurement represents the first time that neutrons have
been measured in coincidence with intermediate-mass fragments observed
at large angles.

These neutron kinetic energy spectra were fit with a two-source
moving source model [Ja83]. This model provided an excellent
parameterization of the data in terms an associated multiplicity, an ef-
fective temperature parameter, and a source velocity for both a target
residue source and a pre-equilibrium source. The associated neutron
multiplicities for neutrons in coincidence with 6L1, 7L1, aLi, 7Be, ’Be,
‘°Be, ‘°B, and “8 fragments are reported in Tables III.3.1 and III.3.2.
For E/A=35 MeV, the target residue multiplicity is typically 6 to 7

(depending primarily on the type of fragment with which the neutrons

83

84

were in coincidence) while the PE multiplicity is about 2. For the
E/A=20 MeV data these values are 4 to 5 and 1, respectively. No depend-
ence is seen on fragment angle for angles greater than 0=50°. No
preference is seen for the neutrons to be emitted either on the same
side or on the opposite side of the beam as the observed fragment. An
out-of-plane anisotropy is observed. It is approximately 20% for the
target residue source and about 50% for the PE source. The measured
multiplicities are used to replace estimates used by Boal [8084b] to
determine the effect of final state interactions on bound excited state
population measurements. While the observed multiplicities are sig-
nificantly different than those estimates, the model is fairly
insensitive to these values in this region, and the correction to its
effects are negligible.

A physically significant interpretation of the source velocities
and effective temperature parameters can be made. For the target
residue source, the velocities are 65% and 80% of the center of mass
velocity for E/A=35 MeV and E/A=20 MeV, respectively. The corresponding
effective temperature parameters (from the fits) are 3 and 2.5 MeV.
These values are typical of what would be expected for incomplete fu-
sion. For the PE source, the velocities are approximately 35% of the
beam velocity for both beam energies. The corresponding effective tem-
perature parameters are approximately 12 and 10 MeV. These values are
are similar to values obtained for particle inclusive measurements of
fragments from 2:1 to 2:7.

Finally, by integrating the moving source model's analytic ex-
pression for the neutron spectra over solid angle an expression for the

neutron energy distribution, g—g, is obtained. With the above moving

85

source fit parameters, this energy distribution is then readily compared
to predictions made by a Harp-Miller-Berne Exciton Model as modified for
heavy ion induced reactions by Blann [8181]. Reasonable agreement is
obtained for exciton number, no, equal to either the number of beam
nucleons, Ap, or for no=Ap+3. The agreement is both in the shape of the
energy distribution (i.e. its energy dependence) and in the overall nor-
malization (i.e. associated multiplicity). This is in contrast to
several similar works [Ga81, Aw82, H083, H086].

In addition to measurement of the associated neutron multi-
plicities, quantitative observations were made of several particle
unbound excited states in the intermediate mass fragments using a tech-
nique developed by Kiss et al. [K187]. Specifically, the neutron decays
of the 7.456 MeV excited state of ’Li, the 2.255 MeV excited state of
“Li, the 7.371 MeV excited state of ”Be, the 3.89 MeV excited state of
“Be, and the 3.388 MeV excited state of ”B were observed. These ob—
servations were used to determine the population of the excited state
relative to the ground state and any existing bound excited state
population measurements, where possible. By assuming a Boltzmann dis-
tribution of excited state populations, these measurements were used tx>
obtain temperatures. Neglecting the effects of sequential decay on such
measurements [M085, Ha86], the extracted temperatures were around 2 or 3
MeV. Finale, while quantitative results were not possible, it appears
the decay of the 1.69 MeV excited state of ’Be has been observed.

In addition to interpreting the unbound excited state population
measurements in terms of temperature, they are also measurements of
feeding due to sequential decay. This mechanism is considered to sig-

nificantly alter the observed population ratios, especially for ratios

86

involving the ground state or states of small excitation energy [M085,
Ha86, Xu86]. This thesis reports the measured extent of feeding from
sequential decay for a system previously used in a bound state tempera-
ture measurement [8186]. This was done via a measurement of the neutron
decay of the 2.255 MeV excited states of ‘Li nuclei observed from the
reaction of "'N+Ag at E/A=20 and 35 MeV. This decay feeds the ground
state of 7Li by 7% for E/A=35 MeV and by 41 for E/A=20 MeV. These
measured feedings were compared to predictions made by Hahn and
Stocker's Quantum Statistical Model [Ha86]. Quantum-statistical cal-
culations predict that the 2.255 MeV state of 8Li will account for 10 to
20% of the total feeding to the ground state of 7L1. The observed de-
gree of feeding via that channel (71 and 4%) clearly indicates that
sequential decay can significantly alter the observed population of
states, particularly that of the ground state. The results are used to
estimate the temperature (4 and 3 MeV are the predictions for the two
beam energies) and to estimate the total feeding to the 7Li ground state
(551 and 311, based on the estimated temperatures) to correct the ex-
cited state population temperature measurements. In most cases, the
corrected excited state population measurements are significantly higher
(than the uncorrected version) and are all somewhat self consistent.
The resulting temperatures are also consistent with charged-particle
correlation measurements [P085a, Ch86a]. In this way, some of the
originally observed discrepancies are explained.

In order to compare ’Li excited state production to that of the
ground state, the “’Li energy spectrum is corrected for contamination by
pairs of 0 particles from the ground state decay of °8e [8186] . This

correction is based on a previous measurement for the same reaction (at

87
E/A=35 MeV). For the E/A=35 MeV data, the contamination is about 20%,

while it is about 131 for the E/A=20 MeV data.
v.2 Conclusions

An important component of heavy ion reactions in this energy

region (10 MeV S E/A S 100 MeV) has been the observation of intermediate
beam) at large angles in the lab (9»egrazing)

[Me80, We82, We84, W085, F186]. Since this is the first measurement of

mass fragments (4<A<A

neutrons in coincidence with fragments of this type, many interesting
conclusions can be drawn.

A logical comparison to make is between the results presented
here and those from neutrons in coincidence with IMF's at forward angles
(projectile-like fragments). In Re86, a definite increase in the ob-
served target residue associated neutron multiplicities is seen as a
function of IMF angle. The lack of dependence on fragment angle in the
data presented here indicates that for any given angle, the events rep-
resent a range of impact parameters. As the fragment angle is
increased, this range is biased towards more violent collisions, up to a
maximum angle. After that point, it appears the collisions are all
characterized by fairly central collisions (giving rise to the highest
average associated multiplicities). Generally, the1observed multi-
plicities are also consistent with those seen from neutrons in
coincidence with evaporation residues for similar reactions [Ho83,
H086].

The moving source model is generally successful at1describing

the energy spectra of fragments emitted from such reactions. The

88

present data are no exception, with excellent fits to the in-plane data
provided by a two source description. However, in that model the ther-
mal assumption implies that the emission is isotropic in the rest frame.
In that sense, the model is in direct conflict with the observed data.
The measured out-of-plane anisotropy proves the emission in not
isotropic. For that reason, one should be very wary of interpreting the
source parameters (particularly the source velocity and the effective
temperature parameter). As shown by Chitwood et al., the observed
parameters can vary significantly if similar models with different as-
sumptions are adopted [Ch86b]. For this particular case, a preferred
plane of emission is probably due the angular momentum of the system.
Certainly a relatively low energy intermediate mass fragment does not
determine the reaction plane as well as a fragment of larger mass and of
relatively high energy (observed at a large angle). The implication of
this is that the observed anisotropy is a lower limit. It is likely
that the coincident fragments were not as effective in determining the
reaction plane as evaporation residues could be.

For this data, the HMB exciton model also provided a good
description. Essentially, this model makes several assumptions about
the physics of the problem, and then makes predictions without any ad-
justable parameters. If the predictions match the data well, one would
hope to be able to conclude that the physical approximations are fairly
reasonable. However, recently attempted applications of the basic model
have been somewhat unsuccessful [Ga81, Aw82, H083, H086]. In order to
explore the possibilities, adjustments in the parameters have been in-
troduced [Aw82, Ho83, H086]. These include letting the exciton number

be a free parameter, generally energy dependent, adjusting the

89

intra-nuclear transition rates, and including arbitrary overall nor-
malizations to the cross section. While these may aid in describing the
data, it is not clear that any conclusions can then be made regarding
the physics. Finally, it is possible that such adjustments may not be
necessary. It may be that agreement with the data is actually being ac-
complished with offsetting adjustments. This is suggest by Blann [8185]
as the explanation for the result obtained by Holub et al. [H083] . In
particular, large values of no can be offset by arbitrary normalizations
of the cross section combined with different intra-nuclear transition
rates. However, such a cancellation of errors is more easily obtained
when observing only the PE contribution to the neutron spectrum. By in-
cluding the neutrons from both sources, the problem becomes more
constrained. The agreement obtained here with the HMB model is both for
the spectrum shape and the multiplicity. Furthermore, the model
predicts the time development of the neutron spectrum.

One application of the associated neutron multiplicities is in
calculating the effects of final state interactions on bound excited
state population measurements. Boal made such a calculation using a
relatively simple model [8084b] and estimated associated fragment multi-
plicities. The measurement of these associated PE neutron
multiplicities combined with measurements of the associated PE multi-
plicities for light charged particles for similar reactions [F186]
allowed Boal's calculation to be redone with more accurate estimates 01‘
the necessary parameters. The model is very insensitive to the multi-
plicities in this region, however, and the results are little changed.

Basically, Boal was able to conclude that final state interactions could

90

lower the observed temperatures by an order of magnitude from the emis-
sion temperature. Based on the model he used, this result remains.
However, as pointed out in M085, that model of cooling is one limiting
case. In their work, Morrissey et al. also present a model at the op-
posite limit (predicting the minimum cooling instead of the maximum).
Now that reasonable estimates of the associated multiplicities are
available a more sophisticated model would be very useful.

The second type of result presented here are excited state
population measurements. These can be interpreted as a nuclear tempera-
ture under the assumption that the distribution of nuclei in their
various quantum states is given by a Boltzmann distribution. At this
point, the temperatures obtained have no significance. Previous
measurements of this type [M084, M085, Po85b, 8186, Ch86a, $086, Xu86]
have yielded inconsistent results, both with each other and with respect
to the observed particle inclusive slope parameters from moving source
fits. Currently, significant effort is being spent in an attempt to
reconcile the various temperature measurements. With a limited amount
of data the1possibility exists that more than one solution would appear
feasible. 8y expanding the data base, it may be possible to determine a
unique solution. Quantitatively, the observed temperatures agree with
the trends observed to date. Temperatures extracted from measurements
of unbound excited state populations are consistently higher (3 to 5
MeV) than those extracted for bound excited state population measure-
ments (~0.5 MeV). Furthermore, population ratios not involving the
ground state and ones involving a state with a very high excitation
energy give higher temperatures than ratios not in these categories.

The present results adhere to these trends.

91

Generally, the largest uncertainty in the above population
measurements (and hence the extracted temperatures) is in determining
the absolute geometric efficiency of the system. In this work, the ef-
ficiencies were calculated based on the measured geometry. Under the
best circumstances this technique will always be subject to large uncer-
tainties. Ideally it would be best to measure directly the geometric
efficiency during the experiment. A technique to do this would greatly
reduce the uncertainty of the measurement.

Finally, one of the most significant results reported here is
the measurement of the feeding from sequential decay, for several
specific channels. For most of the feedings listed in Table III.3.5, no
corresponding temperature measurement exists. The exception is for the
neutron decay of the 2.255 MeV excited state in I’Li to the ground state
of 7Li. A significant portion of the observed ’Li yield comes from this
one branch. This is absolute proof that feeding from sequential decay
plays a major role in the observed population ratios (at least in some
cases). By requiring the predictions made by the quantum statistical
model [H386] to match the feeding from this one branch (by adjusting the
model parameters), the temperatures based on 7L1 populations can be cor-
rected for feeding from sequential decay from all known branches.
Generally, this proved successful. For the E/A=35 MeV data, the cor-
rected temperatures are reasonably consistent. The results are not as
good for the E/A:20 MeV data, but there are several possible explana-
tions. For one, the temperatures are very sensitive to the feeding
corrections. A change by a factor of two in the feeding can result in a

temperature change of over an order of magnitude. Secondly, there are

92

large uncertainties in the data which make accurate predictions dif-
ficult. It should be remembered that the corrected temperatures and
their uncertainties given in Table IV.4.3 do not include any uncertainty
in the model predictions. Reasonable estimates of those uncertainties
would lead to completely undetermined temperatures. The quantum statis-
tical model itself is certainly only an approximation in this energy
regixni. The model was intended to make predictions at much higher tem-
peratures (where the energy per nucleon is well beyond the binding
energy per nucleon). Considering these limitations, the results ob-
tained are quite consistent.

For the other isotopes for which bound state population measure-
ments exist (°L1, °Li, and “’Be) such a complete picture does not exist.
The only other measurement of feeding from sequential decay is from the
7.456 MeV state of “’Li to the ground state of 6Li. While the excited
state fraction predicted by the quantum—statistical model (which in-
cludes the effect of feeding from sequential decay) for any temperature
from 1 to 5 MeV is larger than that observed, there are considerable un-
certainties in both the measurement and the model predictions. In
particular, the model has not yielded particularly good predictions for
the isotope distributions (at least for the parameter ranges consider in
this paper), and there is considerable debate about the proper value of
the density parameter. In light of the sucess in describing the “’Li
system, it.is possible that the excited state populations of other sys-
tems will also be understood in terms of temperature as more data
becomes available. At this point, the validity of the temperature as-
sumptions in this area is far from settled. Hopefully, the additional

unique data reported here will help facilitate such a determination.

APPENDIX A: aBE CONTAMINATION OF 7LI SPECTRA

Recently reported measurements of the production of excited
states of 7L1 and 7Be nuclei emitted at large angles from the reaction
of "'N+Ag at E/A=35 MeV [M084, M085] indicated a slight discrepancy
(about 2 standard deviations) between the temperatures determined from
the excited state populations of these two nuclei. The fraction of the
population of the ’Li excited state indicated a temperature of 340150
keV while the same measurement for 7Be nuclei indicated 5301150 keV.
Very similar results are expected for these two mirror nuclei since they
are a mirror pair. However, this discrepancy was ignored then; the in-
teresting fact was that they both indicated temperatures much lower than
the 10 to 12 MeV expected. In a subsequent experiment [M086], the cause
of this 2 standard deviation discrepancy became a much more important
discrepancy.

Initial analysis (unpublished) of the data obtained by Morrissey
et al. indicated that for 112 MeV 1"N on C, the excited state fraction
for 7Be was roughly five times greater than that for 'Li. In M086, the
authors explain that this prevented them from including results based on
7L1 observations. The clue to solving this huge discrepancy was found
in the 7Li coincident Y-ray spectrum, shown in Figure A.1.1. In addi-
tion to the peak at 478 keV corresponding to the first excited state of
7Li is a peak at 718 keV, which happens to be the first excited state of

”B. For the reaction of 112 MeV 1"N on C, the reaction partner of

93

Counts / keV

60
50

40

30
20
10

15_

94

E /A=8 MeV

 

I I I I r I I I I I I r I I I I I I

1

.—-1

-1

-—1

“1.1....1” '
f T I I I T I 1 I I I I

 

 

 

 

12C(1‘N,7Be)19F, 7

 

 

 

l I

250 500 750 1000

Energy (keV)

Figure A.1.1 Y rays in coincidence with fragments identified as 7Li and

’Be from 1"N+C at E=112 MeV.

95
’L1 is "Ne which has no such Y ray in its decay chain. Conversely, the
reaction partner for 1“B should be ”0. Indeed, what was thought to be
1Li sometimes was actually a misidentified product from the decay of “0
which was in coincidence with ”8 and hence the Y ray from 108. (The
spectrum of Y rays in coincidence with “’8e is shown in Figure A.1.1 for
comparison).

In most cases, the identification of an isotope in a AE-E
silicon telescope is unambiguous. However, this is not true for 1Li.
In the previous measurements [M084, M085], the ’Li spectra included
misidentified “Be decay products. Ground state “Be nuclei decay into
pairs of alpha particles with a Q value of 92 keV. This low relative
energy between the 0 particles (compared to typical “8e kinetic energies
of 30 MeV) means that they will continue along trajectories almost iden-
tical to that of the initial “Be. There is, therefore, a high
probability that both 0 particles from a “Be fragment will be detected
in a single silicon telescope [W072]. As discussed in 8186, when both
of the 0 particles pass through a silicon detector, they produce a
specific ionization approximately 2% different from that of a ’Li frag-
ment, which is much less than the spread in the AE signal due to
straggling. In the reaction of "‘N+"C -> ‘°B+“0, it is very likely
that the excited “0 nuclei will break up into either two “Be or ”C+a.
In this latter case, the 12C can then break up into “Be+a. So in each
case, the “0 provides a source of “Be which will decay into 0. pairs
which are easily mistaken for “’Li. This explains how ”’8 Y-rays are in
coincidence with fragments identified as 7[.1 from the reaction "'N+C.

Also, the propensity for that reaction to give ‘°B+“0 as opposed to

96
'Li+"Ne was responsible for the fact that 0. pairs overwhelmed 1Li by
roughly 4 to 1 in the ’Li particle identification gate.

Clearly any “Be fragments which are identified as 7Li increase
the denominator of the fraction and thus reduce the inferred tempera-
ture. In the reaction of 112 MeV “'N on C, 70-90% of the particles
identified as 7Li were actually 0 pairs from “Be decay. (This result
depends on the solid angle of the silicon detectors. The results given
here are for a 25 msr detector). The size of the contamination in that
particular system made it impossible to determine accurately the number
of 7L1 particles. However, the “Be to ’L1 ratio is not so great in the
reaction of "'N+Ag at E/A=35 MeV. In 8186, measurements of the yields
of 6L1, 7L1, and ’Be fragments from the reaction of E/A=35 MeV ‘“N+Ag as
a function of detector solid angle allowed a determination of the extent
of the contamination of the “’Li spectrum by “Be decay. In that case,
only 33% of the events identified as 'Li were actually 0 pairs, and it
was possible to correct the measured excited state fraction and the
resulting temperature. The corrected values gave excellent agreement
between the temperatures extracted from 'L1 and 7Be.

Part of the experiment described in 8186 determined what portion
of the particles identified as 7Li was actually (1 pairs from “Be decays
for the reaction "‘N+Ag at E/A=35 MeV. The extent of such a contamina-
tion was determined by varying the solid angle of the silicon detectors,
since the yield of 7Li fragments detected is linearly proportional to
the solid angle while the yield of 0 pairs from “Be decay is not. This
difference is due to the fact that the alpha particles are emitted

within a cone of finite opening angle along the “Be trajectory, and

97
therefore both particles will not always enter the detector. The ob-
served "Li differential cross section is then the sum of the true 7Li
differential cross section plus a solid-angle-dependent differential
cross section of 0 pairs. This is represented by the equation:
dzo

- dzo . dzo
7 .. 7
dEdg( Llobs) 1‘ dE - —_(dEdQ L1) x dE + —dEdo(a+a) x dE, (11.1)

 

where the double-differential cross sections are of the products in

 

parenthesis, ’Liobs represents any particle which identifies as a 7Li,
2
and me is a coincidence of two 0 particles in one detector. 3E30(a+a)

has an implicit dependence on solid angle, AO, from the dependence of
the relative efficiency for detecting both 0 particles in the single
detector. This is generally less than one, due to the fact that the al-
pha particles have a finite opening angle. This relative efficiency,
EA0(E)’ is a function of the original a8e energy, E, and the solid angle
of the detector [Me74]. For a given A0, E, and 0, the angle between the
original “8e trajectory and the detector axis, a Monte Carlo calculation
was used to determine the probability, PAQ(E,0), that both alpha par-
ticles, emitted isotropically in the moving “Be frame, would enter the

detector. Then, EAQ(E) is given by the following integration:

0
211 ° .
EAQ(E) - A!) x 0 PAQ(E’G) x Sin(0) x d0, (A.2)
which was computed numerically (see the Fortran code at the end of this

appendix), where Go is the half angle of a detector with solid angle A0,

given by:

Relative a—Pair Efficiency

98

 

MSU-BO-148
1.0 I I l I I I I l I T 1
0.8 ”' “1
. 24 msr

0.6 '2
0.4 '-
0.2 —

 

 

 

l l 1 L J l l l l J l l l I I

0 20 40 60 80
8Be Energy (MeV)

.1.
100

 

.9
0

Figure A.1.2 EAQ(E) for AO=5, 9, 22, and 24 msr.

0o 2 cos-‘(1 - - . (A.3)

The results of such a calculation for the solid angles used in the
present measurement are shown in Figure A.1.2. Since 6150(8) is the
relative efficiency for detecting both 0 particles from a “Be decay,
i.e. the probability of detecting both 0 particles given the initial “Be
trajectory was within the detector's angular acceptance,

dzo _ d’0
dEdQ(0+0) - dEdQ(“8e) x €A0(E) (A.4)

 

 

must hold and can be inserted into equation A.1. By assuming the shape
of the ’Li and “Be spectrum with arbitrary normalizations m and b
respectively the resulting equation can be integrated over an ap-

propriate energy range to yield

U = m x V + b x W, (A.5)
where
-d207 .1 (12—07-
U - dEd§( Liobs) x dE, V - m x dEdQ( Li) X dE, (A.6a,b)

and

_,_ dzo
W - b x EEa§(“8e) x EAQ(E) x dE, (A.6c)

100
all of which are known. (U is a measured quantity, V and W are
calculated). At this point, U and W depend on A9. Dividing equation

A.5 by W gives:

YzmxX-I-b, (A.7)

where Y=U/W and X=V/W both depend on AD but are known quantities for any
A0 (assuming U is measured for each A0). Then by determining X and Y
for more than one A0, a linear fit will give m and b. Since m is the
magnitude of the 7Li cross section, and the shape of the spectrum is as-
sumed, the true 7Li spectrum is determined and can be compared to the
observed ’Li spectrum to determine to what extent the observed spectrum
is contaminated by the decay of “Be.

In 8186, the shape of the “Be kinetic energy spectrum was as—
sumed to be given by a Coulomb-shifted Maxwell-Boltzmann function fit to
the 9Be spectrum. Similarly, the shape of the true 7Li spectrum (with
no contamination from 0 pairs) was assumed to be given by the shape of
the “Li spectrum. Then, the values given in that paper for b and m are
relative normalizations between “Be and “8e and between 7Li (the true
spectrum) and “Li, respectively. Strictly speaking, they are only valid
for that reaction (“‘N+Ag at E/A=35 MeV) and for the kinetic energy
range observed. Particle singles data as a function of detector solid
angle was not obtained for beam energies other than E/A=35 MeV, and
therefore a definite measurement of the level of the a-pair contamina-
tion of the 7Li particles does not exist for this reaction at E/A=20
MeV. On the assumption that the mechanism for producing these fragments

does not change drastically over this energy range, and since in this

101
work the observed energy ranges are very similar (the AE and E elements
of the silicon detectors are nearly the same thicknesses), the same
values for m and b (m=1.22:0.10 and b=2.1:0.5) will be used. (In 8186,
the data for "'N+Ag at energies of E/A=20 and 25 MeV were consistent
with the same solid angle dependence of the relative yields at E/A=35
MeV, which indicates that it is reasonable to assume that the a-pair
contamination is not a strong function of beam energy). Therefore, the

true 7Li yield is "m" times the “Li yield, as given by

Y(’Li) = m x Y(“Li), (A.8)

where Y(“Li) is the yield of “Li, integrated ever the energy range of
the 7Li fragments with which the obServed neutrons were in coincidence.
Comparison of 1.22 times the “Li spectrum to the observed "Li spectrum
indicates that the latter include a contamination from “Be decay of
20(2) percent for E/A=35 MeV and 13(1) percent for E/A=20 MeV. So,
everywhere in this thesis that excited state ’Li yields are compared to
total 7Li yields, which are identified only by silicon telescopes, the
observed yield is reduced by multiplying by either 80(2) or 87(1) per-
cent (depending on the beam energy). Ground state 7Li yields, are
obtained by subtracting excited state yields from the corrected total
yield.

There is one instance where the "Li yield is not corrected. In
determining the associated neutron multiplicity for neutrons in
coincidence with "Li, the uncorrected ’Li yield (including 0 pairs from
the decay of “Be) is used. Presumably “Be has a comparable associated

neutron multiplicity, and there is no way to discriminate (in general)

102
neutrons in coincidence with “Be from those in coincidence with 7Li. So
the associated multiplicities given for 7Li are actually a weighted
average of the associated multiplicities for 7Li and “Be.

There is one final instance where the misidentification of 0
pairs from the decay of “Be complicates the data. In the relative
velocity histograms of neutrons in coincidence with 7Li (see section
4.4) there is a strong possibility for contamination. 9Be can decay via
neutron emission. In that case, the neutron will be emitted with a very
small velocity relative to the remaining “Be. The “Be will be in its
ground state and decay to a pair of 0 particles, which will appear to be
a "Li in the silicon detectors. Thus the decay of the first excited
state of ’Be will appear to be a "Li in coincidence with a neutron at
low relative velocity. This will be confused with the decay of the
third excited state of “Li, which is identified by a 7L1 in coincidence
with a neutron at low relative velocity. As of yet, there is no
measurement to indicate to what extent this contamination takes place.
For that reason, the error this misidentification causes (overestimation

of the population of the third excited state of'“Li) remains uncor-

rected.
The following program was used to calculate EAQ(E):
PROGRAM BE8_MONTE
C This MONTE-CARLOS the efficiency for detecting a pair of alpha
C particles if a “8e was heading into a detector.

CHARACTER FNAME*12
FNAME='MSROO.DAT'
S:SECNDS(O.)
III=INT(S)

103

p1=3.1415926 !n
Q = .0919 !Q-value for “Be decay
DV = SQRT(Q)

TYPE *,' ENTER THE SOLID ANGLE IN MSR.‘
ACCEPT *,S_ANGLE

ENCODE (2,1003,FNAME(4:5)) NINT(S_ANGLE)
OPEN (UNIT=11,FILE:FNAME,STATUS='NEH')
TYPE *,' The output will be in a file named:',fname

s_angle=s_angle/1000. !converts to steradians
THETA_MAX=acosd(1.-s_angle/(2.*pi)) !half angle
delta:THETA_MAX/100. !angle integration step size.

Select Be-8 energy...
Do 199 i_energy=0,19

energy=5.+5.*real(i_energy)
V=SQRT(ENERGY)

Select Be-8 direction...

Do 150 jthetaz0,99
thetazdelta/Z.+delta*real(jtheta)

Weight is the fraction of the total "IN" 8e-8's that are in this
direction (less factor of 2*pi/s_angle, added later).

weight:cosd(theta-delta/2.)-cosd(theta+delta/2.)
arg=SQRT(ENERGY/Q)*sind(theta_max-theta)

if (arg.GE.1.) then
PERCENTzl.
ELSE
DO 1:1,1000 !Monte-Carlo over alpha directions
theta_a=90.*RAN(III)
phi_a =180.*RAN(III)
dx=dv*cosd(theta_a)*sind(phi_a)
dy=dv*sind(theta_a)*sind(phi_a)
dz=dv*cosd(phi_a)

x = v*sind(theta) + dx
Y = dy
z = v*cosd(theta) + dz

rho = sqrt(x*x + y'y)
rho_max = z*tand(theta_max)

if(rho.le.rho_max) then !one alpha in...
x = v'sind(theta) - dx
y=—dy
z = v*cosd(theta) - dz

150

199

1001
1003

104

rho = sqrt(x*x + y'y)
rho_max = z*tand(theta_max)

if(rho.le.rho_max) then
COUNT=COUNT+1.
ENDIF
ENDIF
ENDDO

PERCENT=COUNT/IOOO.
COUNT =0 .

endif

probability:probability+weight*percent

percent=0.

probability=2.“pi’probability/s_angle
write(11,1001)energy,probability

probability=0.
CLOSE (11)

format(2f)
format(I2)

stop
end

I BOTH ALPHAS IN !

APPENDIX B: CALCULATION OF RELATIVE VELOCITY GEOMETRIC EFFICIENCIES

The number of neutrons observed from the decay of the 7.456 MeV
state of ’Li observed in coincidence with “Li depends on three quan-
tities: the population of the state in question, the geometric
efficiency for observing such coincidences, and the neutron detector ef-
ficiency. We have measured the number of such neutrons for the decay of
several excited nuclei, and wish to deduce the population of the states
in question. This is possible by calculation of the two efficiencies
mentioned. The neutron detector efficiency has been calculated, as dis-
cussed in section 111.1. This quantity gives the probability that a
neutron which enters the neutron detector will produce a signal larger
than the threshold set. For a given detector, this efficiency is a
function of the threshold and the neutron kinetic energy. The purpose
of this appendix is to discuss the geometric efficiency mentioned.

The geometric efficiency is the probability that if the fragment
from such a decay enters the silicon detector, the neutron enters the
neutron detector, regardless of the signal produced. This efficiency
accounts for the geometric and kinematic effects of the decay. The
geometric factors include the solid angle of both the silicon detector
and the neutron detector, and their positions relative to one another.
The kinematic considerations include the velocity or kinetic energy of

the original fragment (before decay), the decay energy in that frame

105

106

(i.e. the Q value), and the relative masses of the two decay products
(the neutron and the remaining fragment). This geometric efficiency,
E(E,Q,m,M,AO,,AQ,,A0), is then a function of the original fragment
energy, E, the Q value, Q, the neutron mass, m, the mass of the remain-
ing fragment, M, the solid angle of the silicon detector A0,, the solid
angle of the neutron detector, A02, and the angle between the axes of
the two detectors, A9. The calculation of this geometric efficiency is
actually a generalization of the problem discussed in Appendix A. In
that case, the efficiency was for detecting both 0 particles from the
ground state decay of “Be. Since both fragments were observed in the
same detector, AO,=AO,, and A9=0. Also, the Q value was fixed at 92 keV
and the two masses were constant and identical. Then,
e(E,Q,m,M,AO,,AOo,A9) could be written as eAQ(E). A more general code
was written to allow for different Q values, different masses, two dif-
ferent solid angles, and a finite angle between the two detector axes.
The calculation, however, basically remained unchanged. There is a
subtle difference in what efficiency was being calculated. In the case
of the “Be decay, particle inclusive measurements were being studied.
The efficiency there gave the probability that both (1 particles from a
given “Be would be detected. The neutron case is a coincidence measure-
ment. It is assumed that the decay fragment is detected in the silicon,
and the probability that the neutron will enter the neutron detector is
computed.

For a given decay (i.e. initial fragment and state -- this fixes
Q, m, and M), A0,, A02, E, A9, and 0, the angle between the original
fragment (either 7L1, “L1, ”Be, 1‘Be, or ‘28) trajectory and the

silicon detector axis, a Monte Carlo calculation was used to determine

107
the probability, P(E,Q,m,M,AO,,AOo,A0,0), that if the decay fragment
(“L1, 7Li, “8e, ‘°Be, or “B, respectively) entered the silicon detector
the neutron would enter the neutron detector, under the assumption of
isotropic emission in the moving frame of the original fragment. Then,

E(E,Q,m,M,AO,,A02,A0) is given by the following integration:

211
A0

 

9.
e(E,Q,m,M,AO,,A02,A0) = 2x10 P(E,Q,m,M,A0,,AOo,A0,0)xsin(0)Xd0, (8.1)
which was computed numerically (see the Fortran code at the end of this
appendix), where Go is the half angle of the neutron detector with solid

angle A92, given by:

Go = cos-‘(1 - g?“- . (8.2)
This geometric efficiency, e(E,Q,m,M,AQ,,AOo,A0), was determined
separately for neutrons emitted in the direction of the moving system
and for neutrons emitted in the opposite direction. The value of A0 is
discussed later in this appendix.

Figure 8.1.1 shows the geometric efficiency for detecting
neutrons (in coincidence with ‘Li) emitted from the 7.456 MeV state of
7L1 as a function of the kinetic energy of the emitting 7Li for the
solid angles of silicon telescope-1 and neutron detector-1. Both the
efficiency for neutrons emitted in the direction of the moving system
and for neutrons emitted in the opposite direction are shown. For each
of these calculations (i.e. for all five systems being considered and
for each direction of neutron emission), an average geometric ef-

ficiency, (c(Q,m,M,AO,,AOz,A9)>, was then obtained by weighting

108

 

 

 

 

 

12 ' l r I ' 1 ' l ' l ' 1

A Dashed - backward direction '

O
5 1 O L Solid — forward direction A
>\ e
o

:1 8 r- _.
cu
.Fq .
o
31::
w-a 6 — --
El

0 .1
’E
+2 4 _

g . .
o ._ _
<1) 2
CD .

O 1 I I I 1 I 1 I 1 I 1 I

0 20 40 60 80 100 120
7L1 Energy (MeV)

Figure 8.1.1 6 (E) for neutrons in coincidence with “Li, forward and
backward relative velocity peaks.

109
c(E,Q,m,M,AQ,,AOz,A0) by the kinetic energy spectrum of the parent frag-
ments, Y(E), which was determined from inclusive data, integrating over

energy and dividing by the total yield. That is,

I::(I:;,Q,m,M,A01,A02 ,A0)Y(E)dE

<E(Q,m,M,AO,,AOo,A0)> = IY(E)dE . (8.3)

(For simplicity, this geometric efficiency and the related average ef-
ficiency are referred to as €n(E) and <2“), respectively, throughout
this thesis, except in this appendix). This average efficiency had to
be calculated separately for each system, for each direction of neutron
emission (forward and backward), and for both beam energies used. The
geometric efficiency was the same for each beam energy, but the charged
particle singles spectra were different. The resulting values for the
average efficiencies are listed in Table III.3.3.

Since the silicon telescope and the neutron detector were
colinear for the cases under consideration, ideally A0=0. As discussed
in section 111.4, the uncertainty in this alignment was 20.1“. The
geometric efficiency obtained when A0:0.1° is slightly smaller than that
obtained when A0=0.0°. A much greater effect on the efficiency is
caused by the finite-sized beam spot and possible error in centering the
beam. The axis of each detector is the line from the fragment source (a
point-like target) to the center of the detector. The angle between the
two detector axes depends on the position of the point-like fragment
source on the finite sized target. Averaging over all possible posi-
tions for the point-like source (as limited by the estimated size of
the beam spot and beam spot position, as described in section 111.4)

yields an average effective detector misalignment of about 0.6 degrees.

110

This is the value of A0 used in the calculations of the geometric ef-

ficiency. The uncertainties given with the average geometric

efficiencies reflect the uncertainty in this value of A9.

The following program was used to calculate

E(E,Q,m,M,AO,,AO,,A0):

CO

C

PROGRAM geo_eff
Nov. 8, 1986. C. Bloch

(1,2) —-> (1-1,2) + n

This MONTE CARLOS the efficiency for detecting a neutron emitted from
a FRAG(A), given a FRAG(A-1) was detected.

CHARACTER FNAME*20,dir*1

number of integration steps...

Input

ntheta=100
monte=1000
nphi=1

S:SECNDS(O.)

III=INT(S)

p1=3.1415926

OPEN (UNIT:5,STATUS='OLD',READONLY)

parameters...
TYPE *,' Enter the solid angle (in msr) of the neutron

1 detector'

READ(5,*) s_angle

TYPE *,' Enter the solid angle (in msr) of the silicon

1 detector'

READ(5.*) sil_sa

type *,' Enter the angle (deg) between the two detectors.’
READ(5.“) dtheta

type *,' Enter the name of the output file.‘
read(5. 1010) mame

type *,' Enter the energy (in MeV) of the decay.‘
READ(5.*) Q

C

111

type *,' Enter A for the fragment before decay.‘
READ(5,*) a_parent

type *,'Enter # of integration steps for fragment theta.‘
READ(5.*) ntheta

If the angle between the two detector axes is zero, the problem has

C azimuthal symmetry, and nphi should be left equal to 1

00000

type *,' Enter # of integration steps for fragment phi.‘
type '.' ( for azimuthal symmetry, enter 1).
READ(5,*) nphi

type *,'Enter # of neutron decays for each frag direction.‘
READ(5,*) monte

type *,' Enter F for forward peak, 8 for backward peak.‘
READ(5.1010) dir

CLOSE(5)

if(dir.eq.'F'.or.dir.eq.'f') then !forward peak
sgn=1.

else
sgn=-1.

endif

A for daughter...
a_daughter = a_parent - 1.

Velocities in frame of parent
dV_n = sqrt(2.*Q/(1./(a_daughter*931.5)+1./939.55))/939.55*30.
dV_Frag = 939.55*dV_n/(a_daughter*931.5)

Determine the condition for "forward" or "backward". For dtheta=0,
the plane separating these hemispheres is determined by the detector
normal. For non-zero dtheta, the normal is between the two detector
normals. Using small angle approximations, the change of the normal
from the frag-det. normal is given by...

dtheta=dtheta*pi/180. !change to radians
theta_norm=(dV_n*dtheta-dV_frag*(1.-cos(dtheta)))/

1 (dV_n+dV_frag)
theta_norm=theta_norm*180./pi !converts back to degrees

type *,' theta_norm=',theta_norm

solid angle stuff...
theta_max = acosd(1.- sil_sa/(2000.*pi))
theta_test = acosd(1.-s;angle/(2000.*pi))

angle integration step size...
dcos (1.-cosd(theta_max+theta_norm))/real(ntheta)
dphi 360./real(nphi)

OPEN (UNIT:11,FILE:FNAME,STATUS:'NEH')

112

Do ifake=0,1
write(11,1001)Ifake,0,0.0
enddo

C Select parent energy...
Do i_energy=2,127 !begin energy loop

E_parent = real(2*i_energy)
V = sqrt(2.*E_parent/(A_parent*931.5))*30. !cm/ns

C Select parent frag direction...

Do Jtheta=0,ntheta-1 !begin parent theta loop
domegazdcos/Z.+dcos*real(Jtheta)
theta:acosd(1.-domega)
do iphi=0,nphi-1 !begin parent phi loop

phi=dphi/2.+real(iphi)*dphi

DO I=1,monte !monte carlo over neutron directions
theta_n = acosd(RAN(III))-theta_norm
phi_n = 360.*RAN(III)

C Check to see if daughter is in silicon detector:
dx:-sgn*dV_Frag*cosd(phi_n)*sind(theta_n)
dy:-sgn*dV_Erag*sind(phi_n)*sind(theta_n)
dz=-sgn*dV_Erag*cosd(theta_n)

x = v*cosd(phi)*sind(theta) + dx
y = v”sind(phi)*sind(theta) + dy
z = v*cosd(theta) + dz

rho = sqrt(x*x + y’y)
rho max = z*tand(theta_max)

if(rho.le.rho_max) then !Frag in...
denom:denom+1.

C Check to see if neutron is in NEUTRON detector:
C Shift to new frame, z-axis in neutron detector direction...

dx=sgn*dV_n*cosd(phi_n)*sind(theta_n)
dy=sgn*dv_n*sind(phi_n)*sind(theta_n)
dz=sgn*dV_n*cosd(theta_n)

x
Y
z

v*cosd(phi)*sind(theta) + dx
v”sind(phi)*sind(theta) + dy
v*cosd(theta) + dz

xprime
yprime
zprime

x'cos(dtheta) + z*sin(dtheta)

Y
-x*sin(dtheta) + z*cos(dtheta)

rho = sqrt(xprime*xprime + yprime*yprime)

113
rho_max = zprime*tand(theta_test)

if(rho.le.rho_max) then ! neutron in too!
COUNT:COUNT+1.
ENDIF
ENDIF
ENDDO !End Monte Carlo over neutron directions

IF(DENOM.EQ.O.) THEN
PERCENTzo.
ELSE
C denom=# frags detected, count:# neutrons detected, out of #:monte
C decays.
PERCENT=COUNT/denom
ENDIF
denom=0.
COUNTzO .

probability:probability+percent

percentzo.
ENDDO !End loop over parent phi
enddo !End loop over parent theta

probability=probability/real(ntheta*nphi)
write(11,1001)I_ENERGY,NINT(probability*1000OO.),0.0

probability:0.

ENDDO !End loop over parent energy
CLOSE (11)

1001 format(I,2X,I,2X,f)

1003 format(IZ)

1010 format(a)

stop'PROGRAM DONE'

end

A38“
A385
Aw79

Aw80

Aw81a

Aw81b

Aw82

Ba80

Ba83
Be83
8176

8181
8185
8186

8187a

3187b

8080

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