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WESIS

 

 

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5’73? 9‘9“ Michigan State
University

 

 

 

This is to certify that the
dissertation entitled

Low-Temperature Measurement of the Giant Dipole
Resonance Width in Sn

presented by

Paul R. Heckman

has been accepted towards fulfillment
of the requirements for the

PhD. fl degree in Physics

41/4 (1;

Major Professor’s Signature
(/23 /03

Date

MSU is an Affirmative Action/Equal Opportunity Institution

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINE return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 cz/CIRC/DateDUGpGSp 15

 

Low-Temperature Measurement of the Giant
Dipole Resonance Width in Sn
By

Paul R. Heckman

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

2003

ABSTRACT

Low-Temperature Measurement of the Giant Dipole
Resonance Width in Sn

By

Paul R. Heckman

Theoretical calculations within the adiabatic thermal shape fluctuation model predict
differences in the behavior of the Giant Dipole Resonance (GDR) width between nuclei
with and without shell effects. At low temperatures, in nuclei with strong shell effects,
the width is predicted to be suppressed relative to nuclei where shell effects are weak.

Studies have been performed on the GDR properties of nuclei with strong shell
effects (2°8Pb), and weak shell effects (Sn and Cu). The data for nuclei where shell
effects are weak show a deviation from predictions at low temperatures. To investigate
this discrepancy, an experiment was performed to measure the GDR width in 120Sn
at lower temperatures than have previously been measured.

The width of the GDR built on excited states in 120Sn was studied by means of
inelastically scattered 170 particles. This technique allowed for the first measurement
of the GDR width at a temperature as low as 1 MeV in Sn. A GDR width of 4 i 1 MeV
consistent with the GDR width of the ground state was extracted. This result does
not confirm the adiabatic coupling calculations of the evolution of the width as a
function of temperature, and indicates an overestimation of the influence of thermal

fluctuations.

To my wife, Karen

iii

ACKNOWLEDGMENTS

The completion of this thesis marks the end of my life as a graduate student. It has
been along, and sometimes frustrating experience. That being said, it has also been a
very rewarding experience personally. I am indebted to many for their contributions.

First and foremost I would like to thank my advisor, Dr. Michael Thoennessen.
This thesis would not have been possible if not for your guidance and support over
the past few years. It has truly been an enjoyable experience working with you.

I am also grateful to all that helped in the running of the experiment. This includes
everyone from our group, the S800 group, ORNL, University of Washington, and the
N SCL staff. The running of this experiment was a group effort.

The lengthy data analysis relied heavily on the computing power here at the
NSCL. The computer department and support staff has done a wonderful job making
sure that the necessary resources were always available. For this, I thank you.

Finally, I would like to thank everyone that has made my time as a graduate
student more enjoyable. You know who you are! I am not even going to try and list

everyone. There are many of you, and undoubtedly I would miss someone.

iv

Contents

1 Introduction
1.1 Background ................................
1.1.1 GDR Built on Ground States ..................
1.1.2 Macroscopic Picture .......................
1.1.3 Microscopic Picture ........................
1.1.4 GDR Built on Excited States ..................
1.1.5 GDR Width ............................
1.2 Motivation .................................
1.3 Experimental Considerations .......................
2 Experimental Details
2.1 Detectors and Experimental Devices ..................
2.1.1 BaF2 Scintillators .........................
2.1.2 CsI Array .............................
2.1.3 S800 Magnetic Spectrograph ...................
2.2 Electronics .................................
2.2.1 BaF2 Electronics .........................
2.2.2 CsI Electronics ..........................
2.2.3 S800 Electronics ..........................
2.2.4 Trigger Box Electronics ......................
3 Data Analysis
3.1 Calibrations ................................
3.1.1 BaF2 Array ............................
3.1.2 CsI Array .............................
3.1.3 CRDC Detectors .........................
3.2 8800 Analysis ...............................
3.2.1 Particle Identification .......................
3.2.2 Fragment Energy Loss ......................
3.3 BaF2 Array Analysis ...........................
3.3.1 Selection of 7 Rays ........................
3.3.2 Shower Reconstruction ......................
3.3.3 'y-ray Decay Spectra .......................
3.4 CsI Array Analysis ............................
3.4.1 Identification of Events ......................

Hommmwwwu

|-*

17
17
18
19
21
22
23
23
26

28
28
28
31
33
33
33
37
40
4O
41
44
49
49

3.4.2 Proton Spectra ..........................

4 Tools to Interpret the 7-ray Spectra

4.1 Statistical Model Calculations ......................
4.1.1 Initial Population of Nucleus ...................
4.1.2 Decay Rates ............................
4.1.3 Level Density ...........................
4.1.4 GDR Width ............................

4.2 Bremsstrahlung Radiation ........................

4.3 GEANT Simulation ............................

4.4 Nuclear Temperature ...........................
4.4.1 Formalism to Calculate the Temperature ............
4.4.2 Relevant Quantities ........................

5 Interpretation of the 'y-ray Spectra
5.1 20—30 MeV Energy Loss Spectrum ...................
5.2 Higher Energy Loss Data .........................

6 Conclusions
Bibliography ...................................

vi

51

57
57
58
63
65
67
68
69
73
73
76

80
80
83

87
92

List of Figures

1.1 Cartoon of Steinwedel and Jenson model ................ 4
1.2 Cartoon of Goldhaber and Teller GDR vibrational model ....... 4
1.3 Free energy surfaces for 120Sn and 208Pb ................ 8
1.4 Data and theory for Sn and Pb nuclei .................. 10
2.1 Schematic of the experimental setup .................. 14
2.2 Schematic of the BaF2 array ....................... 15
2.3 Perspective drawing of the S800 target chamber door ......... 16
2.4 Photo and top view of the CsI array .................. 16
2.5 Perspective drawing of an individual BaF2 scintillator ......... 18
2.6 Diagram of the Ban electronics ..................... 24
2.7 Diagram of the CsI electronics ...................... 25
2.8 Diagram of the trigger box ........................ 27
3.1 88Y and PuBe calibration spectra .................... 29
3.2 Energy calibration curve for a BaF2 detector .............. 30
3.3 Calibrated cosmic-ray spectra ...................... 30
3.4 Time spectra used to calibrate the BaF2 array ............. 31
3.5 Calibrated time spectrum from the CsI detectors ........... 32
3.6 Proton and a calibration curves for the CsI array ........... 33
3.7 Mask spectrum for CRDCl position calibration ............ 34
3.8 Plots used to adjust the T OF parameter for particle identification . . 35
3.9 Initial plots used for particle identification ............... 36
3.10 Final plot used for particle identification ................ 37
3.11 S800 singles energy-loss spectrum .................... 39
3.12 Plots used to eliminate high-energy neutrons from the analysis . . . . 40
3.13 Plots used for final y-ray selection .................... 42
3.14 Schematic to demonstrate the shower reconstruction process ..... 43
3.15 Spectra from PuBe data to show the effects of reconstruction ..... 44
3.16 Spectrum used to exclude decays to the ground state ......... 45
3.17 20—30 MeV energy loss y-ray spectrum breakdown ........... 46
3.18 Raw and random y-ray spectrum for 80—90 MeV energy loss ..... 46
3.19 y-ray decay spectra. ........................... 47
3.20 Ground state 7-ray decay spectra .................... 48
3.21 CsI fast vs. slow spectra ......................... 50
3.22 Illustration the CsI E fast transformation ................ 51

vii

3.23 Transformed CsI plots for charged-particle identification .......
3.24 Plot of energy loss vs. proton energy ..................
3.25 Projection of energy loss from Fig. 3.24 .................
3.26 Plot of energy loss vs. proton energy for a forward and backward CsI

detector ...................................
3.27 Proton energy spectra ..........................

4.1 Spectrum of inelastically scattered 170 particles in coincidence with ”y
rays with E, 24 MeV ...........................
4.2 Distribution of E“ resulting from a given energy loss ..........
4.3 Distributions of E‘ used in this work for energy losses greater than
30 MeV ..................................
4.4 S800 singles energy loss spectrum ....................
4.5 Cartoon of inelastic-scattering process .................
4.6 Population of the target nucleus in terms of energy and angular mo-
mentum ..................................
4.7 Level density parameter comparison ...................
4.8 GDR width descriptions incorporated into CASCADE .........
4.9 Energy resolution of the BaF2 array ...................
4.10 Comparison of source data and simulation ...............
4.11 Response of the BaFg arrays as simulated by GEANT .........
4.12 Distribution of 'y rays emitted in the GEANT simulation .......
4.13 Response of the Ban array to specific energies .............
4.14 Example to demonstrate the effects of folding .............
4.15 Temperature comparison for various level density descriptions
4.16 Low energy region of exact temperature calculation ..........

5.1 Result of the fits to the 20—30 MeV energy loss spectrum .......
5.2 Comparison of data and theory for Sn .................
5.3 Comparisons of the expected spectral shapes and data ........
5.4 Effects of the initial excitation energy distributions ..........

6.1 Microscopic correction to the ground state energy ...........
6.2 Theoretical predictions and data for Pb, Sn, Cu, and Au .......
6.3 Comparison of Sn data and microscopic model predictions ......

viii

54
55

59
60

62
63

64
66
68
70
70
71
72
72
73
75
75

81

88
89
90

List of Tables

1.1
2.1
3.1
4.1

4.2
4.3

Summary of temperatures associated with each curve in Fig. 1.3 . . . 8
Lab angles of the CsI detectors ..................... 17
Parameters to adjust the TOP parameter for particle identification . 36

Summary of the correlation between projectile energy loss and target

excitation energy. ............................. 59
Sample population matrix from CASCADE .............. 77
Summary of nuclei populated along decay ............... 78

ix

Chapter 1

Introduction

Giant resonances are an important topic in nuclear physics. These resonances are
called “giant” due to their collective nature. More specifically, all of the nucleons take
part in the resonance. Several giant resonances have been identified, resulting in two
classifications.

The first classification of giant resonances is electric vibrational modes. Several of
these modes have been found. In order of their discovery, they are the giant dipole,
quadrupole, monOpole, and octupole resonances. These terms arise from the names
for electric fields of a given spatial complexity [1]. For example, the motion of protons
in the nucleus vibrating in the dipole mode give rise to an oscillating electric field
that resembles the field generated by two poles, or point charges.

The second classification of giant resonances is magnetic vibrational modes. The
magnetic giant resonances involve the spin orientation of the nucleons. In this type
of giant resonance, there is a coordinated precession of the nucleons. As a result,
the nucleus can acquire a net spin 0r net magnetic moment that oscillates at the
precession frequency. The names of the giant resonances in this category are the
giant Gamow-Teller and giant magnetic-dipole resonances.

In this thesis, the giant dipole resonance (GDR) built on excited states will be

investigated. The study of this resonance can provide nuclear structure information.
For example, the strong nuclear forces that hold the nucleus together can be probed.
The study of this resonance also provides an experimental check on the validity of
various theoretical models. The adiabatic thermal shape fluctuation model will be

tested in this thesis.

1 . 1 Background

1.1.1 GDR Built on Ground States

The first measurements of the GDR built on nuclear ground states were in the mid-
1940’s [1]. The experiments were performed with the use of photonuclear cross-section
measurements [2]. The photo-absorption cross section (cabs) is given by

(E ) — ___4”62h]_V_Z 1 531”
0.1113 7 _ MC A F (E3 — E50102 + EH2,

 

(1.1)

where E7 is the y-ray energy, EGDR is the resonance energy, E is the resonance width,
M is the mass of a nucleon, N is the number of neutrons, Z is the number of protons,
and A is the number of nucleons. This functional form of cab, provides a good descrip-
tion of the shape of the GDR in medium and heavy nuclei by treating the resonance
energy, width, and sum rule strength as energy-independent, empirically adjustable

parameters [3]. The sum rule strength is defined with the following expression:

°° 27r262h NZ NZ
_— “E E: —_— —MV . 1.2
07» /0 ab( 7)d 7 Mc 60 ( 6 mb) ( )

 

This expression corresponds to a classical E1 sum rule, and is referred to as the
Thomas-Reich-Kuhn (T RK) sum rule [4].
The GDR splits into two components for axially symmetric deformed nuclei, cor-

responding to oscillations along the short axis (high-energy component) and long axis

2

(low-energy component). The ratio of the strength for the two components provides
a sense of the deformation (i.e. prolate or oblate deformed), and the energy splitting
is related to the magnitude of the deformation [3]. For the case of deformed nuclei,

Jab, can be generalized to include two Lorentzian components.

1.1.2 Macroscopic Picture

The easiest way to describe the motion of the GDR is macroscopically. The center of
mass is fixed, and the protons move collectively as a group, as do the neutrons.

One macroscopic description is named after Steinwedel and Jenson [5]. In this
model, the motion is thought of as density vibrations of neutron and proton fluids
against each other with the surfaces fixed [6], as depicted in Fig. 1.1. This description
leads to a form for the resonance energy in terms of the number of nucleons A given
by

EGDR O< 24—1/3- (13)

A second description is named after Goldhaber and Teller [7]. Here, the pro-
tons and neutrons behave as two separate rigid but interpenetrating density distri-
butions. These rigid distributions undergo a harmonic displacement with respect to
each other [6], as depicted in Fig. 1.2. This mode also leads to an expression for the

resonance energy, and has the following form:

EGDR QC 24—1/6. (1.4)

The GDR can also be described as a superposition of the above two modes [6]. The
superposition of these two modes leads to the following equation for the resonance
energy:

EGDR = (1.13 x 10-4/1”3 + 7.34 x 10-4A1/3)-1/2. (1.5)

 

Figure 1.1: Cartoon of Steinwedel and Jensen model to show GDR vibrational motion.
The protons are shown in blue, and the neutrons in yellow. Images in this dissertation
are presented in color.

..

T l

   

     

Figure 1.2: Cartoon of Goldhaber and Teller GDR model. The rigid proton distri-
bution is shown in blue, while that of the neutrons is shown in yellow. The inter-
penetrating area is shown as green. The center of mass is fixed and shown as the
cross.

The ratio of the contributions from the GT and SJ modes is

GT
S—J = 6.49 X A—1/3, (1.6)

and the contribution from the SJ mode becomes more significant with increasing

mass [4].

1.1.3 Microscopic Picture

The microscopic picture of the GDR is more complicated than the macroscopic pic-
ture. In the microscopic picture, the collective oscillations of the nuclear system are
described in terms of particle-hole excitations, obtained by promoting nucleons from
occupied shells to unoccupied shells [8]. In order to describe the resonance in this
way, the particle-hole interaction has to be taken into account. This can be done by
using the random-phase approximation (RPA) [8]. Examples of this treatment can be
found in Refs. [8—10].

Microscopic models have been applied to various nuclei. Despite this, the micro-
sc0pic picture has limitations. As energy increases, it becomes extremely difficult to
perform microscopic calculations. This is due to the fact that all energetically allowed
channels must be considered. These channels can include three, four, or more frag-
ments. Presently, a calculation with more than three fragments in the continuum is

out of reach at resonance energies [9].

1.1.4 GDR Built on Excited States

The GDR built on excited states differs from the GDR built on nuclear ground states
in that it is built on excited states, as the name suggests. The study of the resonance
built on excited states provides information about the nucleus at temperatures above

0 MeV. This makes this type of study especially useful in determining properties of

nuclei at high temperatures. For example, it is possible to study the shape evolution
of the nucleus with increasing temperature.

The existence of the GDR built on excited states was postulated as early as
1955 by David Brink [4]. He proposed that the energy dependence of the photo-
absorption cross section is independent of the detailed structure of the initial state
of the nucleus [3]. This weak-coupling hypothesis, known as the Brink hypothesis,
implies that Eqn. 1.1 should also apply to the GDR built on excited states.

It was soon realized that the Brink hypothesis together with the existence of a
substantial spreading width for the ground-state GDR meant that the high-energy
7 decay of highly excited compound nuclei formed in nuclear reactions should be
observable and be visible as an enhancement or “bump” at y-ray energies equal
to E0012 [3]. This “bump” was first observed experimentally with proton, 3He, and
4He—induced reactions [11,12]. In these first experiments, the enhancement was only
observed. The first quantitative analysis of a high-energy ’y-ray spectrum was on the
nucleus 252Cf in 1974 [13].

Since the first measurements of the GDR built on excited states, it has been
studied extensively by use of fusion-evaporation reactions [3, 14—22]. More recently,
inelastic scattering has been used to study this resonance [23—27]. The most extensive

studies have been done on Sn isotopes.

1.1.5 GDR Width

The evolution of the GDR width with increasing temperature has been the focus
of many experimental studies [3,14—27]. These studies have resulted in a significant
amount of data covering a relatively large range of temperatures (0 < T< 3 MeV).
The availability of data over such a broad range of temperatures has lead to theories
that predict the width of the GDR as a function of temperature.

In general, the width of the GDR increases with temperature. This increase can

be explained microscopically. The GDR width (I‘GDR) has two components

F0012 = F T +F L (1-7)

where I‘ T is the escape width and I‘ i is the spreading width of the nucleus.

The escape width originates from the decay of the collective doorway state to
residual nuclei with a one-hole configuration resulting from the emission of a proton
or a neutron. In an excited nucleus, the escape width is small, on the order of a
few hundred keV [28]. Thus, the increase of the width with temperature is primarily
due to the spreading width, which is the result of the coupling of the coherent 1p—1h
excitation to 2p—2h and other complicated particle-hole configurations (np-nh) [4].

The magnitude of the spreading width is determined by its coupling with other
nuclear degrees of freedom, such as the nuclear shape. Because of this, shape fluctua-
tions are important in the behavior of the GDR. The shape of the nucleus is sensitive
to the angular momentum and temperature of the nucleus.

The magnitude of the shape fluctuations is determined in part by the free energy.
Several free energy surfaces are shown in Fig. 1.3 for Sn and Pb. The surfaces are
much broader in Sn than in Pb at a given temperature, due to the presence of shell
effects in Pb. As the temperature increases, the thermal fluctuations increase and
the nucleus probes different shapes. The GDR couples to these shape fluctuations
and the resonance prOperties convey information on the time scales of these shape
variations [29].

In most nuclei, the width of the GDR is 4—5 MeV at low temperatures (T w 0 MeV).
The lifetime of the resonance is then on the order of 10‘22 s. As the nucleus gets hot-
ter, the width of the resonance increases, and the lifetime decreases. The lifetime
of the GDR is much shorter than lifetimes of rotational and single-particle states,

which have lifetimes on the order of 10‘1‘1—10‘15 3. These estimates indicate the GDR

 

 

 

 

 

511 .7] Sit TI TI "l ] l
A L (a) - A ~ ] / (b)
7’ 4t i 7» 42 \ ‘ 1
a : 7 5 : . i
E 3C ] E 3f -
o : j a) i 1
f: 2;“ t: 2[ j
m 7 j. in ]: l a
: o l
313.) 1:“ “j 93. 1": 1
LL. ; 4 LL, _ ]
OEM i A; Oil—ll . l.l__1fiuml+_l,li.l-lfl
-0.2 0.4 -0.2 0.0 0.2 0.4

 

l3

Figure 1.3: Free energy surfaces as a function of the quadrupole deformation param-
eter B. The deformation parameter 7 was set to zero. Panel (a) is for 12"Sn and (b)
is for 208Pb. See Table 1.1 for the temperatures associated with each distribution.
lifetime is approximately seven to eight orders of magnitude shorter than those of
single-particle states and rotational states, respectively.

Several models have been proposed that use shape fluctuations in describing the
GDR properties [30]. The model that has been generally adopted is the adiabatic ther-
mal shape fluctuation model. The adiabatic assumption is that the nuclear shape does
not change during the time it takes the GDR to damp. The strength is then a weighted
sum of the strength distributions that correspond to vibrations built on the possible
shapes that the nucleus can have. The increase of the GDR width with increasing
temperature is then attributed to the resonance sampling all possible shapes, which
become more numerous as the free energy surfaces become more broad and shallow.

In some models that use shape fluctuations, the adiabatic assumption is dropped

 

Color 120Sn 208Pb
red 0.0 0.0
blue 1.0 0.5
black 2.0 1.0
green 3.0 1.5
gray 4.0 2.0

 

 

 

 

 

 

Table 1.1: Summary of temperatures in MeV associated with each curve in Fig. 1.3.

at high temperatures. These models take the relative time scales for the shape fluctu-
ations into account [30]. In these models, the time spent in each shape configuration
decreases with increasing temperature, and enough time may not be spent in a given
shape for the GDR to adjust its frequency to the corresponding nuclear shape. As a
result, the GDR only feels the average shape of the nucleus. The implication of this
is motional narrowing [31].

The GDR width has also been modeled without the use of shape fluctuations.
Microscopic calculations based on the linearized Vlasov equation that include the
interplay between one-body Landau damping and two-body collisional damping of

nucleons have been performed [27, 32].

1.2 Motivation

The evolution of the giant dipole resonance (GDR) has been the focus of many ex-
perimental studies. The dependence of the GDR width on temperature and angular
momentum has been of particular interest. Fusion—evaporation and inelastic-scattering
reactions have been used to extract the GDR width at various temperatures [22,25,27]
and angular momenta [20,21], primarily in Sn and Pb.

Shell effects are thought to play an important role in predicting the width of the
GDR [33—35]. The generally accepted model is the adiabatic thermal shape fluctuation
model. In this model, the width of the GDR is determined by averaging over a thermal
ensemble of nuclear shapes. The increase of the GDR width is then attributed with
an increase in shape fluctuations with temperature. In nuclei where shell effects are
weak, such as Sn, the shape fluctuations are expected to behave as determined by a
rotating liquid drop. This is not the case for nuclei with strong shell effects. In nuclei
where shell effects are strong, such as Pb, shell effects must be considered. To take

shell effects into account, Nilsson-Strutinksy calculations are used to determine the

 

' (a) 1 lb)
1 . {it .
g‘ Tl. ‘ 4
‘ 1 e
/ A l ,

  

 

 

 

W11 A LEI—LIXIALJ MlJlJlLL

0.0 0.5 1.0‘1.5‘“i2.6“0.0 0.5 1.0 1.5 2.0
Temperature (MeV)

Figure 1.4: Data and theory for Sn and Pb nuclei. Panel (a) — Sn. Panel (b) - Pb.
The solid curves are adiabatic thermal shape fluctuation calculations. The shapes were
determined using Nilsson-Strutinsky calculations for the red curve, while liquid drop
calculations were used for the gray curve. The calculations are taken from Ref. [35].
The black circles and green diamonds are data points taken from Ref. [35]. The black
circles were measured using inelastic scattering, whereas the green diamonds are from
fusion-evaporation measurements. The blue triangles are taken from Ref. [22]. The
orange rectangles show the range of widths measured for the ground state.

shapes.

Both panels in Fig. 1.4 show adiabatic thermal shape fluctuation calculations.
Calculations were performed where the shapes were determined within the Nilsson-
Strutinsky formalism (red curve) and liquid drop formalism (gray curve). In the
Nilsson-Strutinsky formalism, shell effects are considered, whereas in the liquid drop
formalism they are not. Examination of Fig. 1.4a shows that the calculations are
nearly identical. This suggests that the properties of a rotating liquid drop can be
used to determine the shape fluctuations in Sn, as already mentioned. As discussed
previously, liquid drop predictions cannot be used for Pb. This is evident in Fig. 1.4b.
The initial suppression of the GDR width found in Pb should be absent in Sn.

The existing data for Sn and Pb generally agree with calculations [33-35]. How-
ever, the lowest temperature data point in Sn is on the order of 1—2 MeV lower than

predicted (see Fig. 1.4a). This discrepancy suggests a possibly significant deviation

between theory and experiment. To investigate this discrepancy, the width of the

10

GDR must be measured at even lower temperatures. Thus, the goal of this thesis was

to measure the GDR width at a temperature below 1.3 MeV.

1.3 Experimental Considerations

The majority of experiments performed to measure the GDR width in Sn used fusion—
evaporation reactions. These types of reactions cannot be used to study the GDR at
low temperatures. Traditional fusion-evaporation experiments are limited to higher
temperatures because of the Coulomb barrier in the entrance channel.

Inelastic scattering can be used to study the GDR at low temperatures. Inelastic
a-scattering has been used to measure the GDR width as a function of tempera-
ture [25, 27] in the past. While this type of reaction is not limited to high temper-
atures, there is a difficulty associated with it. Inelastic-scattering reactions have the
disadvantage that it is difficult to determine the initial excitation energy [36,37]. This
is due to knockout reactions and contributions from other reactions that do not lead
to full energy equilibrium of the energy loss of the scattered particle. The latter effect
becomes more important with increasing projectile energy loss. The contribution due
to knockout reactions can be reduced by using heavy-ion scattering as opposed to
a-scattering [24].

The reaction employed in this experiment was 120Sn(17O,17O’). The projectile 17O
was chosen for several reasons. As mentioned above, the contribution from knockout
reactions and other processes that do not lead to full energy equilibrium of the energy
loss of the scattered projectile should be reduced with heavy-ion scattering. The
neutron binding energy of 17O is also very low (4.14 MeV). This is important as
we wish to study target excitations and not projectile excitations. If the projectile
becomes excited in the scattering process, it will emit 7 rays with energies up to the

neutron binding energy. Since the neutron binding energy is low, these 7 rays will have

11

energies below the region of interest. The 7-ray energies probed in this experiment
range from 8-25 MeV. If the projectile is excited to energies above the neutron binding
energy, it will lose the loosely bound neutron to form 16O. These events are easily
discriminated against as we demand an 170 fragment to be in coincidence with the

detected 7 rays.

12

Chapter 2

Experimental Details

The experiment was performed at the National Superconducting Cyclotron Labora-
tory (NSCL). A primary beam of 1"'O was accelerated by the K1200 cyclotron to
80 MeV/nucleon. The beam was sent down the analysis line to the 8800 magnetic
spectrograph. Here the beam bombarded a 7.45 mg/cm2 target of 120Sn.

Three major detector systems were used in this experiment. These systems in-
cluded an array of Barium Fluoride (BaFg) scintillators, an array of Cesium Iodide
(CsI) scintillators, and the S800 spectrometer. The BaF2 scintillators were used to
measure high-energy 7 rays. The CsI scintillators detected charged particles. The
S800 measured inelastically scattered 1"'0 particles and other reaction products. The
8800 focal plane detectors ultimately determined scattered particle energy loss. The
focal plane detectors also allowed for accurate particle identification. A schematic of
the setup is shown in Fig. 2.1.

The Ban scintillators were arranged into two close-packed arrays. Each array
consisted of 68 scintillators. The arrays were placed at angles of i90° with respect
to the target chamber of the S800. The geometry of the arrays is shown in Fig. 2.2.
The scintillators were stacked in a wall type configuration. The gap in the stacking

scheme was necessary because of the design of the S800 target chamber doors.

13

 

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Figure 2.1: Schematic of experimental setup. This drawing is not to scale.

14

 

 

 

 

 

Figure 2.2: Schematic view of one of the Ban arrays. The detectors are shown as the
orange hexagons. The white trapezoids were plastic that aided in the stacking of the
arrays. The aluminum frame used to hold the array together is also evident.

The 8800 target chamber doors were modified in order to get the Ban arrays as
close to the target as possible. Each door had a cavity that extended into the target
chamber. A piece of aluminum was welded to the back wall of the cavity to provide
strength. This piece of aluminum extended into the cavity, and is evident in Fig. 2.3.
As a result, it was necessary to stack the B3F2 scintillators with a gap between two of
the rows. Positioning the arrays closer to the target gives a larger solid angle coverage,
which results in a higher detection efficiency.

The CsI scintillators were mounted inside the 8800 target chamber. There were 11
of these scintillators in all. Nine of these scintillators were attached to the roof of the
target chamber, while the two most forward detectors were attached to the forward
wall. A picture of the CsI array is shown in Fig. 2.4. The most forward detector in
the picture was removed for the run. The array covered scattering angles as indicated

in Table 2.1.

15

 

 

 

 

 

 

 

Figure 2.3: Perspective drawing of the 8800 target chamber door. Notice the alu-
minum extrusion from the door cavity.

 

 

 

 

 

Figure 2.4: The direction of the beam is from left to right in both panels. Left: Photo
of the CsI array. The most forward detector was removed during the experiment.
Right: Top view of the CsI array. The CsI detectors are depicted as green cylinders.

16

 

 

Number 0 (degrees) qb (degrees)
1 30 20
2 60 60
3 90 60
4 120 60
5 150 60
6 180 60
7 -150 60
8 -120 60
9 -90 60
10 -60 60
11 -30 20

 

 

 

 

 

Table 2.1: Lab angles of the CsI detectors. 6 is the scattering angle, and (15 is the
azimuthal angle. The z—axis is given by the direction of the beam. The numbering
scheme is as in Fig. 2.4.

2.1 Detectors and Experimental Devices

2.1.1 Ban Scintillators

BaF2 is an inorganic scintillator. The scintillation light consists of two components,
namely the fast component and the slow component. The fast component has a decay
time of 0.6 ns emitted in the short wavelength (220 nm) region of the spectrum, while
the slow component has a 630 ns decay time at wavelengths longer (310 run) than that
of the fast component [38]. The very short decay time of the fast component makes
BaF2 an excellent sub-nanosecond timing detector. In addition to the excellent timing
capabilities of BaFg, it also has a high density (4.89 g/cm2) [39]. The high density
makes this material good for 7 ray detection.

The two arrays of BaF2 scintillation detectors were assembled and installed at the
NSCL. The BaF2 detectors belong to Oak Ridge National Laboratory (ORN L), Texas
A&M University (TAMU), and Michigan State University (MSU). All scintillators are
regular hexagons. The ORNL and TAMU scintillators have a length l = 19.5 cm and
hexagonal cross section of inscribed radius r = 3.25 cm. The MSU dimensions differ

in that they have l = 24.5 cm and r = 3.00 cm. The various BaF2 detectors were

17

PMT

 

BaF2 Crystal

Figure 2.5: Perspective drawing of a BaF2 scintillator. All components are shown
except for the materials used to wrap the crystal.
stacked into the arrays as follows: 1—15 TAMU, 16-61 ORNL, and 62—68 MSU. The
numbering scheme follows that of Fig. 2.2. All together 136 BaF2 detectors were used.
Each BaF2 detector consisted of a BaF2 crystal, photomultiplier tube (PMT),
strap, frame, and base. The crystal was attached to the PMT by use of optical grease.
This grease is transparent to the ultraviolet light emitted in BaFg. The crystal was
then wrapped in teflon tape. The teflon tape gives the edges of the crystal 3 highly
reflective surface, which results in maximum light collection. Once coated with the
teflon tape, the crystal was wrapped with black electrical tape. The black tape pro-
duced a covering that was light tight. To aid in the strength of the coupling of the
PMT to the crystal, a frame and strap were used. This also helped in the stacking
of the arrays. A base was then attached to the PMT for applying voltage. Fig. 2.5

shows exactly how the various components of the BaF2 detectors were connected.

2.1.2 CsI Array

CsI is an inorganic scintillator. CsI is typically activated with either thallium (T1)
or sodium (Na). The scintillators used in this experiment were activated with T1.

The resulting scintillation light consists of two components, namely the fast and slow

18

component. The fast component has a decay time of 0.68 as, and the slow component
has a decay time of 3.34 as. The two components of light emitted allows for pulse
shape discrimination to differentiate among different types of radiation. The density
is 4.51 mg/cm2 [39]. The scintillators were cylindrical in shape, with a length of 3 cm
and diameter of 1.5 cm.

The CsI scintillators were assembled as follows: first, all but one end of the crystal
was wrapped in teflon tape. As in the case of BaFg, this gave the edges of the crystal
a highly reflective surface. This is important for maximum light collection. Next,
the wrapped crystal was put into an aluminum can. The aluminum can served to
protect the crystal and to seal it from outside light. Finally, a photomultiplier tube

was attached to the end of the crystal not wrapped in tape.

2.1.3 S800 Magnetic Spectrograph

The S800 spectrometer is composed of an analysis line and a magnetic spectrograph.
The analysis line consists of four bending dipoles, one quadrupole doublet, five qua-
drupole triplets, and four sextupoles (See Fig. 2.1). The magnetic spectrograph con-
tains two dipole magnets (D1 and D2), two quadrupoles (Q1 and Q2), and a series
of detectors in its focal plane [40]. The focal plane detectors consist of two cathode
readout drift chambers, an ion chamber, and three plastic scintillators [41].

The magnetic spectrograph bends scattered fragments to its focal plane. The two
quadrupoles focus fragments in the dispersive (x) and non-dispersive (y) directions.
The two dipole magnets have a bending radius of 2.8 m with a maximum central
field of 1.6 T, giving an overall bending power of 4 Tm. This results in an angular
acceptance of 7° and 10° in the dispersive and non-dispersive directions, respectively
[41]. Running the spectrograph in dispersion-matched, energy-loss mode compensates
for intrinsic beam momentum spreading in the dispersive direction, which ideally gives

a zero-width image at the focal plane [40]. The S800 is capable of correcting Ap/p

19

by 1% for every 10 cm at the dispersive image. The overall energy acceptance of

the device is 10%. For a very detailed description of the S800 and its operation see

Ref. [42].

Cathode Readout Drift Chambers

The Cathode Readout Drift Chambers (CRDCl and CRDC2) are position sensitive
detectors in the S800 focal plane. The active area of each detector is 30 cm x 59 cm
with an active depth of 1.5 cm. The volume of the detectors is filled with a mixture
of 80% CR, and 20% C4H10 gas at a pressure of 140 Torr [41].

The gas in the detector volume is ionized by charged particles passing through it.
The electrons created in this process drift through a region with a constant electric
field until they reach a grounded Frisch grid. Once the grid is passed, charge am-
plification (electron avalanche) takes place and the electrons are accelerated towards
the anode wire. The anode wire is typically kept at 1400 Volts. Cathode pads are
located in front of and behind the anode wire. There are 224 cathode pads in all. The
Frisch grid insures that the integration over all pad signals will be independent of the
charged fragment’s interaction distance from the anode. This is due to the fact that
no charge amplification takes place in the region of constant electric field [40].

The dispersive (x) position is determined with a Gaussian fit over non-zero pad
signals. The centroid of the fit gives the position. The non-dispersive (y) position is
determined by measuring the drift time of the electrons from the point of interaction
to the anode. The position resolution of these detectors is designed to be better than

0.48 mm in both directions.

Ionization Chamber

The ionization chamber (IC) is a detector that gives energy loss information. This

detector is a standard Frisch gridded ion chamber that is segmented into 16 one-inch

20

anodes perpendicular to the path of the ions [41]. The IC volume is filled with P10
gas at a pressure of 300 Torr. This gas is 90% argon and 10% methane. Sampling the
energy loss along the path through the IC reduces the noise, and provides an accurate

energy-loss signal.

Scintillation Detectors

The last set of detectors in the S800 focal plane are a series of scintillators. The
scintillators provide fragment energy loss and total energy information. They can
also be used for timing purposes. There are three scintillators in all. The first one
(E1) is 5 cm thick, while the second (E2) and third (E3) are 10 and 20 cm thick,
respectively. All three scintillators are made of plastic. Light guides are attached to
both ends of the plastic, and PMTs are attached to the light guides. The light guides
direct the light created in the scintillation process from the plastic to the PMTs. This
results in higher light collection. The E1 scintillator was also used to determine the

time-of-flight of fragments relative to the cyclotron radio frequency (RF).

2.2 Electronics

This experiment utilized three different electronic systems. These systems correspond
to the BaF2 array, CsI array, and S800 spectrometer. Two different threshold settings
were used in the BaFg electronics. During the run, the BaF2 acquisition was started
if any of the individual detector elements had energy deposition greater than a high
threshold, Th. In the event that Th was exceeded by any of the detector signals, a
high gamma trigger was created. Also, energy and time information was collected for
all detector elements with energy deposition greater than the low threshold, T1. The
CsI acquisition was started based on the energy deposited in the individual detector

elements. If any of the individual detectors had energy deposited greater than the

21

threshold, a CsI master trigger was generated. Additionally, energy and time-of-flight
information was collected for all CsI detectors. The S800 acquisition was started if
both PMTs attached to the E1 scintillator had a signal. If a signal was present in
both PMTs, a 8800 master trigger was generated and information was collected from

all S800 focal plane detector elements.

2.2.1 Ban Electronics

Each of the 136 BaF2 scintillation detectors had two output signals. One of these
signals was delayed and split into two parts, namely the fast and slow signals. The
fast and slow signals were sent to a charge-to—digital converter (QDC) unit. The QDC
units integrated the charge and digitized it to give energy information. The other
output from each detector was used for logic and timing. This signal was attenuated
and fanned into two parts. The signals were attenuated to approximately match the
thresholds from detector to detector. The fanned logic signals were sent to leading
edge discriminators, one with threshold T 1 and the other with threshold T h. The
signals sent to the discriminator with threshold T, were used to generate the low
gamma (lo-7) logic, while the others were used to generate the high gamma (hi-7)
logic. The lo—7 and hi-7 logic was used to generate gates for the various electronic
modules, triggers for the data acquisition, and for timing purposes.

The lo—7 logic path began with the 136 individual detector signals. These signals
were sent to 10 different 16 channel discriminators, all with threshold TI. This formed
10 banks, each with up to 16 detectors. The individual outputs from each channel
were sent to a time-to—digital converter (TDC) unit. These signals were delayed and
served as individual stops to the TDC for each detector element. The TDC unit was
run in common start mode. The common start was provided by the event output from
the trigger box (to be discussed in Sec. 2.2.4). In addition to the individual outputs,

each of the 10 discriminators also had a single output that worked as a logical OR.

22

The logical OR signal from each of the 10 discriminators were input to another logic
unit. This logic unit served as a logical OR to the 10 OR—ed discriminator signals.
This resulted in a single output that was true if any of the 136 detectors fire. It was
this signal, in coincidence with the master event signal, that was ultimately used to
generate the QDC gates. This signal was also used as the lo—7 trigger.

The hi-7 logic path began in the same way as the lo-7 logic. The 136 detector
signals were sent to 10 discriminators, each with threshold Th. As in the case of the 10-
7 logic, each of the 10 discriminators had a logical OR output. The 10 OR—ed outputs
were sent to a logic unit. This unit served as another logical OR. The resulting output
was used to generate the hi-7 trigger.

A diagram of the electronics is shown in Fig. 2.6. The lo-7 and hi-7 triggers were
input to the trigger box used in this experiment. The clears for the TDC and QDC

units came from the computer.

2.2.2 CsI Electronics

The CsI electronics were responsible for reading out energy and time information
from the individual CsI detectors. The readout was triggered based on the energy
deposited in the individual CsI detectors. If any of the detectors had energy deposition
greater than the threshold setting, energy and time information was gathered for all
11 elements. The time was determined with a TDC, where the individual detectors
provided a stop and the master event signal provided a common start. Both the fast
and slow energies were read out with the use of a QDC. A diagram of the electronics

is shown in Fig. 2.7. Clears for the QDC and TDC modules came from the computer.

2.2.3 8800 Electronics

The S800 electronics were responsible for reading out signals from all focal plane

detector elements. The readout was triggered based on the E1 scintillator. If both

23

 

 

 

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Figure 2.6: Diagram of the BaFg electronics.

24

 

 

 

 

   

             

83850
35
an 1.—

SEEECRE

85050
8.5

 

 

 

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asm 3:222:

 

 

Figure 2.7: Diagram of the CsI electronics.

25

PMTs on this scintillator had a signal, the trigger was generated. Specifically, the
gates for the S800 electronics were created by the logical AND of constant fraction
discriminator (CFD) signals from both E1 scintillator PMTs. This signal also served
as the start signal for each CRDC time-to—analog converter (TAC). The stops for
each of these TACs came from the individual CRDC anodes. Additionally, the logical
AND between both E1 PMTs was the stop for a TAC which measured time-of-flight
relative to the cyclotron RF. The cyclotron RF provided the start for this TAC. The
analog signals from each TAC were sent to an analog-to—digital converter (ADC) to

be read by the acquisition. Diagrams of the electronics can be found in Ref. [42].

2.2.4 Trigger Box Electronics

The trigger box (TBSOOO) served as the control system between the various detector
systems and data acquisition. A diagram of TB8000 is shown in Fig. 2.8. TB8000
allowed for easy selection of which events started the acquisition, as the different
triggers were selected with the flip of a switch. It also allowed for downscaling of the
different inputs. Additionally, if the computer was busy, TB8000 was inhibited. This
was to block events that occur while the computer was still processing the current
event. Both raw and downscaled signals were sent to scaler modules.

The trigger inputs to T B8000 were Lo-7, Hi-7, S800 master, CsI master, a coin-
cidence trigger formed between a logical AND between Hi—7 and S800 master, and
a second coincidence trigger formed between a logical AND between CsI master and
S800 master. Several triggers were selected during the experiment. Both coincidence
triggers were used to trigger the acquisition. The S800 master also triggered the ac-
quisition during the run. The S800 master was downscaled by a factor of 128 to give
8800 singles events. The L0—7 trigger was used for source calibration purposes with
the BaFg array. Similarly, the CsI master trigger was used for calibration purposes

with the CsI array.

26

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 TB8000
Inhibit BUSY
2
AND ‘ 3 0R] Master
Out Event
r 4
AND ‘ 5
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H m" Out Reduced Out
Coincidence
Register
Sealer Sealer

 

 

 

 

 

 

Figure 2.8: Diagram of trigger box, TB8000, which controlled the data acquisition for
this experiment. All inputs and outputs are described in the text.

27

Chapter 3

Data Analysis

The experimental data analysis consisted of several parts. First calibrations were
performed. All detectors in the BaF2 array and CsI array were calibrated for time
and energ. The only elements that needed calibration in the S800 focal plane were the
CRDC detectors. These detectors were calibrated for position. After the calibration
process, it was necessary to identify the fragments detected in the 8800 focal plane.
This was to ensure that only inelastically-scattered 170 events were considered. Next,
the 7-ray events detected with the BaF2 array were isolated. The 7 rays were then
correlated with projectile energy loss in order to extract 7-ray spectra corresponding
to various projectile energy losses. Finally, proton events in the CsI array were isolated

from other events. These events were also correlated with projectile energy loss.

3.1 Calibrations

3.1.1 Ban Array

Each of the 136 BaF2 detectors was calibrated for energ. The energy calibration was
carried out by using a source of 88Y and PuBe. These two sources gave calibration

points at 0.898 MeV, 1.836 MeV, 3.927 MeV, and 4.438 MeV. The two lowest energy

28

 

 

 

 

 

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t 1 0.898 MeV 1 l 3 927 Me V 44% MeV 1
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0 20 .40 60 80 100 075 100 125 150 175 200
Slow Signal (Channels) Slow Signal (Channels)

Figure 3.1: Left: 88Y source calibration spectrum. Right: PuBe source calibration
spectrum. The lower energy peak in this plot is the first escape peak.
points were from the 88Y source, while the other two were from the PuBe source.
Fig. 3.1 shows a typical spectrum resulting from the two sources. The first escape
peak is evident in the PuBe spectrum, and gave the calibration point at 3.927 MeV. A
higher energy calibration point was obtained from cosmic rays. The energy deposited
in the individual detector elements from cosmic rays depends on the geometry of the
detectors. Hence, the energy deposited in the ORNL and TAMU detectors was the
same. The detectors belonging to MSU had a lower amount of energy deposition as
compared to the other two types. The energy deposited in the ORNL and TAMU
detectors corresponds to an energy of 40.290 MeV, while in the MSU detector it is
37.930 MeV. These energies are based on simulations run at ORNL. In this analy-
sis, only the slow component was calibrated. A typical energy calibration curve is
shown in Fig. 3.2. A calibrated cosmic-ray spectrum is shown for both an MSU and
ORNL/TAMU detector in Fig. 3.3.

The time calibration of the Ban detectors consisted of two parts. First, all of
the timing channels were gain matched. This was accomplished by using a pulser to
trigger the electronics. With the electronics triggered in this manner, a spectrum was

measured with several peaks (Fig. 3.4). The time between peaks corresponds to 40 ns,

29

 

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0 400 800 1200 1600
Slow Signal (Channels)

Figure 3.2: Typical energy calibration curve for a BaF2 detector. The solid curve is
the result of a quadratic fit through the points shown. The points were obtained as
explained in the text.

 

 

 

 

400 L] l ] l V l l l I | l . l l l [ - l j 500 ti l T l l l [ T T] l l l' l i
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Energy (MeV) Energy (MeV)

Figure 3.3: Calibrated cosmic—ray spectra. Panel (a) is for an ORNL/TAMU detector,
while panel (b) is for an MSU detector.
which was easily determined from the frequency of the pulser. With this information,
the time gains of the individual channels in the electronics were matched. With the
gains matched, a reference point was still needed to complete the time calibration.
The reference point to complete the calibration was obtained from actual run
data. The time spectrum of each individual detector contains a prompt peak as well
as random peaks (Fig. 3.4). The prompt peak corresponds to events that are correlated

with the current beam burst. The random peaks arise because of the width of the gates

30

 

   

 

 

 

 

 

 

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'l ‘, Prompt
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Time Signal (Channels) Time (as)

Figure 3.4: Time spectra used to calibrate the BaF2 array. Left: Pulser data used to
gain match the individual electronic channels. Right: Time spectra from data used as
reference point. The prompt peak is indicated, as is a random peak.

used in the electronics. The width is sufficiently large for events from either previous
or later beam bursts to trigger the acquisition. These events are not correlated with
the current beam burst, and the occurrence of such events is random. The reference
point used in the calibration corresponds to the centroid of the prompt peak.

The time information from the BaF2 detectors was used in conjunction with the
time between the RF and the E1 scintillator in the S800 focal plane. The accuracy
of the Ban time, when measured relative to the E1 scintillator, was insufficient to
resolve the 7 rays from the neutrons. By subtracting the time between the RF and
E1 scintillator from the Ban times, the times were relative to the cyclotron RF. The
resulting resolution with this reference point was good enough to resolve the 7 rays

and neutrons.

3.1.2 CsI Array

The CsI detectors were calibrated for time in the exact same manner as the Ban
array (see Sec. 3.1.1). The individual gains were matched from detector to detector

with pulser data, while the prompt peak resulting from detected charged particles

31

 

1500 L fl

T T: l T T ]' I j
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8 fRandom ] ,
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100 .200 300
Time (ns)

Figure 3.5: Calibrated time spectrum from the CsI detectors. The prompt and random
peaks are indicated in the spectrum.
was used as the reference point. The calibrated time spectrum is shown in Fig. 3.5.
The individual CsI detectors were calibrated for energy. Energy calibrations were
performed for (1 particles and protons. It was necessary to have a separate calibration
for each type of particle as the response of the detector is not the same for different
particles. For the calibration process, the CsI detectors were removed from their
position during the run and stacked into a holder. The holder was then placed into
the path of the beam. To get calibration points, beams of protons and alphas were
used. To get enough points for calibration, the beams were degraded with the use of
aluminum. Additionally, the 8,0 was varied. Two different degraders were used. The
two degraders had thicknesses of 420 mg/cm2 and 209 mg/cm2. The values for Bp
varied between 0.65 Tm and 1.28 Tm. In the case of the a calibration, a source of
232U was also used. A typical calibration for both proton and a particles is shown
in Fig. 3.6. In the case of the protons, a linear fit gave a good fit to the calibration

points. A quadratic fit was needed for the a calibration.

32

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T I 1 I l I I

   

 

 

 

 

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O 1 1 1 141 A 1 l L 1 J '1 1 I 1 l O ; L1 1 1 . 1 l 1 1 1 1 l 1 1 1 1 1 1
0 100. 200 300 400 0 1 00 200 300 400
Fast Slgnal (Channels) Fast Signal (Channels)

Figure 3.6: Calibration curves for one of the CsI detectors. The points were obtained
as explained in the text. The solid curve in each panel shows the resulting fit through
the points. Left: Proton calibration. Right: a calibration.

3.1.3 CRDC Detectors

The two CRDC detectors were calibrated for position in both the dispersive (x) and
non-dispersive (y) directions. This was accomplished with the use of a mask. Each
detector had its own mask, and each mask had holes and slits in it. The position
of the holes and slits was known. With the masks in place, the beam only struck
the detector where the holes and slits reside, as the mask itself was thick enough to
stop the beam. This resulted in a spectrum that was used to calibrate the CRDC
detectors for position. The spectrum used to calibrate CRDCl is shown in Fig. 3.7.
In the figure, the non-dispersive position is given by S801_TAC, while the dispersive

position is given by S801_Cen_Fit.

3.2 8800 Analysis

3.2.1 Particle Identification

The particle identification (PID) in this experiment involved several steps. Typically,

a two-dimensional plot of the energy loss of fragments through the ion-chamber versus

33

 

 

 

 

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l I 1 l l 1 l q
00 100 200 300 400 500
S801_Cen_Fit (Channels)

Figure 3.7: The mask spectrum used to calibrate CRDCl for position in both the
dispersive and non-dispersive directions is shown. The points in this spectrum cor-
respond to holes in the mask, while the vertical bands correspond to slits in the
mask.

the time-of-fiight (TOF) is used for identification purposes. In order for this type of
approach to be useful in this analysis, the TOF had to be adjusted. It should be
mentioned that the TOF was started with the cyclotron RF and stopped by the
signal from the E1 scintillator. The TOF was adjusted in such a way as to eliminate
the dependence on the dispersive angle, 0, for nuclei with similar mass to charge
(m/q) ratios. The T OF was subsequently adjusted to eliminate the dependence on
the dispersive position for CRDCl (S801_Cen-Fit) for similar m/q. The general way
in which this was done was the following: first, a two—dimensional plot of TOF versus
6 (left panel in Fig. 3.8) was created. With this plot, the TOF was adjusted using the

following equation:
TOF’ = TOF[1+ 5(6 — 60) + A(6 — 90V]. (3.1)

The parameters 6, )1, and 60 were determined by reading points from the left plot in

Fig. 3.8. TOF’ was held constant for all points read from the plot for a given m/q in

34

 

 

   

 

 

 

 

 

500.............,
400t- {
A 3 3 P:
- - : =
3 300_— 1 g
V I. ‘ \
8 200: : 5
t— :— I; t—
100} —:
O-llllllllllll I:l O-llllllllllllllllll:
() 100 200 300 100 200 300 400 500
9 (a.u.) S801_Cen_Fit (Channels)

Figure 3.8: Plots used to adjust the TOF parameter for particle identification. Left:
T OF vs. 0. Right: TOF vs. CRDCI dispersive position

this process. Reading off three values for 0, A, and TOF yielded three equations with
three unknowns, which allowed for a simple algebraic solution. The three points were
chosen along the center of one of the bands at the beginning, middle, and end of the
region. The new parameter, TOF’, was further adjusted from a plot of TOF’ versus
8801_Cen_Fit (X). This plot is shown in the right side of Fig. 3.8. The equation used

in this step is similar to Eqn. 3.1, and is:

TOF” = TOF’[1 + ((X — X0)]. (3.2)

This time there are only two unknowns, namely C and X0. These parameters were
determined in the same fashion as ,8, A, and 00. The values found for the parameters
are shown in Table 3.1.

The new TOF parameter, TOF”, in conjunction with the energy loss of the frag-
ments through the ion-chamber (IC-Sum), allowed for the first step in the PID process.
This plot is shown in the right side of Fig. 3.9. Also shown in this figure is a plot of
IC_Sum vs. TOF. This plot shows that the adjustment to the TOF parameter was

indeed necessary, as it was impossible to distinguish between isotopes without it. The

35

 

 

 

 

 

 

 

 

 

 

_ I I ‘ l
200— - 400'
3 150— 3 300
S " E '
' .‘3
ml - ml
E9. 100~ 9 200'
- - 1
50 1 1 1 1 1 100 1 1 1 1 1
400 600 800 200 300 400
TOF (a.u.) TOF" (a.u.)

Figure 3.9: Left: Plot of IC_Sum vs. TOF. Right: Plot of IC_Sum vs. TOF”. This plot
was used initially for particle identification. The gate used is shown. The identified
isotopes are also indicated.
initial gate used for PID is shown in the right side of Fig. 3.9. A new gate was made
for each individual run. This was to account for any drifts in the RF.

A second gate was placed on a plot of IC_Sum versus the geometric mean of E1.
This is shown in the right side of Fig. 3.10. For comparison, the left side of Fig. 3.10

shows the same plot before the gate shown in Fig. 3.9 was implemented. The geometric

mean for E1 is given by:

geometric mean E1 = \/(E1_Up)(E1_Down),

(3.3)

Table 3.1: Parameters used to adjust the TOF parameter for particle identification.
AH units are arbitrary.

 

 

 

Parameter Value
6 5.5X10'4
A 4.17x10'7
60 502.181
C 2.56 x 10'5
X0 5749.65

 

 

36

 

 

 

   

 

 

 

 

 

 

200 L i 200 l
a i Z a I ’
:_ h d a. l-
3 150 — — 8 150 - .1
E ' 4 E L _
s - q s P
ml - . ml . .
2 100 - a B 100 — -
. .4 k .
: _ , 1 : :
0 - l I l l L 50 '- l l l ‘
5 100 200 300 100 200 300
Geometric Mean El (a.u.) Geometric Mean E1 (a.u.)

Figure 3.10: Left: Plot of IC_Sum vs. Geometric Mean E1 before the initial gate
shown in Fig. 3.9 was implemented. Right: Plot of IC_Sum vs. Geometric Mean E1
after the gate shown in Fig. 3.9 was implemented. This plot ultimately gave particle
identification. The gate used for final particle identification is shown.

where E 1_U p and E LDown are the signals from the top and bottom PMTs, respec-
tively. Typically, the geometric mean is not position sensitive; however, this was not
the case in this experiment. 170 fragments that hit the left half of the E1 scintillator
resulted in a different geometric mean than fragments which hit the right half. This
is evident in the right side of Fig. 3.10. Clearly there are two intense regions in this
plot. 170 fragments hitting the center of E1 show up in this plot between the two
regions enclosed by the gate. This effect may have been due to some dead area in the
scintillator. This gate, in conjunction with the other (right side of Fig. 3.9), ultimately

allowed for inelastically scattered 170 events to be isolated.

3.2.2 Fragment Energy Loss

The energy loss of 170 fragments was determined with the $800 magnetic spectro-
graph. The information collected from the CRDC detectors completely determined
the trajectory of fragments reaching the focal plane. The parameters of fragments

reaching the focal plane are given by 12;, 9f, 3),, and (1);. The parameters 3:! and y,

37

give the position at the focus, while 6; and (:5; give the angles of trajectory in the x-z
and y-z planes, respectively. These parameters, along with magnetic field mappings,
were used to determine the energy loss.

The magnetic fields created by the magnets within the spectrograph were mapped
as described in Ref. [42]. With this information, it was possible to analytically recon-
struct the trajectory of fragments with known magnetic rigidity through the 8800.
The ability to reconstruct the trajectory, coupled with the measured parameters at
the focus, allowed for the calculation of quantities that describe the motion of the
fragments as they left the target (6t, 3),, 915,, (it). The quantity 6, is related to the

fragments kinetic energy. Specifically, the quantity (St is given by

 

a. = , (3.4)

where EC is the kinetic energy of fragments traveling along the central axis of the

spectrometer. The quantity EC is determined by

c 2mEC
805800 = I: = - (3.5)
q q

 

The quantities Bpsgoo, m, and q are the magnetic rigidity setting of the S800, fragment
mass, and fragment charge, respectively. The target and focus quantities are related

through the matrix equation

{0A firfl

9
y‘ 2R f , (3.6)
(K51

W W

where R is the inverse matrix, which is calculated by the code COSY INFINITY [43].

 

 

 

 

The parameters 6, and EC are all that is needed to calculate the energy loss of the

38

b LII

J:;_;:3
. #44,; _1_.L L___l___l__l1- 1__;

Counts (104/MeV)
IT$I l (TifT—F—v—j-‘I r T_—'—T I—T—_

   

 

0l1‘ 11-1ng A J_ll 1 11
0 20 40 60 80 100 120

Energy Loss (MeV)

Figure 3.11: The 8800 singles energy-loss spectrum is shown for 170 events. The peak
at ~ 15 MeV is from the ground-state GDR.

fragments. The energy of the fragments, Ep, is given by
Ep 2' 6tEc + EC. (3.7)
The parameter 7 is calculated from this energ. More specifically,

+ 1, (3.8)

where v is the velocity of the fragment and c is the speed of light. Finally, the energy
loss (EL) is given by

EL = fly—62111 - 7), (3-9)

where 70 is calculated in the same manner as 7, except with E? replaced with EC.

The energy-loss spectrum for 8800 singles 170 events is shown in Fig. 3.11.

39

 

.1

 

500 III‘IIII’IIITIIVITIIII]

      

 

 

 

500:1"'I""I""I""I'”‘41 4:
400 L i 400 g
2? 300; ; Z? 300 J
a : 1 s; . i
a I 1 a 1‘
m 200 _ 1 m 200 .
i 1
100 .: 100 ,, J
3 . 1 I 1
.. w : ‘ “S 1

o 100 200 300 400 500 0 100 200 300 400 500

Eslow (a.u.) Eslow (a.u.)

Figure 3.12: Plots used to eliminate high-energy neutrons from the analysis. Both
plots show Epw versus ESlow- Left: Plot for forward detector. Right: Plot for back-
ward detector. The gate used to exclude neutrons is shown in each plot. The bands
corresponding to pile-up, neutron, and 7 events are also indicated.

3.3 BaFg Array Analysis

3.3.1 Selection of '7 Rays

In order to study the evolution of the GDR width with temperature, the 'y-ray decay
spectrum had to be extracted from the data. The excited Sn nucleus predominantly
decays by neutron emission at energies above the neutron binding energy. As a result,
many neutrons were emitted as the nucleus decayed. The neutrons were detected,
along with the '7 rays, by the Ban detectors. If the 7-ray decay of the GDR is to be
studied, the neutron events must be discriminated against, so that only 'y-ray events
are considered. The discrimination of neutrons consisted of two parts.

The first step in selecting 'y-ray events was to take advantage of the two com-
ponents of light emitted in BaFg. The ratio of the fast-to-slow component of light
is different for neutrons than it is for 'y rays. As a result, it was possible to elimi-
nate many of the neutron events by gating on a plot of the fast versus slow signals.

Fig. 3.12 shows such a plot. The gate shown in each side of the plot was used to

40

exclude events. A separate gate was made for each individual detector. Many more
neutrons were emitted in the forward direction than in the backward direction, as
evident in the plot. There is also a region that corresponds to pile-up for the forward
detector. Pile-up occurs when multiple low-energy 7 rays hit the same detector. The
occurrence of pile-up is completely random.

In order to eliminate low—energy neutrons, it was necessary to consider the time—of-
fiight as measured between the individual BaF2 detectors and the RF (TOFBap2). The
flight time should be shorter for 7 rays than neutrons at low energies, because 7 rays
move at the speed of light. Hence, by plotting the energy deposited in each detector
against the TOFBGF” it was possible to eliminate all neutrons from the analysis. The
plot used to do this is shown in Fig. 3.13. Fig. 3.13a shows the overall spectrum, while
the other plots in Fig. 3.13 show smaller ranges of times. Fig. 3.13b shows the region
corresponding to the prompt 7 rays, while Fig. 3.13c is for that of the random 7 rays.
The gate shown in Fig. 3.13b was used for final 7-ray selection. These 7 rays were
ultimately used to create 7-ray decay spectra. In order to determine the background,
and the contribution to the prompt 7 rays from the random ones, a second gate was
implemented. This gate is shown in Fig. 3.13c. The gate shown here is the same gate
as used for the prompt 7 rays, except that it is shifted by the time between beam
bursts from the cyclotron (54.3 ns). This allowed for the creation of another 7-ray
spectrum. This spectrum gave the background and the contribution of randoms. New
gates were created for every run to account for any drifts in the RF. The spectra

shown in Fig. 3.13 are for 10 runs.

3.3.2 Shower Reconstruction

To improve the response of the BaFg array, a shower reconstruction routine was
implemented. All BaF2 events sent to the routine were analyzed in the following way:

first, these events were sorted into descending order. Next, the detector with highest

41

 

 

O 120 160 200 240 280

 

 

 

 

 

 

 

TOFBaF2(ns)
4o_' ,....,.... 4o-~-v~m-_11
: Gate 0’) ‘ Gate (c) I
32 :— 32 ' f
% 2431's % 24 ns —
a : E 75 ‘- -/
‘faN16:— “le6 3‘. j»; . 5
1r :_ 111° , ,. 1.
8 8
o o
180 190 200 210 220 126 136 146 166 186
TOFBaF2 (ns) TOFBali (ns)

Figure 3.13: Plots used for final 7-ray selection. (a) Full spectrum used in the analysis.
(b) Region of spectrum corresponding to prompt 7 rays. (c) Region of spectrum
corresponding to random 7 rays. Neutron and 7-ray events are indicated in panels
(b) and (c). The gates used in the analysis are also shown.

energy was assigned as the primary detector in the primary shower. After this, the
detector with the second highest energy was considered. If this detector neighbored the
primary detector in the primary shower, it was also assigned to the primary shower.
Otherwise, it was assigned as the primary detector in a secondary shower. Then the

detector with the next highest energy was analyzed. If this detector neighbored any

42

 

Ey=14.8 MeV\

/ EY=0.0 MeV

, EY=O.0 MeV

 

 

 

 

Figure 3.14: Schematic to demonstrate the shower reconstruction process used with
the Ban array. An example of both a good shower (yellow) and bad shower (green)
are shown.
detectors already assigned to a shower, it was assigned to that shower. Otherwise,
it was assigned as the primary detector in a secondary shower. This process was
continued until all detectors were considered. Once all detectors were grouped into
showers, the energies of detectors belonging to a given shower were added together.
This sum gave the total energy of the 7 ray (E,). If any detector belonged to more
than one shower, the summed energy of these showers was rejected by setting the
energy to zero. A criterion in the add back process was that the energy must decrease
when moving away from the primary detector. Fig. 3.14 illustrates the process. The
detectors colored yellow were added together, and signify a good shower. The detectors
colored green signify a rejected shower. Analysis of all the data showed that only one
in 600 showers was rejected.

The effect of the reconstruction process is evident in Fig. 3.15. The blue curve in
Fig. 3.15 shows the spectrum resulting from PuBe source data, when no reconstruction

was performed. The red curve in Fig. 3.15 also shows a spectrum from PuBe source

43

u—n
U'c

 

 

E Photopeak ‘ 3
5‘ L 1St Escape \ 0‘ 1
010% Peak / «l
.3 ’1 \ . 1
e r-
3 t WK) 1
.«3 V1 11 3
o . 1
u E A j
l K 1
0l1111l1111l11111111111111111;
2.5 3.0 3.5 4.0 4.5 5.0 5.5

Energy (MeV)

Figure 3.15: Spectra from PuBe source to show the effects of reconstruction. The blue
spectrum is the result of histogramming each individual detector energy, while the
red spectrum uses the reconstruction routine.

data. For this spectrum, events were analyzed using the reconstruction routine. The

first escape peak is significantly lower for the red spectrum as compared to the blue

spectrum. Also, the photopeak is much improved in the red spectrum.

3.3.3 7-ray Decay Spectra

The final step in the BaF2 data analysis was to extract 7-ray decay spectra at various
projectile energy losses. To ensure that detected 7 rays were correlated with the
projectile energy loss, only events where there was both a BaF2 and S800 event in
coincidence were considered. With E, and projectile energy loss correlated, it was
relatively simple to extract decay spectra for different energy losses.

The 7-ray spectra were extracted by making cuts on projectile energy loss. The
cuts were made in 10 MeV steps from 20—90 MeV (i.e. 20—30, 30—40, , 80-90 MeV).
Additionally, the 7-ray spectrum corresponding to decays to the ground state was
measured. In all, eight spectra were extracted. For the 20—30 MeV energy cut, special

care had to be taken.

    

LIL-AJIJIIIAIIIAL

 

40

10 20 30
E7 Sum (MeV)

Figure 3.16: The fragment energy loss is plotted against the sum of detected 7 rays.
This spectrum was used to exclude 7 decays to the ground state. The gate used to
exclude 7-ray events that decay to the ground state is shown.

In the case of the 20—30 MeV energy loss cut, decays to the ground state were of
concern. To study the GDR built on excited states, these events had to be rejected.
The first step in eliminating these events was to sum up all 7—ray energies (E, Sum)
from each event and plot them against energy loss, as shown in Fig. 3.16. This plot
allowed for decays to the ground state to be eliminated by gating on the diagonal
band, as the diagonal band corresponds to these decays. All events in this gate were
excluded from the 20*30 MeV energy loss analysis. The spectra in Fig. 3.17 show the
result of the analysis in the 20—30 MeV energy loss region. The effect of excluding
events in the gate just described only affects the final spectrum for 7-ray energies
greater than 20 MeV. At these energies, the contribution to the final 7-ray spectrum
from the GDR built on excited states is minimal.

The events in the gate shown in Fig. 3.16 allowed for the 7-ray spectrum corre-
Sponding to decays to the ground state to be extracted. The events in this gate were

histogrammed. It should be mentioned that E, was histogrammed, and not the sum

of E7.

45

 

I If I? fil‘l

104.;

103: .

1.1-.1
1 041- .10

Counts
b‘
O
l l ll Ill
.1
~ H—O + 1
N _14_L.m_m_._r_u 1.1.14l _ 1_1 1411. ___J..L_Jl.l.ll. ___J

2 on 101
1- .11....19.

10 i

l

t..-
j.

13Y (MeV)

Figure 3.17: Breakdown of 7-ray spectrum corresponding to 20—30 MeV energy loss.
The solid red circles exclude events from the gate in Fig. 3.16, while the blue circles
are events from this gate. The open black circles show the resulting spectrum if no
gate would have been implemented.

4
10 FWjIITtITl’IIIl’TTII

 

 

 

 

Er
103:- i
.- .+ 3
U)
2 "+
g 10 1- + 3+ 1
C) *’ -+
i +
10;— g“?
1 1 1 1 l1 1 1 1 l 1 1 1 1 114 f1T:
10 15 20 25
137 (MeV)

Figure 3.18: Raw and random 7-ray spectrum for emery losses of 80—90 MeV. The
blue spectrum is the raw spectrum, while the red spectrum is the random spectrum.
The errors in the vertical direction are statistical, while the horizontal error bars are
to show the width of the histogram bins.

46

 

 

     

 

104+. (a) 10 z'. (11H, (c);
E ‘ j E :1 103%— I E
w 3 . 1 m 103‘:— ' 3 m : . 2
E 10 ‘r ? E E e r E » . a
g E 3 g r i g 102; 'u. a
L) 1021; u. 3 0 102g a. 3‘ U E -.. .
l ‘1 L 5 j ’7
10 .O‘O_1 l: .3 :1 10 f— 7 I. A
E _ .4 10 l;— ‘e'j‘ E j E
1L1_1_1_1_1_1J_1_l_1_1_.1_1_1j 51.11.111.1111.3 1@
10 15 20 25 10 15 20 25 10 15 20 25
BY (MeV) 13Y (MeV) 13Y (MeV)
O V
1 (d) : _- (e) 7 3 (03
103'! 3 1037' ' 103—4
m E . 3 m P ' j m 3 .
13 2E ."- 1 E 2: "- 1 E 2: .5
8 10 f ... a 8 10 S e”. “:1 g 10 E— '0'.
. O : : r v
0 1 «a. 1" — j 0 ~ ‘~9;.1
101:— -._3 10;— 6", 10;— 1o—
I .3 E 7 .i E 1 0
1E,11111I1;11,11‘171 1w 11 ‘ ‘7
10 15 20 25 10 15 20 25 10 15 20 2
13Y (MeV) E, (MeV) EY (MeV)
104W 104W
g (g) j 3 (h) j
,2 1031- 1 i9 103;— 31
8 1 ’ 1 8 ‘ ’. 1
U 102% ..o. “:1 U 102? .’
r 1 : 90’ i
L ,. ,1 .1... 3}
, 1 10 : 0 ‘4
1. i , 1 1 ~ 3
10 15 20 25 10 15 20 25
BY (MeV) E, (MeV)

Figure 3.19: 7-ray decay spectra. Panel (a) corresponds to decays to the ground state.
Panel (b) corresponds to enery losses of 20—30 MeV, (c) 30—40 MeV, (CI) 40—50 MeV,
(e) 50—60 MeV, (f) 60—70 MeV, (g) 70—80 MeV, (h) 80—90 MeV.

47

 

 

ITIIITTTTT1

 

 

 

*3 T 1 T r l
A 104 g- - (b) 3‘
> :— . “:
a : 2
:7, 103 :— ' 3
B *2 Z . O o 0 . :
5': =3 - - . *
LL] 8102 E— I “a
“O E ¢ 3
_ , ,
B 10 3" t I?
N .. . ..
.6 — ! L
1 1 1 m l L 1 l i i i t: T111 _1 1 hr 14‘ g; 1 L l m 14 l n l l ‘ —‘
8 10 12 14 16 10 15 20 25
Excitation Energy (MeV) Ey (MeV)

Figure 3.20: Panel (a) shows the ground state 7—ray spectrum measured by Ref. [23]
for 208Pb. The green curve shows a calculation for the yield of direct decays to the
ground state, while the black curve shows compound decays. The solid blue curve
is the sum of the blue and green curves. Panel (b) shows the ground-state spectrum
from this work.

The final 'y-ray spectrum for each energy loss cut was obtained by creating both a
raw and random (background) spectrum. The raw spectrum was made by considering
prompt "y-ray events (gate in Fig. 3.13b). These events were sent to the reconstruction
routine described in the previous section. All 7-ray energies were then histogrammed,
which resulted in the raw spectrum. The background contribution to the raw spectrum
was determined in a similar way, with the difference being which events were sent to
the reconstruction routine. In the case of the background, the events considered came
from the gate shown in Fig. 3.13c. Fig. 3.18 shows both the raw and background
spectrum corresponding to the 80—90 MeV energy-loss region. The final spectrum
was obtained by subtracting the background spectrum from the raw spectrum.

The final 7-ray decay spectra for all energy losses considered are shown in Fig. 3.19.
The v-ray spectrum corresponding to decays to the ground state (Fig. 3.19a) was not
analyzed in this work. Not only does this spectrum contain decays directly to the

ground state, but it also contains decays that first go through excited states before

48

finally decaying to the ground state. It is extremely difficult to disentangle the different
contributions. The only such analysis of this type has been performed on Pb [23].
Despite the fact that the ground state y-ray spectrum was not analyzed quanti-
tatively, it is still interesting to compare this spectrum to the one in Ref. [23]. Both
spectra are shown in Fig. 3.20. The spectrum from this work (Fig. 3.20b) has a very
similar shape to the blue curve in Fig. 3.20a. This indicates the presence of both

direct and compound decays to the ground state.

3.4 (351 Array Analysis

3.4.1 Identification of Events

The CsI array was used to detect charged particles. In order to study the charged
particles, the various particles were identified. In particular, a and proton events were
isolated. As in the case of BaFg, CsI has two components of light (see Sec. 2.1.2),
which allows for pulse shape discrimination. The proton and 0 particles leave a differ-
ent ratio of fast-to—slow energy, and plotting these signals against each other allowed
for the separation of these events. Two such plots are shown in Fig. 3.21. In Fig. 3.21a,
more particles were detected than in Fig. 3.21b. This is as expected, since the detec-
tor corresponding to Fig. 3.21a is more forward in the array. The spectra shown in
Fig. 3.21 are not gated on 170 events. The only requirement in making these plots
was that a charged particle came in coincidence with a fragment in the S800 focal
plane.

The plots in Fig. 3.21 are very useful for identification purposes. However, even
with these plots it is difficult to gate on the different events. The bands in the plots
are very close together. A larger separation between the bands can be achieved by

manipulating the fast signal. The fast signal (Efast) was transformed according to

49

 
   
    

  
  

 

 

 

500 500

(a) : :
400 d’g -} 400 j
1» a’s t's -, “ I o . 1
g 300 \ , N " — g 300 . ._ .
\ ‘ :6 as ‘
n: .i Igndr' ’ - “a N - "
9 200 " p5 ‘ U 200 " \ ' ‘
- — a: . S ..
g jg'y/ . g . r p 1
100 451:3” — 100 .‘7. ‘ -
4‘? 2 .

.” 1 g

0 100 200 300 400 500 O 100 200 300 400 500
ESlow (Channels) Eslow (Channels)

Figure 3.21: CsI fast vs. slow spectra. The spectrum in panel (a) was measured at a
scattering angle of 60°, while in panel (b) the scattering angle was 150°. The bands
corresponding to a, triton, deuteron, proton events are indicated. These plots were
transformed, and used for identification purposes.

Ref. [4]. The transformed signal (Effast) is given by

112-3!
y2-y1

 

E}a,, = (3.10)
The quantities y, yg, and y1 are defined in Fig. 3.22, and are dependent on the
boundary lines (blue lines in Fig. 3.22). The placement of these lines was such that
all data was between them.

The transformation of the fast signal allowed for gates to be made on proton
and 0 particles. The plots in Fig. 3.23 show the result. The separation between the
bands corresponding to the proton and a particles is much better in this plot than
in Fig. 3.21. Ultimately, gates were only implemented for proton events. Once 170
events were gated on, very few 0 particles were detected. Also, only 4% of the events

shown in Fig. 3.21 and Fig. 3.23 were left after gating on 170.

50

Efast

 

 

 

E

slow

Figure 3.22: Illustration of parameters used to transform E fat. The parameters y, y1,
and y2 were used to transform E fast as shown in Eqn. 3.10.

 

 

 

 

 

 

 

500 500 I. I I I I I I I I l I I I I rI I I I I I I I
(a) I I (b) 2
400 p,s —: 400 {- p,s L
2 300 K... -_ 5 sons: ‘ -.
:3 p O c R l ‘ CU {3.4-H ’. ' .,
is) ' ts 3 6 ~f 1
a: 200 1 s: 200 ~..-- ' 1
s (a . -‘ ~ 3 v.5 . .1
100 as j 100 _~ - R 1
j t O. S 1
0 l l I l l l l 1 1 I l l 1 l l l l l l I 1 l 1 l 0 ‘- l l l l I l l l l l l l l l l l l l 1 l 1 1 L 1

O 100 200 300 400 500 0 100 200 300 400 500
Eslow (Channels) Eslow (Channels)

Figure 3.23: 'Dansformed CsI spectra for charged-particle identification. The trans-
formation was performed on the plots shown in Fig. 3.21. As in Fig. 3.21, a, proton,
triton, and deuteron events are indicated. Ultimately gates were places on the proton
bands.

3.4.2 Proton Spectra

Proton events were isolated in order to try to determine the initial excitation energy of
the target nucleus. In a past experiment, the correlation between projectile energy loss

and target excitation energy was studied [36]. It was hoped that a similar approach

51

   
 

   
  
 

120 120
100 g 1 100 '
g 80 ~ 9 80
O -1 O
E 6 ' —1 E 60
.4 ._i
m m

ILJllAl

  

AL'AI

 

 

0 1 l I O I‘m-list.“ "1 . '
O 20 40 6O 80 100 120 O 20 40 60 80 100 120
Ep(M e V) Ep(M e V)

    
 
 

lllle‘lAlllJJAJ_‘_l

|

 

0 L i ' ‘
0 20 40 6O 80 100 120
131, (MeV)

Figure 3.24: Plot of energy loss vs. proton energy for all CsI detectors. Panel (a) shows
the resulting spectrum from prompt events, while (b) shows the random events. Panel
(c) shows the random subtracted spectrum.

could be used here, by measuring proton spectra.

The fragment energy loss was correlated with the detected protons. Since the
energy loss and proton energy were known, it was possible to construct a plot of
fragment energy loss (EL) against proton energy (Ep). This plot is shown in Fig. 3.24,
and allowed for the proton energy spectrum to be extracted as a function of energy

loss.

52

 

Counts
#- U:
C O
O O
I l l l ‘ l I l l
C: t
r.
‘1_L._._l_.L._LLL~iJ__l_LLlJL_L._ l_Ll

200; j L.

3. r” '
100and E
0:Ji 1 i illuli l

0 120' 40 6O 80L106L120
EL(MeV)

.1_._1_J.

Figure 3.25: The fragment energy loss in coincidence with proton events is shown.
This spectrum is the projection onto the energy-loss axis from Fig. 3.24c. The broad
peak at 80 MeV is indicative of pickup-decay reactions.

Protons due to knockout and pickup-decay reactions were of concern. Pickup-
decay reactions occur when the 17O projectile picks up a proton from the target, and
subsequently decays by the emission of a proton. Knockout reactions occur when the
projectile knocks a proton out of the target.

The presence of knockout and pickup-decay reactions was investigated by pro ject-
ing Fig. 3.24c on to the EL axis. This is shown in Fig. 3.25, and gives the energy
loss distribution associated with the detected protons. There is clearly a broad peak
in this spectrum at 80 MeV, which indicates the presence of pickup-decay reactions.
There is also evidence for knockout reactions in Fig. 3.24c. The energy of the emitted
protons ranges from a couple of MeV all the way up to the projectile energy loss. The
presence of knockout and pickup-decay events in the CsI array should be limited to
forward scattering angles. To eliminate these events from the analysis, only backward
detectors could be considered.

Plotting the fragment energy loss against the proton energy for individual de-
tectors gives an indication of whether or not knockout and pickup-decay reactions

can be eliminated by considering only backward detectors. The spectrum shown in

53

 

 

 

   

 

 

 

 

 

 

"I I 'I' I "'l ' I 'l' 'l I "'l
120 r 120 _ —l
: (a) : : .. q}, ,. ._(b) I
. . - . .' .~ - .. 4
100 in}; - 100 : 5N ' 3‘ -:
{by}: : * I: ' . , :
9 80 f2?" 1 9 80 r : ‘ i
‘9 :If’ : ‘9 t :
E 60 :5 1 E, 60} ..
r—1 ’3’? : p—l C 2
m 40 L—"’:'-'-,', — m 40 ~ ., —
:12: 'i; 2 C a 1,, Z
20 54“ -: 20 :— I". -:
nay. ‘ _ ‘1 , ... . .I’ .
0"lullllllll‘lllllllllllll- 0ll‘l.l.ll.lll.llllllllllllll
0 20 40 6O 80 100 120 0 20 40 60 80 100 120

Ep (MeV) 13p ( e V)

Figure 3.26: Plot of energy loss vs. proton energy. Panel (a) shows the spectrum from
the backward most detector, while (b) shows the same for the forward most detector.
Fig. 3.26a was measured at a scattering angle of 180°, while in Fig. 3.26b the scat-
tering angle was 30°. The spectrum measured at backward angles is much different
than the one at forward angles, as the high-energy protons are almost completely
absent from the spectrum from the backward detector. It appears that protons orig-
inating from knockout and pickup-decay reactions can be eliminated by considering
only backward detectors.

The final proton spectra shown in Fig. 3.27 were extracted by only considering
detectors covering scattering angles between 120° and 180°. The proton spectra were
extracted as a function of excitation energy. Unfortunately, the statistics are poor.
As a result of the poor statistics, this data could not be used to determine the initial
excitation energy of the target nucleus.

Although the CsI data was not very useful in this experiment, it does show that
detection of charged particles in the decay of the excited nucleus in GDR studies is
feasible. If a similar approach is to be used in future experiments, the solid angle
coverage of the CsI array should be increased. This is easily accomplished by adding

more detectors to the array. Additionally, the array should primarily cover backward

54

 

 

 

 

 

 

4O :— T T l T L; 7 7 ‘ T ‘r T T 4
c -I .
j: . a it b i
30H I)?J I)q
LIj I. I
20;“ l .6?, *
:I L“, 1 Ian]
. I? I I. 1“. id} .4.
I? ‘1 I
30LIfi T I I I i I I I , fl

—<>—
0..
v

Counts
at I
J 1 _1-J._l_;_l__L_l_L_.__l

I (c) ‘“

 

 

llii

 

 

l

}__
—{
.4-

_i_l_L.llJ_Ll Il I

 

1..
.l

A
(D

v
il.i

ITIYl

‘—-E_‘—..-a
«.fi—l—_—’
C9

 

 

 

 

 

 

9 LI .. i
x 7 “U I . I j
90 o 30 60 9 120
Ep (MeV)

Figure 3.27: Proton energy spectra. The panels correspond to the following projectile
energy losses (a) 30—40 MeV, (b) 40—50 MeV, (c) 50—60 MeV, (d) 60—70 MeV, (e)
70——80 MeV, and (f) 80—90 MeV.

55

angles As mentioned earlier, the presence of knockout and pickup-decay reactions is

very small at backward scattering angles.

56

Chapter 4

Tools to Interpret the y-ray

Spectra

To interpret the results of the data analysis presented in the last chapter, several
tools were needed. It was necessary to perform statistical model calculations. In this
experiment bremsstrahlung radiation was also a concern, and had to be dealt with.
The response of the BaF2 detector arrays was also needed in order to compare theo-
retical calculations with data. Finally, the nuclear temperature had to be calculated
in order to compare this data with previous measurements. In order to calculate the
temperature, it was necessary to determine the mean excitation energy of the nucleus

along the GDR decay.

4.1 Statistical Model Calculations

The fundamental assumption of the statistical model for the decay of an excited
nucleus is that all relevant nuclear degrees of freedom are equilibrated before the
decay can take place [3]. The computer code used to perform the calculations was
CASCADE [44,45]. In this code, the user specifies the initial population of the excited

nucleus in terms of energy and angular momentum. Based on the initial population,

57

the code calculates a final decay spectrum for alpha, proton, neutron, and 7-ray decay.
These spectra are output according to the amount of the total initial cross section
that went into each decay. It was the 'y-ray decay spectrum from these calculations
that was eventually compared with data. The relative probability of a given nucleus
decaying by alpha, proton, neutron, or gamma emission is dependent on the relative

decay rates as calculated in the code.

4.1.1 Initial Population of Nucleus

In past inelastic-scattering experiments, the energy loss of scattered fragments has
been used to determine the initial excitation energy of the nucleus. In these exper-
iments, the initial excitation energy was equated directly to the fragment energy
loss [25,27]. This procedure has since been shown to be inaccurate [36,37]. A signifi-
cant range of energies are populated well below that of the energy losses considered,
as evident by the forward CsI detectors (see Fig. 3.24c). This becomes more and more
problematic as higher and higher energy losses are considered.

An experiment was performed to investigate the correlation of energy loss and
excitation energy. This study was performed with the use of 0 particles as the pro-
jectile, and 209Bi as the target [36,37]. Although the projectile and target used here
differ, the results of the study can be used to aid in the determination of the energy
distribution resulting from a given energy loss. Table 4.1 shows how the projectile
energy loss and average excitation energy (FF) compare. As the table indicates, the
average excitation energy is less than that of the energy loss for energ losses greater
than 55 MeV. The discrepancy between energy loss and excitation energy becomes
larger and larger as the energy loss increases.

In addition to the work of Ref. [36], there is another way to get some indication of
the correlation between initial excitation energy and energy loss. Fig. 4.1 shows the

energy loss spectrum in coincidence with 7 rays with energy greater than 4 MeV. The

58

 

 

 

EL (MeV) E (MeV)
45 45
55 55
65 63
75 68
85 74
95 79
105 84

 

 

 

Table 4.1: Summary of the projectile energy loss and target excitation energy. This
information is taken from Ref. [36], where the reaction 209Bi(a,a’) was investigated.

structures in this plot correspond to the subsequent opening of neutron evaporation

channels, and indicate a correlation between energy loss and excitation energy [24].

The structures can clearly be identified up to 35 MeV corresponding to the 4n channel.

Thus, the energy loss can be equated directly with the excitation energy up to at least

35 MeV. For energies higher than this, the work of Viesti et al. [36] had to be used.

A distribution of excitation energy was determined for a given energy loss by

Viesti et al. [36]. The distributions relevant to this work are shown in Fig. 4.2 along

 

5[.ll[
I-

—1n

[—

Counts (104/MeV)
N

H

 

l l

l‘ITI[I‘TI[lITI

 

uni Ilml

lil.144

lllllLlllll..ll

 

lIll l._1_.__lllilll ll llnLl ll‘lll

,._

 

ohlillliTT7[l

O

110 20 3o 40 50 60 70 80
Energy Loss (MeV)

\O
C

Figure 4.1: Spectrum of inelastically scattered 1"'0 particles in coincidence with '7 rays
with E7 24 MeV. The successive opening of neutron evaporation channels, up to 4n,

is indicated.

59

 

A

b)

       

EL=65 MeV

   

Relative Probability

fl

N
[7'1" T‘T'TT'TT ['—l TIT—m7— TTET 7m "rm ‘ TT

$1 lllllIJllLl

I l I I I I I I i I I
60 80 100 0 2O 40 6O 80 100 120
Excitation Energy (MeV)

ImJI

20"

1

O

-I
40

C

Figure 4.2: Plots adapted from Ref. [36]. The distribution of excitation energy result-
ing from a given energy loss is shown. The corresponding energy losses are indicated
by the arrows in the plots. The points are data from Ref. [36], while the solid curve
through the points is a fit.

with the corresponding energy loss. All distributions from Ref. [36] have a low energy
tail. This tail is predominantly due to knockout and pickup-decay reactions.

The contribution of knockout and pickup-decay reactions is expected to be much
lower in heavy-ion scattering than in a scattering [24]. Also, the contribution to the
calculated 7—ray spectral shapes from the low-energy tail is negligible for 'y-ray energies
above 8 MeV. As a result, the low-energy tail was not included in the distributions of
excitation energy used in this work. The distributions used are shown in Fig. 4.3. The
corresponding energy losses considered are also shown in this figure for comparison.
The energy loss distributions shown in Fig. 4.3 were determined from the S800 singles
data (see Fig. 4.4). The peak at approximately 80 MeV in Fig. 4.4 indicates the
presence of pickup-decay reactions. For spectra gated on energy losses below 30 MeV,
the energy loss was equated with the initial excitation energy in the calculations.

CASCADE will calculate the initial distribution of angular momentum for a given
energy; however, this calculation is only applicable for fusion-evaporation reactions.

In inelastic-scattering experiments, the excited nucleus populates low angular mo-

60

men]
Whirl

OPTIOI

 

    
  
   

I

A U! Ch
I I I

N U)
IIIIII

Illlllllllllllllllll
III III III II III

p—a
IIlIILLIIIlIiLlII

O

 

 

J> U:
r I l I

Relative Probability
N b.)

—n

,.
IlllI_11J_LlJlLlll111lIII

O

 

 

N U) A U!
AlmigIALLImJnIIII

_-
I

 

 

 

 

 

J60] .
Excitation Energy (MeV)

Figure 4.3: Distributions of E‘ used in this work for energy losses greater than 30 MeV.
In all panels, the red curve shows the distributions used in the calculations, while the
blue curve shows the distribution of energy losses considered, as determined from
the S800 singles data. Panel (a) corresponds to 30—40 MeV, (b) 40—50 MeV, (c)
50~60 MeV, (d) 60—70 MeV, (e) 70—80 MeV, and (f) 80—90 MeV energy losses.

mentum states. CASCADE has the option of reading in a two—dimensional matrix,

which specifies the initial angular momentum and energy. To take advantage of this

option, the initial distribution of angular momentum must be determined.

61

 

 

    

II [I]
III I
EH] ]
5% ix I
5L? [

       

Oflllllllllllllll‘. I
O 20 40 60 80100120

Energy Loss (MeV)

Figure 4.4: The energy loss determined from the 8800 singles data is shown. This
type of spectrum has been used in past experiments [25—27] to determine the initial
excitation energy of the target nucleus.

A range of angular momenta was calculated for a given excitation energy. The
upper limit (Jmam) was determined using the sum of the matter half density radii
(bmax) of the target and projectile nuclei. The lower limit (Jmin) was calculated using

the nuclear interaction radius (bmin). This quantity is defined as:

CT+CP

in = 44 - 1
bm 07“ + CP + 9 6.35

(4.1)

where CT and Cp are the matter half density radii of the target and projectile nuclei,
respectively [4]. The matter half density radius is 5.43 fm for 12”Sn and 2.83 fm for
170. With these quantities determined, it was straightforward to calculate a lower
and upper bound for the angular momentum transferred to the target. The range of

angular momentum (J) of the target after the scattering process is given by:

1

min max = in man: 5, 4-2
J / 197bm / p ( )

62

 

 

 

b

min/max

 

 

 

Figure 4.5: Cartoon of inelastic-scattering process to illustrate the momentum trans-
ferred to the target from the projectile. All quantities are explained in the text. This
figure was adapted from Ref. [4].

where p is the momentum transferred to the target. The value of p is determined by:

19: lle - IE], (4.3)

where 171) and E are the momentum of the projectile before and after scattering,
respectively. A cartoon of the process is shown in Fig. 4.5.

The two-dimensional matrix used for the energy losses of 20—30 MeV is shown in
Fig. 4.6. It is evident from this figure that as the energy loss increases, so does the

angular momentum transferred to the target in the scattering process.

4.1.2 Decay Rates

CASCADE calculates the decay rates from the absorption cross sections for the in-

verse (excitation) process, using the reciprocity theorem [46]. In this model, the ex-

cited nucleus may decay by emission of a proton, neutron, alpha particle, or 7 ray.
The width per unit energy, dI‘x(ex)/dex, for emitting a particle :12 from an excited

nucleus 1 (excitation energy E, angular momentum J1, parity 7n) to form a daughter

63

Relative
Probability
0

 

Figure 4.6: Population of the target nucleus in terms of energy and angular momentum
for the energy losses of 20—30 MeV. The relative population for each energy was
determined by the 8800 singles data shown in Fig. 4.4.

nucleus 2 (at E2, J2, IQ) is then given by [3]:

dI‘(e,,) p2(E2, J2, IQ) ”+5: "+5
= 2 : E : I 4.4
(l8;- 27rp1(SE1IJla7rl) T L(ex) ( )

=lJa- 5:] L: IJI- 5|

 

 

The kinetic energy of particle at is ex = E1 — E2 — Bx, where BJr is the binding energy.
Other quantities in Eqn. 4.4 are the level density (p), orbital angular momentum (L),
channel spin (S 2 J2 + 5;), and transmission coefficients (ij(ex)). The transmission
coefficients are for the scattering of particle :1: on nucleus 2, and the values for these
coefficients are obtained from the optical model.

The width per unit energy, dI‘7/dE,, for E1 7 decay is obtained in a similar way,
and is given by [3]:

dI‘7(E.,) 2 p1(Ez, J2, «2) 054E.) E3
515:, pI(EI,JI,vrI) 3 We)”

 

 

(4.5)

where E, = E1— E2 and J2: J1 or J1 :i:1. The quantity 001,451,) represents the cross

64

section for E1 photoexcitation of a single level, averaged over all levels populated by

7 decay in a given nuclear reaction, and is defined by:

 

 

2 2 S-F-E2
47rehNZZ J J 7 (46)

(E2 — E302 + EII‘I'

1:1

The quantities Sj, Ej, and F,- are the values for the strength (in units of the classical
dipole sum rule), energy and width of the E1 resonance, respectively.

The probability of a nucleus decaying through the available channels (n,p,a,7) is
dependent on the values calculated for the width per unit energy. Specifically, the
relative magnitude of these calculations for the individual channels determines the
percentage of the initial cross section that goes to the various decays. Since this is
the case, it is very important that the quantities used to calculate the width per unit

energy are accurate. Most of the quantities are well known, or can be calculated.

4.1.3 Level Density

It is very important to describe the level density as accurately as possible. The ex-

pression used to calculate the level density in CASCADE is given by [3,44]:

(ll/2(2J-l- 1) 82m

 

p = 1263/2(U + T)2 ’ (4'7)
where,
UzE—A—‘KJQ—Zl—Uzaflfl—T, (4.8)
A = Alf/3 (4.9)
6 = 21,,g,d52, (4.10)
6’ = 6(1+6J2 +8.14). (4.11)

65

 

O\
]

 

 

 

 

.A I I
‘> 14; i
g r ff”:
v13F// i
U I l
12; g
11: II II IIIIII]
0 20 40 60 80 100

Energy (MeV)

Figure 4.7: Level density parameter comparison for 120Sn. The curves correspond to
the following formalisms: green-A/ 8, black—A/Q, blue—A/ 10, and red—Reisdorf.

In the above equations, E is the energy, A is the pairing energy, and T is the nuclear
temperature. In the expression for A, a new parameter is introduced, namely the
constant p, which is 8.5 MeV. The quantity 6 is determined by the rigid body moment
of inertia, while 6’ represents the moment of inertia of a deformable rotating liquid
drop [3]. The only other quantity not defined in Eqn. 4.7 is the level density parameter,
a.

Several approaches have been used to calculate a. In past experiments, this quan-
tity has been fixed over all energies and angular momenta considered. It was not
uncommon to fix the value based on the mass (A) of the nucleus. The typical range
used for Sn corresponds to A / 10—A / 8. In more recent experiments, the formalism set
forth by Reisdorf [47] has been adopted. A comparison of the different formalisms
for the level density parameter is shown in Fig. 4.7. In the Reisdorf description, a
is both energy and mass dependent. Additionally, this description takes shell effects
into account. In the description set forth by Reisdorf, a is calculated in the following
way:

a = 0.04543r3A + 0.1355r3A2/3 + 0.1426roA1/3 (4.12)

66

a = 51(1 + (SD—“,9 (1 — e“U/ED)). (4.13)

The quantities To and ED are constants given by 1.16 frn and 18.5 MeV, respectively,
and (SS is determined by the magnitude of shell effects. The Reisdorf description for
the level density was adopted in the statistical calculations used in this analysis. The
use of this level density description is even more important for nuclei where shell

effects are large.

4.1.4 GDR Width

The width of the GDR is typically held constant throughout the decay process in
CASCADE, and corresponds to an average along the entire decay. The code was
modified to include the option of a non-constant width. In a recent paper by Kusnezov
et al. [35], a parameterization was presented for the width of the GDR as a function
of temperature (T), angular momentum (J), and the mass (A) of the nucleus. The

parameterization is given by:
MT. J. A) = NT, J = o. A) [L (or/(“3’ (4.14)

P(T, J = 0, A) 2 RM) + C(A)In(1+ T), (4.15)

where MM) is the ground state width of the GDR, C(A) a: 6.45 —A/100, { = J/AS/G,
and L(€) — 1 z 1.8[1+e(1'3‘5)/°'2]‘1, as defined in Ref. [35]. This parameterization was
incorporated into CASCADE, and allowed for the width of the GDR to be adjusted
continuously along the decay.

In addition to the parameterization of Ref. [35], a second temperature—dependent
width was incorporated into CASCADE for Sn, as shown by the blue curve in Fig. 4.8.
This curve is an empirical fit to the existing data for Sn. The dependence of the width

on angular momentum was not considered. The excited nucleus in this work never

67

 

 

#l—l 1

1.5 2.0 2.5

i . l 4 i i l i i
0.0 0.5 1.0
Temperature (MeV)

Figure 4.8: GDR width descriptions incorporated into CASCADE. The red curve
was calculated from Eqn. 4.14 at low angular momentum, and the blue curve was
empirically determined from existing data. Both of these curves were incorporated

into CASCADE.

populates angular momentum states higher than 20h, and angular momentum effects
are insignificant below 205 in Sn [33,35]. The width description by Kusnezov et al. is

also shown as the red curve in Fig. 4.8 for comparison.

4.2 Bremsstrahlung Radiation

In addition to the statistical ”y rays, there was also a non-statistical contribution to
the 7—ray spectra. Bremsstrahlung radiation was present in this data, as can be seen
at high 'y-ray energies (see Fig. 3.19). The form of the bremsstrahlung component of
the spectra was assumed to have the form exp(-E.,/E0), where E0 was set to a value
of 25 MeV [48, 49]. This value is smaller than that given in Ref. [48], because the
collision is peripheral [49] in this experiment.

The study of bremsstrahlung radiation is interesting in itself. Numerous exper-
iments have been performed to study bremsstrahlung radiation [48,49]. The 'y-ray
spectra from this work contain bremsstrahlung information; however, statistics are

too poor to perform a detailed analysis.

68

4.3 GEANT Simulation

The response of the BaF2 arrays was simulated with the Monte Carlo code GEANT [50].
This code allows the user to specify the exact geometry of the experimental setup.
The S800 target chamber, target chamber doors, BaF2 arrays, and aluminum used to
hold the BaFg arrays together were specified. GEANT also allows for the materials
used in the experiment to be defined. This is especially important since BaFg is not
one of the standard materials in the code.

In the simulation it is important to take the energy resolution of the Ban arrays
into account. It was not possible to determine the resolution of the arrays as a func-
tion of energy in this experiment. The only data that was available to determine the
resolution was the source data. The highest energy point was only 4.4 MeV. Informa-
tion was needed for energies much higher than this. To account for this, the energy
resolution determined in the work of Ref. [51] was adapted. The detectors used in
Ref. [51] were the same detectors used in this experiment. For this experiment, all
scintillators were recoupled to their photomultiplier tubes. The recoupling resulted
an energy resolution that was slightly better than that of Ref. [51], so the spread (a)
measured by Ref. [51] at a given energy was scaled by 90%. The resolution used in
the simulation is shown in Fig. 4.9.

It was possible to use the same analysis routines from the data analysis in the
simulation. Since GEANT is a Monte Carlo code, events can be tracked individually.
For a given event in the simulation, all detectors were considered. Any detectors that
had energy signals were flagged for event reconstruction (see Sec. 3.3.2). Once the
energy reconstruction was complete, the energies were histogrammed.

The accuracy of the simulation was tested by comparing experimental source data
to simulated source data. This was done for both the 88Y and PuBe sources, and is
shown in Fig. 4.10. The good agreement between data and simulation indicates that

GEANT can be used to generate a realistic response function for the detector arrays.

69

 

0 08 E = 0.0207 + €

 

ll]! lllll

l l l l l A I l
5 10 15 20 25 30
By (MeV)

Figure 4.9: Energy resolution of the BaF2 arrays. This plot is adapted from Ref. [51].
The solid points show where measurements for the resolution of the array were made
by Ref. [51]. The solid curve is the scaled resolution used in this analysis, as discussed
in the text.

 

 

    

 

 

7twv.w,mp.v: 15 w. :
96; 5 ‘ 9 f
o 5: 99 7 cu _
E ‘E 39 El “2
I? 4E 90 : E 3
zyg— : 53 i L: a
2 - s: , ‘2
S r b , 8 l :
U 1[‘ fl 0 £ _
0L. . 0n.m..1..i . '
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
E7 (MeV) E7 (MeV)

Figure 4.10: Comparisons of source data and simulation. Left — 88Y. Right — PuBe.
In each panel, the solid red diamonds are the result of the simulation, and the open
blue circles are the data.

To generate a response fimction for the arrays, it was necessary to emit a 7—ray
with a given energy and plot the resulting detected energy in the Ban arrays. In this
experiment we dealt with energies up to approximately 32 MeV. The response of the
arrays was determined in 100 keV steps up to this energy. This was accomplished by

emitting random energy ”y rays in random directions. A 2-D histogram was created

70

 

Figure 4.11: Response of the BaF2 array as simulated by GEANT.

with the incident 'y—ray energy on one axis, and the detected 'y-ray energy on the other
axis. This histogram is displayed as a surface plot in Fig. 4.11. Since all energies were
random, it was necessary to keep track of the number of 'y rays emitted in each
100 keV interval. This was easily accomplished by histogramming the incident energy
event by event. The resulting distribution of incident ry rays is shown in Fig. 4.12.

Making cuts on the histogram shown in Fig. 4.11 allowed for the response of the
Ban arrays to a given energy to be examined. Several cuts are shown in Fig. 4.13.
These cuts show the overall behavior of the array to a given energy. These plots do not
take the geometric efficiency into account. The response of the array to a given energy
was obtained by making a cut on Fig. 4.11, and scaling by the number of incident 'y
rays at the given energy. The number of incident 7 rays is shown in Fig. 4.12.

The response function of the arrays allowed for the CASCADE calculations to be

folded. When comparing data and theory, it is necessary to either unfold the data,

71

Counts (104/MeV)

 

[[IfiTT It T.TT[T

N

l J 9 1
1411114111 11111 111111111

10 20 3O
Incident Energy (MeV)

 

00*

Figure 4.12: Distribution of 7 rays emitted in the GEANT simulation.

 

 

—0—

 

Relative Probability

 

 

—]"'

fir—

(b)

lLLl llllllllllllllllllllll

L1

lllll

 

_‘

l
l

 

 

l
I

fit
J

 

(C)
l l .

05’. . .WW‘E'M- .1, -
O 5 10 15 20 5
Detected Energy (MeV)

Figure 4.13: The response of the BaF2 array is shown for several energies. Panels (a),
(b), and (c) correspond to incident '7-ray energies of 5, 10, and 20 MeV, respectively.
The incident 7—ray energy is indicated by the vertical line in each panel.

72

 

—n .—n
C). Q
L» --
IT IT T'TT'WT T'TTTTT—"Ylm TT'ITI'TII III?“ 'ITTW—FTWTT‘ 'T

Cross Section (a.u.)

—t
o.
K).

 

,_
,_

m11l411l

1‘0 L13 20 25
E, (MeV)

Jim.
10 5

Figure 4.14: Example to demonstrate the effects of folding. Blue curve — Raw CAS-
CADE calculation. Red curve — Folded CASCADE calculation. The red curve was
normalized to the blue curve at 6 MeV.

or fold the calculations. Since it is very difficult to unfold the data, the calculations

were folded. An example of the effects of folding are shown in Fig. 4.14.

4.4 Nuclear Temperature

4.4.1 Formalism to Calculate the Temperature

The conversion of excitation energy to temperature is necessary if comparisons are

to be made between theoretical predictions and experimental results. The nuclear

temperature (T) is defined as:

T = (3% [171(p)l)—1 , (4-16)

where p is the level density and U is the energy. At high energies, the Fermi gas model

of the nucleus is valid, and the level density has the following form [52]:

p o< exp(2\/av). (4.17)

73

This form of the level density, along with Eqn. 4.16, leads to an expression for the
nuclear temperature given by:

T: 9.
a

(4.18)
The expression given in Eqn. 4.18 has traditionally been used to determine the tem-
perature in GDR experiments [3,16,20,25,27]. It should be noted that the level density
parameter was constant in the derivation of Eqn. 4.18.

The Sn and Pb data existing prior to 1998 have been re-evaluated [35]. In the work
of Ref. [35], the Reisdorf [47] level density formalism was used. Using this formalism,
and the level density in CASCADE (Eqn. 4.7), the temperature was re—calculated
using Eqn. 4.16. The expression obtained by Ref. [35] was:

T=-—5( H555. [E 5—5734, «19>

do c165 U
—=— —1. 41/30 . 4.
dU U2 [ 0+(1.0+E—D)e ] ( 20)

In this derivation, the quantity (U +T) in Eqn. 4.7 was replaced by U. This is justified

where

as T is small compared to U. The expression in Eqn. 4.19 was used to calculate the
temperature in this work.

The calculation of temperature is dependent on the level density description used.
Since different level density descriptions are used in analyzing data, it is important
to determine the temperature in a manner consistent with the data that comparisons
are to be made with. The effect of using different level density descriptions is evident
in Fig. 4.15.

Some care has to be taken when calculating the temperature using Eqn. 4.19. The
determination of the level density (Eqn. 4.7) is not accurate for very low energies.

This is evident in Fig. 4.15. A vertical asymptote is present at ~ 0.32 MeV for the

74

 

 

1

l 1 l 1 ' J l l ‘1 l l ‘ l ‘1

0 20 40 60 80 10
U (MeV)

Figure 4.15: Temperature comparison for various level density descriptions. The blue
curve shows the result of Eqn. 4.18, while the red curve shows the result of Eqn. 4.19.
The black curve was determined with the Bethe [52,53] level density description.

 

 

 

35‘” ‘l‘ ‘ 5
2:— i
-13— 5
a 3
£0? 5
H-l: ]
-_ Asymptote .
-2— J
[ 1
_3‘.. l ..n..-...]
0.0 0.5 1.0
U(MeV)

Figure 4.16: Low energy region of exact temperature calculation (red curve from
Fig. 4.15). The vertical asymptote at U ~ 0.32 MeV is apparent, and shows the
danger in using this approach to calculate the temperature at low energies.
red curve shown in Fig. 4.15. This is clearer in Fig. 4.16.

At energies below ~ 2—3 MeV, the temperature should not be calculated with
Eqn. 4.19. The level density, as calculated in CASCADE, is not accurate at very

low energies. This has been accounted for in the calculations, as discrete levels were

included in the CASCADE calculations. For the experiment discussed here, the lowest

75

energy that had to be converted to a temperature was approximately 9 MeV, and the

problems associated with Eqn. 4.19 are unimportant.

4.4.2 Relevant Quantities

To calculate the nuclear temperature using Eqn. 4.19, two quantities must be deter-
mined. One of these quantities is the mean excitation energy of the nucleus during
the decay. Since the Reisdorf level density formalism is used in this analysis, the

magnitude of shell effects also must be determined.

Mean Excitation Energy

The mean excitation energy (E2)”) of the nucleus along the decay of the GDR is

needed in order to calculate the temperature. The quantity ngf is determined by:

13*” = E,,,, — Emt — EGDR, (4.21)

e avg

where Eavg is the average energy, E23; is the average rotational energy, and EGDR is

the ground state energy of the GDR. It is necessary to subtract E33; and Econ from
Eavg because the energy associated with GDR corresponds to the energy associated
with the states upon which the GDR is built [3]. The rotational energy is calculated

with the following expression:

 

, E (J... +1)
E2”; = g 9,9 , (4.22)
where Tug is the average angular momentum of the nucleus during the decay.
The determination of the quantities Envy and rug is relatively straightforward
from the computer code CASCADE. As discussed earlier, CASCADE calculates an
expected spectrum of 7 rays, which is dependent on the specified initial population

of the nucleus. From this initial population, the code determines the relative popula-

76

 

 

 

 

1311—» 1/2 5/2 9/2 13/2 17/2 21/2 25/2 29/2
50.4 0 1 113 1145 1104 98 1 0
49.4 0 12 576 3941 3473 406 12 0
48.4 0 48 1374 7063 5852 870 36 0
47.4 0 116 2318 9878 7720 1358 69 0
46.4 1 213 3299 12283 9018 1789 116 1
45.4 2 334 4280 14294 9808 2120 167 3
44.4 3 469 5293 15766 10107 2313 207 4
43.4 6 623 6342 16953 10014 2362 229 6
42.4 9 799 7413 17865 9617 2294 235 8
41.4 14 992 8516 18465 9160 2145 227 10
40.4 20 1185 8693 16887 8366 1965 208 10
39.4 28 1269 7287 12903 6985 1748 181 10
38.4 35 1166 5423 8997 5302 1481 153 9
37.4 39 964 3773 5971 3773 1187 128 8
36.4 37 732 2506 3829 2555 888 105 7
35.4 32 510 1591 2371 1644 619 85 6
34.4 25 333 973 1425 1013 408 66 4
33.4 18 210 581 840 608 261 49 4
32.4 13 129 342 489 359 162 35 3
31.4 8 78 199 283 210 99 24 2
30.4 5 46 116 163 122 60 16 2
29.4 3 27 67 94 70 35 10 1
28.4 2 16 38 54 40 21 6 1
27.4 1 9 22 31 23 12 4 1
26.4 1 5 13 18 13 7 2 0
25.4 0 3 7 11 8 4 1 0
24.4 0 2 4 6 4 2 1 0
23.4 0 1 2 3 2 1 0 0
22.4 0 1 1 2 1 1 0 0
21.4 0 0 1 1 1 0 0 0

 

 

Table 4.2: Sample population matrix from CASCADE. The relative probability of
population in terms of energy and angular momentum is shown. The energ, in units
of MeV, is indicated in the left most column, while the angular momentum, in units
of h, is indicated in the top row.

tion of daughter nuclei along the decay. By examining these populations, an average
energy and angular momentum can be determined for each nucleus along the de—
cay. Table 4.2 shows a typical population output from the code. For this particular
example, Eavg=42.39 MeV and Javg=6.87 h.

The average energy and angular momentum of each daughter nucleus along the

77

 

 

Nucleus Envy (MeV) .1an (h) 68 (MeV) 67 Relative Weight (‘70)
12OSn 54.89 6.71 -1.311 0.98 39.46
119Sn 42.39 6.87 -0.483 0.04 30.70
119In 35.47 6.87 0.211 1.96 0.24
“SSH 32.92 6.98 -0.938 1.04 22.66
118In 24.72 6.94 0.605 1.02 0.17
117Sn 21.16 7.02 ~0.361 2.04 5.85
117In 16.26 6.94 0.590 2.02 0.04
116Sn 12.48 6.97 -0.833 3.04 0.54
116Cd 34.98 7.22 0.575 3.02 0.22
“st 23.98 7.22 1.199 4.02 0.10
114Cd 16.04 7.15 0.624 5.02 0.02

 

 

 

 

 

 

 

 

Table 4.3: Summary of nuclei populated along the decay. Several quantities relevant
in calculating the temperature are shown. The quantities are described in the text.

decay allows for the determination of Egg”. To calculate this quantity, the average
energy of each daughter nucleus has to be determined. Calculating Em for each
daughter nucleus is straight forward, as discussed in the previous paragraph. The
weight given to each daughter nucleus in calculating ET”; is determined by the 7—ray
cross section at 15 MeV of that nucleus relative to the total cross section of 7 rays at
15 MeV, as determined by CASCADE. Determining T179 is completely analogous to
calculating m. The 7-ray energy of 15 MeV was chosen because the ground state
energy in 120Sn is 15.4 MeV [54]. Since CASCADE calculates everything in 1 MeV
steps, 15.4 MeV was rounded down to 15 MeV. Table 4.3 shows an example of what
can be expected. In this example, m=4368 MeV and Tw;=6.84 11. With these

quantities determined, it is easy to calculate ngf. It is this value of energy that

should be used to calculate the temperature of the nucleus during the decay.

Magnitude of Shell Effects

The magnitude of shell effects (63 in Eqn. 4.20) is determined by the nucleus which
has the number of protons and neutrons closest to that of TV- and 7. The quantities W

and 7 are determined by performing a weighted average of Z and N. The averaging

78

 

procedure is completely analogous to that in the previous section where Em, and Javg

were determined. The nucleus is then found by defining the quantity 0, where

a: 7—Z] + N—Nz. (4.23)

The quantity 0 can be calculated for each nucleus populated during the decay, as
shown in Table 4.3. The nucleus which has the smallest value of 0 determines (SS. For
the example in the previous section, 77 = 69.03 and 7 = 49.99, which means (SS is

determined by 119Sn.

79

Chapter 5

Interpretation of the 7-ray Spectra

The interpretation of the 7-ray spectra relied on the tools developed in the previous
chapter. The parameters of the GDR are the sum rule strength (S), energy (E3133),
and width (I‘). These parameters were extracted from the data by comparing theoret-
ical calculations with data. The theoretical calculations consist of two pieces. The first
piece is a statistical model calculation performed with CASCADE. The second piece
is a bremsstrahlung calculation. Both of these calculations were folded, normalized
to the data, and added together. This spectrum was then compared to data.

In the case of the 7-ray spectrum gated on energy losses of 20—30 MeV, the data
was fit by varying the GDR parameters in CASCADE to achieve the best agreement
between calculation and data using X2 minimization. The higher energy loss data was
not analyzed in the same manner. Rather, this data was used to check for consistency

between this data and previous measurements.

5.1 20—30 MeV Energy Loss Spectrum

The 20-30 MeV energy loss spectrum is low enough in energy to equate the initial
excitation energy with the energy loss of the scattered 17O. This was discussed in

Sec. 4.1.1, and will not be discussed further here. The initial angular momentum was

80

 

104

103,

lLl-_ __L__J_1 1.1.1 -L1.___l_l._l._i 1-111 __[

 

 

   

L4

10 If 15 20 25
E7 (MeV)
Figure 5.1: The 7-ray spectrum is shown as the solid points for 20—30 MeV energy

losses. The blue curve is the result of the X2 fit, while the red curve is the result of
using the description for the width set forth by Kusnezov et al. [35].

also determined as discussed in Sec. 4.1.1. With the initial excitation energy and
angular momentum specified, CASCADE calculations were performed.

In the calculations, the parameters of the GDR were varied to minimize )8. The
result of the calculations are shown in Fig. 5.1 as the solid blue curve. The parameters
were found to be S = 1.1 :l: 0.2, EGDR = 16.5 i 0.7 MeV, and l" = 4 :l: 1 MeV. For
this case, the mean excitation energy following the GDR decay was found to be
9.7 MeV. This mean excitation energy was converted to a temperature as discussed
in Sec. 4.4. The temperature was found to be 1 MeV. The fitted width agrees with
the ground state GDR width of 4.9 MeV [54]. The fitted resonance energy, EGDR, is
somewhat higher than the ground state value of 15.4 MeV [54]; however, a resonance
energy higher than that of the ground state value was also measured at low excitation
energies in Refs. [25,27].

The low-temperature width is shown in Fig. 5.2 with other existing data points
taken from Refs. [22,35]. The temperature of all data points in Fig. 5.2 was determined

as described in Sec. 4.4. The value of the width at zero temperature was set to the

81

 

 

 

. Temperature (MeV) .

Figure 5.2: Comparison of data and theory for Sn. The red circle is from this work.
The blue circles and green diamonds are from Ref. [35], where the circles are from a-
scattering and the diamonds are from fusion-evaporation reactions. The blue triangles
are from Ref. [22] and are from fusion-evaporation reactions. The orange rectangle
is the range of widths measured for the ground state. The red curve is the adia-
batic thermal shape fluctuation calculation, and the blue curve is the empirical curve
discussed in Sec. 4.1.4.

value of 3.8 MeV [55], as in Ref. [35]. The red curve in Fig. 5.2 shows the adiabatic
thermal shape fluctuation width calculated in Ref. [35] at low angular momentum.
The red curve is generally consistent with the data at higher temperatures, but fails
to describe the data at low temperatures.

The temperature-dependent width shown by the red curve in Fig. 5.2 was incor-
porated into CASCADE (see Sec. 4.1.4). Using this temperature-dependent width,
the expected 7-ray spectrum shape for energy losses of 20—30 MeV was calculated,
assuming EGDR = 16.5 MeV and S = 1.1 as determined in the x2 fit. The result,
shown as the red curve in Fig. 5.1, does not describe the data well. The width of the
calculated spectrum shape is clearly too large, distributing the strength over a larger
energy range than the data.

The empirical temperature-dependent width shown by the blue curve in Fig. 5.2

was also incorporated into CASCADE (see Sec. 4.1.4). If the data from this work is

82

consistent with previous measurements of the GDR width, then the empirical width
description in Fig. 52 should describe the overall behavior of the data at higher

temperatures.

5.2 Higher Energy Loss Data

The higher energy-loss data was used to check for consistency with previous measure-
ments of the GDR width. The 7—ray spectra measured for energy losses higher than
30 MeV were not fit using X2 minimization. Additionally, the width was not held
constant in the CASCADE calculations. Rather, the expected spectral shapes of the
different measured spectra were calculated.

The calculation of the expected spectral shapes involved several steps. The initial
excitation energy and angular momentum of the nucleus were determined as discussed
in Sec. 4.1.1. The width of the GDR in the calculations was adjusted continuously
along the decay as determined by the empirical width in Fig. 5.2. The sum rule
strength, S, was fixed at 100%. The resonance energy, EGDR, was fixed at 16.0 MeV.
N o attempt was made to fit the data. The only free parameter in the calculations was
the overall normalization between the calculation and data.

The results of the calculations are shown in Fig. 5.3. While the agreement is not
perfect between calculation and data, the overall shape of the calculations is similar
to the data. The overall agreement indicates that this data is consistent with previous
measurements.

The effects of using a broad range of energies for the initial excitation energy (see
Fig. 4.3) in the calculations can also be investigated. This is possible by considering
the highest energy loss (80—90 MeV) 7—ray spectrum measured. The highest energy
loss spectrum had the broadest range of energies, and as such the effects should

be largest for this spectrum. The effects should be evident by performing a second

83

   

A
9)
v

._L_._L LLLLJll—J .L_l_._l LLLL._ _l___l_L 21..-;

 
  

 

 

 

 

 

 

 

 

 

 

l
104'_T_fT T T111111 ' I rd:
. (C) ]
.4 1 1 .8
C 2 7 G
g 10 E 5: 3
O t 1 U
10:; -{1
1 ’TH
.1[1
104,1 [5+ 1511 1% 53]
3
. (e) ]
1031 1
102% g
[i 4
101 ']
5 :4
1L11 111 111111 111111.117
25 10 15 20 25
E7 (MeV) E7 (MeV)

Figure 5.3: Comparisons of data and expected spectral shapes as calculated with
CASCADE. The 7-ray spectra are gated on the following range of projectile energy
losses: (a) 30—40 MeV, (b) 40—50 MeV, (c) 50—60 MeV, (d) 60—70 MeV, (e) 70—
80 MeV, and (f) 80—90 MeV. In all panels the data is shown as the solid points, while
the calculations are shown by the solid blue curves. The calculations were performed
as described in the text.

84

 

Counts

 

,_
:1»
—(>—
0— 1—

, .
1.11 l.’11111ll1.,,1._]

10 15 20 25 1071151 201 25
E7 (MeV)

' l

 

Figure 5.4: The 80—90 MeV energy loss 7-ray spectrum is shown in both panels. In
panel (a), the initial excitation energy in the CASCADE calculation was set to the
projectile energy loss as shown in the insert. The calculation is shown as the solid red
curve. In panel (b), the initial excitation energy in the CASCADE calculation was
set according to the insert. The resulting calculated spectrum is shown as the solid
blue curve.

calculation, where the initial excitation energy is equated with the projectile energy
loss. This calculation can then be compared with the calculation in Fig. 5.3f.

The result of this second calculation is shown in Fig. 5.4a. The other panel in
this figure is identical to Fig. 5.3f. In both calculations (Fig. 5.4a,b), the width was
adjusted continuously along the decay as shown by the empirical width in Fig. 5.2.
Also, the resonance energy was fixed at 16.0 MeV. The only difference between the
calculations is the initial excitation energy used (see inserts of Fig. 5.4). In the case
where the initial energy was set to the projectile energy loss, it was necessary to reduce
the sum rule strength from 100% to 36%. Both calculations show good agreement with
data, and hence the choice of the initial excitation energy distributions influence the
apparent GDR strength, but has only minor influences on the GDR width. This is
consistent with the findings of Ref. [36].

The broad distributions used for the initial excitation energy extend to much
lower energies than the energy losses considered. The population of lower excitation

energies adds to the statistical 7 rays, and does not influence the high-energy 7 rays.

85

The high-energy 7 rays are predominantly from the highest energies populated. This
results in more statistical 7 rays relative to the high-energy 7 rays, and affects the

overall sum rule strength as noted above.

86

Chapter 6

Conclusions

The GDR was studied by means of heavy-ion scattering using 170. This allowed for
the first measurement of the GDR width at a temperature as low as 1 MeV in Sn.

In the previous chapter, the 7-ray spectra were analyzed. In the case of the spec-
trum where the temperature was found to be 1 MeV, the parameters of the GDR were
extracted. The parameter of main interest was the width. The width (4 i 1 MeV)
extracted for this temperature was compared with previous measurements (Fig. 5.2).
The consistency of this data was then verified by analyzing the higher energy-loss
data.

The GDR width found at a temperature of 1 MeV is significantly lower than
predicted (see Fig. 5.2 or Fig. 6.2b). The discrepancy at this temperature is on the
order of 3 MeV. The difference between theory and experiment is especially striking
when comparing the predictions with the empirical curve in Fig. 5.2. This indicates
that the calculations overestimate the influence of thermal shape fluctuations at low
temperatures.

Further insight into the behavior of the GDR width may be obtained by comparing
Sn with other nuclei. Another nucleus where enough data and theoretical calculations

exist is Cu. This nucleus has weak shell effects (see Fig. 6.1), just as in Sn. Therefore,

87

     
   
 

14° ;- Em1.(MeV)
5 4 I5!
120 E" H
E 0
N 100 E—
5 a -4 "
E E . '
:3 80 :' — .
z E ‘8H J _ Q .
8 5 5
«- 60 :— —
E ~ 1'
40 :—
20 :—
0 I

 

        

20 40 60 80 100 120 140 160 180 200
Neutron Number N

0

Figure 6.1: Microscopic correction to the ground state energy in terms of N and Z.
The larger the absolute magnitude of the correction, the larger the shell effects. This
plot is adapted from Ref. [56].
the shape fluctuations should be determined by the properties of a rotating liquid
drop. The data and predictions for Cu are shown in Fig. 6.2c. The behavior of the
Cu data is similar to that of Sn. The experimental width is nearly constant up to
temperatures of ~1 MeV. Then the width begins to increase. As in the case of Sn,
the liquid drop predictions fail to describe the data, especially at low temperatures.
A measurement of the GDR width in 179Au has also been performed [57]. The
extracted width was found to be 5 MeV, and is shown in Fig. 6.2d. The solid curve in
this figure is a calculation of the width as determined from Ref. [35] with an angular
momentum of 17.5h. Shell effects are weak in 179Au, and just as in Cu and Sn, the
predictions significantly overestimate the width at low temperatures.

The behavior of the experimental data for nuclei where shell effects are small

88

 

 

 

 

l

1.1E11111111411m11m11 l lm1

 

 

 

  

 

 
 
 

 

 

 

1114111411 1111 lll_L 11
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5
Temperature (MeV) Temperature (MeV)
1511? , 1 IITrTIIIIIIIIITT1
A 1
> t
O.)
2 10 ~
L‘ L
5111 1111111L11’1111111111
0 0.0 0.5 1.0 1.5 2.0

1 2 3
Temperature (MeV) Temperature (MeV)

Figure 6.2: Theoretical predictions and data for Pb, Sn, Cu, and Au. Panel (a) —
Pb. Panel (b) — Sn. Panel (c) —- Cu. Panel ((1) - Au. The solid curve in panels (a),
(b), and (c) is an adiabatic thermal shape fluctuation calculation. In panels (a), (b),
and (c) the black circles and green diamonds are from Ref. [35]. The black circles
are from inelastic scattering measurements, whereas the green diamonds are from
fusion-evaporation measurements. The blue triangles are from Ref. [22], and the solid
red circle is from this work. The orange rectangle in panels (a) and (b) is the range
of widths measured for the ground state value. In panels (0) and (d) the ground-
state width is given by the curve at T = 0 MeV. The solid curve in panel ((1) is the
calculated width from Eqn. 4.14. The data point in this panel is from Ref. [57].

(Sn, Cu, and Au) is as predicted for nuclei where shell effects are large (Pb). This is
evident by examination of Fig. 6.2. In the case of Pb, the GDR width is predicted to be
suppressed relative to liquid drop predictions. This suppression is attributed to shell

effects. While it is clear that shell effects limit shape fluctuations at low temperatures

in Pb, it is not clear that these effects are responsible for the suppression of the GDR

89

 

 

 

 

111L1111L41

1114—1111

0.0 0.5 1.0 1.5 2.0 2.5
Temperature (MeV)

Figure 6.3: Comparison of Sn data and microscopic model predictions. The solid blue
curve shows the predicted GDR width as determined from the microscopic model
discussed in the text. The data is as in Fig. 6.2b.

width. In fact, the interpretation that shell effects are responsible for the suppression
of the GDR width in Pb at low temperatures has to be questioned.

The suppression of the GDR width at low temperatures is evident in the exper-
imental data for all nuclei discussed here (Sn, Cu, Au, and Pb). In the case of Sn,
Cu, and Au, shell effects are weak. Despite this fact, the behavior of the GDR width
is as predicted for nuclei with strong shell effects. It appears that the GDR with is
suppressed at low temperatures regardless of whether shell effects are present of not.

The thermal shape fluctuation calculations neglect pairing effects. Pairing effects
are predicted to be unimportant at the energies explored in this experiment. It is
thought that pairing effects are only important for very low energies. Still, it would
be interesting to have a calculation where pairing was included.

Another attempt to predict the GDR width is based on the interplay between
one-body Landau damping and two-body collisional damping of nucleons [27, 32].
The predicted width from this theory is shown in Fig. 6.3, along with the data. The
calculation was shifted such that the ground state value (T = 0 MeV) for the width
was 3.8 MeV. At low temperatures (T < 1 MeV), this theory describes existing data;

however, the agreement at higher temperatures (T > 1 MeV) is poor.

90

It is clear that the existing theories to describe the GDR width are not very ro-
bust. In fact, based on the lack of agreement between theory and data, it is fair to
say that the evolution of the GDR width with temperature is not well understood.
At this point, more theoretical work is needed. If the adiabatic thermal shape fluctu-
ation model is to be used, the way in which the shapes are determined needs to be

reconsidered. Possibly more effects could be included.

91

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