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This is to certify that the

dissertation entitled

"Giant Dipole Resonance in Highly Excited Lead—208 Nuclei“

presented by

Easwar Ramakrishnan

has been accepted towards fulﬁllment
of the requirements for

Ph.D . degree in Ehysi cs

 

1 ﬂ 4; // 517/

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Ma jOl’ professor

Date May 2' 1995

 

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

 

 

 

 

 

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Michlgan State
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ABSTRACT

GIANT DIPOLE RESONANCE IN HIGHLY EXCITED 208Pb NUCLEI

By

Easwar Ramakrishnan

The giant dipole resonance (GDR) built on highly excited states of 208Pb was
measured in order to study the evolution of the resonance with excitation energy.
The nucleus was excited by inelastic scattering of 40 MeV / nucleon a particles. High
energy '7 rays from the decay of the resonance built on excited states were measured
in coincidence with the inelastically scattered projectile nuclei. Target excitation
energies in the range of 40 to 110 MeV were chosen by gating on the energy loss of
the scattered projectile. Inelastic scattering populates low angular momentum states
in the target. The resonance properties were thus measured as a function of excitation

energy with very little influence from angular momentum.

The analysis of the measured 7-ray spectra was performed within the standard
statistical model. Resonance parameters were extracted by comparing the measured
spectra to calculations performed with a modiﬁed version of the evaporation code

CASCADE.

The width of the resonance was observed to increase systematically with increasing
excitation energy from the ground state value of 4 MeV to ~ 8 MeV at the highest
measured energy. The measured widths were well reproduced by a model calculation
of the resonance cross section that considered the adiabatic coupling of the collective

excitation to the free energy surface of the nucleus at ﬁnite temperatures.

To my parents

iii

ACKNOWLEDGEMENTS

First and foremost of all, I would like to thank Michael Thoennessen for his guid-
ance during my stay at the NSCL. I have greatly beneﬁted from the encouragement
and inspiration that he provided during the course of this work. His cheerful disposi-
tion combined with his willingness to help solve problems at all times made working

with him to be a very enjoyable experience.

I thank professors Walter Benenson, Pawel Danielewicz, Carl Bromberg and Ger-
ald Pollack for being on my guidance committee. I am also indebted to Prof. Julius
Kovacs and Prof. Subendra Mahanti for their help during my ﬁrst year of grad—
uate study. I thank my collaborators Jim Beene, Mel Halbert, Robert Varner,
Dan Stracener and Paul Mueller from Oak Ridge, and Lee Sobotka, Bob Charity,
Demetrios Sarantites and James Dempsey from St. Louis. Erich Ormand deserves a

special thanks for providing the theoretical calculations.

The staff at the N SCL were always very friendly and helpful. I wish to especially
thank Dave Sanderson, and members of the operations group for their assistance

during the experiments.

I greatly enjoyed working with members of our research group, Shigeru Yokoyama,
Afshin Azhari, Bob Kryger, Thomas Baumann and Peter Thirolf. Afshin, Shigeru
and Thomas made life at the NSCL to be quite an interesting experience. I also
had the good fortune of interacting with John ‘Ned’ Kelley, Stefan Hannuschke, Wen
Chen Hsi, Raman Pfaff, Tiina Suomijarvi, Robert Pak, Eugene Gualtieri, Mathias
Steiner, Mike Fauerbach, Damian Handzy, Quibauo Pan, Brian Young, Larry Phair,
Tong Li, Mike Lisa and many others. Many thanks to ‘Ned’ for keeping the humour
going in our corner of the lab, and to Stefan for putting up with the interruptions in

our ofﬁce.

iv

On a more personal note, I wish to thank my beloved wife Hema for her support
and encouragement during the past two years of my student life. My dear friends
Ramkumar and Iyer deserve special mention for making my stay in Michigan a mem-
orable one. Prof. A. A. Rangwala, Prof. R. J. Kulkarni, and Dr. H. C. Pradhan of
Bombay University were instrumental in my decision to pursue a doctoral degree. Fi-
nally, I wish to acknowledge my family and friends back home for their moral support

and for helping me face many odds in my pursuit of a higher education.

Contents

LIST OF TABLES viii
LIST OF FIGURES ix
1 Introduction 1
2 Giant Dipole Resonance in Excited Nuclei 6
2.1 Introduction ................................ 6
2.2 Giant Dipole Resonance ......................... 6
2.3 GDR Built on Excited States ...................... 9
2.4 Statistical Modeling ............................ 10
2.5 Evolution of the Resonance with Excitation .............. 12
2.6 Excitation by Inelastic Scattering .................... 18
2.6.1 The Inelastic Continuum ..................... 18

2.6.2 Comparison to Fusion-Evaporation Reactions ......... 22

3 Experimental Setup 27
3.1 Introduction ................................ 27
3.2 Detectors ................................. 27
3.2.1 Ban Detector Arrays ...................... 28

3.2.2 Dwarf Ball/Wall CsI Array .................... 28

3.3 Electronics ................................. 30
3.4 Data Acquisition ............................. 36

4 Data Analysis 37
4.1 Introduction ................................ 37
4.2 Particle Spectra .............................. 37
4.2.1 Particle Identiﬁcation ....................... 37

4.2.2 Calibration of the DWARF Ball/Wall Array .......... 38

vi

4.2.3 Resolution, Efﬁciency and Response ...............
4.3 Coincidence y-ray Spectra ........................
4.3.1 Energy Calibration ........................
4.3.2 Neutron Separation ........................
4.3.3 Region Sum for Improved Response ...............
4.3.4 Resolution, Efﬁciency and Response ...............
4.3.5 7-ray Spectra for Different Target Excitations .........
4.3.6 Background Subtraction .....................
4.3.7 Absolute Normalization .....................

5 Modiﬁcations to the Standard CASCADE Code

5.1 Level Density Parametrization ......................

5.2 Input Population for Statistical Calculations ..............

6 Results and Discussion

6.1 Particle Spectra ..............................
6.1.1 Singles a Spectra .........................
6.1.2 Coincidence a Spectra ......................
6.1.3 Knockout and Pickup-Decay Contributions ...........

6.2 Coincidence 7-ray Spectra ........................
6.2.1 7-ray Spectra as a Function of Target Excitation .......
6.2.2 Statistical Model Calculations with CASCADE ........

6.3 Resonance Width .............................

6.4 Pre—equilibrium Emission .........................

7 Summary and Conclusions

LIST OF REFERENCES

vii

41
41
42
42
43
46
46
48
51

53
53
62

67
67
68
70
74
81
81
83
98
104

113

116

List of Tables

6.1
6.2
6.3
6.4
6.5

DWARF WALL array angles ....................... 67
DWARF BALL array angles ....................... 68
Contribution to the 7-ray spectrum from individual decay channels . 87
GDR parameters ............................. 94
Calculation of nuclear temperature ................... 96

viii

List of Figures

2.1
2.2
2.3

2.4

3.1
3.2
3.3

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

5.1
5.2
5.3
5.4
5.5
5.6
5.7

5.8

6.1

Damping of the giant dipole resonance ................. 15
Free energy surfaces for Pb isotopes. .................. 19
Angular momentum imparted to target in fusion reactions and inelastic

scattering ................................. 24
Comparison of angular momenta in the excitation plane . .I ...... 25
Schematic diagram of the B&F2 packs in the setup ........... 29
The DWARF WALL array as seen by the beam ............ 31
Block diagram of BaF2 electronics .................... 32

Geometric transformation for particle identiﬁcation in DWARF detectors 39
Particle identiﬁcation plot from a DWARF WALL detector ...... 40
Energy versus time of ﬂight plot from a forward angle Ban detectors 44

Resolution of time of ﬂight measurement in BaF2 detectors ...... 45
Response of a Ban detector to 15.11 MeV 7 rays ........... 47
Extraction of *y-ray spectra for different target excitation energies . . 49
Comparison of 7-ray contributions from real and random time gates . 50
Contribution from nuclear bremsstrahlung at high 7-ray energies . . . 52

Level density parametrization employed in standard CASCADE code 55

Level density surface calculated using standard CASCADE code . . . 57
da parameter calculated using Residorf parametrization ........ 60
Level density surface calculated using Reisdorf parametrization . . . . 61
Obtaining input population for statistical calculations ......... 63
Calcuation of angular momentum transfer ............... 64
Angular momentum transferred to target as a function of excitation

energy ................................... 65
Initial population of nuclei in neutron decay channels ......... 66
Singles 0 spectra from the WALL array ................. 69

ix

6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10

6.11
6.12
6.13

6.14

6.15
6.16
6.17
6.18
6.19

6.20

6.21
6.22

6.23
6.24
6.25
6.26

Differential cross section data for elastic a scattering ......... 71
Absolute cross section for inelastic a scattering ............ 72
Coincidence (1 spectra from the WALL array .............. 73
Neutron emission probability compared to particle coincidence spectrum 75
a-proton coincidence events in the DWARF array ........... 77

Kinematics of free proton knockout events seen in the DWARF array 78

Pickup-decay and knockout contributions to the singles a spectrum . 80
Comparison of 7-ray spectra from different detection angles ...... 82
Comparison of 7-ray spectra from two different target excitation energy

ranges ................................... 84
Coincidence 7-ray spectra for various target excitation energies . . . . 85
Contributions to the 7-ray spectra from different decay channels . . . 86
Contributions to the calculated 7-ray spectra from individual neutron

channels .................................. 88
Contributions to the 7-ray spectrum from statistical and non-statistical

processes .................................. 90
Comparison of 7-ray spectra and model calculations .......... 91
Comparison of 7-ray spectra and calculations on a linear scale . . . . 93
Resonance width as a function of excitation energy .......... 95
Resonance width as a function of temperature ............. 97
Comparison of measured resonance width to adiabatic coupling calcu-

lation .................................... 101
Comparison of measured resonance width to collisional dynamics cal-

culations .................................. 103
Singles 0 spectra at low a energies ................... 105
Comparison of 0 singles spectrum with calculated a evaporation spec-

trum .................................... 106
a spectra in the BALL array ....................... 108
High energy background in 7-ray spectra compared to particle singles. 109
7-ray spectra in coincidence with low energy a particles ........ 110
Resonance width at large projectile energy losses ............ 112

Chapter 1

Introduction

The giant dipole resonance (GDR) is a collective excitation of the nucleus. In the
macroscopic picture the resonance is described as a vibration of all protons versus all
neutrons within the nucleus. The GDR built on the nuclear ground state has been
studied over a wide mass range by means of cross section measurements employing
(7,n) reactions [Die88]. The measured resonance energies exhibit a dependence on
the nuclear mass described empirically by the relation EGDR = 77 x 14-1/3. Since the
nuclear radius is related to the mass number by Roc A1/3, the resonance energy scales
as the inverse of the nuclear radius. The GDR thus couples strongly to the nuclear

shape and is therefore sensitive to changes in the shape induced by excitation.

The existence of giant dipole resonance built on excited states of the nucleus was
proposed in 1955 by David Brink [Bri55]. The ﬁrst evidence for excited state GDR
was observed in (p,7) scattering studies performed on light nuclei [Sin65]. Excited
state GDR was subsequently observed in heavy nuclei formed by fusion-evaporation
reactions [New81]. Fusion reactions populate compound nuclei with high excitation
energies and angular momenta. The GDR built on the excited states is measured by
detecting the high energy 7 rays that emerge from the decay of the resonance. These
7 rays are emitted in competition with particle and ﬁssion modes of decay. The 7

rays are emitted during the early stages of the decay and are therefore sensitive to the

1

nuclear properties of the excited states on which the resonance is built. Giant dipole
resonance spectroscopy thus provides the means for the study of nuclear shapes at
high excitation energies and angular momenta. This is an area of high current interest

in nuclear structure physics.

Excited state GDR has been studied in nuclei over a wide mass range using fusion
evaporation reactions [Sno86, Gar92]. In the A < 170 mass range, the most system-
atic study of excited state GDR has been performed in Sn isotopes [Cha87, Gar86].
Excitation energies ranging up to 600 MeV have been studied, thus probing the lim-

iting temperatures for the existence of the nucleus as an ensemble [Gar87, Suo94].

In deformed nuclei the GDR energy splits into two components corresponding to
nuclear radii parallel and perpendicular to the principal symmetry axis. Measurement
of the two energy components and the angular distribution of the emitted 7 rays
provides information on the extent and shape of the deformation. For instance, high
energy 7-ray measurements in excited Er isotopes revealed prolate nuclear shapes
similar to the ground state shapes at temperatures of ~1 MeV and a spin range of
0-25 h [G0385]. The study of excited state GDR was extended to heavier masses in
the measurement of deformation in Pb isotopes [But90]. Large prolate deformations

(ﬂ ~0.43) that persisted to high excitation energies were observed in 200Pb nuclei.

Since the high energy 7 rays are emitted from the early stages of formation of
the excited nucleus, GDR spectroscopy provides information on the time scales in-
volved in the de-excitation process. In the Thorium mass range, high energy 7-ray
measurements have been performed to determine the time scale of the ﬁssion process
in excited nuclei [Tho87, Pau94]. The high energy 7-ray spectrum from nuclei un-
dergoing ﬁssion has contributions from the compound nuclear system and from the
excited ﬁssion fragments. Since the dipole resonance energy in the ﬁssion fragments

is well separated from the resonance energy in the compound system, it is possible to

analyse the 7-ray spectra in terms of pre— and post-ﬁssion contributions. The analysis

revealed a strong hindrance in the ﬁssion process at high excitation energies.

The GDR as a clock has also been applied to the study of reaction dynamics
in fusion-evaporation reactions forming Yb and Sn isotopes [Th093, Th094]. High
energy 7 rays from 164Yb nuclei formed by fusion reactions exhibited a dependence
on the entrance channel. The spectra from an asymmetric entrance channels could
be described within the standard statistical model whereas the spectra from a more
symmetric entrance channel could not be described. This behaviour was observed
earlier in the measurement of neutron multiplicities [Jan86, Ruc86]. The discrepancy
in the 7-ray spectra have been explained in terms of a long formation time in the more
symmetric fusion channel. Particle and 7—ray emission during the formation time
lead to a different compound nuclear population in the symmetric entrance channel
compared to the asymmetric channel, thus leading to differences in the measured
7-ray spectra. The 7-ray spectra could be described within the statistical model by
treating the emission from the formation stage and from the compound nuclear stage

separately.

Measurements of excited state GDR have thus provided valuable information on
the properties and dynamics of nuclei at high temperatures. The measurements
discussed so far have all been performed on compound nuclei populated in fusion
evaporation reactions. Fusion reactions populate compound nuclei over a wide range
of angular momenta due to large momentum transfers in the entrance channel. It
is thus not possible to study the evolution of the nuclear shape as a function of
excitation energy alone decoupled from spin effects. Theoretical understanding of the
nuclear surface requires the possibility of experimentally studying nuclei populated in
narrow cells of excitation energy and angular momenta [Gar92]. Furthermore, fusion

reactions produce compound nuclei that are neutron deﬁcient. It is therefore not

possible to apply fusion reactions to study shape changes in stable nuclei with a view

to compare the properties with known ground state systematics.

An alternative to fusion reactions is to excite the nucleus by means of inelastic
scattering with hadronic probes. Inelastic scattering has been an important tool in
the study of structural properties of nuclei. For moderate projectile energy losses
up to ~30 MeV, structures observed in the inelastic particle spectra have been well
understood in heavy nuclei in terms of giant resonance excitations of various mul—
tipolarities built on the nuclear ground state. For instance, inelastic excitation has
provided information on the strength function of the giant monopole resonance in nu-
clei that leads to the estimation of nuclear compressibility [You76, Sh194]. Recently,
particle and 7-ray measurements in coincidence with the scattered projectiles have

been employed in the study of the decay properties of collective excitations in heavy

nuclei [Wou88, Fra88, Bee89].

Recent measurements of heavy ion inelastic scattering have revealed structures
in the inelastic continuum that have been interpreted in terms of multiphonon ex-
citations [Fra88, Bee94]. The double dipole excitation of GDR x GDR in 208Pb for
instance occurs at an excitation energy of ~27 MeV. The study of multiphonon excita-
tions provides a unique way of understanding properties of collective states in nuclei.
Precise measurements of the multiphonon energy states can lead to the estimation of

anharmonicities in giant resonance excitations.

Beyond the collective excitations built on the nuclear ground state and the mul-
tiphonon excitations, the high energy continuum observed in inelastic scattering is
not well understood [Tsa75]. The inelastic scattering process does not transfer high
angular momenta to the target. Thus if the high energy continuum in the particle
spectrum does correspond to high target excitation states, inelastic scattering pro-

vides the exciting possibility of studying the evolution of nuclear shapes as a function

of excitation energy with little inﬂuence from angular momentum. The giant dipole
resonance built on the excited states could be studied by measuring high energy 7

rays in coincidence with the scattered projectile.

In the present measurement, the GDR built on excited states of 208Pb are studied
by exciting the nucleus with inelastic a scattering. 208Pb has a doubly closed shell
structure in the ground state and therefore exhibits a deep minimum in the potential.
This minimum broadens rather rapidly beyond nuclear temperatures of ~1 MeV due
to the vanishing of shell effects. The GDR couples to the potential landscape and the
resonance width increases with temperature, reﬂecting the broadening of the potential

surface.

On the theoretical front, the evolution of the resonance with nuclear excitation has
been described by different models. Adiabatic models that consider shape ﬂuctuations
in the nuclear surface to be a slow process compared to the damping of the GDR,
argue that the measured resonance width is a superposition of the widths arising
from the coupling of the resonance to all possible shape degrees of freedom [Br092].
Dissipative models on the other hand treat the damping of the resonance in terms of
two-body collisional dynamics that depend only on the nuclear temperature [Sme91].
These model calculations are in agreement with resonance width measurements from
fusion reactions. The inelastic excitation process populates low angular momentum
states. Thus the validity of these models at high excitation energies and low spins

can be studied.

Chapter 2

Giant Dipole Resonance in
Excited Nuclei

2.1 Introduction

The GDR built on highly excited states of the nucleus is studied by measuring the
high energy 7-rays from the decay of the resonance. In the following sections the
properties of GDR built on the ground state and excited states of the nucleus are
discussed. The statistical model employed to analyse the data is reviewed. The
process of target excitation by inelastic scattering is discussed and is compared with

fusion-evaporation reactions.

2.2 Giant Dipole Resonance

The giant dipole resonance (GDR) is a collective mode of excitation of the nucleus.
In a macroscopic picture, the GDR has been described by two different models. The
Steinweld-Jensen (SJ) model describes the GDR as a dipole oscillation of the proton
ﬂuid against the neutron ﬂuid inside a rigid spherical shell [Ste50]. The restoring
force for the oscillation is the symmetry energy of the nucleus which is proportional

to the term (N — Z )2 / A. This model yields an expression for the resonance energy

as a function of the mass number A given by
EGDR o< R“ oc A-1/3. (2.1)

Here the nuclear radius is related to the mass number by R = To A’”, where

1‘0 = 1.2fm.

The second macroscopic model by Goldhaber and Teller (GT) describes the GDR
as an oscillation of rigid interpenetrating neutron and proton spheres [Gol48]. The
restoring force in this description arises from the surface symmetry energy. The mass

dependance of this surface resonance is given by

R2 —1/6
EGDR CC 71— O( A . (2.2)

These two descriptions have been combined by Myers et al. in their droplet model

[Mye77]. The resonance energy in the Myers model is given by

EGDR = (1.13 x 104/W3 + 7.34 x 10’4A1/3)‘1/2. (2.3)

The ratio of the contributions from the GT mode to the SJ mode in this model is

9—7: = 6.49 x A‘”3

SJ (2.4)

Thus the contribution from the SJ mode becomes more signiﬁcant at heavier
masses. The Myers description is in good agreement with the experimentally observed

values of the resonance energy over a wide range of nuclear masses.

In the microscopic picture of the nucleus the GDR can be described as a superpo-
sition of one particle-one hole (lp-lh) conﬁgurations. This superposition is referred
to as a collective particle-hole doorway resonance. The term doorway emphasizes the
point that the excited nucleus passes from the entrance channel through the doorway

state before the full complexity of the compound nuclear states could be generated

[Fes92]. The energy for this lp-lh excitation in the independent-particle shell model
should correspond to the relative spacing of the major shells which is 1 Eco = 41A-I ” ,
since the E1 matrix elements for single particle excitation from one major shell to
the next one are very strong. Repulsive interaction between the particle and hole
states shifts this energy to the observed value of ~ 27w [Sno86]. The p-h doorway
resonance mixes with other complicated conﬁgurations like the 2p-2h excitation, and

these admixtures contribute spreading width to the resonance.

The GDR built on the ground state of stable nuclei have been extensively studied
and documented [Die88]. The ﬁrst observation of the ground state GDR was from
photonuclear cross section measurements. The photo absorption cross section of the

GDR may be expressed as a Lorentzian

47r62h ﬂ 1 ng‘2
MC A F (E3 —’ E50102 + 13,3]?2

 

0.5.(E7) = (2.5)

where EGDR is the resonance energy, F is the resonance width and M is the nucleon

mass.

Integrating the above expression over all E, yields for the total 7 absorption cross

section [J ac75]

21r262h NZ NZ
Me —A— — 607( MeV mb). (2.6)

 

0T = [0 0.5,(E,)dE, :-
This expression corresponds to a classical E1 sum rule, referred to as the Thomas-

Reich-Kuhn sum rule.

As was described earlier the resonance energy EGDR depends on the mass number
of the nucleus. Typical values range from ~24 MeV in 160 to ~14 MeV in 208Pb.
The resonance width F varies from ~ 4 to 8 MeV. The most narrow widths have been

observed in magic nuclei.

Since the resonance energy depends on the nuclear radius through the mass num-

ber A, a single component Lorentzian is appropriate only for spherical nuclei. In

deformed nuclei the GDR energy splits into different energy components along the

principal axes of the nucleus.

The nuclear deformation can be expressed in terms of the mean radius R0 and the
deformation parameters ,6 and 7 [Boh75]. The deviation in the nuclear radius along

the three principal axes is given by

612,, = @ﬂRo cos (7 — 5231) (2.7)

where NET-1,2,3 is the axial index. If the deformation is axially symmetric, there will
be one principal axis R”, and two degenerate axes R i parallel and perpendicular to

the principal axis respectively. These axes are related to the deformation parameter

- R. (”75.) .2...

R.=R.(._1 4%.). (2.9)

ﬂ and the mean radius R0 by

and

2

2.3 GDR Built on Excited States

The existence of the GDR built on excited states of the nucleus was postulated as
early as in 1955 by David Brink [Bri55]. Brink proposed that the, energy dependence
of the photo absorption cross section should be independent of the detailed structure
of the initial state of the nucleus. Thus the lorentzian form of equation 2.5 should de-
scribe the correct photon energy dependence for all initial states. This weak-coupling

hypothesis is referred to as the Brink hypothesis.

The evidence for the existence of the GDR built on excited states was ﬁrst seen

in detailed (p,7) studies in light nuclei [Sin65] where GDR peaks displaced upward

10

in excitation energy were observed. The energy shift corresponded to the energy of
low lying discrete states in the nucleus. The resonance energy for the GDR built on

the excited states was thus the same as that for the GDR built on the ground state.

Due to the weak coupling hypothesis, in excited medium and heavy nuclei formed
in nuclear reactions, one should observe an enhancement in the multiplicity of high
energy 7-rays from the decay of the nucleus at an energy of E, = EGDR. This en-
hancement was ﬁrst observed in the study of 7-rays from the spontaneous decay of
252Cf [Die74] and later on in the high-energy 7-ray spectra from the decay of excited
nuclei formed in heavy-ion fusion reactions [New81]. Since then the evolution of the
GDR as a function of nuclear excitation and spin has been studied in nuclei over a

wide mass range [Sno86, Gar92].

2.4 Statistical Modeling

The decay of the excited nucleus can be described by the statistical model with the
fundamental assumption that all nuclear degrees of freedom are equilibrated prior
to the decay [Sto85]. The channels for the decay of an excited nucleus are particle
emission, 7-ray emission and ﬁssion. The emission of high-energy 7-rays from the
decay of the GDR occurs in direct competition with the particle evaporation and
ﬁssion channels. The branching ratio for 7-ray emission compared to particle emission

at the GDR energy EGDR is m 10‘4 to 10‘s.

In the analysis of the data, the statistical model calculations were performed with
the evaporation code CASCADE [Pul77]. The main aspects of the statistical model

are described below.

The decay of an excited equilibrated compound nucleus is independent of its

formation. Thus, using the principle of detailed balance, the decay can be calculated

 

11

using absorption cross sections for the different channels.

For a nucleus with an initial excitation energy and spin (E5, 1,), the particle decay

rate to the nucleus with ﬁnal state (Ef, If) is given by

1 Pf(EfaIf)
dE = d .
12,, ,9 27m p;(Es,I.-) T(Ep) Ep, (210)

 

where p,- and pf are the level densities of the initial and ﬁnal nuclei and T(Ep) is
the transmission coefﬁcient for the emitted particle. The transmission coefﬁcient is
obtained by summing over all possible angular momentum values that are consistent

with the initial and ﬁnal angular momenta of I,- and I f.

The 7 decay rate can be calculated in analogy to the particle decay rate. Applying
Brink’s hypothesis that every nuclear level has a GDR built on it, the width for E1
7 decay from an initial state (E;, I.) to the ﬁnal state (Ef, If) in the same nucleus is

given by

—"(Ef’1f)"°”’ E3 dE. (2.11)

IW(E7)_ p(E,',I,°) 3 (’ll'hc)2 7

 

For a spherical nuclear shape, the 7 absorption cross section can be substituted

from equation 2.5. The 7 decay rate is then given by

F1 p(Ef11f) 1

 

 

3
=—: d .
12.21153, h p(E;, 1.) 27m fGDR(E,)E., E,, (212)
where
862 NZ E r
E = s “’ 2.13
km“ 7) 3hMc3 0"” A (Eton-E$)2+E$F2 ( )

is the GDR strength function. The quantity SGDR is the strength in terms of the clas-
sical E1 sum rule. Fusion reaction studies show that the GDR strength exhausts the
energy weighted sum rule, corresponding to a value of SGDR 2: 1 . Equation 2.12 was
derived only for E1 radiation and higher multipolarities such as the giant quadrupole
resonance have not been considered. The strength function for other multipolarities

could be included in the expression for 7 decay width [Cha87]. Nevertheless, in the

12

energy range of interest, the quadrupole radiation strength in nuclei is a few orders

of magnitude lower than the dipole strength, and has not been observed [Cha87].

The ﬁssion decay rate for the nucleus, derived using the liquid drop model [B0h39],

is
1
27thp(E,', 1;)

 

EI’EB(Ii)
Rﬁ” = /0 p(E,' — EB(I,) — Ekin(1i)) dEkin (2.14)

where Em is the kinetic energy of the nucleus at the saddle point and E'B(I.°) is
deﬁned as the sum of the angular momentum dependent ﬁssion barrier Em and
the rotational energy. For the decay of excited 208Pb considered here, there is no

appreciable contribution to the decay cross section from the ﬁssion process.

The level density p(E,I) of the nucleus is an important input to the statistical
model calculation. A consistent level density description over the whole range of
excitation energies and spin involved in the decay is necessary. This issue is addressed

in detail in chapter 5.

2.5 Evolution of the Resonance with Excitation

The properties of nuclei at high excitation energy and Spin have been studied by
measurements of high energy 7-rays from the decay of the GDR built on these excited
states. The time scale for the damping of the resonance is short enough for the 7-
ray emission to compete with the other decay modes of the nucleus. The resonance
shape of the GDR exhibits a well localized strength in the otherwise exponential
continuum of 7-rays from the decay of the nucleus. Furthermore, the 7 rays from
the decay emerge unhindered by the surrounding nuclear medium. High energy 7-
ray measurement thus provides a clean probe for the study of GDR built on excited
states. Since the GDR couples strongly with other degrees of freedom such as the

nuclear shape, the evolution of the GDR in the nucleus offers information about

13

nuclear properties at ﬁnite temperatures and angular momenta.

So far, the properties of the GDR in excited nuclei have been studied over a wide
mass range by fusion reactions [Sno86, Gar92]. The most comprehensive measure-

ments have been performed in Sn isotopes in the mass range of ~110 [Gar86, Cha87,

Gar87, Bra89].

The parameters that characterize the resonance are the resonance energy EGDR,
the resonance width 1‘ and the fraction SGDR of the E1 sum rule strength. These
quantities are extracted by treating them as free parameters in the statistical model

calculation performed to ﬁt the 7-ray spectra.

The resonance energy EGDR extracted from excited nuclei over a wide mass range
exhibits no appreciable deviation from the systematics of the corresponding ground
state GDR. This implies that the main physical quantities responsible for the reso-
nance, namely the symmetry energy and the volume energy, do not change appreciably

with nuclear excitation.

For the GDR built on the ground state of nuclei, the resonance is seen to exhaust
the full sum rule strength predicted by the classical Thomas-Reich-Kuhn equation.
Fusion-evaporation measurements of the GDR built on excited states show that the
sum rule strength is still fully exhausted for excitation energies up to ~ 100 — 200
MeV. Early on it was expected that the study of GDR could lead to the determination
of a limiting temperature for the existence of the nuclear ensemble. However, fusion
measurements in the Sn region for excitation energies above ~300 MeV have observed
a saturation of the GDR strength [Bra89, Gar87]. These measurements suggest a
limiting temperature for the existence of the GDR of Tz4.5 MeV, which is lower
than the limiting temperature of ~10 MeV for the existence of the nucleus. Collective

excitation is thus expected to disappear before the nucleus as an ensemble ceases to

14

exist.

Fusion measurements in excited nuclei exhibit a strong increase in the GDR width
F with increasing excitation energy. For instance in Sn isotopes the width increases
from the ground state value of I‘=5 MeV to ~12 MeV at an excitation energy of
around 150 MeV. At excitation energies beyond ~200 MeV, measurements exhibit a
saturation of the resonance width [Bra89, Gar87]. High excitation energies in such fu-
sion measurements implicitly correspond to high angular momentum states populated
in the compound nucleus. The observed increase in width has been empirically linked
to the excitation energy and angular momentum in many studies. For instance in Sn
isotopes the width has been parameterized as I‘ = 4.8 + 0.0026 E26 for excitation
energies below ~150 MeV [Cha87].

To understand the increase in the resonance width with excitation, it is useful to
invoke the microscopic description of the resonance. The width I‘ of the GDR in the

nucleus has two components

I‘ = 1“I + I“. (2.15)

The quantity PI is the escape width of the resonance and it 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.

The quantity I‘1 is the spreading width that arises from the coupling of the co-
herent lp-lh excitation to 2p-2h and other complicated particle-hole conﬁgurations.

This process is illustrated in ﬁgure 2.1.

The 1p-1h doorway resonance corresponds to a single component in the energy
spectrum. Coupling of the doorway state to 2p-2h conﬁgurations results in the frag-

mentation of the resonance strength. The coupling to compound nuclear np-nh states

15

 

L/ w

 

 

 

 

 

 

 

 

 

 

 

 

 

lp—lh 2p—2h np—nh

- bi - -ullllll llllllllll ........... L I

0 10 BO 30 40 O 10 30 30 40 0 10 20 30 40
E (MeV) E (MeV) E (MeV)

 

 

 

 

 

020040000030010001200020040030000010001200020040000000010001200
time (frn/c) time (fm/c) time (fm/c)

 

 

 

 

 

 

 

 

Figure 2.1: The damping of the GDR arises from its coupling to the compound nuclear
states. Displayed here are the energy and time behaviour of resonance from three
different stages. The ﬁrst column displays the coherent 1p—1h doorway state that has
a single energy component. Coupling of the 1p-1h states to the 2p-2h conﬁgurations
results in the fragmentation of the resonance as shown in column 2. Finally, coupling
to the complicated np-nh compound state conﬁgurations smoothes each fragmented
component resulting in a spreading width in the energy which is responsible for the
damping of the resonance. This is displayed in the third column.

16

smooths each fragmented component resulting in a spreading width for the resonance.
This spreading process results in the damping of the giant dipole resonance in the
nucleus. In heavy nuclei the major contribution (~ 80%) to the resonance width

arises from the spreading process [Ber83].

In an excited nucleus the escape width corresponding to direct particle emission
is small, of the order of a few hundred keV [Sme91]. Thus the observed increase in
resonance width with excitation energy should be due to an increase in the spreading
width. The spreading width of the GDR arises from its coupling with other nuclear
degrees of freedom such as nuclear shape. Shape ﬂuctuations thus play an important
role in the behaviour of the GDR in excited nuclei. In other words, the GDR exhibits

a strong dependence on the temperature and angular momentum of the nucleus.

The free energy distribution of nuclei in the ground state exhibit deep minima
that corresponds to the ground state shell conﬁgurations, especially in nuclei at and
around closed shells. In an excited nucleus, even at moderate temperatures of T21
MeV, the shell effects disappear and the free energy surface no longer exhibits deep
minima. The surface broadens considerably and thermal ﬂuctuations in the shape
degree of freedom become important. The GDR couples to these shape ﬂuctuations
and the resonance properties convey information on the time scales of these shape

variations [Goo88].

There are several models that incorporate the shape ﬂuctuations in describing the
resonance properties [Gar92]. The adiabatic model assumes that the time scale of
shape ﬂuctuations is long compared to the damping time of the GDR. In this model,
the GDR strength measured in an experiment is a superposition of the strength dis-
tributions that correspond to vibrations built on all possible nuclear shapes, weighted
by the probability of the nucleus for assuming that shape. The systematic increase in

the resonance width seen in measurements are thus attributed to the resonance sam-

 

17

pling all possible deformations over a shallow free energy surface at high excitation

energies and angular momenta.

In contrast to the adiabatic model, dynamical models take into account the relative
time scales for shape ﬂuctuation in the nucleus. In this picture the time spent by
the nucleus in a given shape conﬁguration decreases with increasing temperature.
Thus the nucleus may not spend long enough time at a given point in the free energy
surface for the dipole vibration to adjust its frequency to the corresponding nuclear
shape. Thus the GDR never explores extreme shape transitions but only feels the
average shape of the nucleus. This leads to a substantial reduction in the effect of
shape ﬂuctuations [Alh90, Orm90]. This effect, referred to as motional narrowing,
has been offered as an explanation to the observed saturation in the GDR width at

very high excitation in measurements performed on Sn isotopes.

The analysis of the evolution of the GDR in terms of shape ﬂuctuations is compli-
cated by the introduction of high angular momentum states in the compound nucleus.
The increase in excitation energy of the nucleus is associated with an implicit increase

in the angular momentum transferred from the entrance channel in fusion reactions.

It is thus highly desirable to perform experiments that selectively populate nuclei
in narrow ranges of excitation energy and spin to provide detailed information on the

nuclear surface for understanding shape ﬂuctuations.

This work focuses on the study of nuclei at high excitation energies populated with
very low angular momenta via the mechanism of inelastic scattering. The evolution of
the GDR is studied as a function of excitation energy alone, with little inﬂuence from
angular momentum effects. The measurements were performed on excited states of
208Pb nuclei. The ground state conﬁguration of 208Pb exhibits a very deep minimum

due to the existence of doubly closed shells. Figure 2.2 displays the free energy

18

surface for a few Pb isotopes calculated at different temperatures, assuming zero spin
[Wer94]. The energy scale for the calculations have been translated such that the free

energy is 0 MeV for zero deformation.

A deep minimum is observed in 208Pb at zero temperature due to the doubly
closed shell conﬁguration. The minimum is less prominent in the other neutron
deﬁcient isotopes. The ﬁgure shows that the deep minimum in 208Pb broadens rather
rapidly with increasing temperature. The study of shape evolution of the GDR in this
nucleus should thus provide interesting information on how the nuclear free energy
surface evolves with temperature and how the giant dipole resonance couples with

the nuclear surface.

2.6 Excitation by Inelastic Scattering

2.6.1 The Inelastic Continuum

Inelastic scattering has been an important tool in the study of the structural prop—
erties in nuclei. A wide variety of hadronic probes have been employed to study the
scattering process. For instance, neutron and proton resonance scattering have been

employed to reveal individual compound nuclear states in nuclei.

The absorption of neutrons and protons in the interior of the nucleus is a weak
process. But the absorption is strong for composite hadronic probes like a-particles
and heavy ions. Composite probes do not penetrate much into the nuclear interior of
the target. They are more sensitive to the surface properties of the nucleus and can
therefore preferentially excite the vibrational modes of the nucleus [Fe392]. Inelastic
scattering with composite probes can thus be employed to study collective excita-
tions like the giant dipole resonance in nuclei. Furthermore, the angular momentum

transferred to the target in the scattering process is low.

19

 

 

Free Energy (MeV)

 

 

 

 

 

Figure 2.2: Free energy surfaces for isotopes of Pb at temperatures of 0 MeV (dots),
0.5 MeV (dashes), 1.0 MeV(long dashes), 1.5 MeV (dot-dashed) and 2.0 MeV (solid).
The calculations were performed assuming zero angular momentum. The parameter
,8 is a measure of the nuclear deformation. Negative values of )8 correspond to oblate
deformation and positive values to prolate deformation. The energy scale for the
different temperatures were translated so that the free energy is 0 MeV for zero
deformation. The free energy in 208Pb exhibits a deep minimum at zero temperature
due to the doubly closed shell structure. This minimum broadens with increasing
temperature. The minimum in less prominent in the other isotopes.

20

Heavy ion inelastic scattering along with the coincidence measurement of particles
and 7-rays has been applied in recent years to study the decay of giant resonances in
nuclei [Bee89, Wou88]. For moderate excitation energies in the target up to ~20 MeV
the structures in the particle spectra have been well understood in inelastic scattering
studies on heavy nuclei. These structures correspond to localized strengths of giant
resonances, mostly the isovector giant dipole resonance (IVGDR) and isoscalar modes

like the giant quadrupole (GQR) and the giant monopole (GMR) resonances.

Beyond the structures seen at the lower end of the excitation spectrum inelastic
scattering studies exhibit a broad continuum in the particle spectrum that correspond
to higher energy losses of the projectile. There is not much experimental information
on the nature of target excitations that can contribute to this particle continuum.
Theoretical calculations predict that this continuum may correspond to poorly lo-
calized distributions of higher multipolarities [Tsa75]. Recently particle and 7-ray
coincidence measurements have been performed to search for structures in the con-
tinuum that correspond to localized multiphonon strength such as the two phonon
GDR X GDR excitation [Blu88, Fra88, Bee94]. The identiﬁcation and characteriza-
tion of the wide variety of collective modes of excitation that exist in the continuum
region of the excitation spectrum is a major task in experimental nuclear structure

physics.

A recent experiment employing the inelastic scattering of 84 MeV/ A 17O on 208Pb
searched for giant dipole resonance built on highly excited states of the target in the
inelastic continuum [Th091]. High energy 7-ray spectra measured in coincidence with
the scattered projectile nuclei showed an enhancement in the 7-ray multiplicity in the
giant dipole resonance energy region. Furthermore, the inelastic particle spectrum
in coincidence with high energy 7-ray emission exhibited structures corresponding

to the individual neutron decay channels of the excited nucleus. This observation

21

is evidence for equilibrated emission from the excited target. Statistical model cal-
culations are thus applicable to the analysis of the excited states populated by the

inelastic scattering process.

A main criterion in the selection of the inelastic probe is that there are no contri-
butions to the 7-ray spectrum from projectile excitation. Projectiles with low nucleon
binding energy are thus a good choice. The outgoing particle in the inelastic scatter-
ing process needs to be isotopically identiﬁed. Such measurements warrant the use
of a high resolution spectrometer. In the absence of a large solid angle spectrometer
to isotopically identify the scattered projectile, it becomes necessary to use discrete
particle detector arrays employing silicon or organic scintillators. The choice of the
projectile nuclei is then restricted to those that can be isotopically identiﬁed in the

detector system.

In this work the giant dipole resonance excitations built on highly excited states
of 208Pb were studied with inelastic scattering of 40 MeV/ A a-particles. There are
no experimentally know bound excited states of the a-particle. Contamination from

projectile excitation is thus eliminated.

The giant dipole resonance excitation is an isovector mode and is therefore charac-
terized by an isospin transition of AT = 1. The a—particle, being a Z = N nucleus,
has an isospin value of T = 0. Exciting giant dipole resonance states by means of
inelastic a scattering is inhibited due to the isospin selection rules. Nevertheless,
isospin is a good symmetry only in light nuclei [Sn086]. In excited heavy nuclei, the
isospin mixing process results in the possibility of exciting isovector modes by means

of a T = 0 probe [Won90].

22

2.6.2 Comparison to Fusion-Evaporation Reactions

The GDR built on excited states in nuclei have been conventionally studied via fusion-
evaporation reactions. For energies above the coulomb barrier the fusion cross section
for such reactions is relatively large (~1 barn). The formed compound nuclear system
equilibrates rapidly and the excitation energy is shared amongst all available degrees
of freedom. Statistical model calculations are thus applicable to the study of such

systems.

One drawback in using fusion-evaporation reactions for the study of collective
excitation modes like the GDR is that the compound system is formed with large spins
due to the angular momentum transfer from the incoming projectile. Furthermore,
the range of angular momenta populated in the fusion process is rather large. Thus
is becomes difﬁcult to study the properties of collective excitations as a function of

excitation energy alone, decoupled from spin effects.

Figure 2.3 compares calculated angular momenta populated in inelastic scattering
and fusion reactions. The calculations are shown for two different excitation energies.
The inelastic scattering calculation was performed for 40 MeV / nucleon a-particles on

208Pb. The angular momentum transfer in the inelastic process is given by
I : thgth (2.16)

where the momentum transfer to the target, pm, is the difference in the momenta of
the projectile between the incoming and outgoing channels. The impact parameter
b was varied between the sum of ‘matter half density’ radii of the nuclei and the

‘nuclear interaction radius’ [Wi180].

The fusion reaction calculation was done for a typical reaction of 19F+181Ta form-

23

mg 200Pb. The cross section for the fusion reaction is given by
W 00
of... = p 2(21 +1)T,, (2.17)
:0
where the transmission coefﬁcient T1 is parametrized in the sharp cut-off model in

terms of the maximum angular momentum [max and diffuseness 61, and is given by

I "" Imam _1
T1 = (I + exp (T)) . (2.18)
I

It is clear from the ﬁgure that the angular momenta populated in the inelastic
scattering process are much smaller, and are spread over a rather narrow range,

compared to the population in the fusion channel.

In the inelastic scattering approach, the statistics of 7 rays in coincidence with the
scattered projectile is rather poor. Thus it is not possible to look at a very narrow
range of target excitation energies. Rather, a 10 MeV wide bin in the excitation
energy is chosen. Figure 2.4 compares the nuclear population in the excitation plane
for the fusion and inelastic processes. The fusion process creates a compound nuclear
population with a narrow spread in excitation energy, but with a large spread in
angular momenta. The inelastic scattering process populates nuclei in a narrow cell

in the excitation plane, over small ranges of excitation energy and angular momenta.

Fusion-evaporation reactions often produce nuclei that are neutron deﬁcient. The
N /Z ratio for the projectile and the target in the entrance channel are usually lower
than the N /Z ratio of the stable isotope of the product nucleus formed. Thus it
is not possible by means of fusion reactions to measure the collective properties in
stable nuclei at high excitation energies and compare them with known ground state

properties.

Another advantage of inelastic scattering is that different excitation energy ranges

in the target can be studied by applying excitation energy cuts in the inelastic particle

24

 

1000

800

600

 

400

 

200

 

500

 
 
  

400 100 MeV

300

 

200

Cross section (arb. units)

100

 

 

 

l
20 40 60

Angular momentum (h)

n-
p-

 

O

o ﬂTIIIIIIIIIIIlIIIIITIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIII
m Jlllllllllllllllllllllllllll llillllllllllllll1111111111

C

Figure 2.3: Comparison of angular momenta imparted to the target in fusion reac-
tions versus inelastic scattering. The comparison is shown for two different excitation
energies. The histograms are the angular momenta calculated for inelastic a scatter-
ing on 208Pb at 40 MeV/nucleon. The solid lines are angular momentum transfers
computed for a typical fusion reaction of 19F+181Ta forming 200Pb. The angular
momentum populated in the inelastic scattering is low. In the fusion channel, the
angular momentum is rather large and is spread over a broad range.

80

4O

20

Excitation energy (MeV)

Figure 2.4: Distribution of excited nuclei populated in fusion reactions (left) and
inelastic scattering (right) plotted on the excitation plane. The yrast line corresponds
to the minimum excitation energy in the nucleus for a given angular momentum. The
fusion population is shown for 200Pb nuclei at 60 MeV excitation energy. The angular
momentum in the fusion channel is large and is spread over a broad range. In the
inelastic scattering method, a range of excitation energies is selected in the analysis.
The population shown here is for inelastic a scattering at 40 MeV/ nucleon on 208Pb
forming excited target nuclei in the energy range of 50-59 MeV. Since the angular
momenta p0pulated are very low and the excitation energy bin is only 10 MeV wide,
the population of excited nuclei is restricted to a rather narrow cell in the excitation

plane.

25

 

60‘

IIIIIIIIIIIIIII’IIIIIITII

d

db

Fusion—Evaporation

   

 

 

lllllllllllllllllll

 

IIIIIIIIIIIIIIIIIIIIIIII

—

‘IH

Inelastic Scattering _

   

 

 

lllllllllllllllllll

 

10 20 3O 40 O

10 20 30 40 50

Angular momentum (h)

26

spectrum. Thus the nuclear properties as a function of a wide range of excitation

energies can be measured in a single experiment.

Chapter 3

Experimental Setup

3.1 Introduction

A 3 mg/cm2 thick isotopically enriched 208Pb target was bombarded by a
40 MeV/nucleon a beam from the K1200 Cyclotron. The target was mounted in
the center of a scattering chamber that housed an array of particle detectors. High
energy 7-rays from the decay of the excited target nucleus were measured in coin-
cidence with inelastically scattered projectiles. The 7-ray detectors were arranged
outside the scattering chamber. The residual beam was stopped in a shielded fara-
day cup and the beam current was monitored during the experiment. Typical beam

currents were around 3 pnA.

The following section describes the details of the detector systems used in the

experiment.

3.2 Detectors

The 7-ray measurement required good energy resolution as well as good timing reso-
lution to allow 7-neutron discrimination. Only moderate energy resolution was neces-
sary for the particle detectors, however particle identiﬁcation with isotopic resolution

was essential.

27

28

3.2.1 BaF2 Detector Arrays

The high energy 7 rays were measured with Ban scintillator detectors. These de-
tectors have a very fast response which allows sub-nanosecond timing [Nov87]. This
is necessary in discriminating 7 rays from fast neutrons by time of ﬂight. The setup
consisted of 95 hexagonal BaF; crystals arranged in 5 packs of 19 detectors each.
Four of these packs were from Oak Ridge National Laboratory (ORNL) and the ﬁfth
pack was from MSU. Figure 3.1 shows a schematic diagram of the BaF2 packs in the

experimental setup.

The ORNL detectors were each 20 cm in length with a face dimension correspond-
ing to an inscribed circle of 6.5 cm diameter. The MSU detectors were 25 cm in length
and the diameter of the inscribed circle was 6 cm. The ﬁve packs were placed around
the target at a distance of ~ 40 cm and were centered at laboratory angles of 60°(2),

72°(2) and 112°. The solid angle coverage was ~ 17% of 471'.

3.2.2 Dwarf Ball/Wall CsI Array

The inelastically scattered projectiles and other light charged reaction products were
detected using the Washington University DWARF BALL and DWARF WALL 47r
CsI(Tl) array [Str90]. In the present experimental setup the DWARF WALL con-
sisted of 35 CsI(Tl) plastic phoswich detectors, each 20 mm thick, arranged in four
rings centered at laboratory angles of 14.78°, 22.39°, 23.18° and 31.03°. The angular
coverage in the lab was from ~ 9° to ~ 36°. The detectors were at a distance of 13
cm from the target and the total solid angle covered was ~0.8 ster. The scintillators
were thick enough to stop the highest energy 0 particles of 160 MeV corresponding
to the initial beam energy. High energy Z = 1 particles could not be stopped and

they punched through.

29

 

 

 

 

 

 

Figure 3.1: Schematic diagram showing the positioning of the BaF2 packs in the
experiment. The beam direction is along the Z axis. The DWARF scattering chamber
was placed at the center of the co-ordinate system.

30

Figure 3.2 shows the beam’s eye view of the DWARF WALL array. The numbers

in the ﬁgure indicate the ring numbers that were assigned to the detectors.

In our setup the DWARF BALL consisted of 64 close packed CsI(Tl) detectors ar-
ranged in thirteen rings covering laboratory angles of ~ 36° to ~ 160°. The detectors
were at a distance of 4 cm from the target. The thickness of the scintillator crystals

varied from ~8 mm at forward angles to ~4 mm at the most backward angle. The

WALL and the BALL arrays together covered a solid angle of ~ 95% of 4n.

3.3 Electronics

Figure 3.3 shows the schematic block diagram of the BaF2 electronics used in the
experiment. A schematic of the DWARF ARRAY electronics can be found in reference

[Str90].

The ORNL detectors were equipped with photomultiplier tubes that provided two
anode signals. The photomultiplier tubes for the MSU detectors provided only one
anode signal which was split to provide two identical signals. For the analog path
of the electronics, one copy of the PMT signal from each detector was fed to ‘Delay
and Splitter’ boxes. These boxes grouped the 95 detectors into seven ‘banks’. The
signals were delayed by 500 ns and then split to provide two outputs. One output
was fed to the ‘E FERA’ LECROY 4300B modules and the other output was fed
to the ‘AE FERA’ LECROY 4300B modules. The pedestals for these modules were
subtracted on-line. The light output from the BaFg crystal has two components: a
fast component with a decay time of 0.6 us at a wave length of 220 nm, and a slower
component with a decay time of 620 us at a wave length of 310 nm [Kn089]. The gate
signal for the ‘AE FERA’ was set to a width of 50 ns, with a lead time of 15 us. The

integration was thus performed on the ﬁrst 35 us of the detector signal, yielding the

31

10cm

 

 

 

Figure 3.2: The DWARF WALL array as seen by the incoming beam. The top ﬁgure
is a schematic view of the WALL array. The bottom ﬁgure shows the numbering
scheme employed for the detectors. The rings were centered at laboratory angles of
14.78°, 22.39°, 23.18° and 31.03°.

32

 

 

 

 

 

 

@1 “u

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

323.3
I .25

AI
AIR

 

 

 

 

 

 

 

 

 

 

 

 

 

. z .m.
3: augcll _ so .3;
0: 8530500 - “#230 so... 5

T

.35 I 8.0... LI. .050
. «SEE—.5
‘1

 

 

 

 

 

 

 

 

 

 

9.88.3
. LI.. .350
, .3: IT Secon—
3054 A . .32.:

a

3.2.5.?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

32:3 .582

 

.050

a 5..
58 I

 

 

 

 

Figure 3.3: Block diagram of the electronics for the BaF2 detector arrays.

 

 

 

33

energy in the fast component. The ‘E F ERA’ modules integrated the entire signal

over 1.5 psec, yielding the total energy deposited in the crystals.

The second copy of the PMT signals were used for the logic path of the electronics.
These signals were ﬁrst fed to attenuator modules that were used to gain match the
fast light output of the different PMT signals. The output of the attenuators were
fed to linear fanout modules which produced three copies. One copy of each signal
was fed to a bank of linear multiplexer modules. The output from the multiplexer
bank was patched through to the counting area. The multiplexers could be addressed
through CAMAC commands thus allowing any one of the 95 linear signals to be mon-
itored on the oscilloscope in the counting area during the experiment. The second set
of outputs from the linear fanout modules were fed to linear summing ampliﬁers. The
signals of the 19 detectors within each array were added in the summing modules.
The summed outputs from the ﬁve groups were fed to a LECROY 4413 discrimina-
tor module. This module allowed setting thresholds on these individual ‘pack sum’
signals. The thresholds on all the packs was set at ~4 MeV. The bus output of the
‘pack sum’ discriminator was daisy chained to a scaler module and to a LECROY
4448 coincidence register to record Ibit information on which array ﬁred in an event.
The ‘pack sum’ discriminator also provided a N IM output which was the OR of all the
ﬁve array discriminators. This output served as the high threshold 7 trigger which

was required for a coincidence event.

The third and the last copy of the linear fanout modules were grouped in seven
‘banks’. The signals in each ‘bank’ were fed to LECROY 4413 discriminator modules.
These modules set the individual thresholds on all the 95 detectors. The thresholds
were set at ~500 keV. The bus outputs of these ‘bank’ discriminators were fed to
CAMAC delay modules which delayed these logic signals by 250 nsec. The output

of the delay modules were used as the stop signal for the TDC modules to record

34

event timing for each detector. The common start signal for the TDC came from a
coincidence of the Cyclotron radiofrequency signal and the mastergate signal from the
trigger box. The outputs of the delay modules were also daisy chained to LECROY
4448 coincidence register modules to record bit information on which detectors ﬁred
in an event. A second set of bus outputs from the ‘bank’ discriminators were fed
to scaler units and to a bank of logic multiplexers. The output of the multiplexer
bank was patched to the counting area. It was thus possible to monitor the logic
signals from all detectors during the experiment. The OR outputs from each ‘bank’
discriminator were fed to a logic OR module to create a logic signal when any one of
the 95 detectors had a signal pulse that crossed the individual thresholds. The output
of this OR module thus formed the low threshold 7 trigger. This trigger was used
mainly for calibration purposes. The gate signals for setting the integration times for
the FERA units for each ‘bank’ were derived from the OR output of the discriminator
for that ‘bank’. The ‘bank’ discriminator OR outputs were ﬁrst fed to coincidence
units that allowed the gates to be vetoed when the computer was busy. Gates for the
F ERA units were thus produced only when the computer was ready for processing

the event.

The BaF2 detectors were gain matched in energy by adjusting the high voltage
inputs to the PMT’s so that the calibration peaks lined up in the same data channel
for 7-rays of the same energy. This energy gain matching was performed with data
acquired from the radio-active sources. It was also necessary to gain match the fast
component of the light output from the detectors so that common trigger thresholds
applied to the signals in the logic path of the electronics have a uniform effect. This
was achieved as follows. After gain matching the detectors for the total energy,
cosmics data was acquired for all detectors by setting the common trigger threshold

at an arbitrary value. The threshold cutoff point in the AE channel was recorded for

35

all detectors. These cutoff points were used to decide the settings for the attenuator

modules in the logic path thus yielding matched signal amplitudes.

For the DWARF electronics, the signal from the PMT of each detector was split to
provide three copies. The light output from the CsI(Tl) crystal has two components.
The ﬁrst component has a decay time of 0.3-1.0 ps depending on the particle type, and
the second component has a decay time of 7 ps independent of the particle [Kno89].
Two copies of the PMT signal were fed to two different set of FERA modules, one for
the ‘Slow’ integration and the other for the ‘Tail’ integration. For the ‘Slow’ F ERA’s
the gate was set to integrate over a time period of ~340 ns, leaving out the ﬁrst ~35
ms of the signal. The gate for the ‘Tail’ F ERA’s were set to start 1.5 ps after the
start of the signal pulse and the integration time was 1.5 as. In the logic path, the
signals from the 35 DWARF WALL detectors were fed to logic ‘OR’ units to form
a ‘DWARF WALL OR’ trigger. This trigger was used to form the coincidence with
the high threshold 7 trigger yielding the ‘Coincidence Trigger’ for the experiment.
A copy of the ‘DWARF WALL OR’ trigger was scaled down by a factor of 64 and
was used as a ‘DWARF Singles’ trigger to record singles data from the DWARF
array. The individual detector event times for the DWARF array were recorded using
‘Time to F ERA’ converter modules. These modules were operated in a common start
mode. The stops came from the individual detectors, and the start signal was derived
from the coincidence of the ‘DWARF WALL OR’ and the high threshold 7 trigger.
Information on which DWARF detectors were present in an event was recorded using

LECROY 4448 bit register modules.

During the experiment, the active triggers were the ‘Coincidence Trigger’ and
the ‘DWARF Singles’ trigger. The energy and time information for the DWARF
BALL/ WALL detectors that ﬁred in an event were recorded for both the ‘DWARF

Singles’ trigger and the ‘Coincidence Trigger’. The energy and time information for

36

the Ban detectors that ﬁred were recorded for events in which the ‘Coincidence
Trigger’ was present. Furthermore, for each event the time of the mastergate signal

relative to the Cyclotron radio-frequency signal was recorded as well.

3.4 Data Acquisition

The NSCL acquisition system was used to set up the CAMAC electronics for the
experiment. All the electronics was set up inside the vault. To monitor detector per-
formance, the analog and logic signals from the two detector systems were multiplexed
andrpatched through to the counting area. The Ban electronics and the DWARF
Array electronics were integrated in one CAMAC branch and were controlled by a
front end code that was written speciﬁcally for the experiment. For each event the
front end code identiﬁed the detectors that were present in the event from bit reg-
isters. The code then read the modules associated with those detectors and wrote
them to the data stream together with a number that was assigned to each detector. ‘
Event type was also recorded. The data stream was routed to a taping process, and

was also monitored by an on-line data analysis program.

Chapter 4

Data Analysis

4.1 Introduction

The off-line analysis of the data was performed with a modiﬁed version of the NSCL
data analysis program SARA. The modiﬁcations were necessary because of the differ-

ent data structure created by the customized front end code used in the experiment.

Initially the data was scanned and particle identiﬁcation (PID) histograms were
created for both the DWARF detectors and Ban detectors. Gates were drawn on
these PID plots to identify different isotopes in the DWARF detectors, and 7 and
neutron events in the BaF2 detectors. All the data sets were then scanned with the
PID gate conditions and a ﬁltered output was created. For each event, only those
detectors that had clean particle identiﬁcation were written out. Subsequent analysis

of the data were performed using these ﬁltered data tapes.

4.2 Particle Spectra

4.2.1 Particle Identiﬁcation

Particle identiﬁcation in the DWARF detectors was obtained from the ‘Slow’ and

‘Tail’ energies recorded for each event. A two dimensional plot of the ‘Tail’ versus the

37

38

‘Slow’ parameters was not sufﬁcient to clearly identify the a events from 3He and to
distinguish between p, d and t events in the detectors. In order to draw unambiguous

gates for particle identiﬁcation, the DWARF parameters were transformed as follows.

First, a two dimensional plot of the measured ‘Tail’ versus ‘Slow’ parameters
was created for each detector. Boundary lines were drawn on these plots to include
the data range of interest. For each data point within the boundaries, a new ‘Tail’
parameter was computed as shown in ﬁgure 4.1. Two dimensional plots of the new
‘Tail’ parameter versus the recorded ‘Slow’ parameter were then created. Particle
identiﬁcation gates were drawn on these transformed plots. Figure 4.2 shows the

‘Tail’ versus ‘Slow’ plots before and after the transformation.

4.2.2 Calibration of the DWARF Ball/Wall Array

The WALL array was calibrated by a beams of various energies. The primary a beam
from the cyclotron was degraded using aluminum absorbers of various thicknesses in
the A1200 beam analysis device [She92]. The degraded beams were also subject to
momentum cuts of ~ 1% in the A1200. The beams were then tuned to the vault
and 0: singles data was recorded for all the WALL detectors. Beam energies of 21.6,
27.19, 31.72 and 36.07 MeV/nucleon were used for the calibration. The calibration
data was scanned back, the elastic peaks were corrected for F ERA pedestals and a

second order ﬁt was employed to yield calibration curves for each detector.

Since down scaled particle singles in the DWARF detectors were recorded during
the experiment it was possible to monitor gain shifts in the WALL detectors by
monitoring the peak position of the elastically scattered a-particles. Gain shifts in

the WALL array were thus corrected for in the analysis.

Since the grazing angle for the a scattering at the calibration energies was small

39

Etall

 

 

 

slow

Figure 4.1: Geometric transformation employed to obtain particle identiﬁcation in
DWARF array detectors. For each detector a two dimensional plot of the measured
Emu energy versus the Emu, energy were plotted. Two boundary lines were drawn
on the plots as shown in ﬁgure. For each measured point, a new Emu parameter
was computed.Two dimensional plots of the new Ema parameter versus the E310.”
parameter were created to obtain better particle identiﬁcation.

40

 

 

 

 

 

2 25°?
0 p
C :
5 a”:
.l: _
3 C
if .3.
100:—
5°:—

— 1"]l|lll1|lllillllllltlllll|1||I

50 100 . 150 Z1!) 25!! m0

450:—
400:—
350:—
: E
o aoo~
: :
c :
.3 25°.—
0 h
v :
.1 “r
150"—
.
too}:
[2
Eli’-

 

 

 

(channel)

Eslow

Figure 4.2: Two dimensional plots of the tail parameter versus the slow parameter
from a typical DWARF WALL detector. The top panel shows the plot before the
geometric transformation explained in text was applied. The bottom panel shows the
plot after the geometric transformation. The improvement in particle identiﬁcation
is clearly seen.

41

(~ 15° at the lowest energy), it was not possible to observe elastic peaks in detectors
beyond the WALL array. The BALL array was thus not calibrated during the experi-
ments. In the offline analysis, scanning the singles data from the BALL array yielded
information on proton punch through points. From the thickness of the CsI crystals
and the punch through points, it was possible to obtain a rough calibration for pro-
tons in the BALL array. This calibration was used to look at kinematics of a-proton
coincidence events to yield information on background processes like knockout and

pickup-decay.
4.2.3 Resolution, Efﬁciency and Response

The resolution of a typical CsI detector in the WALL array was 3.2% for a-particles at
160 MeV. This resolution was sufﬁcient because the (1 spectra from the WALL array
were binned in broad intervals of 10 MeV to obtain the coincidence 7-ray spectra.
The geometric efﬁciency of the WALL array was ~ 6% of 41r. The count rates in
the WALL array detectors were maintained at around 3000 counts / second or less in

order to avoid degradation in the response due to pile up.

4.3 Coincidence 7-ray Spectra

The energies and times measured by the Ban detectors were recorded for coincidence
events where a particle was detected in the WALL array and the high threshold 7
trigger was present. The 7-ray energies of interest ranged from a few MeV up to ~30
MeV. The following subsections discuss various aspects of the analysis of the 7-ray

Spectra.

42

4.3.1 Energy Calibration

The low energy range of the 7-ray spectra was calibrated with radio-active sources.
Known 7-ray transitions from 2°7Bi(569.65 keV, 1063.64 keV), 228Th(26l4.5 keV) and
a Plutonium-Beryllium source (3928 keV, 4439 keV) were used for calibration energies

in the range of ~500 keV to ~4.5 MeV.

The GDR energy for the target studied is peaked around 13 MeV. Thus it was
important to obtain a calibration point in this mid energy range. Inelastic a scattering
on a thick l"’C target excited the 15.11 MeV level in carbon and the subsequent 7-ray

decay of this state was detected.

An additional calibration point around 40 MeV was obtained from the measure-
ment of cosmic muons in the detectors. Data was collected with all detector packs
in the horizontal position. The interaction of the cosmic muons in the detectors was
simulated using the monte carlo code GEANT [Bru86]. The detector geometry was
put in explicitly in the simulation and the peak energy for the cosmics interaction

was obtained.

Pedestal subtraction for the BaF2 F ERA’s was done on line. The calibration data
were binned in 100 keV bins and a second order ﬁt was employed to yield calibration

curves for each detector.

4.3.2 Neutron Separation

A major source of contamination to the 7-ray spectrum can come from fast neu-
trons. The 13an arrays were placed as close as ~40 cm from the target. With a
40 MeV / nucleon beam, neutrons with energies close to the beam energy per nucleon
take ~5 ns to reach the detectors. A 7-ray takes 1.33 us to traverse the same distance.

Hence it is important that one obtains good timing discrimination between 7-ray and

43

neutron events in the detectors. BaFg detectors have an inherent time resolution of
less than a nanosecond. This coupled with a sub-nanosecond beam timing resulted
in obtaining good n-7 separation. In the analysis, 7 ray events were distinguished
from neutrons from a two dimensional plot of the energy deposited in the detector
versus the time of ﬂight. The time of ﬂight was measured relative to the cyclotron
radio-frequency signal. Figure 4.3 shows this two dimensional spectrum from one of

the forward angle detectors. The 7-ray and neutron groups are well separated.

Figure 4.4 shows the projection of the energy versus time of ﬂight plot on the
time axis from two different 13an detectors. The detectors were placed at laboratory
angles of 60° and 112°. The projection was done for events with energy above the
high energy trigger threshold of ~ 4 MeV. The 7-ray peak is sharp in both detectors

and has a full width at half maximum of ~1 ns.

4.3.3 Region Sum for Improved Response

To obtain the 7-ray spectrum for each detector pack, a region summing technique was
employed. The detector with the largest 7-ray energy was identiﬁed for each event.
Then the energies deposited in the nearest neighbour detectors were added yielding
a. region sum. At the high 7-ray energies measured, the predominant mechanism
of interaction in the detectors is by production of electron-positron pairs [Kno89].
Due to the limited size of an individual detector, one often encounters a loss in the
measured energy due to the escape of one or both of the 511 keV photons from the
annihilation of the positron. It is then most probable that the escaped photon is
detected in a nearest neighbour detector. Thus it is only necessary to add back the
energies from the nearest neighbours and not from all the detectors in the pack. In

Contrast to adding all the energy within one pack, this reduces the chance of pileup.

44

 

..
.
400 — '7:
I ’
— ~ 1 -
10'
- u“. *
.s
)- ' "'U
.
A.
b w- ‘
‘
o .. U- .
35 -
”fa A
)- v .. ...
v
.. - ..
b v
"f5 s-
‘vuﬂ.
)- K...“ 1'
:\*:.
_ 3.3;“ “h...
in at" T
s - ..
300 — .6”:-
’ﬁuﬁu
.‘ C“ d
._ .. -
.‘A. ‘
"‘ ﬁ’ .‘ I
.' .
- - .
..
” ~ : ‘2 4% ~
.. ‘1'“...
u ’v f“
A ’- ’ M
R
' 250 — W... -‘.«- . * '0
S ~J$ﬁ a u. v
0 3. ~10-(‘-
an.
\ " Quays-v, ..
a__ U V
> . - . .:- *.
‘34,“. r”
~ '5... xii“)... '
x i- 0“ C “'3. “it:
w“:
_ ~ - 1'."
o.“
1-
v

 

 

 

Time (250 pslch.)

]Figure 4.3: A two dimensional plot of the measured energy versus time of ﬂight in a

aFg detector at a forward angle of 60°. The time of ﬂight was measured relative to
the cyclotron RF signal. The group with the lower value of time of ﬂight is from 7
rays and the broader group to the right is from neutrons. The two groups are well
S‘31)erated leading to unambiguous determination of event type in the BaF2 detectors.

45

 

1500 ' ' '

1000

500

IIIIIIIIIIIII]

 

 

Counts

2000

1500

1000

500

IIIIIIIIIIIIIIIITVIIII

 

 

IlililllllllllllllllllIlllillllllllli

 

l l L 1 1 L l J_ L I J l l l 1 l l l l I l l l i

9380 400 420 440 460 430
Time of flight relative to RF (250 ps/ch)

 

Fi glue 4.4: Time of ﬂight in Ban detectors measured relative to the cyclotron radio

r eQuency signal. The top panel is the time spectrum from a detector placed at an
a'1131e of 60° in laboratory and the bottom panel is the time spectrum from a detector
at 1 12°. The neutron peak is more prominent in the forward angle detector. The
'7‘.1‘a.y peak is sharp and is well separated from the neutrons in both cases. The full
wldth at half maximum of the 7-ray peak is ~1 nanosecond.

46

4.3.4 Resolution, Efﬁciency and Response

The resolution in a typical Ban detectors for a 2.61 MeV 7 ray from a 228Th source
was ~ 6.4%. The detector efﬁciency and response to 7 rays of energies in the range

of interest were obtained by simulations using the monte carlo code GEANT [Bru86].

The simulations included the geometry of the pack consisting of 19 detectors. The
response function for the pack for 7 rays from 100 keV to 25 MeV were calculated in
100 keV steps. The data from the simulations were compiled in a 250x250 matrix. It
is rather difﬁcult to uniquely unfold the response of the detector from the measured
'y-ray spectrum. Instead, the results of the model calculations were folded with the
response matrix before comparing them with the measured spectra. The intrinsic
efﬁciency of the detectors was included in the response matrix. The intrinsic efﬁciency

of the detector pack geometry was ~ 60% at 15 MeV.

Figure 4.5 compares the 7—ray spectrum seen in a single BaFg detector to the sim~
ulation performed with GEANT. The histogram in the ﬁgure is the energy spectrum
measured from the decay of the 15.11 MeV state in 12C excited by inelastic a scat-

tering. The solid line is the simulation in which the geometry of the single detector

and the trigger threshold were included.

In the experimental setup the ﬁve detector packs were each placed at a distance
of ~40 cm from the target. The geometric efﬁciency of the packs was thus ~ 17% of
47r.

4.3.5 7-ray Spectra for Different Target Excitations

In order to obtain coincidence 7-ray spectra as a function of target excitation energy,
the data was scanned and a two dimensional histogram of the 7-ray energy versus the

01 energy for coincidence events was created. The a—particle energies were grouped

47

 

I I I I I I I I I I I I I | I T I I I I I I I I I I I

1250

1000

750

Counts

 

500

250

 

   

 

0‘ l l 14L 1 I l I 1 l I l I
5.0 7.5 10.0 12.5 15.0 17.5 20.0

E., (MeV)

 

 

Flglue 4.5: The response a Ban detector to 15.11 MeV 7-rays. The histogram is
the energy spectrum seen in a single BaF2 detector from the decay of the 15.11 MeV
Staste in 12C excited by inelastic a scattering. The solid line is the response calculated
1131113 the monte carlo code GEANT. The simulation took into account the crystal
gecﬂnetry, the efﬁciency and the trigger threshold.

48

in bins of 10 MeV each by applying gates on the two dimensional histograms. For
each 0 energy bin, the corresponding 7-ray spectrum was projected from the two
dimensional plot.

The top panel of Figure 4.6 shows the two dimensional plot for coincidence events
with a prompt time gate on the 7-ray detectors. The bottom panel shows the pro-
jection on the 7-ray energy axis for an 0 energy cut of 91 MeV to 100 MeV. Since

the beam energy was 160 MeV this a energy cut corresponds to a target excitation

range of 60—69 MeV.

4.3.6 Background Subtraction

Random subtraction for the data was performed as follows. The data was scanned
twice, once with the condition that the 7-ray event fell within the prompt time gate
and then with the condition that the event fell in the random time gate. The 7-ray
Spectra were extracted as a function of the target excitation energy for both scans.
The random time gated data was then subtracted from the prompt time gated data
to yield the ﬁnal random corrected 7-ray spectra for the different excitation cuts.
Figure 4.7 shows the comparison of 7-ray spectra from the real and random time cuts

for a. typical target excitation range of 50-59 MeV.

The peak position for the interaction of cosmic muons in the detectors was around

40 MeV. No signiﬁcant counts were seen in the 7-ray spectra in this energy region.

At the higher energy end of the 7—ray spectrum there could be contributions from
1111Clear bremsstrahlung. The bremsstrahlung process produces a 7-ray spectrum of
the form exp(—E.,/Eo). The slope parameter E; is dependent on the beam energy.
From systematics of bremsstrahlung 7-ray spectra studied at various beam energies,

the slope parameter E; for the current beam energy of 40 MeV/ nucleon is ~14 MeV

49

 

  

 

 

 

 

 

 

 

m —
100 "—
100 E
E 140 _— 10'
é: 120 _
x 100 E
.8. so :— .
V _ to
u? so :—
40 :—;
20 :—
I 10
20 40 so so 100 120 140 160
Ea(MeV)
10‘;
:_ ..
10 Etgt' 60- 69 MeV
33 5
§ 10’.—
O E
0 :
10 "E-
’ :— WIIIIIIIIILIIIUIIIIIIIIII
‘...1....11.71
so 100 150 200 250 300
Ey (100 keV/ch.)

Figure 4.6: Top panel shows a. two dimensional plot of the total 7—ray energy in the
Ban detectors versus the (1 energy in the WALL array, for coincidence events with
the prompt time gate. The bottom panel shows the projection of the two-dimensional
plot on the 7-ray energy axis for an 01 energy range of 91—100 MeV. The corresponding
target excitation is 60—69 MeV.

50

 

4T1]! If Till [III TTI Illl
1° 1“) 1 1 '1

lLllllll

1 11111111

   
      

 

 

 

(D
‘63
:1 102 E“ *2
O I I
U : :
101 E- 1
l— ' -1
.- II III. I|:|1'l I11] ﬂ
' " IIJIII II
100 1 1 1 1 l 1 1 1 1 111111111Ll|1 1 1 1 1 1
5.0 7.5 1C1.0 12.5 15.0 17.5 20.0
E, (MeV)

Figure 4.7: Comparison of 7-ray contributions from real (solid) and random (dashed)
time gates. The spectra show here are for a target excitation energy range of 50~59
MeV. The random contribution was subtracted from the spectrum for the real time
gate to yield random corrected spectra for the different target excitation energy cuts.

51

[N if90]. Figure 4.8 shows the measured 7-ray spectrum for a target excitation range
of 70—79 MeV. A bremsstrahlung spectrum calculation with a slope parameter of 14
MeV is shown as a solid line. The calculation was normalized to the data points in
the range of 20-30 MeV. This normalization range was applied to spectra from all
excitation energy ranges. Rather than subtracting the contribution of bremsstrahlung

from the measured spectra they were added to the statistical model calculations.

4.3.7 Absolute Normalization

The initial population for the statistical model calculations were derived from the
particle singles spectra. For each 10 MeV wide target excitation cut the singles counts
in all the WALL detectors for the corresponding 01 energy range were extracted. The
number of 0 singles events in each 1 MeV bin from this range was spread over a
range of angular momenta. The angular momentum range was computed taking into

account the energy loss of the outgoing a-particle.

The 7-ray spectra from statistical calculations performed with the input popula-
tions derived from the singles cross section should match the measured 7-ray spectra.
Any excess measured yield is then due to background processes like pickup-decay and
nucleon knockout. The contribution from these processes can at best be estimated

since not all detection angles were covered and since neutrons were not detected in

the DWARF array.

52

 

l lllllll

“II
1—
103 __ _
1- -i
p -
D .4
1— -I
1— -!
_ q
- I. d
F- d
2 __ .' __
10 P" . -
h- d
1— ﬂ
1— -4
I- -l
)- _.
” IIq. ‘
h— —I

1...

O

p
T I [Till]
I llllllll

Cross section (arb. units)

 

 

 

5. .
0 __ 3" __
1° 1 I i
: l I II .
10—1 1 1 1 1 1 1 1 1 1 L 1 I 1 IRE
10 20 30
E, (MeV)

Figure 4.8: The 7-ray spectrum for a typical target excitation energy range of 70-79
MeV is shown as ﬁlled circles. The nuclear bremsstrahlung contribution was assumed
to have an exponential form with a slope parameter of 14 MeV as explained in text.
The solid line in the ﬁgure shows this exponential form normalized to the data in the
energy range of 20—30 MeV.

Chapter 5

Modiﬁcations to the Standard
CASCADE Code

5.1 Level Density Parametrization

The nucleus, being a many body system, can experience many different conﬁgura-
tions even for small amounts of excitation energy. The level density in nuclei thus
increases rapidly with excitation energy. Statistical model calculations are therefore

appropriate and necessary to study the decay of excited nuclei [St085].

For low excitation energies information on nuclear level densities is available from
experimentally measured energy levels and from neutron resonance data. These mea-
sured level densities near the nuclear ground state show extreme sensitivity to proper-
ties like pairing, vicinity to closed shell and nuclear deformation. At higher excitation
energies there is hardly any direct experimental knowledge of level densities in nuclei.
Effects like pairing and shell closure are expected to vanish with increasing excitation.
A liquid drop description of the nucleus becomes appropriate as excitation energy in-
creases. The validity of a statistical model thus depends on how well the known level
densities at lower excitation energies are described and how good the extrapolation

to regions of high excitation and angular momentum are.

The statistical model calculations in the analysis were performed with the code

53

54

CASCADE. The modiﬁcations made to the standard version of the code are described

here.

The level density parametrization in the standard version was modiﬁed to correctly
describe the level densities in nuclei near closed shells. The input section of the
code was modiﬁed to accept a population distribution spread over a range of target

excitation energy and angular momenta.

In the statistical model code CASCADE the level density as a function of excita-

tion energy E and angular momentum I is given by

 

 

_ 21 + 1 exp(2\/aU)
p(E?I)_1203/2\/E (U+T)2 , (5'1)
where
U=E—A—I(I+1)/0’=aT2—T, (5.2)
0’:6(1+612+6'14), (5.3)
and
0 = 2J,.,-g,-d/h2. (5.4)

Here, E and I are the excitation energy and angular momentum of the nucleus, and
T is the nuclear temperature. The quantity U is the effective excitation energy of the
nucleus which is obtained by subtracting the rotational energy from E. Jn-ggd is the
rigid-body moment of inertia and 0' is the moment of inertia of a deformable rotating
liquid drop with deformation coefﬁcients 6 and 6'. The parameters a and A are ﬁxed

for the individual nuclei.

For low excitation energies below a cutoff value, CASCADE derives these parame-
ters from a ﬁt to the values from Dilg et al. [Dil73]. Figure 5.1 shows the level density
parameter a as a function of mass number over a wide range of nuclear masses. The

open circles in the ﬁgure are from Dilg et al. who performed an empirical ﬁt to the

55

 

 

 

 

 

*- T If I I I I r I I I I I I I I I I I I l' I I I I I I _.
CU ’ .
L1 f a
B 30 F 0 Data points from Dilg et.al. ——
CD + a
E - 0 CASCADE Parametrization gig 0 ~
(U 0000
In _ 0% ‘
0‘3 — a

20 —- ——

>~ — l
rt: .
U) "’ _
a _ 93" _
0)
CD r a
.—1 10 '_ I -—
0)
:> - a
(D _ a
.4

p _

O l l l L 1 EL 14 4 l l l l l l l l l L J l l l l i l
0 50 100 150 200 250

Mass number A

Figure 5.1: Level density paramter a as a function of mass number A at low excitation
energies. The open circles are data from Dilg et al. and the closed diamonds are
a parametrized ﬁt to these points used in standard CASCADE calculations. The
discrepancies near closed shells, particularly near A = 208, is clearly seen.

56

low energy level and neutron resonance data from nuclei over a wide mass range.
The ﬁlled diamonds are a result of the parameterization used in the standard CAS-
CADE code. It is obvious that though the CASCADE parameterization reproduces
the general trend in the level density parameter over the mass range, the values are
very different for mass numbers near the doubly magic nucleus 208Pb. This is not

surprising since the CASCADE code was written initially for the lower mass region.

At excitation energies above a cutoff value speciﬁed in the input ﬁle, the CAS-
CADE code uses a liquid drop description of the nucleus. The parameters a and A
are assumed to have a smooth mass dependance. The level density parameter in the
liquid drop model is given by

a = A/da, (5.5)

where A is the mass number and da is a ﬁxed value over all mass ranges.

The parameter A is assumed to be the difference between the experimental and
liquid drop binding energies of the nucleus, without taking into account pairing or

shell effects.

The level density parameter for intermediate energies that fall between the two
cutoff values is obtained by interpolation. This approach could lead to a level density
description which is not smooth over the range of excitation energies considered.
Figure 5.2 shows a typical plot of the level density in 208Pb nucleus as a function of
excitation energy and angular momentum calculated using the standard CASCADE
level density parametrization. The lower and upper cutoff energies were 20 MeV and

30 MeV respectively. The non-uniformity in the level density is clearly seen.

To achieve a smooth description of the level density parameters over the entire
range of excitation energies involved, another semi-empirical level density formula

developed independently by Reisdorf, Schmidt et al. and Kataria et al. was imple-

57

I
I
I
I
I
I
'1
I
0:
:1 I
I
0'
I
1"
9101

3101

0
511.8an 191x91

 

Figure 5.2: Level density surface in 208Pb calculated as a function of excitation energy
and angular momentum using standard CASCADE parametrization. The interpola-
tion region, as explained in text, was 20—30 MeV. The discontinuity in the surface is

aPParent.

58

mented [Kat78, Rei81, Sch82, Ki087]. In this description the level density parameter
a depends on the ground-state shell correction energy 6 U and the excitation energy
of the nucleus. For a given excitation energy E and angular momentum I and for

both parities, the level density formula is given by

 

 

2I + 1 exp(2VaU)
p(E? 1) = 1203/2 ﬂ U2 3 (5'6)
where the effective excitation energy U is
U=E—I(I+1)/9'+6P, (5.7)
and
6 = 2J..-,.-d/h2. (5.8)
The energy dependence of parameter a is deﬁne by
aU=Ez[E—I(I+1)/0+6U+6P]—&6Uexp(—7U). (5.9)
Using the expression for U from equation 5.7, the above equation becomes
6U
a = 6 1+ 7(1— exp(—7U) . (5.10)
The quantity ii is deﬁned as
Z: = A/da'. (5.11)

where the value of da' is ﬁxed so as to reproduce the known level densities in 208Pb

at low excitation energies.

The quantity 6P is the pairing correction for the ground state masses. An odd-

mass reference system is used, which is consistent with the Myer’s droplet model for

mass calculation in the CASCADE code.

Thus, (SP is given by

6P 2 —pA1/2 for even-even nuclei, (5.12)

59

= +pA1/2 for odd-odd nuclei,

= 0 for odd-mass nuclei.

where A is the nuclear mass.

At higher excitation energies the shell and pairing effects are cancelled by the term
6U + (SF in equation 5.9. This is similar to the —A term in the Piihlhofer descrip-
tion used in standard CASCADE. The dependence of the level density parameter on
shell effects is introduced by the additional energy backshift term [(36 U exp( —'7 U )]
in equation 5.9. This term decreases exponentially with excitation energy U, thus
yielding a smooth description of the level density over the entire range under consid-
eration. The quantities 7 and p were varied to obtain the best ﬁt to the measured
y-ray spectra. The parametrization was also checked by comparing the calculated

level densities with known values in nuclei near the closed shell.

Figure 5.3 shows the parameter da 2 A / a as a function of excitation energy for
nuclei from 208Pb to 198Pb calculated using the Reisdorf parametrization. The effect
of shell closure at low excitations is evident near 208Pb. At higher excitations, the
parameter da approaches the liquid drop value of ~9 which is consistent with sys-
tematics for nuclei in this mass range. The overall normalization for the damping was
ﬁxed by choosing the value of da to be 20.76 at the excitation energy of U=1 MeV

for 208Pb [Dil73] .

Figure 5.4 shows the level density in 208Pb as a function of excitation and spin,
calculated with the new parameterization. The level density surface is smooth over

the entire excitation energy. Thus this description was used for the analysis.

60

 

 

 

 

 

 

I I I I l I l I I I I I I I 1 I I I I I
20
_ 208
g Pb
\ _.
7f 15
(U ..
“U _
10 — _ __
l l l 1 l l l l L l l l l l I l l L l i
o 25 5o 75 100

Excitation energy (MeV)

Figure 5.3: da parameter as a function of excitation energy calculated using Reis-
dorf parametrization for isotopes of Pb from 208Pb to 198Pb. The parameter varies
smoothly as a function of excitation energy for all the nuclei. The inﬂuence of shell
effects near the closed shell of 208Pb is clearly seen. The shell effects damp out as
excitation energy increases. Also the shell effects vanish for nuclei farther away from
the closed shell. The value of the da parameter converges to ~9 at high excita-
tion energies and in nuclei away from the closed shell. This value is consistent with

systematics for nuclei in this mass range.

61

\1
~:
:
~:
I
I...“
.I
I
' I
I
I
I
1...
.‘.,,Iﬁ
910‘ Gear

‘I
I
I
I
i:
'0
I
I
'0
I
h.
I
'i
ii
i
210‘

gOI

I . _
‘ v v y

'0
human 191x91

fOI

I A
' ‘ I I

 

,5
5?
I
I
oOI

Figure 5.4: Level density as a function of excitation energy and angular momentum
calculated using Reisdorf parametrization. The level density surface is smooth over

the entire range of excitation and spin.

62

5.2 Input Population for Statistical Calculations

The input section of CASCADE was modiﬁed to incorporate the initial population

distribution of the compound nuclei.

The population ﬁles were derived from the particle singles spectra. The singles
spectra from the four rings of the WALL array were ﬁrst summed together and then

divided into ‘10 MeV wide’ bins corresponding to target excitation energy ranges of

40-49 MeV, 50-59 MeV, 60-69 MeV and so on as shown in ﬁgure 5.5.

In a given bin the number of nuclei for each MeV step was taken and distributed
uniformly over an angular momentum range. The upper limit of the angular mo-
mentum was calculated using the sum of the ‘matter half density radii’ of the target
and projectile nuclei as the impact parameter. The lower limit was computed using
the ‘nuclear interaction radius’ as the impact parameter. The interaction radius is
deﬁned as [Wil80]

CT + CP

Ring = CT + C13 + 4.49 — W (5.13)

where CT and Cp are the ‘matter half density radii’ of the target and the projectile
nuclei in fm. For the scattering of a-particles on 208Pb, the sum of the ‘matter half
density radii’ is 11.25 fm and the nuclear interaction radius is 8.03 fm. Figure 5.6
shows the geometric calculation of the momentum transferred to the target for spe—
ciﬁc values of projectile energy loss and impact parameter. Since the exact process of
angular momentum transfer in the inelastic scattering is not known, the incoming and
outgoing impact parameters were approximated to be equal independent of the scat-
tering angle. The angular momentum transferred to the target is then the difference
between the angular momenta in the incoming and outgoing channels. A dependence
on the scattering angle should result in a decrease in the momentum transfer with

increasing scattering angle. The momentum transfer calculated here is thus an upper

63

 

 
  
   

    
  

  

    
 

 

 

 

6 100 . 80 60 40 20 O
10 T I I I I I I I I I Tﬁ I I T I I I I I I I I I

5 I I I I I I j
5 :— J
' 3 % =3 e % =3 ‘
- I I I I I -
2 g a s 2 s s _

ré é é é 5% s

U) 5 I I II II II I
E 10 :—H5 a? a? as his his .—::
:1 I I
O 5 -— _
2 I __

I l |
I | I I
104 :— I I I I :
I- l I -
5 Ln1 1 1 111 1 i 1 11 1 1 l 1 1 L 1 l 1 1 1 1 l 1 1-
60 80 100 120 140 160
Ea (MeV) --———>

Figure 5.5: The singles spectrum from the WALL array was divided in ‘10 MeV wide’
bins. Shown here is the singles spectrum from ring 1. The dashed lines show the
boundaries of the a energies for different target excitation bins. The corresponding
target excitation energy values are also shown.

64

 

Momentum transferred to target

 

U'

 

i

p =l—p1fl-lp2

 

 

Figure 5.6: Calculation for angular momentum transferred to the target for a speciﬁc
projectile energy loss and speciﬁc impact parameter. The impact parameter was
varied between a lower and upper limit as explained in text.

limit.
The angular momentum of the target for a momentum transfer p and impact

parameter b is

1
L— 19—70ph (5.14)

Here, 19 is in units of ‘MeV/c’ and b is in units of ‘fm’.

Figure 5.7 shows the distribution of the calculated angular momentum transfer to

the target for excitation energies of 40 to 100 MeV.

Figure 5.8 displays the input population of 2°8Pb nuclei for excitation energies in
the range of 80-89 MeV spread over the calculated range of angular momenta, and
the subsequent populations generated by CASCADE for nuclei in the neutron decay

channels.

65

 

gee
nr
.mmm
“my.
atn
my...“
.cwo
nln
was
dew
nmd
01 d
60.1
on
umIsa
niw
ol‘Mlo
t o
eD.s.m
m. 1”...
aLda
gr
erme
hafh
ttSt
macmm
t
d ty
emmg
Hana
e tn
mam.
anmn
re .w
m.mm.n
r
mimam
wﬁrme
mmeg
oeaom
ms;
nhw
1&on
mowtel
nnwm
Amtm
Hha.mv.
awwm
ewni
re.lC
mochm
mmmm

66

 

Figure 5.8: Initial population of nuclei in neutron decay channels calculated by CAS-
CADE. The starting population in 208Pb is derived from the singles cross section as
explained in text and is fed as input to the code. The subsequent nuclei are popu-

a'ted following neutron evaporation. The populations shown here are for an excitation

energy of 80—89 MeV in 2°8Pb.

Chapter 6

Results and Discussion

6.1 Particle Spectra

In this section the singles and coincidence particle spectra are presented. The DWARF
array detectors were organized in rings centered at various laboratory angles. To
simplify the discussions the rings from the WALL and the BALL array have been
numbered. Tables 6.1 and 6.2 list the numbering scheme and the angular information
for the rings. Detectors that exhibited non-linearities and large gain shifts were not

included in the analysis. The tables reﬂect the actual number of detectors from which

the data sets presented here are derived.

 

 

Ring no. No. of dets. Lab. angle Total solid angle
1 6 14.78° 0.1398 sr
2 8 22.39° 0.1848 sr
3 5 23.18° 0.1290 sr
4 10 31.03° 0.2200 sr

 

 

 

 

 

 

Table 6.1: Table showing ring numbers, angles and solid angle coverage for the

D WA RF WALL array.

67

68

 

 

Ring no. No. of dets. Lab. angle
5 5 41.59°
6 8 49.51°
7 5 63.43°
8 5 67.93°
9 9 7752"
10 5 87.30°
11 4 92.70°
12 5 102.48°
13 5 112.07°
14 5 116.57°
15 5 130.49°
16 5 138.41°
17 4 155.58°

 

 

 

 

 

Table 6.2: Table showing ring numbers and angles for detectors in the DWARF BALL
array.

6.1.1 Singles (1 Spectra

The 0 singles spectra from the four rings of the wall array are displayed in ﬁgure 6.1.
The elastic scattering peak is seen prominently at the beam energy of 160 MeV at
all four angles. At energies below the elastic peak there is a broad continuum from
inelastic processes. This continuum decreases rather slowly with decreasing 0: energy.

At the lower energy end of the 0 spectra the cross section increases with decreasing

(1 energy. This feature is discussed in section 6.4.

At an or energy of ~148 MeV an enhancement is seen in the singles spectra. The
Corresponding target excitation energy is ~12 MeV. This feature is more prominent
in the outer rings due to the reduced elastics cross section. The enhancement cor-
responds to the ground state GQR and GMR excitations in 20813b with resonance
en'Eel‘gies of 10.9 and 13.9 MeV respectively [Ber80]. Since the a-particle has a T20

grol1nd state, the GDR built on the ground state of the target is not excited in the

s .
cattermg process.

69

 

1000

100

10

 

50

r I I IIIII III" I IIIIIIII I IIIIIIII I I

  
  
  

10

AAAAAAAAAAAAAA

 

llLLl l Lilllk J 1 l l l

100

I IIIIIIII III III

10

Counts (X103)

I I IIII

 

#UIODKI

 

 

 

 

80 100 120 140 160 180
Ea (MeV)

Figure 6.1: 0 singles spectra from the four rings of the WALL array.

70

The absolute cross section for the inelastic scattering was estimated from the
elastic scattering cross section. The calculation was performed for ring 1 of the
WALL array. First, the area under the elastic scattering peak was estimated from
the singles spectrum. This area was compared to the absolute elastics cross section

data from scattering measurements of 166 MeV a-particles on a 208Pb target [La382].

The elastics cross section in units of ‘millibarn (mb)’ for ring 1 of the WALL array

is thus given by
27:15? (L) sin0d6

d0
27r [:12 sin 0 old

The integral in the numerator was evaluated numerically after obtaining an exponen-

 

0(Ring 1) = 0(Ring 1), (6.1)

tial ﬁt to the elastic scattering cross section data from [La382] shown in ﬁgure 6.2.
Angles between 9° and 20 ° were integrated, corresponding to the angular coverage
of ring 1. Q(Ring1) is the total solid angle covered by detectors of Ringl. The singles

spectrum was scaled by the factor

_ 0(Ring1)

S
Nelastics

(6.2)

to yield absolute cross section in units of ‘mb/MeV’.

Here Nam,” is the total counts under the elastic scattering peak of the singles

Spectrum from ring 1.

Figure 6.3 shows the absolute cross section derived as explained above. The cross
Section is comparable to inelastic a scattering measurements made at similar angles

and beam energies on 208Pb targets [Ber80].

6.1.2 Coincidence a Spectra

The coincidence 0 spectra were obtained with the condition that a 7-ray of energy
greater than ~4 MeV was observed in coincidence with the a-particle. The spectra

from the four rings of the WALL array are displayed in ﬁgure 6.4.

71

 

 

 

 

.- I I I I I I I I I r I I I I I I I r—
+
+
4 __ _
1: 1° +.
U)
\
,o
3.3.
‘3 +
,3 102 —— ——
+
O +
a) +
m +
m _ + -
+ +
m
0 +-
3.. + +
0 10° —— + —
+
+
++++ +
+
.— l l I l l l l l l l L l l l l l I i 1‘
10 20 3O 40

Lab. angle (deg)

Figure 6.2: Differential cross section for elastic a scattering on 208Pb from [La882]
and ﬁt to the data in the angular range covered by ring 1 of the WALL array. This
data was used to estimate the cross section for inelastic scattering.

72

 

 

 

 

 

50.0 I I I I I I I I I I I r I I I I I I I
_ l l l l -
1
A
>
G)
2 10.0 __
\ I
Q -
E 5.0 —
v d
C} _
o _
"-4
4.:
8
(I) 1.0 —E
a I
O 0.5 _.
L4
0 ..
0.1 1 1
80 100 120 140 160 180

Ea (MeV)

Figure 6.3: Absolute cross section for inelastic scattering of a on 2°8Pb. The cross

section was estimated for ring 1 of the WALL array which covers laboratory angles
of 9° to 20°.

73

 

IIIIIIIIIIIIIIIIIIII

 

  

 

 

 

 

 

40000 9 —§
20000 E— —:
: i
0 I Jr“
10000 — —j
m - .
E i 1
:5 O_HHIH+I|LIHIIHHIH
10000 _— 4n n ~
0 '- l I I I I I I I l I I I I IL I I I I I I II‘
- Ring 4 a
10000 :— —-
WW :
O .— l l l l I l l l J i 14 l l l l l I I4 I-1

80 100 120 140 160

Ea (MeV)

Figure 6.4: a spectra in the four rings of the WALL array for coincidence events with
’7-rays of energy greater than ~4 MeV. The structures seen in the coincidence spectra
are evidence for equilibrated emission from an excited target nucleus.

74

The spectra exhibit structures up'to a energies of ~110 MeV. These structures
arise due to the successive opening of neutron evaporation channels in the decay
of the excited target nucleus. When a new neutron channel is available for decay,
the probability of 7-ray emission is reduced and therefore the 7-ray multiplicity is
reduced. Since the a spectrum is measured in coincidence with the 7 rays, the a-
particle multiplicity also goes down. The structures seen in the coincidence 0 spectra
are thus strong evidence for equilibrated emission from an excited target nucleus.
At higher target excitation energies the increase in the cross section for neutron
emission above the individual evaporation thresholds becomes less and less steep and
the structures therefore do not show prominently. These structures in the particle

spectra have been previously observed in the inelastic excitation measurement of

208Pb with 170 projectiles [Th091].

The probabilities for neutron emission can be computed as a function of target
excitation energy. The top panel in ﬁgure 6.5 displays this probability calculated using
the CASCADE code. The inﬂuence of individual neutron evaporation thresholds is
clearly seen. The bottom panel of the ﬁgure displays the ratio of the coincidence a
Spectrum to the single a spectrum from ring 1 of the WALL array. The dashed lines
mark the excitation energies corresponding to the onset of new evaporation channels.
The peak positions in the ratio spectrum are in good agreement with the threshold

energies for the 3n, 4n and 5n neutron evaporation channels.

6.1.3 Knockout and Pickup-Decay Contributions

Contributions to the particle spectrum other than inelastic scattering could arise from
knockout and pickup-decay processes. In knockout processes, the incoming projectile
kn0cks out a proton or a neutron from the target. Pickup-decay processes occur when

the incoming a-particle picks up a proton or a neutron from the target forming 5Li or

75

 

  
   
   

 

 

 

 

Ej r I I I I I I I I I I I I I I I I T E

1.0 —_Zn 3n 4n _:

f; E 2

:3: 0.8 :- '1

E 3 ‘
g 0.6 L'—
e 0.4 :—

D-. E _

0.2 _— —_

0.0 _ I I I I + I I IT+ T I I T1 I I I :

- I l . l I .

: I l I .-.o."o '1

' 0.8 _ I | I . .00 .—

20 :0? C I... .,O......‘.. o :

a a _ I . o I I ..

'- l 0.. l l "

\. :3 0 6 T'I I I _.

C. .o -' I I I -

. L -

8 E r 3n 4n 5n .

U V 0.4 _— 1

0.2 h l l l l l l J l l I l l l 1 I L I l l _

20 30 40 50 60
Etgt (MeV)

Figure 6.5: The neutron emission probability as a function of target excitation energy
18 compared to the particle coincidence spectrum. The top panel displays the prob-
ability for neutron emission computed using the CASCADE code. The probability
distribution exhibits the inﬂuence of individual neutron evaporation channels. The

Ottom panel displays the ratio of coincidence to singles a spectra from ring 1 of
the WALL array. The dashed lines mark the energies corresponding to the onset of
Various neutron evaporation channels.

76

5 He, respectively. The nucleus formed then decays back to a proton or a neutron and
the a-particle. These processes are included in the measured 0 singles spectra and
thus contribute to the measured cross section. It is therefore important to analyse

these processes and to estimate their contribution to the cross section.

Since neutral particles were not detected in the DWARF array, pickup-decay and
knockout processes were studied by analysing events in which an a-particle and a
proton were detected in coincidence. Figure 6.6 displays two dimensional spectra of
proton energy versus or energy for a-proton coincidence events. The plots correspond
to events where the a-particle was detected in ring 1 of the WALL array and the
proton was detected in rings 1 through 12. Events where the a-particle was detected

in the outer rings 2,3, and 4 did not have appreciable statistics.

One prominent feature of the spectra shown in ﬁgure 6.6 is that for the higher end
of the 0 energy spectrum, irrespective of the angles, the counts are predominantly in a
region which corresponds to the kinematic limit where the outgoing a and the proton
share all the available energy. These events do not leave the residual target nucleus
in excited states and therefore do not contribute to the coincident 7-ray spectra. At
the lower 0 energy end of the spectra, contributions from pre-equilibrium processes

are seen. These are discussed further in section 6.4.

The prominent bands seen in the spectra for protons detected in rings 5 through
9 correspond to knockout events. These events seem to arise as a result of free proton

knockout from hydrogen contaminants in the target.

A kinematic calculation was performed to study the process of free proton knock-
OUt by the a-particles of the beam. Results of the calculation are shown in figure 6.8
Where the angle of the outgoing proton is plotted against the angle of the outgoing

Q"Particle for different energies of the outgoing a-particle.

77

 

 

 

 

 

 

 

 

 

 

 

‘I
00.
oo-
40,“
20 '-
i“
‘f‘
80 7. 7~ 0p=31 09:42" 0P=50'
\-

60
407'

§ 2...

E .

v AM L_‘¥

c IW
%

mi 007 8P=63° 7 9P=68' 0P=78'
go.
40
2° ‘ 1‘
100 A +
00 0P=BT 7 0,:93' 7 9,,=102'
60-
‘0.
201,}. . a

50 75 100 125 150 75 100 125 150 75 100 125 150

Figure 6.6: Two dimensional plots of proton energy versus or energy for a—proton
Coincidence events in the DWARF array. The plots shown here correspond to events
Where the a particle was detected in ring 1 and the proton was detected in rings 1
through 12 of the WALL/BALL array.

78

 

 

 

 

r I I I I I I T I ﬁr I I I I I I I I 1 I
80 __ I . I I
r? .. Ea=155MeV . I | _
an _ ' ' -
a) ' I I
"U 7- CI I -
V _ I . I _
. 60 — I . I __
g _ . . . _
.— I 0 I
.. . .4
| I
.9. - , . , _
_ I .. I -
g 40 7— I o I _
4..) _ I O | _
8 _ I .0 I _
I I
:3: — . - . .
.. I O l _
O 20 _ l C I .—
2 — ' o ' —
DO I l
CI ' _ I I '
<1 Ea— souev I I , -
_ I J ‘
0 I I l I l I r r J l 1 I l I l I I l 4 I l I I
0 5 10 15 20 25

Angle of alpha in lab. (deg)

Figure 6.7: Results of kinematic calculation for free proton knockout events. The
a'Ilgle of the outgoing proton is plotted against the angle of the outgoing a for outgoing
a energies of 155 MeV to 60 MeV in steps of 5 MeV. The dashed lines mark the angular
acCeptance limit of ring 1 of the WALL array.

79

Figure 6.7 shows that the events in which the a-particle is detected in ring 1 of
the WALL will correspond to protons emerging at angles of ~ 16° to ~ 70°. Thus
free protons that are knocked out should be observed in the angular range covered
by ring 1 through ring 9. The energy of the protons emerging in the angular range
covered by rings 1 through 4 is too large (E0, 2 90 MeV). These protons therefore
punch through the detector volume and thus cannot be identiﬁed. The above angular
dependence is seen in ﬁgure 6.6. The knockout band is present from the ﬁfth plot
onwards. Further, ring 9 is the last ring in which the knockout band is seen. The
data that fall in the knockout bands were also analysed for angular correlation. It
was observed that in these events the a and the proton were measured in detectors
that were diametrically opposite to each other in a plane perpendicular to the beam

axis. This angular correlation is consistent with the knockout process.

The bands observed in the ﬁrst four spectra in ﬁgure 6.6 where the proton is
detected in rings 1 through 4 of the WALL correspond to pickup-decay events. No
angular correlation is seen for these events thus ruling out knockout type reactions.
Again the counts are dominant at the kinematic limit corresponding to the total
energy being shared by the a-particle and the proton. Contributions to the coincident

’y-ray spectra are therefore minimal.

Figure 6.8 displays the knockout and pickup-decay contributions to the a spectrum
from the events around the kinematic limit, in comparison to the a singles spectrum
in ring 1.

The pickup-decay spectrum was obtained by summing events where the a-particle
Was detected in ring 1 and the proton was detected in rings 1 through 4. The knockout
SPectrum corresponds to events where the a was detected in ring 1 and the proton
in rings 5 through 9. From the ﬁgure, the knockout contribution can be estimated to

be at most ~ 8%. The pickup-decay contribution is at most ~ 5%. This corresponds

8O

 

     

105

I IIIIIIIl
l llllllll

104

I I IIIIII

   

l llllllll

Counts

  

 

 

 

103 :— —:

I— 1"L\‘l~\rl§;:l pfl 'I
2 I' J I' 41%

.._. ,. .Ih '3 'l __

10 E n Jlflu I" :
E I 1 I
_ IIJ1| H 'I
- a 1 q

I \rl
- I I”L | _
'I . n
101 l l 1 ll 1 L l 1 4 I 'll 1 l l l l l r 11 l i l 1 l J
50 75 100 125 150 175
E 0, (MeV)

Figure 6.8: Pickup-decay and knockout contributions compared to the singles a spec-
trum. The solid histogram is singles cross section. The dotted histogram shows con-

tI‘ibutions from free proton knockout and the dashes histogram shows contribution
r0111 proton pickup-decay events.

81

to events in which the incoming a picks up a proton. Since events where a neutron is
picked up were not detected, the contribution estimated from proton pickup should
be scaled to account for neutron pickup. There are about 1.5 times as many neutrons

as there are protons in 208Pb. The total contribution from pickup-decay and knockout

can thus be approximated to ~ 20%.

6.2 Coincidence 'y-ray Spectra

6.2.1 7-ray Spectra as a Function of Target Excitation

In this section the 7-ray spectra measured in coincidence with a-particles in the WALL
array are presented. The data were sorted to create 7-ray spectra as a function of

a energy, ring number of the coincidence WALL detector, and pack number of the
Ban detectors. .

To obtain the 7-ray spectra as a function of target excitation, the a spectra were
binned in 10 MeV wide cuts in (1 energy as explained earlier in chapter 4.

The 7-ray spectra were measured in Ban detectors placed at three different mea-
surement angles of 60°, 72° and 112° in the laboratory. The left panel in ﬁgure 6.9
displays the 7-ray spectra for detection angles of 60° and 112° for a target excitation
energy range of 80—100 MeV. There in no appreciable difference in the spectra from
the two angles.

The 7-ray spectra as a function of the a detection angle are displayed in the right
Panel of ﬁgure 6.9, for the same target excitation energy. Again the spectra exhibit

n0 shape differences.

Since no appreciable angular dependance was seen in the spectra as a function of
V‘ray detection angle or as a function of a detection angle, the data from the different

detection angles were summed together to yield the ﬁnal y-ray spectra.

82

 

 

 

 

:IIIIIIIIIIIIIIIIIIIIIIIIIIIIIEIIIIIIIIIIIIIIIIIIIIIIIIIIWII:
3 (a) (b) “
-3 WP. _
10° 5" "'55“ i
E 0 5E . i
_ _ r _
B r ? _.__ I _
Cl 2 .— —_:- 8 —:
=1 1° E 93. 32 ' 3
8 : ‘5 i: as! ;
7 a“. " is, ‘
_ 09 -- 0; 7
09 g;
101 — . ——- Q —
a 90 55 ll 2
; T; g I: g I
: i g I f ‘
+ I III
100 .

5.0 7.5 10.0 12.5 15.0 17.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0
E7 (MeV)

Figure 6.9: 7-ray spectra corrseponding to different 7-ray and a particle detection
angles for a target excitation energy range of 80-100 MeV. (a) The open squares are
the spectra from the two Ban packs at laboratory angle of 60° and the closed circles
are data from the pack at detection angle of 112°. The spectra were normalized in the
range of 7—10 MeV. (b) The open squares are spectra in coincidence with a particles
detected in ring 1 of the WALL array and the closed circles are spectra in coincidence
with rings 2 and 3. The spectra were normalized in the range of 7—10 MeV.

83

‘ Figure 6.10 shows the 7-ray spectra for 0 energy ranges of 111—120 MeV and
61—70 MeV. These correspond to target excitation energies of 40—49 MeV and 90—99
MeV respectively. The enhancement in the giant dipole resonance energy region is
clearly seen in both spectra. Furthermore the spectrum from the higher excitation
energy range has signiﬁcantly more counts in the GDR region compared to that from
the lower excitation cut. This is a clear evidence for increase in target excitation with

increase in the energy loss of the projectile.

Figure 6.11 shows the 7-ray spectra for various target excitation energy ranges
corresponding to a energies from 111 MeV to 61 MeV. Below an 01 energy of ~50 MeV,
the singles cross section rises signiﬁcantly with energy loss. The target excitation in

this region can be inﬂuenced by pre-equilibrium type processes.

6.2.2 Statistical Model Calculations with CASCADE

The 7-ray spectra were compared to statistical model calculations performed with

the modiﬁed version of the CASCADE code.

The contribution to the total 77-ray spectrum for all excitation ranges arises pre-
dominantly from the neutron channels in the decay of the excited target nucleus.
Figure 6.12 shows the calculated spectra for target excitation energy range of 80—89
MeV. The open circles represent the total calculated 7-ray spectrum. The ﬁlled di-
amonds are the contribution from neutron evaporation in Z = 82 isotopes. It can
be seen from the ﬁgure that the contribution from the neutron channels accounts for
almost all of the cross section. The summed contributions from other decay channels
are show as open diamonds in the ﬁgure. This contribution is at least 2 to 3 orders

of magnitude smaller.

The dominant contribution to the 7-ray spectrum in the GDR energy range results

84

 

104 TI IrTI IIII IIII IITT VIII
I I I I I

 

 

fl 5

:9 r.

I- a -I

10:3 E- B —:

E . E

_ D _

I- . -I

C: 102 —— 03'. _.
S E .. i
O : an .. j
0 — a .0. ..
_. DD . _.

I— DO .. —

101 _ DD 0 _

E ODD "' E

I Q i "

” §§§ Q i ii

100 14 L l I 1 lJ_LI l l l l I l 1 1J I l l l [fli%l§l%

 

5.0 7.5 10.0 12.5 15.0 17.5 20.0
E, (MeV)

Figure 6.10: 7-ray spectra 'from two different target excitation cuts of 40—49 MeV
(open squares) and 90—99 MeV (ﬁlled circles). Data have been normalized in the
range of 6—7 MeV. Figure shows the enhancement of counts in the GDR energy
region in the spectrum from the higher excitation energy over the spectrum from the
lower excitation energy.

85

 

       
  
 

 

 

  
   
 
   

104 . I I I I l I I I I I I F I j . I I I I I T I I I I 1 I I fr I I I I I I I I I I r
103 F Em=40—49 nev Em=50—59 uev i skew-59 MeV
102 g—
101
.53 I .
I: 0 III IIII III I'
:3 10
0 I
U I
103 Em=80—89 uev Em=90—99 MeV a
103 1

 

H
O
H

I [turn] I [III

 

  

I

l I I

100 llllIllllI [MIIIIIILLIJ llllIllllIl IIIII
5 10 15 5 10 15 5 10 15 20

E7 (MeV)

Figure 6.11: Coincidence 7-ray spectra for various target excitation energies from

40—49 MeV to 90—99 MeV.

86

 

 

 

 

'- I I l I I I I I I I I I I T I I I I I I I I I l I I I I 1
104 ©©© ~
1.7 ©
+2 7 ©© -
.H O 0
S 102 — ° 0 © —
. 0 ©
2 © -
ﬂ ° ©©©©
(Q
g — ° o o ©© -
H 0
20410—2 __ o o ©© —I
0 0 ©
0) 0 G)
V) " o ©© -1
0
$3104 —— ° ©© —
o 0 ©
L4 _ 0 ©@_
0 ° 0 GD
10‘6 —— 0 _
l l l L I I I l L I L 1 l J I L4 1 l I I l L Y L l l l I
0 5 10 15 20 25 30
E7 (MeV)

Figure 6.12: Contributions to the '7-ray spectra from neutron evaporation channels
compared to contribution from other channels for a typical target excitation range
of 80-89 MeV. The open circles are the contribution from all channels. The closed
diamonds are the sum contribution from just neutron evaporation channels. The open
diamonds are the sum contrinution from all other decay channels.

87

 

 

n channel Percentage
In 21
2n 19
3n 17
4n 15
5n 12
6n 9
7n 6
8n 1
9n 0

 

 

 

 

Table 6.3: Percentage contributions to the 7-ray spectrum at 13 MeV from individual
neutron decay channels calculated using CASCADE. The target excitation energy was

80-89 MeV.

from the ﬁrst few steps in the decay of the target nucleus. The contributions to a
typical calculated 77-ray spectrum from the different decay channels are displayed in

ﬁgure 6.13 for a typical target excitation energy of 80—89 MeV.

The contribution to the GDR region is mainly from the neutron evaporation chan-
nels 011 through 5n. Table 6.3 lists the percentage contribution to the 7-ray spectrum
at 13 MeV from the individual channels. The low energy slope of the spectrum is

dominated by the contributions from the last few steps of the decay.

The non-statistical background in the data was accounted for by a simple ex-
ponential ﬁt to the high energy region of the measured 7-ray spectrum. An expo—
nential of the form exp(—E.,/Eo) was used with a slope parameter of E0=14 MeV
obtained from bremsstrahlung systematics for the experimental beam energy of 40
MeV/nucleon [Nif90]. This exponential was normalized to the data points in the
energy range of 20—30 MeV where the contributions from GDR are negligible. The
statistical calculations performed with CASCADE were ﬁrst folded with the detector
response function and then normalized to the measured spectra in the low energy

range of 7-8 MeV. The normalized non—statistical contribution was then added be-

88

 

H

O
.p.
I
/
I

H

O H I-b
I O O
N o N
I I I

O

I!

m

:3
/

/

I I

Cross sectlon (arb units)
/
/
/
/
/
/

H
“’1
4:.
I
(D
D
‘1
O)
:3
/
/
I

 

 

H
C
I
03
_|
I.
F
_
p
r-
I-
I-——
p
b
I-
I-
)—

 

Figure 6.13: Contributions to the calculated 7-ray spectrum from individual neutron
decay channels in 2282 nuclei. The dashed line is the calculated total 7-ray spectrum.
The solid lines are from the nuclei 208Pb to 199Pb. The calculation was done for target
excitation range of 80—89 MeV. Contributions to the GDR region arise mainly from
the ﬁrst few decay steps. The low energy slope is decided by the contributions from
the last few nuclei in the decay chain.

89

fore comparing to the measured spectra. The GDR strength function inﬂuences the
region of statistical 7-rays below 8 MeV. It is thus important to obtain a good ﬁt to
the data over the entire 7-ray energy range of ~5 MeV to ~25 MeV. A least squares
ﬁt approach is not sensitive to the GDR energy region due to the exponential nature
of the 7-ray spectrum. The best ﬁts were therefore obtained by varying the resonance

parameters and by choosing the ﬁnal ﬁt by visual inspection.

Figure 6.14 shows the 7—ray spectrum for a target excitation energy range of 70—79
MeV and the calculations for the statistical and non-statistical contributions. The
ﬁlled circles are the data points plotted in 1 MeV wide bins. The dashed line is the
output of the statistical model calculation performed with CASCADE. The dotted
line is the exponential exp(—E.,/E0). The solid line in the ﬁgure is the sum of the
statistical and the non-statistical contributions and is in good agreement with the

data. The contribution from bremsstrahlung at 13 MeV is ~ 15%.

The above mentioned procedure was applied to the 7-ray spectra from all excita-
tion energy ranges. Figure 6.15 shows the 7-ray spectra compared to the calculations
for the excitation energy ranges of 50—59 MeV to 90—99 MeV. The calculations are in

good agreement with the data in the GDR energy region and at lower 7-ray energies.

The data and calculations were compared on a linear scale by dividing them by
an additional statistical model calculation performed with a constant dipole strength
function. The strength was chosen arbitrarily to be 0.2 Weisskopf units. The division

results in a strength function given by

f (E ) = IVY(E7) ~ fGDR(E7) = E’YF
ave ’7 Fconst(E7) fconst(E'y) (E3 —’ E3)2 'I" E3112

 

(6.3)

The statistical calculation with the constant strength function was normalized

ﬁrst to the data in the energy range of 7-8 MeV and the bremsstrahlung contribution

90

 

104 -- I I I I I I I I I f T I I I I I I I I I I I I

l I 111111

  
   
  
 

103

I I IIIIIII
l lLllILlI

I I IIIIIII

l l lllllII

IIIIII
I l I lllllI

  

I
/

ll
'0
.....
u._
‘-
I

Cross section (arb. units)

I I IIIIIIl’

 

 

 

H
“I
H

F-
>-
I.
I.
__
,—
r.
I.
#—
..__
I.
._
I.
I.
I
_
..
I.
.—

01
H
O
p...
01
N
O
N
01
00
C

Figure 6.14: The 7-ray spectrum for target excitation energy of 70—79 MeV is com-
pared to calculations. The dashed line is the result of a calculation performed
with CASCADE. The dotted line is the non-statistical contribution from nuclear
bremsstrahlung. The solid line is the sum of the statistical and non-statistical con-
tributions.

91

104 Em= 50- 59 MeV Em= 80- 69 MeV Em= 70— 79 MeV

Q 9

Counts

Em= 80- 89 MeV Em= 90— 99 HOV Em=lOO—109 MeV

. -...-.l - .

.ul

 

 

A4 1 AAA A lug—AAA] Ann-44A AA AL 1 A AAA 1A

5101520 5101520 510152025
E7 (MeV)

Figure 6.15: The 7-ray spectra for various target excitation energy ranges are com—
pared to the model calculations. The ﬁlled circles are the measured 7-ray spectra and
the solid line is a sum of the statistical model calculation and the bremsstrahlung

component as explained in text.

92

was added to it. The resulting spectrum was used to divide the measured data and
the model calculation including the GDR strength to yield the linearized plots. The

linearized plots for various target excitation energy ranges are displayed in ﬁgure 6.16.

The resonance parameters extracted from the ﬁts to the 7-ray spectra are listed in
table 6.4. The error bars quoted in the table were estimated by varying one parameter

at a time and visually inspecting the quality of the ﬁt.

A dipole resonance energy value of 15.0 MeV was used in the statistical calcu-
lations for all the target excitation energy ranges. This value is 1.5 MeV above the
ground state resonance value of 13.5 MeV. The quality of the ﬁts did not vary ap-
preciably for resonance energies in the range of 14.5 to 15.5 MeV. No systematic
dependence is observed in the resonance energy as a function of target excitation
energy. The resonance energy parameter input to the statistical calculations can be
inﬂuenced by uncertainties in the level density parametrization. For the range of
resonance energies considered in the ﬁtting procedure, the extracted resonance width

stayed within the estimated error range listed in table 6.4.

The resonance energy extracted from measurements of excited state GDR in fu-
sion reactions have exhibited deviations from the ground state value. For instance,
measurements in excited Sn isotopes yielded a resonance energy parameter 1 MeV
lower than the energy of the ground state resonance [Cha87]. No systematic depen-
dence is observed over the mass range. The deviations observed in fusion-evaporation

measurements have not been studied in detail.

The parameter SGDR is the fraction of the classical E1 sum rule strength input
to the statistical calculation. This parameter is seen to decrease from a value of
1.0 at low excitation energies to ~05 at higher energies. This decrease in the sum

rule strength may be due to processes in the inelastic scattering that do not induce

93

 

l

IIII

4IIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIII

-

50- 69 MeV 60- 89 MeV 70- '79 MeV

IIII
Ill]

1 l

   

J
l

  

I—.—4

llll

   
 

IIII

 

  
   
    

N
LIWIIIIIIIIIII
v——.——c
o—.——-c
111
O——.—¢
I-—.—l
llllllllll

 

l

 

In
111

 

 

 

 

 

 

 

 

fave(E./)(arbitray units)

 

   
  

 

 

II III llllllll ll]|llll"‘"llll [Ill 11]] I
II III III III IIIIIIIT IIIIIIII IIII IIII IIII IIT
u-l- —(I— -
L—n u-II— -- q
_ BO- 89 NOV ‘_ 90- 99 HOV __ 100-109 HOV q
u— .1— "P 1—1
3 — —— —II——- —
p- -— -I- ‘
h —u— -h— cl
1— db— —1— —:
I— .0— —II— —I
2 _ _— —_ —
- c-l-n our ‘
y.- —I— d; d
b d- “F + -
1 —. -c

 

  
 

  
 

llllllllllll+léllllll llllllllllllllLll llllllllllllllLLlll
5101520 5101520 5 10152025

E7 (MeV)

Figure 6.16: The 7-ray spectra for various target excitation energy ranges are com-
pared to the calculations on a linear scale. The linearized plots were obtained on
dividing the data and the calculations by a second model calculation employing an
energy independent dipole strength.

94

 

Excitation PGDR SGDR
Range (MeV) (MeV)
40-49 5.7:l:0.5 1.00:1:0.1
50-59 6.0i0.5 0.80:1:0.1
60-69 6.5:l:0.5 0.80:1:0.1
70-79 6.5:l:0.5 0.55i0.1
80—89 7.2i0.5 0.45i0.1
90-99 7.0i0.5 0.55i0.1
100—109 8.0:t0u5 0.70:1:0.1

 

 

 

 

 

 

Table 6.4: GDR parameters extracted for various target excitation energy ranges.

collective excitations in the target, but however contribute to the 7-ray spectra in
the energy region below ~ 8 MeV. A lower sum rule strength is therefore required to

obtain a good ﬁt to the 7-ray spectra in the range of 5—30 MeV.

The resonance width extracted from the ﬁtting procedure is seen to increase sys-
tematically with increasing target excitation energy. The excitation energy is given
by

E... = E... — E... (6.4)

where Emma is the mean energy of the input population derived from the particle
singles spectrum and E... is the rotational energy corresponding to the mean angular
momentum of nuclei in the input population. Table 6.5 lists the above mentioned

quantities for the different target excitation energy ranges.

Figure 6.17 displays the resonance width as a function of excitation energy E...
The data points are shown as ﬁlled circles. The ﬁlled square is the width of the
resonance built on the ground state [Die88]. The width values are well described by
a linear dependence on the excitation energy. The solid line in the ﬁgure is a linear

ﬁt to the data points including the ground state point and is given by the expression

I‘GDR(E.I) = (3.42 i: 0.13) + (0.044 :I: 0.003) x E. (6.5)

 

95

 

10 I I I I I I I I I I I I I I I I I I I I I I I I I I r I

PGDR (MeV)

 

 

 

1. _
l- —1
" W
4 — _
_ J
2 1 1 1 1 l 1 1 1 1 l 1 1 m 1 l 1 1 1 1 l 1 1 J 1 l 1 1 1 1
0 20 4O 60 80 100 120

Eex (MeV)

Figure 6.17: The resonance width as a function of exciation energy in 208Pb. The
excitation energy was obtained by subtracting the rotational energy from the mean
energy of the input population derived from the 0 singles spectra. The solid circles
are the widths obtined from ﬁtting the calculations to the data and the solid square
is the width of the resonanace built on the ground state. The line is the result of a
linear ﬁt to the data set including the ground state point.

96

 

 

Excitation Em.“ mean Em a(Ecﬂr) T
Range (MeV) (MeV) (5) (MeV) (MeV‘l) (MeV)
40—49 44.38 8 0.28 16.27 1.34
50-59 54.35 10 ‘ 0.45 17.54 1.49
60—69 64.42 12 0.66 18.54 1.62
70—79 74.42 14 0.91 19.31 1.74
80—89 84.47 17 1.36 19.93 1.85
90—99 94.55 19 1.71 20.44 1.95
100—109 104.64 21 2.31 20.84 2.05

 

 

 

 

 

 

 

 

Table 6.5: Calculation of nuclear temperature from the effective excitation energy.
The rotational energy and the GDR energy were subtracted from the mean excitation
energy and the temperature was calculated with an energy dependent level density
parameter.

The nuclear temperature in 208Pb for the different excitation energies was com-

puted using the expression

Egg
—— (6.6)
“(13:17)
where Egg is the effective excitation energy given by
Eeﬂ : Emean — Erot _ EGDR~ (6.7)

The quantity 0(Eeg) is the energy dependent level density parameter that was ob-
tained using the parametrization described in chapter 5. The temperature T corre-

sponding to each target excitation energy range is listed in table 6.5.

The width as a function of the temperature in 208Pb is plotted in ﬁgure 6.18. The
solid line in the ﬁgure is a second order ﬁt to the data points including the ground

state width, and is given by the expression

ram.(T) = (4.0 :1: 0.1) + (0.89 :1: 0.07) x T2. (6.8)

97

 

10 I I I I I I I I I I I I I I I I

FGDR (MeV)
l
l

 

 

 

Figure 6.18: The resonance width as a function of temperature in 208Pb. The temper-
ature was obtained from the effective excitation energy by using an energy dependent
level density parameter as explained in text. The solid circles are the widths obtained
from ﬁtting the calculations to the data and the solid square is the width of the res-
onance built on the ground state. The line is the result of a second order ﬁt to the
data set including the ground state point.

98

6.3 Resonance Width

The measured resonance widths can be compared to model calculations that describe
the evolution of the giant dipole resonance with increasing excitation energy and

angular momentum.

One such model attributes the evolution of the resonance width as due to the cou-
pling of the collective degrees of freedom to the nuclear potential landscape [Br092].
At low excitation energies the contribution to the width arises from small amplitude
quantal ﬂuctuations in the potential surface. These ﬂuctuations in shape are induced
by the zero point motion of a harmonic vibrator in the deformation degrees of free-
dom. The resonance width from quantal ﬂuctuations accounts for the majority of
the ground state width in heavy nuclei. In excited nuclei, other than the quantal
ﬂuctuations of the surface, there are also large amplitude thermal ﬂuctuations where
nuclear shapes over the entire (5,7) deformation plane are sampled. These thermal

ﬂuctuations result in a broadening of the width of the GDR [Pac88, Bor89].

Ormand et al. have performed detailed calculations of the evolution of the reso-
nance in excited 208Pb nuclei by considering the coupling of the collective excitation
to the nuclear free energy surface [Orm95]. The coupling was assumed to be adiabatic
in nature such that the time scale of the shape ﬂuctuations are large compared to the

damping time of the GDR.

In their model, the probability that a given deformation a in the (3,7) plane is

experienced by the nucleus at a temperature T, is given by the Boltzmann factor
1002) «x exp {—Fcr, an, (6.9)

where

F(T,a)=E—Ts—f-.:3 (6.10)

99

is the nuclear free energy. Here, E is the excitation energy, 5 is the entropy, T is the

angular momentum and L3 is the rotational frequency [Gar92].

The observed GDR cross section is then written as a weighted average over the

deformation parameter as

0(E.) = ; [01a10(a.E.) eXP[—F(T.a)]. (6.11)

where E, is the photon energy and
z = / D[a] exp [—F(T,a)] (6.12)

is the partition function. The quantity D[a] is the volume element for the integration
in the ﬁve dimensional space formed by the deformation parameters ﬂy) and the
three Euler angles that deﬁne the orientation of the nucleus with respect to 0'5 [Ga185,
Pac88, Alh90]. The deformation dependent cross section 0(1), E,) for the GDR was
computed using a harmonic oscillator model that considers vibrations along the three
principal axes of the deformed nucleus, with frequencies corresponding to the inverse
of the radius for each axis. The intrinsic resonance width for each resonance energy

component E,- was parametrized by a power law [Alh90]

, 1.6
13:1“0 (if) , (6.13)

where F 0 is the ground state width and E0 is the ground state resonance energy. Such
a parametrization is necessary because no fundamental microscopic description of the

dipole resonance widths that reproduce the experimental data is currently available.

The nuclear free energy plays an important role in the determination of the GDR
cross section in hot nuclei. The free energy as a function of temperature T and
deformation 8 was evaluated using the Nilsson—Strutinsky procedure [Str68]. This

procedure assumes that the global bulk properties of the nucleus are well described

100

by the liquid drop model, while local shell effects are accounted for by the Strutinsky
shell correction applied to the Nilsson hamiltonian. The free energy was parametrized
by functions that mimic the behaviour of the Nilsson-Strutinsky calculations as close
as possible. A simple and accurate evaluation of the free energy for a wide range
of deformations and temperatures was thus achieved without having to explicitly

perform a Nilsson-Strutinsky calculation at each deformation point.

Figure 6.19 displays the width of the GDR obtained from the calculated cross
sections, in comparison to the measured data. The angular momentum of the nucleus
was assumed to be zero. The calculated width does not change appreciably up to a
temperature of ~1 MeV due to the persistence of shell effects in 208Pb. Beyond 1
MeV, the shell effects vanish and the width increases with increasing temperature.
The surface energy plots in ﬁgure 2.2 displayed this feature. There the free energy

surface was seen to broaden rather rapidly between 1 and 2 MeV.

The main goal of this measurement was to study the evolution of the Width as a
function of excitation energy with very little inﬂuence from angular momentum. In
fusion-evaporation reactions large angular momenta are populated in the nucleus over
a broad range of values. The width increase observed in fusion measurements have
been attributed mainly to angular momentum, with a less signiﬁcant contribution
from excitation energy [Br092]. Inelastic scattering populates low angular momentum
states and thus the properties of nuclei in a narrow range of excitation energy and
spin can be studied. In the absence of large spins the width of the resonance should
increase rather slowly with increasing excitation energy. The calculated widths exhibit

a dependence on the nuclear temperature given by FGDR ~ \fT.

The calculation is in good agreement with the data over the range of temperatures
observed in the measurement. Clearly more data is needed at temperatures beyond 2

MeV to compare the behaviour of the resonance with calculations at higher excitation

101

 

12

 

 

 

F I I I I I ‘IiI I I I I I I I I I I

10— —

9 8—— ——
<1) ~ _
2 ~ i _
V __ _
8 6*— _

L. ~ .
4— I —+

2_I I I I I I J I l I J I I I I I I l I-

0 2 3
T (MeV)

Figure 6.19: Measured resonance width compared to calculations that consider the
coupling of the GDR to the nuclear free energy surface. The ﬁlled circles are the
widths obtained from ﬁtting the 7-ray spectra. The open diamonds are the model
calculations performed by Ormand et al. The ﬁlled square is the ground state reso-
nance point. The calculation is in good qualitative agreement with the data.

102

energies. Temperatures below 1 MeV are not accessible for study using giant dipole

resonance measurements.

Smerzi et al. have proposed an alternate theoretical description for the evolution
of the resonance width with excitation [Sme91]. In their model the damping of the
resonance is treated purely in terms of nucleon-nucleon collisional dynamics. The
effect of one- and two-body dissipation is studied by solving a semiclassical Vlasov
equation including a collisional relaxation time. The relaxation time is the time
required for the perturbed system to reach a new equilibrium under the effect of

two-body collisions.

The relaxation width as a function of temperature is expressed in their model as

 

 

e
FR(T) = I112030) [1 + —T , (6.14)
6D
where
71'2T2
= .1
6T 46F (6 5)
is the thermal energy density, and
E

is the collective energy density. The quantity 6}? is the Fermi energy.

Such ﬁnite temperature relaxation widths are employed in solving the collisional
dynamics. The results of their calculation for 208Pb is displayed in ﬁgure 6.20 in com-
parison to the data. A rapid increase in the width is seen at lower temperatures. The
calculated resonance widths are rather large compared to the data. For temperatures
above 2 MeV, the calculated widths display a saturation effect. They attribute the
saturation to the slow disappearance of the GDR strength with increasing excitation
energy. The observed dipole strength at high excitation energies in their model thus

corresponds to cooler nuclei that are populated subsequent to particle evaporation.

103

 

 

 

 

If I I I I I I I I r I I T ﬁ I I I

15— —

9 ‘ 4

(D 10— _

2 _ _
V

D: " E -1
a

L? * HE i

5— .—

.. I _.

I i I 4 I I I I I I I I L L I L I I I

O 1 2 3

Figure 6.20: Measured resonance width compared to calculations performed using
collisional dynamics model. The ﬁlled circles are the data points from the experiment.
The ﬁlled square is the ground state width. The open diamonds are results of the
model calculation by Smerzi et al. The calculations predict resonance widths that
are much larger than those obtained from experiment.

104

6.4 Pre-equilibrium Emission

At the lower energy end of the particle spectra processes other than inelastic scattering
contribute to the measured cross section. The cross section is seen to rise with
increasing projectile energy loss for a energies below ~50 MeV. The target excitation

energy in this region cannot be deduced purely from the energy loss of the projectile.

Figure 6.21 shows the 01 singles spectra from the four WALL rings in the low
energy range. The cross section rises with decreasing 0 energy in this range in all

four rings.

Previous measurements of inelastic a scattering on 208Pb did not observe this

behaviour due to higher thresholds on the particle detectors [You76, Ber80].

The slope of the cross section at lower energies is too shallow to be accounted for
by the statistical emission of a-particles in the decay of the excited target nucleus.
Figure 6.22 shows the cross section of a-particles from the decay of equilibrated 212Po
formed by the fusion of 40 MeV/ nucleon a-particles on 208Pb in comparison to the
measured inelastic spectrum from ring 1. The evaporation calculation was performed
with CASCADE. The angular distribution of evaporated emission is isotropic. The
calculation was scaled to account for the solid angle acceptance of the detectors. It
is clear from the ﬁgure that though the cross section for the evaporation process
is comparable to the measured cross section, the evaporation spectrum has a much

steeper slope than that of the measured a spectrum.

The shape of the a spectrum at low energies is due to pre—equilibrium processes
occurring in the scattering. For sufﬁciently low impact parameters the incoming a-
particle could undergo multiple interactions with the nucleons of the target. As a
result of these interactions one or more particles could be emitted from the target

before equilibration of the energy is achieved. It is possible that a proton or a deuteron

105

 

_
—<
q
—
d
1
I-
-

IIIIJ"

0.5

I IIIII4

I

0.1

 

1
.1
_

q
_

d

4
.-

ﬁ

4
--ﬁ-—

4

4
c-Ib-

4L

0.5

I IIIIIJIIII
[1111 III“

0.1

 

I I III 11111

0.5

I IIIII IIIII
4
.4
i
.1

I 4. I
d

4» 1. «b
1! ii 4!
D (b «p
d- ‘h 1b
p I. db
4» 1h 1»
1 up 1-
q q: >
d - P
4- <>
1 1- '
<1- 5 <-
D up 4F
5 'lP 4h
Ah 4» p
u up >
in It P
(I 1» db
uh db -
in d. uh

uh Iv
ii in db

I l I I

0.1

 

Gib-
4
1
l
-ﬁF—

0.5

I I IIII..IIIII

I I IJJI IlILI

   
 
 

I

1

0.1 Ring 4

A ‘4, I l l A A l A 1 1 I l l 441 1 L l l A A A l 1 l l A l j

20 30 40 50 6O 70
Ea (MeV)

IIII

 

 

”I III

 

Figure 6.21: 0 singles spectra in the four rings of the WALL array at the low energy
end is displayed. The spectrum from ring 1 was converted to absoulte cross section
scale as described in section 6.1.1. The spectra from rings 2 to 4 were scaled to
absolute cross section by normailizing the solid angles of these rings to the solid angle
of ring 1. The cross section is seen to rise with decreasing (1 energy in all four spectra.

106

 

FT
.1
an
-I
u—

—l
q
q
-|
_1
.4
_1
—
n—

-——1
.-
—4

L

I
l

H
O
H

I IIIIIIII
I IIIIIIII

H
C
O

I IIIIIII

L I IIIIII

I
I

Cross section (mb/MeV)
o
I

I ITIIIII

I JJIIIIII

I

 

 

 

H
°.
N

 

Figure 6.22: The calculated a evaporation spectrum from the decay of 212P0 formed
by the fusion of 40 MeV / nucleon a on 20'E‘Pb (histogram) is shown in comparison to the
a spectrum measured in ring 1 of the WALL array from the inelastic scattering (solid
line). The evaporation calculation was done with CASCADE. Evaporated (1 particles
have an isotropic distribution. The calculation was scaled to correspond to the solid
angle acceptance of ring 1. Though the evaporation cross section is comparable in
magnitude to’the measured cross section, the slope of the evaporated (1 particles is
much steeper compared to the slope of the measured spectrum at low energies.

107

or another a-particle is emitted from the pre-equilibrium stage.

Emission from the pre-equilibrium stage should be forward focussed. Figure 6.23
shows that this feature is observed in the data. The ﬁgure displays the a spectra
from various rings of the BALL array which were measured in coincidence with an
a-particle in the WALL array. The pre-equilibrium signature is seen in the forward
rings of the BALL. As the measurement angle becomes more backward, the spectral

shape approaches that of evaporated a-particles from an excited target nucleus.

Another signature for pre—equilibrium processes can be seen in the high energy
region of the coincidence 7-ray spectra. For 7-ray energies above ~20 MeV, there
is no signiﬁcant contribution to the spectra from the GDR. This region is therefore
indicative of processes like nuclear bremsstrahlung that generate high energy 7 rays.
If the incoming a-particle interacts strongly with the target nucleus, the nuclear
bremsstrahlung contribution should increase. Figure 6.24 displays the integrated
counts in the 7-ray spectra in the 20—30 MeV energy range in comparison to the
singles cross section. The ﬁgure shows that as the measured 0 energy decreases
the high energy 7-ray contribution increases, and reaches a maximum in the pre-
equilibrium energy range. This indicates that at lower at energies the interaction
of the projectile with the nucleons of the target increases, and this could result in

enhanced pre—equilibrium emission.

Statistical model calculations can be performed to ﬁt the 7-ray spectra in coinci-
dence with the a-particles from the pre—equilibrium region. Figure 6.25 displays the
7-ray spectra in coincidence with a energies of 21-30 MeV, 31—40 MeV and 41—50
MeV. The apparent target excitation energies are 130—139 MeV, 120—129 MeV and
110—119 MeV respectively. Statistical model calculations assuming these excitation
energies are shown in the ﬁgure along with the linearized plots. The width of the

resonance as extracted from these ﬁts does not increase with excitation energy, and

108

 

p‘VU'l‘VV'lVﬁ'T'I'Vr'IIIYY TYT‘I'V‘UIVVVUIVIVIIIIII III'I'UVIIYI'UIVIVII‘FVT 'V'VIIVYUIV'III'I'IIIVT
p

102 Rings Ringo Ring? Ringa1

I "nl

F 4
n 1
4

100

102

Counts

101 :-

1_A 11“

Rin316'1
q
1

‘1

 

 

 

I

20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100120
Ea (MeV)

Figure 6.23: a spectra from various rings in the BALL array. These spectra were
measured in coincidence with an a particle detected in one of the WALL rings. The
pre-equilibrium feature of the spectra disappears as the detection angle becomes more
and more backward. At the most backward angles the spectra are similar to that
obtained from evaporation calculations.

109

 

 

 

 

 

 

1.0 -
C.‘ 0.75
.2 ”
E z; 0.5-
.. g —
II)
E! 1
8 v 0.3
63
0.2- s
-5ﬁ i . 4 = i + 4 1 v* s i - i 1
o A
'3 - i f .
‘3 —<
a :3 2.0T i
w e
8 3 1.0 : :
{‘3 I 2
0.5: I
I 4 I J 1 1 I 1 1 1 1 I 1 1
25 50 75 100 125
Ea (MeV)

Figure 6.24: The high energy background in the 7-ray spectra are compared to the
singles cross section. The top panel shows the singles spectrum from ring 1 of the
WALL array. The bottom panel displays the integrated counts from the 20—30 MeV
region of the 7-ray spectra, for each 10 MeV wide target excitation energy cut. The
summed counts were normalized by dividing with the singles cross section. The
normalized high energy 7-ray background increases with increasing projectile energy
loss, and is strongest in the pre-equilibrium region.

110

 

 

 

 

   

 

 

 

 

 

 

104 IIIIIIIj—IIIIIIIII . TIIIIIIIIIIIIITI ﬁIIIIIIIIIIIII rII
103 i E,= 41— 50 nov i 2,: 31- 40 MeV E.= 21- 30 MeV
33 mar-7.5 MeV rgdr=7.0 uev Pgdr=7.5 uev
g 102
O
U
101 .
O
o IIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIJ_L IIIIIIIJIILIII LLI
10 IIIIIIIIIIIIjIIIIII__IIIIIIIIIIIIIIIIIh-_r1IIIIIII|IIrrIIIII
$3.0 4:— g:—
It’. -- 0-
.4— .4.—
g} 53-5 ‘25— “E?
>, 2: Z:
‘1: :32") 2: ::
g .‘3 1: :2
1... 31.5 7:.— ‘2.—
; H .25 EE
V1.0 .1
0.5 IIIIIIIIIIIIIIIIIII IJIILlIIIIIIIIIIIII IIIIIIIIIIIIIIIIIII
10 15 20 5 10 15 20 5 10 15 20 25
E7 (MeV)

Figure 6.25: The 7-ray spectra in coincidence with 0 particles of energies 21-30
MeV, 31-40 MeV and 41—50 MeV. Apparent target excitation energies as 130—139
MeV, 120—129 MeV and 110—119 MeV respectively. The statistical model calculations
performed assuming these excitation energies are shown as solid lines in the upper
panels. The lower panels display the corresponding linearized plots. The resonance
width stays at a value of ~ 7.5 MeV indicating that the 7-rays are emitted by cooler
nuclei that are populated after pre-equilibrium emission.

111

stays at a value of ~ 7.5 MeV. These widths are compared in ﬁgure 6.26 to the res-
onance widths extracted for excitation energies where pre-equilibrium contributions
are negligible. The saturation in the width at apparent high excitation energies indi-
cates that the 7—rays arise perhaps from cooler nuclei that are populated subsequent

to particle emission in the pre-equilibrium stage.

112

 

 

 

 

_I I I I If I I I I I I I T I I I I I I I I I I I I I I I_
9 — _
- 1
8 _ -——4
A ’- ..
> _ _
cu _ _
E 7 — __
m _ -
Q ' -
U - —1
L1 _ _
6 '— _
5 — _
"1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 4 I 1 1 1 1 l 1 1"

40 60 80 100 120 140

E... (MeV)

Figure 6.26: The resonance widths at large projectile energy losses are compared to
the widths at lower excitation energies. The open circles are the widths extracted
from 7-ray spectra for a energies in the range of 21—50 MeV. The apparent target
excitation energies are 110—139 MeV. The ﬁlled circles are the widths for excitation
energies from 40-109 MeV where the pre—equilibrium contributions are negligible.
The widths at apparent high excitation energies exhibit a saturation effect since they
correspond to the GDR in nuclei populated subsequent to particle emission in the
pre-equilibrium stage.

Chapter 7

Summary and Conclusions

In this measurement, the evolution of the giant dipole resonance in 208Pb was studied
as a function of excitation energy with very little inﬂuence from angular momentum.
This was achieved by exciting the nucleus with inelastic scattering of a-particles. The
GDR built on highly excited states of the nucleus was observed by measuring the high
energy 7 rays from the decay of the resonance in coincidence with the inelastically

scattered projectiles.

The enhancement due to the GDR was observed in the coincidence 7-ray spec-
tra at all measured excitation energies. Furthermore, the a spectra measured in
coincidence with the high energy 7 rays exhibited structures that corresponded to
individual neutron evaporation channels in the decay of the excited target nucleus.
These observations were evidence for equilibrated emission from a highly excited tar-

get nucleus.

The 7-ray spectra were compared to statistical model calculations performed us-
ing the CASCADE code and resonance parameters were extracted as a. function of
excitation energy. The width of the GDR was observed to increase with increasing
excitation energy from a value of 4 MeV at the ground state to ~8 MeV at the highest

measured energy.

113

 

114

The measured widths were compared to the results of an adiabatic model cal-
culation for the resonance energy cross section that took into account the coupling
of the resonance to the nuclear free energy surface. The calculation predicted an
increase in the resonance width with excitation energy for temperatures beyond ~1
MeV, subsequent to the disappearance of shell effects in 208Pb. The calculated widths
were in good agreement with the data over the range of temperatures observed in the

measurement.

This was a ﬁrst measurement of the GDR built on excited states of a stable nucleus
studied by means of inelastic light ion scattering. The observation of width evolution
in this study was strongly inﬂuenced by the presence of shell effects in 208Pb at lower
excitation energies. It would therefore be interesting to measure the resonance width
in other nuclei where shell effects are not prominent. Nuclei with deformed shapes in
the ground state form an interesting choice since the shape evolution can be studied

independent of spin.

Recently angular distribution measurements have yielded additional information
for the determination of nuclear shapes. A larger solid angle coverage for the 7-ray
detectors can yield sufﬁcient statistics to perform angular distribution analysis of the

data which is valuable in the study of shape evolution in excited nuclei.

Presently the use of discrete particle detector arrays limits the ichoice of projectile
nuclei to those that could be isotopically identiﬁed. Measurements at very small
scattering angles where the inelastic cross section is larger are also not possible due to
signiﬁcantly large elastic scattering cross sections. These limitations can be overcome

in the future by the use of magnetic spectrographs.

The choice of a-particles as the inelastic probe in this study ensured that there

is no contamination to the 7-ray spectra from projectile excitation since there are

115

no bound excited states in the projectile. However, pre-equilibrium effects at large
projectile energy losses posed a problem. The cross section for pre—equilibrium emis-
sion may be much suppressed for the less bound system of 3He, thereby making this
nucleus a better choice for the inelastic probe. Calculations that consider emission
from the pre-equilibrium stage could conﬁrm this speculation. Other light ion probes

such as 7Li that have low particle separation energies could also be chosen.

More systematics on the evolution of the GDR width as a function of excita-
tion energy in nuclei over a wide mass range are required to perform comparisons
with model calculations. Coincidence measurement of 7 rays with inelastic light ion

scattering can serve as an important tool towards achieving this goal.

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