MEASUREMENT OF CAPTURE EXCITATION FUNCTIONS WITH

NEUTRON-RICH NUCLEI

By

Nathan Watwood

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Chemistry – Doctor of Philosophy

2021

MEASUREMENT OF CAPTURE EXCITATION FUNCTIONS WITH NEUTRON-RICH

ABSTRACT

NUCLEI

By

Nathan Watwood

The study of heavy and superheavy elements is important for understanding nuclear

structure at the limit of stability where macroscopic and microscopic effects are delicately bal-

anced. It is a benchmark domain for a rich variety of calculations including time-dependent

Hartree-Fock (TDHF) and density functional theory (DFT). One difficulty in studying these

nuclei is the low formation probability. There is limited reliability in models to predict the

outcome of superheavy particle formation due to the significantly large number of degrees

of freedom. The fusion-fission process is a key reaction to access heavy element formation.

Experiments were performed at the National Superconducting Cyclotron Laboratory

(NSCL) at Michigan State University and at the Heavy Ion Accelerator Facility at Aus-

tralian National University to measure fusion-fission excitation functions of two different

combinations of Ca+Sm and K+Pb with varying neutron-richness. The excitation functions

were measured at center-of-mass energies ranging from 1.1% to 0.9% above and below the

predicted barrier heights. Measured cross sections were found to be comparable above the

barrier regardless of neutron-richness. At and below the barrier, cross sections were enhanced

for systems with positive Q-value neutron transfer channels.

Furthermore the experiment performed at the NSCL was the first measurement of fusion-

fission cross sections using the Active-Target Time Projection Chamber. This experiment

demonstrated the successful reconstruction and identification of fission tracks and established

the viability of performing similar experiments in the future.

Copyright by
NATHAN WATWOOD
2021

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

Chapter 1

1.1 Heavy Ion Reactions

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Capture and Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
1.1.2 Fission and Evaporation Residue
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Classical Approach - Single Barrier . . . . . . . . . . . . . . . . . . .
2.1.2 Quantum Mechanical Approach - Single Barrier . . . . . . . . . . . .
2.2 Modelling Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Nuclear Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 General Description of Fission Observables . . . . . . . . . . . . . . .
2.3.2 Decay of Excited Nuclei
. . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 GEMINI++ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3 Michigan State University Experiment . . . . . . . . . . . . . . .
3.1 Active Target Time Projection Chamber . . . . . . . . . . . . . . . . . . . .
3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1
Ionization Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Time projection chambers . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Active Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Structure of AT-TPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inner and outer gas volumes . . . . . . . . . . . . . . . . . . . . . . .
3.3.1
3.3.2 Micromegas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3
Sensor plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.5 Tilting the Detector
. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.6 Electric and Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . .
3.3.7 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Experimental Setup of the AT-TPC . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Rare Isotope Beam Production . . . . . . . . . . . . . . . . . . . . .
3.4.2 ReA3 Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 Characteristics of the Reaction Projectiles . . . . . . . . . . . . . . .
3.4.4 Beam Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.5 Detector Gas
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.6 Reaction Target and Window . . . . . . . . . . . . . . . . . . . . . .

iv

1
2
3
3
4

7
7
7
10
10
17
17
18
19

21
21
21
21
22
23
24
24
26
27
28
29
30
33
34
34
35
37
38
38
40

3.6 AT-TPC Fission Analysis

3.4.7 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Analyzing AT-TPC Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Pedestal Subtraction and Charge Extraction . . . . . . . . . . . . . .
3.5.2
3D Track Reconstruction - RANSAC . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1
Identifying Fission Fragments . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Elastic Scattering Normalization . . . . . . . . . . . . . . . . . . . . .
3.6.3 Beam Impurity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.4 Differential Cross Section . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 4 Measurement of Fission Fragment Tracks . . . . . . . . . . . . .
4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Comparison to SRIM . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 5 Australian National University . . . . . . . . . . . . . . . . . . . .
5.1 Heavy Ion Accelerator
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Structure of CUBE Detector . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Electronics and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Analyzing CUBE Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1.1 Position Transformation . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1.2 Time of Flight
5.4.2 Kinematic Reconstruction . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2.1 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2.2 Mass Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2.3 Time Calibration . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Fission Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 6 Cross Section Determination . . . . . . . . . . . . . . . . . . . . .
6.1 Differential Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Cross Section Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Establishing Variables
6.2.2 Lab Frame to Center of Mass Frame
. . . . . . . . . . . . . . . . . .
6.2.3 Mass-Angle Distributions (MADs) . . . . . . . . . . . . . . . . . . . .
6.2.4 Experimental Differential Cross Sections . . . . . . . . . . . . . . . .
6.3 Cross Section Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1 Evaporation Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Barrier Height and Interaction Radius Extraction . . . . . . . . . . . . . . .
7.2.1 Reduced Excitation Functions . . . . . . . . . . . . . . . . . . . . . .
7.2.2 Competing Fission Modes
. . . . . . . . . . . . . . . . . . . . . . . .
7.2.3 Comparison to Models . . . . . . . . . . . . . . . . . . . . . . . . . .

41
42
42
43
45
45
47
49
52

56
56
58
60

65
65
68
70
71
72
72
73
74
74
76
76
77

81
81
83
83
84
85
86
86

91
91
93
97
99
99

v

Chapter 8

Interpretation and Future Work . . . . . . . . . . . . . . . . . . . 103

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

vi

LIST OF TABLES

Table 1.1: Barrier height comparison between stable and neutron-rich RIB reactions
[9, 10, 15] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

Table 3.1: Table of different window material considered for AT-TPC entrance window 41

Table 7.1: Experimental barrier heights in comparison with calculated barriers [105].

96

Table 7.2: Experimental interaction radii in comparison with calculated radii [106].

.

96

Table 7.3: Q-values for neutron and proton pick-up channels from the heavy to the
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

light reaction partner.

Table 7.4: Q-values for neutron and proton stripping channels from the light to the
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

heavy reaction partner.

98

98

vii

LIST OF FIGURES

Figure 1.1: Depiction of the possible processes in a heavy ion capture reaction.

. . .

2

Figure 1.2: Description of the total interaction potential for a capture reaction to
occur [7]. Nuclei with enough energy to overcome the fusion barrier VB
at a radial separation RB will result in capture (shaded). . . . . . . . . .

Figure 1.3: Reduced excitation functions for 32,38S + 208Pb,181Ta, where the capture
cross section is reduced by the interaction radius and the center of mass
energy (Ec.m) is reduced by the barrier height (VB). [9, 10]
. . . . . . .

Figure 2.1:

(a) Depiction of the total interaction potential of colliding nuclei when
angular momentum l=0 (black) and l>0 (grey) as a function of radial
separation with contributions from Coloumb repulsion (dashed), centrifu-
gal repulsion (double dot dashed), and nuclear attraction(long dashed).
RB is the capture barrier radius. (b) Depiction of the total interaction
potential along increasing angular momentum l. As angular momentum
increases, the barrier increases and the potential well becomes more shal-
low. The potential well disappears at a critical angular momentum lcrit.

Figure 2.2: Example of the potential energy surface of 180Hg as a function of nuclear
. . . . . . . . . . . . . . . . . . .

deformation and mass asymmetry [24]

Figure 2.3:

Illustration of 1-dimensional interaction potentials for Cf, Pu, and Th
nuclei as a function of deformation using the liquid drop model (top),
shell effects (middle), and the combination of the both (bottom). [34] . .

Figure 2.4:

Illustration of the angular momentum vectors at the saddle configuration
for a fissioning nucleus. In the transition-state model for fission, the an-
gular distribution of fission fragments can be expressed as a function of
the total angular momentum J and the projection of J onto the fission
axis K at the saddle point if the projection of J onto the space fixed axis
(here the beam axis) M=0.
. . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.1: Schematic view of the Active Target Time Projection Chamber. The
outer shielding was made transparent and a quarter section of the inner
volume was cutout to make the details more visible. The beam enters the
detector through the beam duct at the right-hand side and travels towards
the sensor plane on the left. Some of the electronics described in Section
3.3.4 are shown mounted on the left-hand side . . . . . . . . . . . . . . .

4

6

9

11

14

16

25

viii

Figure 3.2:

Illustration of Micromegas operation within the TPC. The electric fields
will vary depending on the details of the experiment. This image is not
to scale.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.3:

Illustration of AT-TPC sensor plane. The bottom right image is a zoomed
cutout of the sensor plane showing the transition between large and small
pads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.4:

Illustration of electronic hierarchy used for the AT-TPC. The illustration
only shows the inside of one AsAd, but it is important to note that 40
AsAds and 10 CoBos are used during experiments . . . . . . . . . . . . .

Figure 3.5: Logic diagram of the Application Specific Integrated Circuit for GET elec-
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

tronics (AGET) [67].

Figure 3.6:

Illustration of the AT-TPC tilted inside the solenoid magnet. The detector
can be tilted up to 6◦ and the magnet can reach a uniform magnetic
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
strength of 2T.

Figure 3.7: Picture of the rings of the field cage inside the inner volume of the AT-TPC
detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.8:

Illustration of the NSCL beam-line, with different regions labelled. The
beam for this experiment is produced by a room temperature ECR (RTECR)
and superconducting ECR ion source (SuSI) and accelerated sequentially
by the K500 and K1200 cyclotrons. The beam is then separated by the
A1900 fragment separator, stopped and re-accelerated by ReA3, and is
delivered to the AT-TPC in the ReA3 experimental hall.
. . . . . . . . .

26

27

29

30

31

32

35

Figure 3.9: A1900 fragment separator in conjunction with the twin cyclotrons . . . .

36

Figure 3.10: Oscilloscope trace of the 46K beam structure (green) delivered to the AT-
. . . . . . . . . . . . . . . . .

TPC. The duty cycle of the beam is 5%.

Figure 3.11: Drawing of ionization chamber used for beam identification. The ioniza-
tion chamber was filled with 10 torr of isobutane which resulted in a total
thickness of 500µg/cm2.
. . . . . . . . . . . . . . . . . . . . . . . . . . .

38

39

Figure 3.12: Drift velocity dependence on electric field for P10 gas [74].

. . . . . . . .

40

Figure 3.13: Left: A data set of 2D points that can be used as input for the RANSAC
algorithm. Right: Output of the RANSAC algorithm. The blue line is
the estimate that RANSAC found to be reasonably good. The blue points
are part of the consensus set or inliers. The red points are outliers.
. . .

44

ix

Figure 3.14: Left: X-Y projection of charge on the pad plane from a spontaneous fission
event. Right: Total charge as a function of time from a spontaneous fission
event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.15: TRIM calculation of the energy loss profile of a typical 252Cf fission frag-
. . . . . . . . . . . . . . . . . .

ment with 100 MeV in P-10 at 100 torr.

Figure 3.16: Left: X-Y projection of charge on the pad plane from an event of the
primary experiment. Right: Total charge as a function of time from an
event of the primary experiment. Note that the direction of the x-axis is
opposite to that of Figure 3.15.
. . . . . . . . . . . . . . . . . . . . . . .

Figure 3.17: Left: Total charge of single particle events measured in the AT-TPC as
a function of angle. A visual cut (solid red) is made on beam particles
elastically scattered off of the 208Pb target. Right: Ranges of single par-
ticles events measured in the AT-TPC after visual cut. The black curve
is the maximum ranges the AT-TPC can measure for events originating
from the window. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

cross sections reduced by Rutherford scattering cross sections

Figure 3.18: Measured (blue square) and optical model (gold circle) elastic scattering
. . . . . .
Figure 3.19: Ranges of single particle events in the AT-TPC at 0◦. Each run (left to
right) is further along in experiment time. Each peak was fitted with a
separate Landau curve (solid red line) and summed. X-axis was inverted
. . . . . . . . . . . . . . . . . . . . .
in order to fit with Landau curves.

Figure 3.20: Percentage of beam impurities over the duration of the 46K + 208Pb ex-
periment. The most likely impurities are the primary decay of the beam,
46Ca.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.21: Differential cross sections of the 19F + 208Pb reaction measured by the
AT-TPC as a function of center of mass energy (ECM )and approximated
cross sections from Legendre polynomials.
. . . . . . . . . . . . . . . . .

Figure 3.22: Fission cross section for the 19F + 208Pb reaction measured by the AT-
TPC as a function of center of mass energy (ECM ) compared to previous
measurements [80].
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.23: Left: Differential cross sections measured by the AT-TPC as a function
of center of mass angle (θCM ) and approximated cross sections from Leg-
endre polynomials. Right: Reduced capture cross sections for 39,46K +
208Pb reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

47

48

49

50

51

52

54

55

55

x

Figure 4.1: Picture of the opened pAT-TPC with the 252Cf source attached to the
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

center of the cathode.

57

Figure 4.2:

Illustration of the electric fields inside the holes of a ThGEM during op-
eration [83]. An electric potential is applied between the faces, generating
a strong dipole electric field inside the holes, depicted by the large con-
centration of electric field lines.
. . . . . . . . . . . . . . . . . . . . . . .

Figure 4.3: Pad signals from a fission fragment measured by the pAT-TPC. Each color
is representative of one of the four quadrants into which the pad plane is
separated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.4: Oscilloscope view of the signal from the gamma-ray detector (yellow) in
coincidence with the mesh signal of the fission fragments from the pAT-
TPC (blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.5: Left: Calculated energy loss of 102Ru at 100MeV as a function of en-
ergy fitted with a polynomial function. Right: Energy loss of 102Ru as a
. . . . .
function of range interpolated from the polynomial fit from (a).

Figure 4.6: Ratio of experimentally measured energy loss curve of a fission fragment
. . .

with the calculated energy loss curve (SRIM) of 102Ru at 100MeV.

Figure 4.7: Left: Ratio of experimental and calculated (SRIM) energy loss curves of
fission fragments. Right: Y-projected data of (a) between the ranges of
45-55cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

59

60

62

63

64

Figure 5.1: Schematic view of the ANU Heavy Ion Accerlator Facility beam line

. .

67

Figure 5.2:

(a) Orientation of the front and back MWPCs with respect to the beam
and target (b) Orientation of the back and small back MWPCs with re-
spect to the beam and target
. . . . . . . . . . . . . . . . . . . . . . . .

69

Figure 5.3: Schematic breakdown of the front or back MWPC.

. . . . . . . . . . . .

70

Figure 5.4: Electronics schematic of signal processing from the MWPCs and monitors
to the DAQ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

Figure 5.5: Full active area of the front MWPC in Cartesian coordinates . . . . . . .

72

Figure 5.6: Full active area of all three MWPCs in polar coordinates . . . . . . . . .

73

Figure 5.7: Timing of particle detection in MWPCs in conjunction with RF signal
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

and beam-target time.

74

xi

Figure 5.8: Vector breakdown of fission fragment velocities, with the origin at the
. . . . . . . . . . . . . . . . . . . . . .

reaction center on the beam axis.

75

Figure 5.9: Experimentally derived perpendicular fission fragment velocities (vperp)
as a function of parallel velocity (vpar) subtracted the velocity of the
compound nucleus (vcn) after time parameter optimization for the 48Ca
+ 144Sm reaction at 201.0 MeV. This data includes fission events as well
as elastically scattered events. . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.10: Visual cuts applied to mass ratio MR spectra in order to isolate fission
fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

80

Figure 6.1:

(a) Scatter plot of θlabvs.θc.m. with only full momentum transfer (FMT)
events. The efficiency corrected yield ηf is
cube is represented on the z-axis.
(b) The active area of the small back and back detectors represented in
spherical coordinates from an elastic scattering calibration run; the results
of which provide solid angle normalization coefficients S(θlab) shown in (c). 88

Figure 6.2: Top: Experimental mass ratio data for 40Ca + 144Sm reaction with ap-
plied mirror line. Bottom: Reflection of experimental mass ratio data
across mirror line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.3: Fission angular distributions for 40,48Ca + 144Sm and 39K + 208Pb reac-
tions over all experimental energies. . . . . . . . . . . . . . . . . . . . . .

Figure 7.1: Experimental ER cross sections measured by Hinde [102] with Monte
Carlo calculations, including PACE4 and implementations of the Decay
of Excited Nuclei by the Nuclear Reactions Video website and LISE++.

Figure 7.2: Experimental fission cross sections for 39K + 208Pb and 40,48Ca + 144Sm
reactions compared to calculated total capture, fusion-fission, and fusion-
evaporation cross sections from the Decay of Excited Nuclei Monte Carlo
. . . . . . . . . . . . . . . . . . . . . . . . . .
implemented by LISE++.

Figure 7.3: Measured cross sections as a function of 1/Ecm fitting with the classical
equation Eq. 2.6 with points high above the barrier. The inverse of the
x-intercept yields the experimental barrier height and interaction radius.

Figure 7.4: Comparison of the reduced excitation functions of this work, 40,48Ca +
144Sm, and by J. J. Kolata, 40,48Ca + 124,132Sn. Top: Light ion is iden-
tical while changing the heavy ion. Bottom: Heavy ion is the same with
different light ions.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

90

92

94

95

97

xii

Figure 7.5: Reconstructed TKE and mass distributions of 40Ca + 144Sm at 186 MeV.
Top left: TKE distribution with a two-Gaussian fit and partition into high
and low TKE regions. Top right: Fission fragment mass distribution with
projected TKE partitions based on two-Gaussian fit. Bottom: Projected
fission fragment mass distributions above T KEhigh and below T KElow
with best fit descriptions by either one- or two-Gaussian fits. . . . . . . . 101

Figure 7.6: Experimental fission fragment mass distributions compared to mass dis-
tributions calculated by Monte Carlo codes GEF and Gemini for 40,48Ca
+ 144Sm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Figure 8.1: Experimental fission cross sections of 40Ca + 144Sm (blue circles) com-
pared to calculated cross sections using FRESCO (gold triangles) without
coupling to open transfer channels.

. . . . . . . . . . . . . . . . . . . . . 104

xiii

Chapter 1

Introduction

Naturally occurring abundant elements found on Earth range from hydrogen to uranium; any

heavier element is man-made and created in nuclear facilities. The primary goal of creating

these super heavy elements (SHE) is to study the stability and structure of these nuclei,

which exist in a domain that delicately balances macroscopic effects (Coulomb repulsion,

surface tension) together with microscopic effects (shell and pairing effects). Because of this

delicate balance, predicting the stability of these nuclei is difficult and is very sensitive to

the quality of the model. As such, SHEs are benchmarks for nuclear models. Some models

suggest the likelihood of stable SHEs with nuclear magic numbers at Z = 114, 120, 126 and

N = 184 [1, 2]. In fact four new elements, Z = 113, 115, 117, 118, were added to the periodic

table by the IUPAC (International Union of Pure and Applied Chemistry) in 2016 alone [3].

There is the possibility that the periodic table can even extend beyond. The study of SHEs

and their creation is essential to explore this domain.

The main difficulty in SHE synthesis is the extremely low cross sections, which are of the

order of picobarns [4]. There is limited reliability in models that can be used to successfully

predict the outcome of such heavy particle formation due to the significant number of degrees

of freedom. As heavy-ion beam facilities, such as FRIB, begin to produce neutron-rich rare

isotope beams (RIBs) with high beam intensities, it opens the door to new possibilities.

One possibility is the production of a group of long lived neutron-rich SHEs not accessible

1

with stable beams [5]. These nuclei will be important for the study of atomic physics and

chemistry at the limit of stability as well as nuclear spectroscopy [6].

1.1 Heavy Ion Reactions

The primary method of SHE synthesis is through heavy ion fusion reactions. The process of

fusion entails a projectile and target nuclei colliding and forming a single compound nucleus.

In Figure 1.1 are shown the possible outcomes in a heavy ion fusion reaction. The projectile

and target come into contact forming a dinuclear system (capture) and can either reseparate

(quasi-fission) or form an equilibriated compound nucleus (fusion).

Figure 1.1: Depiction of the possible processes in a heavy ion capture reaction.

After fusion, the compound nucleus (CN) has a variable amount of excitation energy and

can follow two primary exit channels in order to dissipate that energy. The first is light

particle evaporation, where light particles such as neutrons, protons, gamma rays, and alpha

particles are ejected from the CN, carrying with them part of the excitation energy. The

2

result is a heavy or super-heavy element with an N,Z slightly lower than that of the CN.

The second exit channel is the binary separation of the CN nucleus into two particles with

similar mass, called fission.

1.1.1 Capture and Fusion

The interaction between the projectile and target nuclei can be expressed by an interaction

potential along their relative motion (r12). A barrier is formed at a certain distance through a

combination of Coulomb, centrifugal, and nuclear potentials where the repulsive electrostatic

and centrifugal, and nuclear attractive forces are equal. This barrier determines whether

capture can occur and depends on the kinetic energy of the projectile nuclei and, to a lesser

degree, on the probability of quantum tunneling. Figure 1.2 describes the barrier in terms

of potential energy.

Nuclear fusion is the creation of, through the capture process, an equilibrated CN gen-

erated by irreversible energy dissipation. When a compound nucleus is formed, all specific

information on the entrance channel is lost [8]. Only the conserved quantities, such as energy

and linear and angular momentum, are preserved in the compound nucleus.

1.1.2 Fission and Evaporation Residue

After compound nucleus formation and equilibrium, the compound system is in a highly

excited state. The two main exit channels this system can take is the evolution to fission or

to evaporation of light particles resulting in an evaporation residue. The excited compound

nucleus can deform, thus decreasing the nuclear Coulomb energy. The nuclear surface en-

ergy increases until the system reaches the saddle point configuration. At saddle point, or

3

Figure 1.2: Description of the total interaction potential for a capture reaction to occur [7].
Nuclei with enough energy to overcome the fusion barrier VB at a radial separation RB will
result in capture (shaded).

transition state, the rate of change between these two energies are equal. The decay of this

state may lead to the separation of the compound nucleus into two smaller fragment nuclei,

or fission fragments. Alternatively, if a nucleon or group of nucleons obtain enough energy

to overcome the separation energy of the compound nucleus, they are evaporated from the

compound nucleus and de-excite the system. A further look into these exit channels are

discussed in Section 2.

1.2 Motivation

In a series of experiments by Loveland et al.

[9] and Zyromski et al.

[10, 11], the above

barrier capture excitation functions using a degraded neutron rich RIB (38S + 208Pb,181Ta)

4

were measured. Figure 1.3 shows the reduced excitation functions compared to the same

reaction with a stable 32S beam. In a reduced excitation function, the center of mass energy

is scaled by a calculated fusion barrier from Bass systematics [12, 13] and the cross section is

scaled by the interaction radius (πR2). This eliminates the expected changes in cross section

when increasing the mass of the system and the two excitation functions should overlap. It

was experimentally found that the capture cross sections with the more neutron rich 38S

show an increase in cross section with respect to the 32S beam. The fusion barrier heights

were also measured in these experiments and compared to barrier heights calculated by Bass

systematics and can be found on Table 1.1. The Bass barrier heights are expected to be

higher than experimental barriers, but the change in barrier height when increasing the mass

of the system should be accurately predicted [14]. The experimental results show a much

larger decrease in barrier height when changing the beam from 32S to 38S than predicted by

the Bass systematics. This leads to the possibility that neutron-rich beams add possibilities

to the synthesis of heavy and super-heavy nuclei. The formation at lower excitation energy

also might allow for higher survival probabilities of the evaporation residue.

Table 1.1: Barrier height comparison between stable and neutron-rich RIB reactions [9, 10,
15]

The aim of the experiments discussed in this thesis is to establish the AT-TPC as a

5

Figure 1.3: Reduced excitation functions for 32,38S + 208Pb,181Ta, where the capture cross
section is reduced by the interaction radius and the center of mass energy (Ec.m) is reduced
by the barrier height (VB). [9, 10]

reliable fusion-fission detector, and in turn explore other systems nearby the 32,38S + 208Pb

reaction and identify the possibility of enhancements using neutron-rich RIBs.

6

Chapter 2

Theory

2.1 Fusion

2.1.1 Classical Approach - Single Barrier

The relationship between two colliding nuclei can be classically represented as an interaction

potential, with contributions from repulsive Coulomb and centrifugal forces and an attractive

nuclear force,

Vtotal(r) = VCoul(r) + Vcent(r) + Vnuc(r)

(2.1)

A simple expression for the Coulomb potential between two nuclei at a distance r is given

by

VCoul(r) =

e2
4π
0

Z1Z2

r

(2.2)

where the atomic number of the colliding nuclei are represented by Z1,2. The centrifugal

potential takes into account the angular movement of the colliding nuclei in non head-on

collisions and is expressed as

Vcent(r) =

L(L + 1)¯h2

2µr2

7

(2.3)

where L is the orbital angular momentum and µ is the reduced mass of the system. A

simple version of the attractive nuclear force uses the Woods-Saxon potential [16]

Vnuc(r) =

−V0

1 + exp[(r − R0)/a0

(2.4)

with a potential depth V0 and diffuseness parameter a0. R0 is proportional to the radius

of the colliding nuclei

R0 = r0(A

1/3
1 + A

1/3
2

).

(2.5)

with a radius parameter r0. An example of the sum of these three potentials is illustrated

in Figure 2.1a. At a specific distance RB, the sum of these three potentials forms a potential

barrier, known as the capture barrier VB. Within the barrier is a potential well wherein

the projectile and nucleus irreversibly form into a compound nucleus. Both barrier height

and well depth are dependent on angular momentum and can be seen in Figure 2.1b. At a

critical angular momentum lcrit the well and the barrier disappear.

Using this classical approach of a single barrier, the capture cross section can be expressed

as

σ(E) =

πR2

0,

B(1 − VB

E ), E ≥ VB

E < VB

(2.6)

where RB is the interaction radius of the barrier at l = 0. This indicates the capture cross

section is inversely proportional to the energy with no capture possible below the barrier. It

has been used to describe capture cross sections with energies above the barrier in the region

l < lcrit [17, 18] and is also used in this work to extract barrier heights and interaction radii.

8

Figure 2.1: (a) Depiction of the total interaction potential of colliding nuclei when angular
momentum l=0 (black) and l>0 (grey) as a function of radial separation with contributions
from Coloumb repulsion (dashed), centrifugal repulsion (double dot dashed), and nuclear
attraction(long dashed). RB is the capture barrier radius. (b) Depiction of the total interac-
tion potential along increasing angular momentum l. As angular momentum increases, the
barrier increases and the potential well becomes more shallow. The potential well disappears
at a critical angular momentum lcrit.

As mentioned in Section 1.2, maximizing capture cross sections is important for SHE

production. Using this classical approach, the capture cross sections can be increased by

using neutron-rich projectiles. The interaction radius is proportional to the sum of the radii
of the projectile and target nuclei, RB ∝ (A

). Due to the third root, RB will

1/3
p + A

1/3
t

increase and an increase in capture cross section is expected for more neutron rich nuclei of

a particular element. Additionally, the barrier height is proportional to both the Z and A of

9

the colliding nuclei VB ∝

ZpZt
1/3
p +A

(A

1/3
t

)

. Therefore, increasing the total mass of the system

without affecting Zp,t, the energy required for capture is decreased.

2.1.2 Quantum Mechanical Approach - Single Barrier

While the classical approach can be accurate in predicting fusion cross sections above the

barrier, it becomes unreliable for reactions with energies at or below the barrier due to barrier

penetration (tunneling). To account for this, an angular momentum dependent transmis-

sion coefficient Tl is used to represent barrier penetrability and reflection probability. The

quantum mechanical approach then represents the capture cross section as

∞(cid:88)

l=0

π
k2

σ(E) =

(2l + 1)Tl(E)

(2.7)

where (k = 2π/λ) is the wave vector inversely related to the de Broglie wavelength λ.

The transmission coefficient can be calculated using the parabolic barrier approximation,

Wentzel-Kramers-Brillouin (WKB) approximation, or the optical model [19, 20].

Heavy ion fusion experiments in the 1970’s and 1980’s found that measured capture

cross sections were significantly higher than the predicted cross sections using this quantum

mechanical single barrier penetration model and thus subsequently revealed that nuclear

structure had a profound effect on fusion reactions [21, 22, 23].

2.2 Modelling Fission

The nuclear matter within an equilibrated CN with some excitation energy, angular momen-

tum, shape, and fissility, will be expected to fluctuate shape with various oscillations that

10

can lead to deformations of the CN. These deformations can cause the splitting, or fissioning,

of the nucleus into two or more fragments of similar mass. This process is contingent on

the potential energy landscape described by the shape deformation of the CN and the mass

asymmetry of the fissioning system. During deformation, the repulsive forces between con-

stituent nucleons counteract the restoring nuclear forces that are responsible for the surface

tension of the nucleus. Figure 2.2 shows an example of a potential energy surface (PES) of a

CN as a function of deformation and mass asymmetry [24]. An adequate excitation energy

is required for the evolution of the CN from the equilibrated initial state to the saddle point

and finally to fragment separation, although quantum tunneling through the potential bar-

riers is also possible [25]. The optimum fissioning path is then an evolution of deformation

configurations within the valleys of minimum potential energy leading to scission.

Figure 2.2: Example of the potential energy surface of 180Hg as a function of nuclear defor-
mation and mass asymmetry [24]

Fission is a complex, dynamical process that cannot be described perfectly by macroscopic

models and is typically too complex to be solved accurately by microscopic many-body

calculations [26]. As a result, the PES of a fissioning system is often described by mean-field

11

theories or macroscopic-microscopic models [27, 28, 29, 30]. In the macroscopic-microscopic

models, the macroscopic potential may be generated from the liquid drop model (LDM)

[31] and corrected by microscopic shell-structure and pairing effects [32]. Even these models

must be considered as approximations, since the generated PES is a static representation of

a time-dependent process.

The LDM describes three main contributions to the potential energy of deformation:

the Coulomb repulsion between nucleons within the nucleus, the surface tension on the

outside of the nucleus stemming from attractive nuclear forces, and angular momentum,

which energetically favors large moments of inertia. For small quadrupole distortions, the

radius of a nuclear sphere at the lowest order is expressed as

R(θ) = R0(1 + α2P2(cosθ))

(cid:114) 5

4π

α2 =

β2

(2.8)

where P2 is the Legendre polynomial and β2 is the quadrupole deformation parameter.

The Coulomb Ec and surface Es energies can then be represented by quadrupole deformation

parameters as

Ec = E0

Es = E0

c (1 − 1
5
2
5

s (1 +

α2
2)

α2
2)

(2.9)

E0

c and E0

s are the energies of a uniformly charged sphere and can be represented as

E0

c =

3
5

E0
s = 4πR2

Z2e2
R0A1/3
0SA2/3

(2.10)

where R0 is the radius of the sphere, S is the surface tension energy parameter, A is the

12

nuclear mass, Z is the atomic number, and e is the charge of an electron. Using the above

terms, the deformed LDM energy is

ELD = E0

LD +

2(2E0
α2

s − E0
c )

1
5

(2.11)

When the changes of the Coulomb and surface energies are the same, the CN becomes

unstable and the relation between the uniform surface and Coulomb energies becomes

x =

E0
c
2E0
s

= (

ac
2as

)(

Z2
A

) = (

Z2
A

)/(

Z2
A

)critical

(2.12)

where ac = 3e2/5R0, as = 4πR2

0S, ( Z2

A )critical = (ac/2as)−1, and x is the fissility

parameter. The fissility parameter is used to determine if a CN will fission; if x > 1, the CN

will fission, if x < 1, the CN will equilibrate as a spherical or moderately deformed nucleus.

This description is true only in macroscopic conditions as it doesn’t account for pairing or

shell effects. As mentioned in Section 1, SHE production is difficult due to the extremely

low cross sections. Using the expression for fissility, increasing the mass of the system with

a near constant Z (neutron-rich beam) would lead to a decrease in fissility of the CN, which

would increase the survival chance of a SHE’s.

The LDM, using macroscopic effects, can describe the fission barrier with basic features

like in Figure 2.3. However, to get a more accurate representation of the fission barrier,

shell effects and pairing corrections need to be included. Strutinsky proposed a technique

for including these microscopic effects into the total energy of the compound nucleus by

(cid:88)

E = ELDM +

(δS + δP )

(2.13)

(p,n)

13

where the sum of the shell effects and pairing corrections (δS + δP ) are added to the

energy of the LDM (ELDM ) [33]. The addition of these effects produces a more complex

fission barrier for heavy nuclei and is illustrated in Figure 2.3. A double humped or even

triple humped barrier can exist with deep secondary and tertiary minima. The addition

of asymmetric and symmetric deformations transforms the barrier into a multidimensional

surface, making calculation of the barrier height a complex task.

Figure 2.3: Illustration of 1-dimensional interaction potentials for Cf, Pu, and Th nuclei as
a function of deformation using the liquid drop model (top), shell effects (middle), and the
combination of the both (bottom). [34]

The fission decay width can be described by Bohr and Wheeler’s transition-state model

14

(TSM) [35, 36]. The transition-state model can be used to describe the CN at the saddle

point as a transition state between scission and the equilibrated CN and the decay rate

depends on the level density of states above the fission barrier. This model characterized

the fission process as having to compete with other modes of nuclear de-excitation, and that

the decay width could be written as

Γf =

Nf

Nf + Nn + Nγ + Nch.p

(2.14)

where Nx = 2πΓ/D is the level density of exit channels for each de-excitation channel.

The calculation of Nf requires an evaluation of the level density of the transition state

nucleus.

The transition-state model calculates the decay width of fission using three quantum

numbers: 1) the total angular momentum of the system J, the projection of J onto the

nuclear symmetry axis K, and the projection of J onto the fixed space axis M. (Figure 2.4).

This model makes the assumption that fission fragments separate along a nuclear symmetry

axis that remains unchanged throughout the fission process. Quantum numbers J and M are

conserved throughout this process and K is determined at the saddle point configuration.

Using this model, the decay width of a CN can be expressed as

ΓBW
f =

1

2πρ(Ei)

Tsadρ(Ei − Bf )

(2.15)

where Tsad is the nuclear temperature at the saddle point. The nuclear temperature

describes the kinetic energy of the system or the velocity in which the fragments cross the

saddle point, therefore can be represented as the transition rate. Bf is the fission barrier

that can be calculated by Sierk’s finite-range drop model [37] with corrections from the

15

Figure 2.4: Illustration of the angular momentum vectors at the saddle configuration for
a fissioning nucleus.
In the transition-state model for fission, the angular distribution of
fission fragments can be expressed as a function of the total angular momentum J and the
projection of J onto the fission axis K at the saddle point if the projection of J onto the
space fixed axis (here the beam axis) M=0.

ground-state shell structure. The TSM can also be used in predicting the fission angular

cross sections[38] and is described in more detail in Section 6.3

Using a one dimensional diffusion model, Kramers [39] formulated a similar representation

of the fission decay width. For a large viscosity, the width is expressed as

ΓKramers(E∗, J) = fkΓBW
)2 − γ
ω

fk =

f

(E∗, J),

(cid:114)

1 + (

γ
ω

(2.16)

where γ is the magnitude of viscosity and ω is the curvature of potential energy at saddle

point.

A simple approach to the kinetic energy of fission fragments is the result of Coulomb

repulsion after scission and can be expressed as

T KE =

Z1Z2
1/3
1/3
1 + A
2

)

r0(A

(2.17)

where r0 = 1.8 instead of the typical value of 1.2 due to the highly deformed fragments

16

at scission. More empirically derived representations of fragment TKE are given by Viola

et. al [40]. The excitation energy of the fission fragments can be calculated as the difference

between the Q value of the reaction and the TKE of the fission fragments.

2.3 Nuclear Codes

The fusion-fission process can be modelled through a number of different codes [41, 42, 43,

44]. This section describes the relevant codes used in this analysis.

2.3.1 General Description of Fission Observables

The GEneral Description of Fission Observables (GEF) is a model that utilizes a large body

of empirical fission observables for a general description of the fission process. It provides

a reliable prediction of fission observables for fissioning nuclei ranging from Polonium to

Seaborgium with excitation energies up to 100 MeV. GEF uses the Monte Carlo method

to calculate event by event fission observables of two fragments at fission, as well as the

nuclear de-excitation of the fragments, including prompt gamma and neutron emission. The

potential energy surface is calculated using the macroscopic-microscopic approach, relying

on the “separability principle” to empirically determine the stiffness of the macroscopic

potential and the position and strength of fragment shells.

The fission decay width is calculated using a primarily macroscopic approach by Hasse

[45] with a few extensions and is expressed by

Γf =

FrotTf

G · exp(Bmax/Tf

)

(2.18)

where Bmax is the maximum value of the inner and outer fission barriers, Tf is the

17

nuclear temperature of the compound system at Bmax. Frot is the influence of the rms

angular momentum distribution, which is dependent on fissility and nuclear temperature. G

considers the collective enhancement of the level densities at the top of the inner and outer

barriers as well as barrier penetrability.

The excitation energy partition between the fragments is determined through statistical

mechanics, where the assumption is made that all energetically possible configurations in

the system have equal probabilities to be populated. The average excitation energies can be

determined with a probability distribution that is a product of the level densities of each

fragment

< EL >=

(cid:82) E∗
(cid:82) E∗

0

intr

ELρL(EL)ρH (E∗
ρL(EL)ρH (E∗

intr − EL)dEL
intr − EL)dEL

intr

0

(2.19)

where ρL and ρH are the level densities of the light and heavy fragments respectively,

and E∗

intr is the intrinsic excitation energy determined from the sum of the excitation en-

ergy above the barrier plus the dissipated potential energy after the saddle point. Further

explanation of GEF can be found in the documentation by K. H. Schmidt [46, 47, 48].

2.3.2 Decay of Excited Nuclei

In this work, the Decay of Excited Nuclei is described by a Monte Carlo method for calcu-

lating the evaporation residue cross sections as utilized in LISE++. It randomly selects an

exit channel based on a probability distribution that is expressed as

Pb =

Γb

Γtotal

, b = n, p, α, γ, f ission

(2.20)

18

The decay widths for particle emission are described as

(cid:90) E∗

Bb

0

l

(cid:88)

Tl(eb) · I=J+l(cid:88)

I=|J−l|

ΓC→B+b(E∗, J) =

2sb + 1

2πρC (E∗, J)

ρB(E∗ − Bb − eb, I)deb

(2.21)

where sb is the spin of emitted particle b, Bb is its binding energy, and Tl(e) and eb

are the transmission coefficient and kinetic energy of the particle respectively. The fission

barrier used is the sum of the LDM barrier height plus the shell corrections corresponding

to the ground state Q-value. Further documentation can be found [49].

2.3.3 GEMINI++

Gemini++ is a statistical model calculation for the evaporation of high spin CN. The evap-

oration of light particles is implemented within the Hauser-Feshbach formalism [50] in which

spin degrees of freedom are taken into account. The partial decay width of a CN with

excitation energy E∗ and spin JCN for a light particle i is

Γi(E∗, JCN ) =

1

2πρCN (E∗, JCN )

(cid:90)

∞(cid:88)

JCN +Jd(cid:88)

J+Si(cid:88)

Jd=0

J=|JCN−Jd|

l=J−Si

d


Tl(
)ρd(E∗ − Bi − 
, Jd)

(2.22)

where Jd is the spin of the resulting nucleus, Tl is the transmission coefficient, Si, J, l are

the spin and orbital and angular momentum of the evaporated particle, and 
 and Bi are its

kinetic and separation energies respectively. The level densities are approximated using the

Fermi-gas form [51], which is obtained using a spherical nucleus with constant single-particle

19

level densities in the independent particle model and is expressed as

ρF G(E∗, J) =

√
24

2J + 1
2a1/4U 5/4σ3

exp(S)

(2.23)

where σ2 is the product of the moment of inertia of a rigid body, S is the nuclear entropy,

U is the thermal excitation, and a is the level density parameter.

The model calculates the fission decay width using the Bohr-Wheeler formalism using the

angular momentum dependent fission barriers of Sierk [52], assuming the level densities from

ground-state to saddle-point are identical except for a scaling factor. Further explanation is

provided by R.J. Charity [53, 54].

20

Chapter 3

Michigan State University

Experiment

3.1 Active Target Time Projection Chamber

The main goal of the experiments described below was to measure fission fragments for

the first time using the Active Target Time Projection Chamber (AT-TPC). This chapter

will consist of a brief summary of time projection chambers (TPCs) and a more detailed

description of the AT-TPC.

3.2 Background

3.2.1 Ionization Chambers

An ionization chamber is a simple radiation detector that measures ionizing radiation with

no electron amplification. It consists of a gas filled chamber with an applied voltage across

an anode and cathode, creating a uniform electric field. The electrodes can be oriented in

either a parallel plate configuration or a cylindrical orientation where a wire anode runs

coaxially through the center of the detector. When an incident ionizing particle enters the

chamber, the particle will produce an ionizing track in the detector gas, creating ion pairs.

21

The number of electron-ion pairs generated is dependent on the density, atomic number, and

the ionizing potential of the gas as well as the atomic number and energy of the incident

particle. Under the influence of the electric field, the positive ions and the freed electrons

will move towards the oppositely charged electrodes with a drift velocity that is dependent

on the electric field and type and pressure of the gas. In general, the typical drift velocity of

electrons (10’s of cm/µs) is much slower than the speed of the incoming particles (0.3c) and

the drift velocity of the positive ions is typically a factor 100 smaller than the negative ions

[55]. This generates a small ionization current that can then be measured by an electrometer

circuit.

The energy loss of ionization radiation in a gas has been studied and modelled to a good

precision. Several tools allow for the prediction of energy loss of particles in mediums; the

program TRIM (TRansport of Ions in Matter) utilizes data to infer energy loss. A simpler

approach is the Bethe-Bloch formula, which expresses the stopping power S as

(cid:21)

(3.1)

(cid:20)

S =

4πZ2e4
mv2 Z2

1

ln

2mv2
< I >

− ln(1 − β2) − β2 + Ψ(Z1)

Given a velocity of the incoming particles in a detector gas, the energy loss of an in-

coming particle is proportional to the square of the number of protons of a particle. Hence,

ionization chambers can provide energy loss and total energy. This information can be used

to determine the Z and mass/charge of the beam, respectively.

3.2.2 Time projection chambers

A time projection chamber is a gas filled chamber used to detect charged incoming particles.

It was originally invented in the 1970s by David Nygren [56] and was used to study high

22

energy electron-positron collisions at Lawrence Berkeley Laboratory. When a charged parti-

cle enters the detector, it ionizes a number of the atoms of the chamber’s gas proportionally

to the amount of energy the charged particle loses in the gas. The result is a trail of free

electrons that will then drift in a mostly uniform electric field produced by an anode and

cathode within the detector. Near the anode of the chamber there is electron amplification

and a position sensitive readout that measures the number of electrons. This is where it

differs from an ionization chamber

The 3-dimensional coordinates of the electrons are measured; 2-dimensions coming from the

2D-position sensitivity of the readout, and the 3rd dimension can be reconstructed from the

timing of the signals from the electrons relative to the timing of the trigger signal. Because

the drift velocity of the free electrons is constant in a gas in a homogeneous field, the timing

of each signal is equivalent to a space coordinate, hence the title ’time projection’ chambers

[57].

3.2.3 Active Target

In order to fully observe the products of a nuclear reaction within a TPC, the target of the

reaction needs to be inside the detector where the beam particles enter. One way to do this

is by making the ionizing gas and the target gas the same, or an active target [58]. There are

advantages to using this method over the traditional solid target. Reaction detection solid

angle is essentially 4π. Without any compromise on target thickness, reactions can happen

anywhere in the detector volume, resulting in the measurement of a reaction at a continuum

of energies as the beam traverses the detector, instead of measuring just one energy with a

thin target. As a result, excitation functions of reactions can be measured without changing

the initial beam energy.

23

There are some constraints to this method as well. Primarily the inner volume gas needs

to have good electron transport and amplification properties and it must contain the target

nuclei of interest. A thin solid target was introduced for this experiment as 208Pb does not

exist in gaseous form. This will be discussed in more detail in Section 3.4.6.

3.3 Structure of AT-TPC

The AT-TPC is a variation of a TPC that mainly is used in the active target mode. In the

instance of this experiment, as solid target was used. The following section comprises a brief

description of the AT-TPC. A more complete description of the half-scale prototype version

(pAT-TPC), which was also used in experiments described in this dissertation, can be found

in the dissertation by Carpenter et al.

[59] and in the articles written by Suzuki et al [60,

61]. The full size detector is described in depth by the dissertation written by Bradt et al

[62]. A schematic of the detector can be found in Figure 3.1.

3.3.1 Inner and outer gas volumes

The inner volume of the detector is contained in an epoxy coated fiberglass cylinder with a

radius of 29.2 cm and a length of 1 m. The inner volume is ended on the downstream end

by an aluminum frame that supports the sensor plane which operates as an anode. On the

upstream end there is an aluminium plate that acts as the cathode. Within the center of the

cathode is a 1 cm hole where the beam enters the detector. A thin foil window is mounted

over this hole to seal the chamber from the high vacuum beam line, allowing the beam to

enter with a minimum energy loss.

The outer volume of the AT-TPC is a stainless steel cylinder with a diameter of 50

24

Figure 3.1: Schematic view of the Active Target Time Projection Chamber. The outer
shielding was made transparent and a quarter section of the inner volume was cutout to
make the details more visible. The beam enters the detector through the beam duct at the
right-hand side and travels towards the sensor plane on the left. Some of the electronics
described in Section 3.3.4 are shown mounted on the left-hand side

centimeters and a length of 1.4 meter that encapsulates the inner volume. The purpose of

the outer volume is two-fold. First, the inner volume usually operates below atmospheric

pressure and must be pumped down to a vacuum in order to be filled with the working

gas. The thick stainless steel outer volume can withstand these pressure differentials and

protects the less robust inner volume from being damaged by pressure. Second, the outer

volume isolates the high electric potential produced by the cathode from the environment.

The outer volume is filled with an inert gas with a high dielectric constant such as nitrogen

in order to prevent sparking or arcing. The detector is designed for cathode voltages up to

150kV at 1 atmosphere. It is important to maintain the purity of the inner volume gas in

order to maintain a constant drift velocity and amplification. The outer volume pressure is

kept at a slightly lower pressure than the inner volume in order to prevent contamination of

25

the inner volume caused by micro-leaks .

3.3.2 Micromegas

On the downstream side of the detector near the sensor plane, ionized electrons are amplified

by a fine conductive mesh called a Micromegas (“micro-mesh gaseous structure”) [63]. A

Nickel grid is placed 100µm above the sensor plane and a negative voltage of the order of

500V is applied to the grid. This produces a large electric field gradient between the mesh

and sensor plane of the order of 50kV/cm. An electron passing through the mesh causes an

electron avalanche before reaching the sensor plane, which amplifies the signal of that single

electron by a factor of up to 106. An illustration of the process can be found in Figure 3.2.

Figure 3.2: Illustration of Micromegas operation within the TPC. The electric fields will
vary depending on the details of the experiment. This image is not to scale.

26

3.3.3 Sensor plane

The sensor plane is a circular printed circuit board with a radius of 27.5 cm and consists of

10,240 gold plated conductive pads. The plane is arranged with an hexagonal inner region of

triangular pads with a height of 0.5cm surrounded by a circular region of triangular pads with

a height of 1.0cm. A depiction of the sensor plan can be found in Figure 3.3. The pads are

triangular in order to maximize spatial resolution. As a track of electrons from an ionizing

particle reaches the sensor plane, the charge deposited on the sensor plane will be sampled by

these triangular pads. The charge measured by each pad will change drastically depending

on the location of the track on the triangular pad. With a detailed fitting procedure a

localization much finer to the dimension of the pad size may be achieved.

Figure 3.3: Illustration of AT-TPC sensor plane. The bottom right image is a zoomed cutout
of the sensor plane showing the transition between large and small pads.

27

3.3.4 Electronics

The electronics used for the AT-TPC data collection are the General Electronics for Time

Projection Chambers (GET), which were developed by a collaboration [64]. These electronics

are used for amplification, digitization, and storage of data from every pad on the sensor

plane. GET is divided into a number of modules. The first module is the Application Specific

Integrated Circuit (ASIC) for GET electronics (AGET). This chip shaped, amplified, and

sampled 64 channels at a frequency of 25MHz and stored them in a Sampling Capacitor

Array (SCA) that acts as a circular buffer[65, 66]. The chip also compared the signal to a

set threshold to generate a leading edge discriminator signal.

Four of these AGET chips are mounted on an AsAd (ASIC Support and Analog to

Digital Conversion) board. The ADC, mounted along with the four AGET chips, digitizes

the multiplicity of the leading edge discriminator of each AGET and transmits it to a different

module, the CoBo. When a trigger signal is sent, the ADC is switched to digitize the signals

stored in the SCA of the four AGET chips and transmits them via serial link.

The data from the AsAd boards are passed to the CoBo’s (Concentration Boards, devel-

oped at the NSCL), which can house up to 4 AsAd’s, which is 1024 channels. Each CoBo

calculates the number of channel triggers digitized by the AGET chips and can be used to

issue a global trigger. When a global trigger is issued, the CoBo reads the data in the SCAs

from each AsAd, applies a local timestamp, and builds and stores the event on a cluster of

computers. An illustration of the electronics can be found in Figure 3.4 and a logic circuit

of the AGET chip can be found in Figure 3.5.

28

Figure 3.4: Illustration of electronic hierarchy used for the AT-TPC. The illustration only
shows the inside of one AsAd, but it is important to note that 40 AsAds and 10 CoBos are
used during experiments

3.3.5 Tilting the Detector

While the AT-TPC is usually aligned such that the beam traverses the center of the detector,

there is the possibility of tilting the detector. The AT-TPC support can tilt the anode of the
detector up to 6◦ around the entrance window with regard to the beam axis. This orientation

of the detector can be beneficial for post-experiment analysis for a couple reasons. The first

is that forward angle charged particle tracks are extended over a number of pads instead of

just one or two in the centered orientation. This will lead to better measurements of reaction

products at small angles. Another benefit for a tilted orientation is that events with multiple

incoming beam particles, or pileup events, can be separated from each other, as events that

occur farther away from the window will have an origin farther away from (0,0) on the pad

plane. An illustration of this orientation can be found in Figure 3.6.

29

Figure 3.5: Logic diagram of the Application Specific Integrated Circuit for GET electronics
(AGET) [67].

3.3.6 Electric and Magnetic Fields

A uniform electric field is generated within the detector in order to transport the free electrons

towards the sensor plane for detection. This is done by applying a potential difference

between the cathode at the upstream end of the detector and the anode at the downstream

end. Uniformity of the field is obtained by a field cage consisting of 50 concentric ring

electrodes through the length of the detector that are attached to a chain of resistors. The

chain of resistors decreases the voltage across each ring as it progresses from the upstream

end to the downstream end. A picture of the field cage can be seen in Figure 3.7 while the

detector was being assembled. There are two rows of rings, one inside and one outside of

the field cage. Each inner ring is in electric contact with an outer one to keep homogeneity

of the electric field.

A coaxial magnetic field can also be applied to the detector by placing the detector in a

large bore solenoid magnet. At the NSCL, a re-purposed MRI magnet was used, allowing

for fields up to 2T. The magnetic field will bend the charged particles; if the range of the

particle is long enough and the radius of curvature is small enough, they will spiral down

30

Figure 3.6: Illustration of the AT-TPC tilted inside the solenoid magnet. The detector can
be tilted up to 6◦ and the magnet can reach a uniform magnetic strength of 2T.

the length of the detector as they lose energy in the gas. A charged particle with velocity v,

mass m, and charge q in a magnetic field B will move in a circle radius

ρ =

mv
Bq

.

(3.2)

With the particles kinetic energy being E = 1/2mv2, the measurement of the magnetic

rigidity by the curvature of the track allows for a precise energy measurement by

E =

B2ρ2q2

2m

=

B2ρ2Z2e2

2Amp

.

(3.3)

The AT-TPC inside a magnetic field is also the only way to identify particles that do

not completely stop within the detector. Without collecting all of a particles energy in the

gas, measuring the radius of curvature is the only way to identify the particle and measure

31

Figure 3.7: Picture of the rings of the field cage inside the inner volume of the AT-TPC
detector

32

its momentum. For this experiment the magnetic field was not used.

3.3.7 Trigger

Before a trigger is produced, the GET electronics is used to execute two tasks in the waiting

phase: 1) writing all channels in their circular SCA and 2) digitizing the leading edge dis-

criminator signals and sending the result to the CoBo. A trigger signal will be produced if

there is an event of interest. When it is delivered to the GET electronics it 1) stops writing

in the SCA and 2) starts the digitization readout of all the sampling capacitors.

There are several primary triggers that can be used for the data acquisition of the AT-

TPC; the specific setup varies with the goal of each experiment and on other ancillary

detectors used in conjunction with the AT-TPC. The first trigger originates from the output

of the Micromegas mesh. The mesh receives the sum of the current of all the pads (with

opposite sign). This current is passed to a preamplifier-amplifier chain. A single channel

discriminator may then select an experimentally set amplitude window that is dependent on

the specific experiment. The output of the discriminator is then sent to the data acquisition

as a trigger signal.

A second possible trigger is an internal multiplicity trigger within the GET electronics,

which operates as a “number of pads with a signal” trigger. As mentioned in Section 3.3.4,

the ASIC chip can compare the signal of each pad to a set threshold and generate a leading-

edge trigger. In each CoBo a channel trigger threshold can be manually set, where if a certain

number of channel triggers occur within a time period, 6µs for the fusion-fission experiment

described in this dissertation, then the CoBo outputs a trigger signal. The trigger outputs

of each CoBo are then set in an OR logic circuit, and the output of the OR circuit are

sent to the data acquisition as a trigger signal. This signal can also be coupled with the

33

mesh trigger. Alternatively, a global multiplicity signal can be produced by the MuTAnt

(Multiplicity, Trigger, and Time) module that can sum the multiplicity of all the CoBos [68].

Eventually, coincidence will be required between the different trigger signals and external

detectors such as an ionization chamber or MCP.

3.4 Experimental Setup of the AT-TPC

The AT-TPC was chosen for this experiment essentially for its 100% detection efficiency.

The AT-TPC will detect every ionizing particle that enters the detector, which ensures no

loss of incoming particles. This is especially important when performing experiments that

measure differential and total cross-sections as this eliminates any need for normalization.

In respect to the fission experiment itself, with a solid target the detector will have a solid

angle efficiency of 2π which will ensure the detection of one if not both fission fragments in

a fission event. Finally, the difference of the ranges in the detector volume will make the

identification of beam particles and fission fragments straightforward.

3.4.1 Rare Isotope Beam Production

A beam of 46K was produced by the Coupled Cyclotron Facility at the National Supercon-

ducting Cyclotron Laboratory at Michigan State University [69]. The layout of the beam-line

can be found in Figure 3.8. A primary beam of 48Ca, ionized in a superconducting ECR

(Electron Cyclotron Resonance) ion source, was accelerated to an energy of 140 MeV/u after

the two coupled cyclotrons. The primary beam was then fragmented by a stable beryllium

target in order to produce a large number of isotopes, including the desired 46K. The cock-

tail beam is then delivered to the A1900 fragment separator [70], where four dipole magnets

34

separate the beam based on momentum over charge (magnetic rigidity). A sketch of the

A1900 fragment separator can be found in Figure 3.9. Once the secondary beam is filtered,

it exits the fragments separator with an energy much higher than desired for the scope of

this experiment. As a result, the beam is stopped and re-accelerated to the desired energy,

which is done using the ReA3 facility.

Figure 3.8: Illustration of the NSCL beam-line, with different regions labelled. The beam
for this experiment is produced by a room temperature ECR (RTECR) and superconducting
ECR ion source (SuSI) and accelerated sequentially by the K500 and K1200 cyclotrons. The
beam is then separated by the A1900 fragment separator, stopped and re-accelerated by
ReA3, and is delivered to the AT-TPC in the ReA3 experimental hall.

3.4.2 ReA3 Accelerator

As mentioned earlier, the secondary beam exiting the A1900 can be very energetic (∼50-140

MeV/u). In order to reach the energy desired for this experiment (4.5 MeV/u), the beam

needs to be slowed down. One way of doing this is by using a degrader. The disadvantages

of using a degrader are that this will decrease the intensity and the momentum dispersion

of the beam in the transverse direction. This will result in a loss of energy and angular

35

Figure 3.9: A1900 fragment separator in conjunction with the twin cyclotrons

resolution. The ReA3 facility eliminates the disadvantages of using a degrader by stopping

the beam and re-accelerating it, however there will be a loss of beam intensity.

For this experiment, the beam that entered the ReA3 facility [71] is stopped in a linear

gas stopper filled with helium gas. The thermalized 1+ ions are then cooled, accelerated
(to ∼30kV) from the gas stopper and transported using electromagnetic elements into an

electron beam ion trap (EBIT). The ions in the trap are traversed by a high intensity electron

beam for a few milliseconds and undergo electron impact ionization, increasing the charge

of the ions for re-acceleration. They are then ejected and transported to a Q/A separator

for charge selection. After this they are injected into the linear accelerator to reach a final

energy of 4.5 MeV/u for this experiment.

46K is an unstable isotope with a half-life of 105 seconds. During the time it takes for

the secondary beam to be delivered, some of the 46K can beta decay into 46Ca. There is

a dipole magnetic along the beam line from the gas cell to the EBIT that can separate

contaminants from the beam, but it doesn’t have a sufficient resolution to separate isobars.

Fortunately the fusion cross-section for 46Ca + 208Pb is orders of magnitude lower than that

of the studied system. The impurities can also be corrected for in the total cross-section

36

calculation. Particles with the same velocity and mass but a different number of protons will

have different track lengths in the inner volume gas of the AT-TPC as it follows from the

Bethe-Bloch formula. As a result it is possible to calculate the percentage of impurity in the

beam based on track length of the incoming beam and subtract it from the total number of

incoming beam particles. This will also be investigated in further detail in Section 3.6.3.

3.4.3 Characteristics of the Reaction Projectiles

Two beams, 46K and 19F, were separately delivered to the AT-TPC during this experiment;

the 46K beam was delivered first for a total of 6 days and the 19F beam was delivered after

for 24 hours. The 46K + 208Pb reaction was the primary focus of this study, the total

fission cross-section and elastic scattering cross-sections had not been previously measured.

Since the 19F + 208Pb reaction is a well studied system [72], the experimental data in this

experiment was compared to this previous data in order to validate the analysis procedures.

The energy of the 46K and 19F beams incident on the 208Pb target were 211.2 MeV and

107.4 MeV respectively, which was the maximum energy that could be achieved by the ReA3

accelerator. Both beams were delivered with a peak rate of about 1000 pps and a duty cycle,

which is the fraction in which the beam is active over one period, of 5% and can be seen in

Figure 3.10. For the 19F beam, the rate of the beam was chosen in order to limit event pileup.

The rate of the 46K beam was limited by the production of the beam and the performance

of the gas cell.

37

Figure 3.10: Oscilloscope trace of the 46K beam structure (green) delivered to the AT-TPC.
The duty cycle of the beam is 5%.

3.4.4 Beam Identification

Both beams were identified using a ionization chamber located just upstream from the AT-

TPC detector. During the data collection for the reaction studies, the ionization chamber

was removed from the beam line in order to decrease the energy loss of the incoming particles

and thus maximize the cross-section of the reaction. A schematic of the ionization chamber

used can be seen in Figure 3.11. The ionization chamber was filled with 10 torr of isobutane

gas, which was chosen for its high density of atoms. This pressure allowed for a sufficient

signal to be achieved. The total thickness of the ionization chamber was 500µg/cm2.

3.4.5 Detector Gas

The inner volume of the AT-TPC detector was filled with 100 torr of P10 (10% methane,

90% Argon) gas. P10 gas was chosen as the ionizing gas due to the fast transport velocity of

electrons at low electric field as well as the quenching ability of the methane. Fast electron

transport in the AT-TPC will decrease the time between particle track creation and the

38

Figure 3.11: Drawing of ionization chamber used for beam identification. The ionization
chamber was filled with 10 torr of isobutane which resulted in a total thickness of 500µg/cm2.

ionized electrons reaching the detector plane, decreasing the event pileup. Figure 3.12 shows

the drift velocity of electrons in P10 gas. The drift velocity of the free electrons in this setup

was approximately 6 cm/µs and as a result it will take 16.6 µs to travel the total length

of the detector. The pressure of 100 torr was chosen in order to balance the ranges of the

beams and of the fission fragments in order to easily distinguish between them. Using SRIM

[73], the estimated ranges of the 46K and 19F beams in 100 torr of P10 gas are 70.8 cm and

110 cm respectively, while the estimated ranges of the fission fragments is 10-20 cm.

There was unexpected detector performance when using P10 gas in these conditions. A

large amount of positive ion flow in the center of the detector due to the slow drift time of

the positive ions resulted in recombination of electrons and ions. This led to a lack of signal

or holes in tracks. This phenomenon is explained in more detail in the analysis section and

in the publication by the AT-TPC group by Randhawaa et al [55].

39

Figure 3.12: Drift velocity dependence on electric field for P10 gas [74].

3.4.6 Reaction Target and Window

The target for the fusion-fission experiment in this paper using the AT-TPC was 208Pb.

Since there is no gaseous form of lead that exists at room temperature, a solid target was

used. The lead was evaporated with a thickness of 0.635 mg/cm2 onto a thin aluminized

polypropylene foil . The foil, glued to an aluminum support, was placed inside the detector

on the cathode and as close to the entrance window as possible. In order to minimize the

energy loss through the entrance window of the detector (1cm diameter), the window material

40

needed to be as thin as possible while holding a pressure differential of at least 100 torr. A

few materials were considered and tested as possibilities, including Mylar, polypropylene,

and para-aramid(PPTA). Table 3.1 shows the variables considered, specifically maximum
pressure differential and energy loss of a ∼5 MeV alpha particle. The energy loss of the alpha
particle was used to estimate the energy loss of the incoming beam since dE/dx ∝ Z2. While

the polypropylene had minimal energy loss of the alpha particle, the aluminized Mylar was

chosen as the window material due to the slightly higher pressure differential. The window

was glued to the window holder using AA-Bond F113 epoxy. This type of mounting results

in a detection solid angle that is limited to 2π.

Table 3.1: Table of different window material considered for AT-TPC entrance window

3.4.7 Trigger

The two main triggers discussed in Section 3.3.7 were used in conjunction in this experiment.

The trigger signal from the Micromegas mesh, or “beam trigger”, was used to count the

number of incoming beam particles and the SCA discriminator was set during the experiment

to be just above the noise. The internal trigger from the GET electronics was set to a specific

number of ”hits” that did not include beam events. As a result, each CoBo was set to generate

a signal if the number of channel triggers was above a lower level that was set just above
threshold. The dead time of the DAQ (∼1ms, stemming from the electronics) and the rate of

the beam need to be considered when setting the trigger thresholds. The product of the dead

41

time plus the trigger rate needs to be substantially smaller than the beam rate (1000pps).

3.5 Analyzing AT-TPC Data

The raw data taken by the AT-TPC DAQ consists of events with 10,240 trace signals cor-

responding to the pads on the pad plane. In this experiment, trace signals with no signal

were suppressed by the DAQ. After amplification and shaping, each trace signal measures

the amount of charge on each pad and is divided into 512 sequential segments of time called

timebuckets. For this experiment, the write sampling rate of the SCA was 25MHz, which

corresponds to 40ns/timebucket. Before an analysis can be conducted on data taken from the

AT-TPC, the pertinent data needs to be extracted from these registered data, or “unpacked”.

The following section describes the unpacking progress.

3.5.1 Pedestal Subtraction and Charge Extraction

About 1000 traces of the 10,240 have an offset of the signal that is non-zero, which allows

for information on variations of the zero offset and pulse undershoots. The zero offset is

measured by averaging of the first 10 timebuckets in each trace signal and subtracting this

average from the full trace. During the setup of the experiment, the signals produced by the

incoming beam particles were centered within the 512 timebuckets. This is done by setting

the value of the delay between the trigger signal and data stop writing signal. This time

window will not only ensure that no information of the incoming particle is lost, but also

guarantees that the first several timebuckets have only the pedestal information used for

subtraction.

Once the pedestal has been subtracted, the charge collected by the pad and average

42

signal time is extracted. This can be done a number of ways, including taking the peak of

the signal, the integral of the signal, or taking the center of gravity. In this experiment, the

center of gravity of the signal was used. The maximum height of the signal is determined and

then the signal a few timebuckets before and after the maximum are used in the weighted

arithmetic mean

¯t =

(cid:80)n
(cid:80)n

i=1 tiai
i=1 ai

(3.4)

where the average timebucket ¯t is weighted by the signal amplitude ai of each timebucket

ti. The average timebucket and corresponding signal height are then assigned to the pad

number that each trace belongs to and will be used for track reconstruction.

3.5.2 3D Track Reconstruction - RANSAC

The information from the track of the incoming particle is represented by (xi, yi) coordinates

given by the centroid coordinates of the corresponding pad number, the time ti that the

information was received by each pad in units of timebuckets, and the signal height ai,

which corresponds to the energy loss of the particle. The timing of the signal, in reference

to the timing of the trigger signal, can be converted into a z-coordinate zi by measuring the

drift velocity of the electrons in the active volume vd and using the ADC clock frequency ν

in the equation

zi =

vdti
ν

(3.5)

After this process, there is a sufficient amount of information to reconstruct the track

of the particle in 3 dimensions. There are number of approaches for track reconstruction

utilized in the AT-TPC analysis;

in this analysis the approach used is called RANdom

43

SAmple Consensus (RANSAC).

RANSAC is a mathematical algorithm that estimates the parameters of a mathematical

function, in this case a 3D line. An iterative method is used to separate in a data set the

inliers, which are the particle tracks, and outliers, such as noise from the detector. An

illustration of RANSAC can be found in Figure 3.13.

Figure 3.13: Left: A data set of 2D points that can be used as input for the RANSAC
algorithm. Right: Output of the RANSAC algorithm. The blue line is the estimate that
RANSAC found to be reasonably good. The blue points are part of the consensus set or
inliers. The red points are outliers.

The process RANSAC used in the AT-TPC analysis is comprised of two steps that are

then iteratively repeated. The first step is a random selection of two data points in the event

and the construction of a 3D line with corresponding parameters. The second step involves

checking the remaining data points to see if they are compatible with the constructed line

within a chosen deviation. The data points that are considered compatible are called the

consensus set. This process repeats with two outcomes: an estimate is rejected with too

few points in the consensus set, or it is saved with a corresponding consensus set size larger

than the previously saved estimate. Once a reasonably good estimate is established, then

44

the estimate is re-evaluated using all the data points in the consensus set [75]. Once the

estimate is re-evaluated, all points in the consensus set are removed from the event data and

the process is repeated.

In the AT-TPC analysis there are three main adjustable parameters that are set for

RANSAC analysis: 1) the deviation in 3-D of a data point from an estimated model, 2)

the number of data points in the consensus set for a line to be considered good, and 3) the

deviation from one estimate to another [76]. This last parameter is important due to the

chance that multiple tracks can occur within an event at the same time. The parameter

needs to be tuned such that the deviation is small enough as to not reject multiple tracks,

but also large enough not to double count single particle tracks.

The RANSAC algorithm outputs the number of tracks in an event and the respective

data points that belong to each track. From this output, the approximate range of the

tracks can be calculated by finding the distance between the first and last data points and

the approximate charge can be calculated by summing the signal heights of all inlier data

points. The total charge is proportional to the energy loss of the particle in the inner volume

gas and can be compared to known energy loss profiles, such as the energy loss of beam

particles.

3.6 AT-TPC Fission Analysis

3.6.1 Identifying Fission Fragments

Described here is the first experiment observing heavy-ion fusion fission reactions using the

AT-TPC. There was no precedent analysis for fission fragment identification. As a first

approach, before the experiment, a 252Cf spontaneous fission source was placed inside the

45

Figure 3.14: Left: X-Y projection of charge on the pad plane from a spontaneous fission
event. Right: Total charge as a function of time from a spontaneous fission event

detector on the cathode near the entrance window. The data taken from these observed

spontaneous fission events were used as a starting point for the identification of fusion-

fission fragments for the beam induced fission. Figure 3.14 shows plots of a fission event

from the spontaneous fission source. The left plot shows the 2D pad plane and the colors

represent the total charge [arb. units] seen by each pad. The right plot shows the summed

charge of each pad as a function of timebucket and is proportional to the energy loss profile

of the particle. When looking at the energy loss profile from a spontaneous fission fragment

calculated using TRIM, like in Figure 3.15, it can be seen that only the peak of the Bragg

curve of the particle will be experimentally observed. When comparing the experimental

energy loss profile in Figure 3.14 and the calculated energy loss profile from TRIM in Figure

3.15, the two plots are qualitatively consistent. This can also be visualized on the pad plane

in Figure 3.14 (left), where it is observed that a high amount of energy is deposited at the

beginning of the track (0,60) and subsequently decreases sharply.

As a result, these two plots in Figure 3.14 became essential in identifying fission fragments

in the 46K + 208Pb experiment. Figure 3.16 shows the same plots from the this experiment.

46

Figure 3.15: TRIM calculation of the energy loss profile of a typical 252Cf fission fragment
with 100 MeV in P-10 at 100 torr.

When comparing the experimental fission event to the spontaneous fission event and to

TRIM, they are qualitatively consistent, confirming that these were fission fragments.

There were three major observables used in identifying heavy-ion fission fragments in the

primary experiment: 1) total range, 2) total charge, and 3) origin of the particle track. As

discussed earlier in Section 3.4.5, the ranges and energy of the beam and fission fragments are

significantly distinct from one another. Since the detector was tilted, any fission events from

the 208Pb target will originate from the center of the pad plane (0,0) since the target was

placed at the central beam entrance. Any scattering events that occur in the gas will originate

further away from (0,0) the farther the beam particle progresses through the detector before

reacting.

3.6.2 Elastic Scattering Normalization

The elastic scattering of 19F + 208Pb was analyzed in order to normalize the fission cross
sections. Since the range of the 19F particles in the detector is ∼90cm, the observed range of

47

Figure 3.16: Left: X-Y projection of charge on the pad plane from an event of the pri-
mary experiment. Right: Total charge as a function of time from an event of the primary
experiment. Note that the direction of the x-axis is opposite to that of Figure 3.15.

the elastically scattered particles will be constrained to the geometry of the detector. Figure

3.17 shows both the range and summed total charge as a function of lab angle for all events

with a single particle track for all 19F + 208Pb runs. The summed total charge plot (left)
shows a clear restriction of energy as a function of lab angle from 30◦ to 90◦. A visual cut

on the data (shown in red) results in events with ranges that are in agreement with the

geometry of the detector (represented as black curve).

The elastically scattered differential cross sections in the lab frame are calculated by

(cid:12)(cid:12)(cid:12)(cid:12)lab

dσ(θ, φ)

dΩ

=

1

nt∆Ω

Nscat
Ninc

(3.6)

where n is the number density of the target, t is the target thickness, ∆Ω is the finite

angular range, and Nscat and Ninc are the number of scattered and incoming particles

respectively. They are then transformed into the center-of-mass frame by

(cid:12)(cid:12)(cid:12)(cid:12)cm

dσ(θ, φ)

dΩ

(cid:12)(cid:12)(cid:12)(cid:12)lab

=

dσ(θ, φ)

dΩ

48

sinθlab
sinθcm

dΩlab
dΩcm

(3.7)

Figure 3.17: Left: Total charge of single particle events measured in the AT-TPC as a
function of angle. A visual cut (solid red) is made on beam particles elastically scattered off
of the 208Pb target. Right: Ranges of single particles events measured in the AT-TPC after
visual cut. The black curve is the maximum ranges the AT-TPC can measure for events
originating from the window.

where

dΩlab
dΩcm

is the Jacobian and is calculated using LISE++. The elastic differential

cross sections were then normalized to the Rutherford cross sections given by

(cid:18) Z1Z2e2

(cid:12)(cid:12)(cid:12)(cid:12)Ruth

=

(cid:19)2

dσ(θ, φ)

dΩ

1

1

4π
0

4KE

sin4(θ/2)

(3.8)

The elastic scattering cross sections were then compared to cross sections calculated using

the Sao Paulo optical potential and is shown in Figure 3.18. The cross sections in the region
between 50◦ and 70◦ were found to be in good agreement; at more forward angles there is

an increasing background from elastic scattering on the gas (Figure 3.17). As a result, no

further renormalization needed to be applied to the experimental fission data.

3.6.3 Beam Impurity

As mentioned in Section 3.4.2, the 46K beam is a radioactive beam that can decay with its

characteristic lifetime. Also the ReA3 beamline between the gas cell and the EBIT has a

49

Figure 3.18: Measured (blue square) and optical model (gold circle) elastic scattering cross
sections reduced by Rutherford scattering cross sections

magnetic rigidity of only ∼ 1%, which is not sufficient enough to separate isobars. Therefore

the incoming beam is not 100% pure and this implies corrections to cross section calculation.
To assess the purity of the incoming beam, the ranges of single particle events at 0◦ in the

detector was plotted for each run and can be found in Figure 3.19. Although all incoming

isobar particles have the same velocity and therefore energy, the energy loss in the detector

gas will depend on Z. This results in different ranges in the gas where the 46K beam can be

identified. It can be seen in Run 228, at the beginning of the experiment, that three different

species of beams are present. The large peak at 65cm is consistent with the range of 46K

and the secondary peak at 75cm is consistent with the primary decay of 46K, 46Ca. The

tertiary peak at 85cm is consistent with 48Ti. As the experiment progresses, the percentage

50

of beam impurities decreases and reaches a constant impurity of 10%. The cause of this

decrease could have stemmed from the implementation of a beam cleaning method used by

the operators of ReA3 [77].

Figure 3.19: Ranges of single particle events in the AT-TPC at 0◦. Each run (left to right) is
further along in experiment time. Each peak was fitted with a separate Landau curve (solid
red line) and summed. X-axis was inverted in order to fit with Landau curves.

The corresponding peaks were fitted with Landau functions. The integrals of the peaks

and percentage of impurities were calculated for each run and are shown as a function of

experimental run time in Figure 3.20. Each run was one hour in duration, and the number

of incoming particles per run was found to be relatively constant. Since the total number of

incoming beam particles was approximately constant for each run, a total beam impurity of

12% was calculated by fitting two linear equations to the data, one to the large slope between

0-20 hours and a second to the nearly constant percentage of impurity between 20-85 hours,

and integrating.

51

Figure 3.20: Percentage of beam impurities over the duration of the 46K + 208Pb experiment.
The most likely impurities are the primary decay of the beam, 46Ca.

3.6.4 Differential Cross Section

The measured differential cross section of fission fragments for both the 19F + 208Pb and

46K + 208Pb reactions were determined using Equations 3.6 and 3.7.

In order to obtain total capture cross sections from these measured differential cross

sections, the regions beyond the detector’s angular coverage need to be extrapolated. The

method used in this analysis is the transition state model. The saddle point transition model
(SPTS) [78] estimates the anisotropy, the ratio of fissioning events at 180◦ to 90◦, as

< W (180◦) >
< W (90◦) >

≈ 1 +

< I2 >
4K2
0

(3.9)

where < I2 > is the magnitude of the total angular momentum of the fissioning nucleus

52

and K0 is the standard deviation of an assumed Gaussian distribution of K states. Using a

classical approximation, < I2 > is given by

< I2 >≈ [µ(Ecm − Vc)/¯h2](Rt + Rp)2

(3.10)

where µ is the reduced mass, Vc is the Coulomb barrier, and Rt, Rp are the radii of

the target and projectile nucleus respectively. The quantity K2
moment of inertia (cid:61)ef f and the nuclear temperature at the saddle point Tnuc by

0 is related to the effective

K2

0 =

(cid:61)ef f Tnuc

¯h2

(3.11)

where the parallel and perpendicular moments of inertia are used to calculate the effective
moment of inertia (cid:61)ef f = J(cid:107)J⊥/(J⊥ − J(cid:107)). The nuclear temperature at saddle can be

expressed as

Tnuc ≈(cid:113)

(E∗ − Bf − Erot − Eν)/af

(3.12)

where Bf is the fission barrier and af is the level density parameter. A typical value

used for af is ∼ A

8 . Additionally, angular distributions W (θ) are commonly fitted with a

series of Legendre polynomials

(cid:88)

n

W (θ) =

cnP2n(cosθ)

(3.13)

where only even Legendre polynomials P2n are included to conserve forward and back-

ward symmetry [78].

Equations 3.9 and 3.13 can be used to estimate the anisotropy of the the system and

53

predict the full differential cross sections. Figure 3.21 shows that this method (yellow) is in

good agreement with the calculated cross sections of the 19F + 208Pb reaction from the AT-

TPC and from Kapoor et al. [79]. The full experimental capture cross section is calculated

by multiplying by 2π sin θ and integrating the full curve and is found to be in good agreement

within error with cross sections measured by B. B. Back et al [80] in Figure 3.22.

Figure 3.21: Differential cross sections of the 19F + 208Pb reaction measured by the AT-TPC
as a function of center of mass energy (ECM )and approximated cross sections from Legendre
polynomials.

Since this method of total capture cross section determination is found to be in agreement

with past experimental data, it is suitable to be used in cross section calculation for the 46K

+ 208Pb reaction and in future AT-TPC fusion-fission experiments. Figure 3.23 (left) shows

the determined experimental cross sections for this reaction with the aforementioned method

using an approximate anisotropy and angular distribution using Legendre polynomials. The

total capture cross section is shown in Figure 3.23 (right) as a reduced cross section in

comparison with the 39K + 208Pb reaction discussed in Chapter 6.

54

Figure 3.22: Fission cross section for the 19F + 208Pb reaction measured by the AT-TPC as
a function of center of mass energy (ECM ) compared to previous measurements [80].

Figure 3.23: Left: Differential cross sections measured by the AT-TPC as a function of center
of mass angle (θCM ) and approximated cross sections from Legendre polynomials. Right:
Reduced capture cross sections for 39,46K + 208Pb reactions

55

Chapter 4

Measurement of Fission Fragment

Tracks

The identification of fission fragment tracks is an important step in utilizing the AT-TPC as

a fission fragment detector. It would allow for the distinguishing of fusion-fission and quasi-

fission events, since quasi-fission events have Z distributions similar to the Z of the beam and

target compared to fusion-fission Z distributions, as well as fusion-evaporation events during

analysis and provide a more detailed picture of the fusion process. The AT-TPC and pAT-
TPC have energy resolutions of ∼2-5%, suggesting that it could be possible to distinguish

the Z value of the fusion products. The range of the stopped particles can be determined

with a precision of the order of 1mm. The following chapter discusses experiments using the

pAT-TPC measuring fission fragments from a spontaneous fission source and the analysis to

identify these fragments based on energy loss and range.

4.1 Experimental Setup

A 1µCi 252Cf spontaneous fission source was placed inside the pAT-TPC in the center region

of the cathode near the entrance window (Figure 4.1); the fission fragment energies are

expected to range from 70-110 MeV and light fragments are expected to vary from Kr to

Ru. Two separate ionization gases, pure hydrogen (H2) and He-CO2 (90:10) were chosen to

56

measure fission fragments due to their low ionization energies. The low ionization energies

as compared to the total energies will produce a large number of electron-ion pairs generated

by the fragments and result in large signals generated in the electronics. SRIM was used

to determine the pressure of the gases with the restriction that projected range of the light

fragments could not exceed the length of the detector (50cm), with pressures of 400 torr for

pure H2 and 300 torr for He-CO2.

Figure 4.1: Picture of the opened pAT-TPC with the 252Cf source attached to the center of
the cathode.

Micromegas alone and Micromegas+Thick Gaseous Electron Multipliers (ThGEMs) were

used. ThGEMs are robust high gain electron multipliers that are constituted of a double

faced Cu-clad printed circuit board perforated with millimeter to sub-millimeter diameter

holes. An electric potential is applied between the faces generating a strong dipole electric

field, resulting in gas avalanche multiplication of incident electrons. An illustration of the

generated ThGEM electric field can be found in Figure 4.2 and a more complete description

of ThGEMs can be found by A. Breskin and M. Cortesi, et al [81, 82]. Suitable voltages for
these electron amplifiers were ∼300V for the Micromegas and 100V for the ThGEMs with a

cathode voltage of 20kV.

57

Figure 4.2: Illustration of the electric fields inside the holes of a ThGEM during operation
[83]. An electric potential is applied between the faces, generating a strong dipole electric
field inside the holes, depicted by the large concentration of electric field lines.

Events were selected using the Micromegas mesh trigger signal discussed in Section 3.3.7.

Since the only charged particles from the spontaneous fission source are 6.1 MeV alpha

particles and 70-110 MeV fission fragments, it is simple to distinguish between the two

from signal amplitude. An example of a selected fission event is shown in Figure 4.3. The

amplitude and shape closely resemble that of fission events measured in the AT-TPC (Figure

3.14).

4.2 Analysis

The range of the track was determined by the first and last timebucket (T bi) of the fission

fragment signal by

58

Figure 4.3: Pad signals from a fission fragment measured by the pAT-TPC. Each color is
representative of one of the four quadrants into which the pad plane is separated.

vdν−1(T bf − T bl)

cosφ

r =

(4.1)

where ν is the ADC clock frequency, vd is the drift velocity, and φ is the angle between the

track and the vertical axis (parallel to the pad plane). The drift velocity was measured using

a gamma-ray detector (measuring gamma-rays from the spontaneous source) outside the

downstream end of the pAT-TPC and the mesh signal from the Micromegas in coincidence.

Figure 4.4 shows the oscilloscope readout of the gamma-ray detector signals (yellow) in

coincidence with the mesh signals (blue). The measured drift velocities for H2 and He-CO2

using this method were 1.0 and 2.5 cm/µs respectively.

Energy loss calibration is performed with the 6.1 MeV alpha (81.5%) emitted from the

252Cf nucleus. Using SRIM, the energy loss profile of the particle through the detector gas

can be estimated and used to calibrate experimental tracks.

59

Figure 4.4: Oscilloscope view of the signal from the gamma-ray detector (yellow) in coinci-
dence with the mesh signal of the fission fragments from the pAT-TPC (blue).

4.2.1 Comparison to SRIM

In order to identify fission fragments with specific Z, the energy loss profiles of the fission

fragments were collated with an energy loss profile of an expected fission fragment from

SRIM. For this experiment, the energy loss profile of a 102Ru fragment at 100 MeV calculated

by SRIM was used as a standard for comparison. The energy loss curve was fitted with a

high order exponential (Figure 4.5a) giving a continuous curve of energy loss as a function

of energy. This was used to calculate the energy loss in 1mm steps (Figure 4.5b), using the

equation

E2 = E1 − dE
dx

∗ 1mm.

(4.2)

Both experimental and calculated energy loss curves were normalized by dividing each

curve by their respective areas and the ratio between the two curves was used to differentiate

fragments. Figure 4.6 shows an example of this ratio with one experimentally measured

60

energy loss curve. The ratio between experimental and calculated energy loss curves will be

analysed.

Figure 4.7a shows the energy loss ratios for fission fragments. Although there are not

visible discrete bands, it is clear that there is separation in the energy loss curves, with the
greatest separation at ∼50mm. A series of gates on range were applied to this plot and

projected onto the Y-axis in order to differentiate between fragments. Figure 4.7b shows an

example with a range gate of 45-55mm.

If the range ∆R/R and energy ∆E/E resolution of the order of ∼1-2% can be achieved in

the p-ATTPC, it should be possible to determine the Z-value of individual particles. Figure

4.7b shows that this resolution is being approached. The Cf source makes it difficult to obtain

quantitative information due to the broad ranges of A, Z, and kinetic energy that comes with

spontaneous fission sources as well as the energy degradation of the fission fragments as they

travel through the source. One solution is to conduct an experiment with a small accelerator

that can provide beams with well determined A, Z, and energy.

61

(a)

(b)

Figure 4.5: Left: Calculated energy loss of 102Ru at 100MeV as a function of energy fitted
with a polynomial function. Right: Energy loss of 102Ru as a function of range interpolated
from the polynomial fit from (a).

62

Figure 4.6: Ratio of experimentally measured energy loss curve of a fission fragment with
the calculated energy loss curve (SRIM) of 102Ru at 100MeV.

63

(a)

(b)

Figure 4.7: Left: Ratio of experimental and calculated (SRIM) energy loss curves of fission
fragments. Right: Y-projected data of (a) between the ranges of 45-55cm

64

Chapter 5

Australian National University

The motivation of the experiments detailed in this dissertation was to study the possibility

of enhancements of heavy-ion fusion-fission cross sections for more neutron-rich beams in

systems nearby to the 32,38S + 208Pb reaction. The 46K + 208Pb fusion-fission measure-

ment with the AT-TPC determined the cross section for a neutron-rich reaction, however

the measurement of a more stable beam fusion-fission reaction was needed to make a con-

clusion about possible cross section enhancements. Therefore the 39K + 208Pb fusion-fission

excitation function was measured at Australian National University (ANU) with the use of

the Nuclear Reaction Dynamics Group’s CUBE detector. Another nearby system, 40,48Ca

+ 144Sm, was also chosen for fusion-fission excitation function measurement. This chapter

details these experiments at ANU with the CUBE detector and the analysis techniques used

to determine fusion-fission cross sections.

5.1 Heavy Ion Accelerator

Two complimentary experiments were performed at the Australian National University

(ANU) Heavy Ion Accelerator Facility using the 14UD tandem accelerator. The 14UD is a

National Electrostatics Corporation Pelletron accelerator that uses an electric field generated

by an accelerating voltage VA of up to 15MV to accelerate particles for nuclear physics and

applied experiments [84, 85].

65

Negative ions are produced using a SNICS (Source of Negative Ions by Caesium Sputter-

ing)[86]. A Cs oven produces Cs vapour that is then introduced into an ion source chamber.

These Cs atoms can become positively ionized when coming in contact with a hot ionizer. As

a result, the positively charged Cs ions accelerate towards a water cooled cathode containing

a solid sample of the desired beam species. Atoms and ions are sputtered out of the sample

and gain a negative charge by collecting an electron from the layer of condensed neutral Cs
atoms on the surface of the cathode. These negative 1− ions are repelled by the cathode,

refocused, and transported by a positively biased extractor electrode[87, 88]. Then the beam

is accelerated and transported to a mass selection magnet.

The mass selection magnet consists of a dipole magnet that separates beam particles by

momentum over charge. After this selection, the beam enters an accelerator tube located in

the 14UD tank where it undergoes acceleration. The beam accelerates towards a positive high

voltage terminal in the middle of the tank and then passes through a carbon stripping foil,

which changes the beam from negatively charged to positively charged with a distribution

of charge states (Q1+, 2+, .., Q = Z)[89, 90]. The now positively charged beam accelerates
away from the high voltage terminal and enters a 90 ◦ energy selection magnet, where only a

specific charge state is selected [91]. The final energy exiting the accelerator is (1 + Q+)VA.

The beam can either be sent to a superconducting LINAC for further acceleration or directly

to the experimental area. In these experiments, the beam bypassed the LINAC and went

directly to the CUBE detector.

66

Figure 5.1: Schematic view of the ANU Heavy Ion Accerlator Facility beam line

67

5.2 Structure of CUBE Detector

The CUBE detector [92], operated by the reaction dynamics group located at the Australia

National University, is a binary fission spectrometer that reconstructs fission events using

the kinematical coincidence method [93]. It consists of both multi-wire proportional counters

(MWPC) and silicon monitor detectors. Charged particles are detected by three MWPC’s
located at 45◦, 90◦, and 135◦off the beam axis and at a distance of 180.0 - 195.0 mm. The

MWPC’s labelled “Front Det.” and “Back Det.” have a relatively large area of 279.0 mm

x 357.0 mm. The MWPC labelled “Small back Det.” covers roughly half the area as on

of the first two. Figure 5.2 shows the angular coverage of the MWPC’s. The MWPC’s

consists of horizontal and vertical anode wires sandwiching a cathode foil. The anode wires

are 20µm Tungsten wires coated with gold spaced every 1mm. The cathode foil is a 0.9µm
Mylar foil with a thin layer (40µg/cm−2) of gold evaporated onto each side. The cathode

foil is segmented (4 segments for the large detectors, 2 for the small) in order to decrease

the capacitance and increase the pulse height of the signals.

The MWPC’s are filled with propane gas at 4 Torr. As a charged particle passes through

the detector, it ionizes the propane molecules and the resulting free electrons drift towards

the nearest anode wire. The electrons produce an avalanche in the high electric field near

the wires and generate a pulse that is delivered to a readout at the end of the wires. The

crossed wire anodes were used to determine the (X,Y) position and allow for the precise

measurement of the coordinates with a resolution down to 1mm (FWHM) [94, 95]. An

illustration of a MWCP used in the CUBE detector can be found in Figure 5.3

The signal from the particle passing through the cathode and the signal from the pulsed

beam RF are used to produce time of flight measurements of the beam. The charge collected

68

Figure 5.2: (a) Orientation of the front and back MWPCs with respect to the beam and
target (b) Orientation of the back and small back MWPCs with respect to the beam and
target

is proportional to the energy loss of the charged particle. After calibration, the energy loss

of the particle can be used to identify the Z of the particle using the Bethe-Bloch formula,

calculations from SRIM, or simulations from TRIM. The energy resolution of the detector is

not good enough to separate single Z values, but provides an estimate of the distribution. A

target ladder is mounted in the middle of the detector in the path of the beam, oriented at
60◦ to the beam axis in order to minimize the loss of reaction products through the target

and the target frame.

Two Si surface barrier detectors (monitors) are mounted symmetrically around the beam
axis at 25◦ or 30◦ with respect to the beam in order to measure elastically scattered beam

particles. The sum of the counts of the two detectors corrects for minor fluctuations in the

beam spot location. These monitors are used for target thickness measurements, absolute

cross section determination, and tuning the incident beam.

69

Figure 5.3: Schematic breakdown of the front or back MWPC.

5.3 Electronics and Data Acquisition

The signals from the MWPCs and silicon monitors are processed by the electronic setup

in Figure 5.4. The timing signal from the cathode of the front MWPC was in coincidence

with the back and small back MWPC and was then used in an OR logic gate with the

signals of the two silicon monitors. The output of the OR was sent to the DAQ as a trigger

signal. The coincidence of the timing signals between the front and back MWPCs efficiently

decrease the otherwise high trigger rate caused by elastically scattered particles into the front

detector. The signal of the Si monitors is sent to a scaler as well as each MWPC’s signal.

The difference between the scalers and the signal processed in the data acquisition is then

used to determine DAQ dead time. Once a trigger is issued, the DAQ uses analog-to-digital

converters (ADC) and time-to-digital converters (TDC) to process the detector data and

stores all channels from all ADC and TDC modules in an event.

70

Figure 5.4: Electronics schematic of signal processing from the MWPCs and monitors to the
DAQ.

5.4 Analyzing CUBE Data

Data taken from the CUBE detector is analyzed by a fission analysis program ‘dacube’,

which was developed by the reaction dynamics group at ANU [96]. The program is a pack-

age of C/C++ codes with ROOT [97] libraries that reconstructs events, extracts reaction

kinematics, processes event selection, and calculates absolute cross-sections. The following

section describes the procedure ‘dacube’ to process CUBE data.

71

Figure 5.5: Full active area of the front MWPC in Cartesian coordinates

5.4.1 Track Reconstruction

5.4.1.1 Position Transformation

The position of the particles is obtained from the crossing wire planes in each quadrant.

These planes are connected to a delay line that is then read out at each side. This position

is transformed into a physical position by a position calibration, which is done by matching

the physical dimensions of each MWPC to the full active area recorded by the DAQ. Figure

5.5 shows an example of this position calibration with the back MWPC.

The 2D coordinates of each MWPC are then transformed into a 3D Cartesian coordinate

reference frame with respect to the target using the known positions of the detectors in space,

where the z axis aligns with the beam. From here these coordinates are transformed into

spherical coordinates, where the radial coordinate r is the distance between the interaction

of the particle with the MWCP and the origin (target) [98]. Figure 5.6 shows the full active

area of all 3 MWCPs in spherical coordinates.

72

Figure 5.6: Full active area of all three MWPCs in polar coordinates

5.4.1.2 Time of Flight

The time of flight for these experiments is defined as the time of interaction between the

target foil (tinter) and the cathode foil in the MWPCs (tarr

i

). As mentioned in section 5.2,

the information obtained from the experiment is the time between the RF pulse and the

time of interaction with the cathode foil. The true ToF can be extracted by removing the

offset time between the RF signal and the arrival of the beam as well as the offset delay

between each detector by:

T oF1 = T1 − T0 − δT1
T oF2 = T2 − T0 − δT2
T oF3 = T3 − T0 − δT3

(5.1)

Figure 5.7 shows a diagram of the timing for the experiment. During analysis, δT1 is set

to zero and T0 is set to yield the correct time for ToF1. δT2 and δT2 are the offset times

between detectors 2 and 1 and 3 and 1 respectively. (T0, δT2, δT2) are dependent on velocity

73

and this determination is described in Section 5.4.2.3.

Figure 5.7: Timing of particle detection in MWPCs in conjunction with RF signal and
beam-target time.

5.4.2 Kinematic Reconstruction

5.4.2.1 Velocity

Figure 5.8 shows the velocity vectors of a binary fission event and they can be broken down

into parallel and perpendicular components relative to the beam axis:

wi = vicosθi

ui = visinθi

74

(5.2)

(5.3)

Figure 5.8: Vector breakdown of fission fragment velocities, with the origin at the reaction
center on the beam axis.

Disregarding particle evaporation during fission and incomplete fusion, it can be approx-
imated that fission fragments are emitted at 180◦ to each other in the center of mass frame

for binary fission events. The sum of their momentum is always zero, yielding the equation:

ui

w1 − vpar

= −

u2

w2 − vpar

(5.4)

where vpar is the velocity of the compound nucleus parallel to the beam. This equation

can be rearranged to obtain vpar using the measured quantities vi and θi, giving the equation:

vpar =

v1v2sin(θ1 + θ2)
v1sinθ1 + v2sinθ2

The perpendicular velocity of the compound nucleus can be represented by

vperp =

(cid:113)

u1u2sinφ12
2 − 2u1u2cosφ12

u2
1 + u2

75

(5.5)

(5.6)

where φ12 = φ1 + φ2 are the folding angles perpendicular to the reaction plane. While it

is possible to have small perpendicular velocities due to particle emission, measured values

are expected to be centered around zero for full momentum transfer (FMT) fusion reactions.

5.4.2.2 Mass Ratio

The mass ratio of the fission fragments can be described as the mass of one fragment relative

to the combined masses of both fragments and can be calculated using conservation of linear

momentum. :

A1v1cm = A2v2cm

Rearranging this equation and using the definition of mass ratio yields:

MR =

A1

A1 + A2

=

v1cm

v1cm + v2cm

(5.7)

(5.8)

Using the mass ratio, the total pre-neutron emission kinetic energy of the fission fragments

can be estimated assuming both masses sum to the compound nucleus mass by:

2(cid:88)

i=1

1
2

miv2

icm

< T KE >=

(5.9)

5.4.2.3 Time Calibration

The timing parameters discussed in Section 5.4.1.2 were determined by the calculated values

of the velocities of the binary fission fragments. These parameters are considered optimized

when the velocities meet two requirements:

1. < vperp >= 0

76

The average velocity perpendicular to the reaction plane should be zero for FMT binary

fission events. There is the possibility to have small components due to the emission of light

particles, but this will not have an effect on mass ratio calculation.

2. < vpar > −vCN = 0

As a direct result of the first requirement, the average velocity parallel to the reaction

plane should be equal to the velocity of the compound nucleus in the center of mass frame.

The velocity of the compound nucleus can be calculated from experimental values by:

(cid:115)

vCN = 0.982

Ap

Ap + At

2Elab
Ap

(5.10)

where Elab is the energy of the beam in the laboratory frame in MeV and Ap and At

are the masses of the projectile and target respectively. The constant 0.982 is a conversion

factor for converting atomic mass units to MeV/c2.

Figure 5.9 shows a plot of these two requirements with optimized timing parameters for

the 48Ca + 144Sm reaction at 201.0 MeV that was studied for this work.

5.4.3 Fission Selection

With proper reconstruction of events using the methods described in the previous sections,

fission events need to be selected out of the pool of binary events. These binary events can

consist of elastically scattered events with ejected target nuclei, reactions with the target

backing or impurities within the target, coincidences with a single fission fragment and

beam particle, and the desired binary fission event.

The cross-section for an elastically scattered event is orders of magnitude higher than

a binary fission event for these types of reactions. The calculated velocity of the fissioning

77

Figure 5.9: Experimentally derived perpendicular fission fragment velocities (vperp) as a
function of parallel velocity (vpar) subtracted the velocity of the compound nucleus (vcn)
after time parameter optimization for the 48Ca + 144Sm reaction at 201.0 MeV. This data
includes fission events as well as elastically scattered events.

compound nucleus and the reconstructed velocities of both the elastically scattered particles

and fission fragments are approximately equal, so elastic events must be differentiated by

examining the mass ratio and TKE. Figure 5.10a shows the distinction between the two types

of events, where the elastically scattered events are the high density regions at low and high

mass ratio, corresponding with the light mass beam and heavy mass target. The fission events

occur between these two regions. Any reactions with the target backing or impurities in the

target will subsequently have reconstructed velocities much different from the calculated

velocity of the compound nucleus. As a result, these reactions can be differentiated as

vpar/vCN will have a value other than 1.

Variations of the deduced TKE from the expected TKE can also help select binary fission

events from random coincidence events, as well as ensuring proper reconstruction of fission

events. The expected TKE comes from Viola systematics [40], which assumes the projectile

78

kinematic energy is fully dissipated in the compound nucleus. The estimated TKE can be

calculated using Viola systematics using the equation

T KEV iola = 0.1189

Z2

CN
1/3
CN

A

+ 7.3(M eV )

(5.11)

and can be rearranged into an estimate that depends on mass ratio [99]

T KEV iola(MR) =

0.789(1 − MR)Z2
R + (1 − MR)1/3]A

CN

1/3

[M

1/3
CN

(5.12)

A comparison of the experimental TKE to the estimated TKEV iola should result in a

value close to 1 (TKE/TKEV iola = RTKE = 1). Figure 5.10b shows this comparison of TKE

values with the mass ratio. The fission fragments within the predicted mass ratio region lie

along the RTKE = 1 region. The elastically scattered and quasi-fission events are represented

with high intensity near the high and low mass ratio regions. They are elongated along the

TKE axis due to the poor energy resolution of the MWPCs; these events are significantly

faster than fission fragments, resulting in less energy loss in the MWPCs. Events that consist

of a fission fragment in coincident with a fast, projectile-like particle are observed to appear

above fission events with RTKE > 1.

Using these visual aids, a series of gates can be applied to isolate the binary fission events

used in total cross-section calculation and can be seen applied in Figures 5.10a,b with red

polygons.

79

Figure 5.10: Visual cuts applied to mass ratio MR spectra in order to isolate fission fragments

80

Chapter 6

Cross Section Determination

In order to deduce the capture cross-section, all exit channels from the compound nucleus

need to be taken into account, including fission, evaporation, and quasi-fission. This chapter

focuses on extrapolating the fission cross-sections over the full angular range and integrat-

ing to get the total fission cross-section, and incorporating the evaporation cross-section to

determine the total capture cross-section.

6.1 Differential Cross Section

The differential cross section in units of mb/sr for a reaction at a specific angle and beam

energy can be defined as

dσ
dΩ

(θ, E) =

N (θ, E)
IpNtdΩ

(6.1)

where N(θ, E) is the number of particles hitting the detector at a specific angle θ and beam

energy E, Ip is the number of incoming beam particles, Nt is the target density (atoms/cm2),

and dΩ is the solid angle (sr) [100]. Due to the CUBE detector’s large angular coverage and

position sensitivity, the solid angle can be assigned to angle bins within the total coverage

(Figure 5.6) and can be written as

81

(cid:90) (cid:90)

dΩcube =

sinθdθdφ ≈ sinθc∆θ∆φ

(6.2)

where θc is the center degree of a bin with a width ∆θ. The silicon monitor detectors are

not as large and do not have position sensitivity and as such cannot be represented in this

way.

Using Equation 6.1, one can write the differential cross sections for the CUBE detectors

and the silicon monitors as

dσf is
dΩcube

(θc, E) =

N f is

cube(θc, E)

IpNtsinθc∆θ∆φ

dσel
dΩmon

(θm, E) =

N el
mon(θm, E)
IpNtdΩmon

(6.3)

(6.4)

The monitors detect elastically scattered beam particles at forward angles (el), where

θm is the monitor angle, and the CUBE detectors can detect both fission fragments and

elastically scattered particles (f is).

The ratio of the differential cross sections between detectors can be taken and rearranged

to give the fission differential cross section

dσf is
dΩcube

(θc, E) =

N f is
cube
N el

mon

dσel
dΩmon

(θm, E)

dΩmon

sinθc∆θ∆φ

and then multiplied by 2πsinθc to give the angular cross section

dσf is
dθcube

(θc, E) =

N f is
cube
N el

mon

dσel
dΩmon

(θm, E)

82

(cid:124)

(cid:125)

2πdΩmon

∆θ∆φ

(cid:123)(cid:122)

S(θ)

(6.5)

(6.6)

This last term, denoted S(θ), is labelled as the normalization constant per bin and is

determined by measuring the Rutherford scattering in both the CUBE detectors and silicon

monitors at an energy below the fusion barrier. Equation 6.6 can be rearranged to solve for

the normalization constant by replacing f is with el and adding cal for calibration,

(cid:32)

(cid:33)

(cid:32)

(cid:33)

dσcal
el
dΩmon

S(θ) =

N el,cal
mon
N el,cal
cube

dσcal
el
dΩcube

(θc, E)

/

2πsinθc

(6.7)

It is important that when using Equation 6.7 in Equation 6.6 for cross section calculation,

the widths of the angular bins ∆θ and ∆φ must be equivalent.

6.2 Cross Section Code

This section outlines the process of implementing Equation 6.6 in the analysis by resolving

all of the components involved.

6.2.1 Establishing Variables

In order to evaluate the equations in the previous sections, certain variables need to be

defined.

1. Angle bin width (∆θ).

The bin width depends on the statistics of a run along with the solid angle normal-

ization, which is dependent on the type of reaction. For light systems, the angular
distribution for fusion-fission does not vary drastically with angle, so typically 5◦ bins

are used[101]. Heavy reactions, such as in this experiment, tend to have a more drastic
change in angular distribution. As a result, 3◦ bins were used.

83

2. Elastic scattering on the silicon monitors (Nmon).

As mentioned in Section 5.2, two silicon monitor detectors are mounted at forward
angles (θm = 30◦). The sum of these two yields resolves any issue with variations in

beam spot position or entry angle to the first order.

3. Correction of dead time (Nmon and Ncube)

The DAQ used for data collection has a certain dead time which needs to be accounted

for. Figure 5.4 shows the signals from the monitors and MWPCs go to both the DAQ

as well as a scaler module. The ratio of the number of counts from each yields a dead

time correction factor that is then applied to both Nmon and Ncube.

4. Normalization constant per bin S(θ).

This constant is determined by performing calibration runs below the fusion barrier.

These runs were performed using one MWPC at a time and scaled to the back detector

due to differences in time of run and beam current. The angular coverage of the

detectors and the normalization constant can be seen in Figure 6.1.

6.2.2 Lab Frame to Center of Mass Frame

The angular cross sections are evaluated event by event in the lab frame and then converted

to the center of mass frame. The reason for this is two-fold: 1) The solid angles and

normalization constant are measured in the lab frame. This eliminates any unnecessary

transformations that could lead to potential error, and 2) multiple lab angle bins can occupy

a single center of mass bin for reactions with a large range of mass ratios. By making the

transformation event-by-event, this eliminates the potential for round-off error due to the

84

binning effect. Figure 6.1 shows the lab to center of mass transformation. It is important to
note that the nearly full detection in the lab frame has a coverage of about 90◦-160◦ in the
center of mass frame. Since fission angular distributions are symmetric with respect to 90◦

in the center-of-mass frame, the events can be reflected over a “mirror line”

6.2.3 Mass-Angle Distributions (MADs)

Figure 6.2 shows a plot of the normalized fission events seen by the back detector for a run,

specifically the mass ratios and angles of fragments. It is important to note that the DAQ

only records an event when there is a coincidence between the back and front detectors or

the small back and front detectors, as a result there will be complimentary fission fragment

recorded by the front detector. Examples of this can be plotted with black squares and white

circles. If left unchecked, this would produce an excess of identical points when reflected over

the “mirror line”. In order to remove this excess, events are rejected from the front detector

if they lie beyond the mirror line. An acceptable mirror line should run through (0.5,90) and

can be represented in Figure 6.2 by the dashed black line.

The angular distribution can be obtained by projecting the MAD plot onto the y-axis.

For mirrored plots and heavy systems, the mass ratio range should be restricted to either

MR > 0.5 or MR < 0.5. This is applied due to the notable presence of fast quasifission in

heavy systems, which has a strong correlation of emission angles and fragment mass.

85

6.2.4 Experimental Differential Cross Sections

6.3 Cross Section Extrapolation

The CUBE detectors cover only a specific angular range.

In order to calculate the total

fission cross section, the differential cross sections obtained from the angular coverage of the

CUBE detectors need to be extrapolated. The method of extrapolation for this analysis relies

on the transition state model (TSM) introduced in Section 2.2 and utilized in Section 3.6.4.

Due to the broader range of angular cross sections in these data compared to Section 3.6.4,

the application of the TSM is slightly altered. The fission angular distribution, assuming

the projectile and target spins are zero and a Gaussian K distribution, can be expressed by

∞(cid:88)

W (θ) =

(2J + 1)TJ

J=0

J(cid:88)

K=−J

ρJ (K)|DJ

0,K (θ)|2

(6.8)

where ρJ (K) is are the density levels at the transition state and TJ is the transmission

coefficient for fusion of partial wave J. ρJ (K) can be expressed as



ρJ (K) ∝

exp(−K2/2K2
0 )

(cid:80)J
K=−J exp(−K2/2K2
0 )

,

0,

if K ≤ J

K > J

(6.9)

where the variance of the K distribution is expressed as K0 and is characterized by

K2

0 . The K distribution is assumed to be independent of J. K2

0 can be estimated from

the transition state as seen in Equation 3.11 Because these variables aren’t well known for

compound nuclei at the saddle point, K0 is used as a fitting parameter by adjusting the value

for a calculated J distribution until a minimum χ2 fit to the fission angular distribution was

met.

86

Figure 6.3 shows the fits of 40,48Ca + 144Sm and 39K + 208Pb over all experimental

energies using this method. The total fission cross sections are calculated by integrating the
fit from 90◦ to 180◦ and multiplying by 2πsinθcm.

87

Figure 6.1: (a) Scatter plot of θlabvs.θc.m. with only full momentum transfer (FMT) events.
The efficiency corrected yield ηf is
cube is represented on the z-axis. (b) The active area of the
small back and back detectors represented in spherical coordinates from an elastic scattering
calibration run; the results of which provide solid angle normalization coefficients S(θlab)
shown in (c).

88

Figure 6.2: Top: Experimental mass ratio data for 40Ca + 144Sm reaction with applied
mirror line. Bottom: Reflection of experimental mass ratio data across mirror line.

89

Figure 6.3: Fission angular distributions for 40,48Ca + 144Sm and 39K + 208Pb reactions
over all experimental energies.

90

 0 20 40 60 80 100 90 100 110 120 130 140 150 160 170dσ/dΩ [mb/sr]θCM [deg]39K + 208Pb Angular DistributionECM = 164.7 MeVECM = 169.1 MeVECM = 173.3 MeVECM = 177.5 MeVECM = 180.9 MeV 0 20 40 60 80 100 90 100 110 120 130 140 150 160 170dσ/dΩ [mb/sr]θCM [deg]40Ca + 144Sm Angular DistributionECM = 142.3 MeVECM = 144.7 MeVECM = 147.0 MeVECM = 148.2 MeVECM = 155.2 MeV 0 20 40 60 80 100 90 100 110 120 130 140 150 160 170dσ/dΩ [mb/sr]θCM [deg]48Ca + 144Sm Angular DistributionECM = 136.7 MeVECM = 138.7 MeVECM = 141.2 MeVECM = 143.3 MeVECM = 145.4 MeVECM = 147.9 MeVECM = 150.0 MeVECM = 152.1 MeVECM = 154.6 MeVChapter 7

Results

This section describes the processes to extract the total capture barriers and interaction radii

after the addition of evaporation residue cross sections. The data are used for comparison

in reduced excitation functions, models, and competing fission modes.

7.1 Evaporation Residue

The total capture cross section can be described as the sum of the fission, evaporation

residue, and quasi-fission cross sections. The fission and quasi-fission cross sections cannot

be distinguished in the analysis and the evaporation residue cross sections were not measured.

Therefore the evaporation-residue cross-sections need to be estimated from another source

in order to calculate the fusion barrier and interaction radius properly. There have been

no evaporation residue cross-sections measured experimentally for the 39,46K + 208Pb and

40,48Ca + 144Sm reactions. Therefore theoretical models are needed. Two requirements that

need to be fulfilled in order to validate the calculation are that 1) it reproduces the previously

measured experimental fusion-evaporation residue cross-sections of the 28Si+164Er reaction

(the reaction generates the same compound nucleus, 192Pb, as the 48Ca + 144Sm reaction)

and 2) it reproduces experimental fusion-fission cross-sections of the reactions done in this

work. ER cross-sections for the 28Si+164Er reaction are shown below in Figure 7.1 using

a number of different Monte-Carlo calculations and are compared to experimental cross

91

Figure 7.1: Experimental ER cross sections measured by Hinde [102] with Monte Carlo
calculations, including PACE4 and implementations of the Decay of Excited Nuclei by the
Nuclear Reactions Video website and LISE++.

sections measured by Hinde et al. [102]. The implementation of the Decay of Excited Nuclei

implemented in LISE++ [103, 104], mentioned in Section 2.3.2, shows the best fit to the

experimental data, specifically at lower energies. This is important in determining the fusion

barrier, as the method for barrier extraction discussed in the next section is sensitive to cross

sections measured near the barrier energy.

The Monte-Carlo used by LISE++ for the 39K + 208Pb and 40,48Ca + 144Sm reactions

are shown in Figure 7.2. The calculated fission cross sections (black) are adjusted to fit

the experimental cross sections (green) by adjusting the Sierk fission barrier height and

the curvature parameter of the parabolic potential describing the fission barrier. The total

capture cross section (red) is the sum of the fusion-fission and fusion-evaporation (blue)

curves. For these reactions the calculated fusion-evaporation residue cross sections are orders

of magnitude smaller than the fusion-fission cross sections and will should not affect the

capture cross sections. Nevertheless, the calculated evaporation residue cross sections are

92

added to the measured fission cross sections at their respective energies.

7.2 Barrier Height and Interaction Radius Extraction

The barrier heights and interaction radii for the 39K + 208Pb and 40,48Ca + 144Sm reactions

were extracted from the capture cross sections (experimental fission + calculated evaporation

residue) using the 1/Ecm method seen in Figure 7.3. The classical equation for the fusion

cross section above the fusion barrier given in Equation 2.6 is fitted to the high energy

points above the barrier to be extracted. The inverse of the x-intercept of this fit yields

the experimental barrier heights and interaction radii. As mentioned in Section 2.1.1, this

function is for energies above the capture barrier. Therefore the deviation of the cross-

sections at lower energies at or below the barrier from the fitted function is due to quantum-

mechanical effects and cannot be included in the fit.

W. J. ´Swi¸atecki et al.[105] uses an empirical description to represent systematics of

experimental capture barriers as

VB = 0.85247z + 0.001361z2 − 0.00000223z3(M eV )

where the Coulomb barrier parameter z is

z =

Z1Z2
1/3
1 + A

A

1/3
2

(7.1)

(7.2)

Christensen et al.[106] uses an empirical method to derive the radius of the Coulomb

barrier as

93

Figure 7.2: Experimental fission cross sections for 39K + 208Pb and 40,48Ca + 144Sm re-
actions compared to calculated total capture, fusion-fission, and fusion-evaporation cross
sections from the Decay of Excited Nuclei Monte Carlo implemented by LISE++.

94

rB = 1.07(A

1/3
1/3
1 + A
2

) + 2.72(f m)

(7.3)

A comparison of measured and calculated barriers and interaction radii can be found in

Tables 7.1 and 7.2. Measured barriers are in good agreement with calculated values within

2σ and measured radii are between 1-3 fm less than calculated values. The uncertainties in

the measured values were evaluated from statistical uncertainties in the fitted cross sections

and the uncertainty of the fitted function.

Figure 7.3: Measured cross sections as a function of 1/Ecm fitting with the classical equa-
tion Eq. 2.6 with points high above the barrier. The inverse of the x-intercept yields the
experimental barrier height and interaction radius.

95

Capture Barriers (MeV)

System

Experiment

W. J. Swiatecki et al.

39K + 208Pb
40Ca + 144Sm
48Ca + 144Sm

167.0 ± 0.6
141.2 ± 0.2
140.0 ± 0.3

168.0

141.1

138.6

Table 7.1: Experimental barrier heights in comparison with calculated barriers [105].

Interaction Radius (fm)

System

Experiment

Christensen et al.

39K + 208Pb
40Ca + 144Sm
48Ca + 144Sm

9.7 ± 0.3
9.5 ± 0.1
11.1 ± 0.1

12.1

11.4

11.8

Table 7.2: Experimental interaction radii in comparison with calculated radii [106].

96

7.2.1 Reduced Excitation Functions

A comparison of the reduced excitation functions from the systems in this work, 40,48Ca

+ 144Sm, and the excitation functions measured by J. J. Kolata [107] in the neighboring

systems 40,48Ca + 124,132Sn using inverse kinematics can be found in Figure 7.4.

Figure 7.4: Comparison of the reduced excitation functions of this work, 40,48Ca + 144Sm,
and by J. J. Kolata, 40,48Ca + 124,132Sn. Top: Light ion is identical while changing the
heavy ion. Bottom: Heavy ion is the same with different light ions.

Above the barrier Ecm/VB > 1, there are no enhancements observed of the capture cross
for the 38S + 208P b reaction. For Ecm/VB ≤ 1
there is an enhancement of the capture cross sections for 40Ca compared to 48Ca (Figure 7.4

section like observed by Loveland et al.

bottom). Kolata et al. observed that the sub barrier enhancements of 40Ca + 124,132Sn are

due to positive Q-value neutron channels not present in the 48Ca + 124,132Sn systems. This

conclusion can be applied for the 40Ca + 144Sm reaction as well. Tables 7.3 and 7.4 shows the

97

presence of positive Q-value neutron channels for the 40Ca + 144Sm reaction not found with

48Ca + 144Sm, which explains the slight capture cross section enhancement at the barrier.

This enhancement is suppressed when compared with 124,132Sn, and this suppression can

be attributed to the number of open channels. The 40Ca + 144Sm reaction has one extra

positive Q-value neutron channel in comparison to the 48Ca + 144Sm reaction. J. J. Kolata

observed that there are more many more for the 40Ca + 124,132Sn reactions, resulting in a

higher enhancement.

40Ca + 144Sm

48Ca + 144Sm

+1p
+2p
+1n
+2n

+1p1n
+2p2n

-5.2
-5.8
-2.2
+0.7
-3.5
+5

+3.3
+11.2
-5.4
-7.6
-0.5
+7.5

Table 7.3: Q-values for neutron and proton pick-up channels from the heavy to the light
reaction partner.

40Ca + 144Sm

48Ca + 144Sm

-1p
-2p
-1n
-2n

-1p1n
-2p2n

-5.0
-15.5
-8.8
-13.7
-11.0
-10.3

-12.5
-20.7
-3.2
-2.0
-13.7
-17.2

Table 7.4: Q-values for neutron and proton stripping channels from the light to the heavy
reaction partner.

98

7.2.2 Competing Fission Modes

Tseckhanovich et al.[108] observed competition between symmetric and asymmetric fission

modes for the 36Ar + 142Nd reaction by deducing fragment distributions from measured

fragment velocities. Motivated by these observations, a similar analysis was done for the

40,48Ca + 144Sm reactions and an example is demonstrated in Figure 7.5. The TKE spec-

trum, reconstructed in Section 5.4.2.2, for these reactions at different beam energies show a

slight skew that can only be fitted by a two-Gaussian distribution. This fit reveals two TKE

components, T KElow and T KEhigh, which are linked to the symmetric and asymmetric

fission modes. This can be illustrated by the contrast of the shape of the partial mass dis-

tributions reconstructed in the regions above T KEhigh and below T KElow and projected

onto the mass axis (Fig 7.5 bottom). The best fit description of these partial mass distri-

butions are obtained by either one- or two-Gaussian fits, where a one-Gaussian fit implies a

symmetric fission mode and a two-Gaussian fit implies an asymmetric fission mode.

This difference in mass distributions between T KElow and T KEhigh is expected. The

kinetic energy follows T KE ∝

Z1Z2
1/3
1 +A

1/3
2

)

(A

. The highest kinetic energy that can be obtained

from this equation from a fissioning system is when Z1 = Z2, or mass symmetric mode. In
the mass asymmetric mode Z1 (cid:54)= Z2, resulting in a lower kinetic energy. This is observed
in the data, where the higher kinetic energy region T KEhigh has a more symmetric fission

mode and lower kinetic energy region T KElow has a more asymmetric fission mode.

7.2.3 Comparison to Models

A more quantitative interpretation can be obtained by comparing to models. The fission

fragment mass distributions (FFMD’s) for the 40,48Ca + 144Sm reactions are compared to

99

Monte Carlo codes GEF and Gemini (described in Section 2.3) in Figure 7.6. Gemini over-

estimates the symmetric mass yield and under-estimates the heavy fragment yield for the

40,48Ca + 144Sm reactions. GEF predicts an asymmetric yield for the 48Ca + 144Sm reaction

which isn’t reproduced by experiment.

The level density at the saddle point at low excitation energy is heavily influenced by

structure effects, which include shell effects and the Q-values of the splitting system. These

effects begin to disappear at high excitation energy of the compound nucleus. The inaccurate

predictions of Gemini for these compound nuclei at high excitation energies would mean that

Gemini has too low of a transition of level densities with shell effects (low excitation energy)

to level densities without these effects (high excitation energy).

100

Figure 7.5: Reconstructed TKE and mass distributions of 40Ca + 144Sm at 186 MeV. Top
left: TKE distribution with a two-Gaussian fit and partition into high and low TKE regions.
Top right: Fission fragment mass distribution with projected TKE partitions based on two-
Gaussian fit. Bottom: Projected fission fragment mass distributions above T KEhigh and
below T KElow with best fit descriptions by either one- or two-Gaussian fits.

101

Figure 7.6: Experimental fission fragment mass distributions compared to mass distributions
calculated by Monte Carlo codes GEF and Gemini for 40,48Ca + 144Sm

102

Chapter 8

Interpretation and Future Work

The results of fusion-fission experiments performed by Loveland et al. [9] showed important

enhancements to the capture cross sections when using more neutron-rich RIBs, in this case

38S. This opened the prospect of increasing the extremely small cross-sections for super-

heavy element formation and of creating more neutron-rich super-heavy isotopes, which are

studied to better understand nuclear stability, structure, and dynamics. The present study

of similar systems, 39,46K + 208Pb, 40,48Ca + 144Sm, and 40,48Ca + 124,132Sn, reveals that

medium to low neutron excess does not seem to affect the capture cross sections above the

barrier, and the results are consistent with Hinde et al [109].

The fusion excitation functions measured in this work found clear enhancements in the

capture cross sections at and below the barrier for less neutron rich beams due to positive

Q-value neutron pickup channels not present in the more neutron rich beams. Preliminary

results from FRESCO calculations reinforce this conclusion. Figure 8.1 shows a clear en-

hancement of the experimental cross section when compared to the calculated cross sections

without the inclusion of open transfer channels. Alternatively, Q-value calculations of much

more neutron-rich beams, 50Ca + 144Sm for example, result in positive Q-value proton

pickup channels, which could yield enhancements to capture cross sections at and below the

barrier as well.

The introduction of the Facility for Rare Isotope Beams (FRIB) at Michigan State Univer-

103

Figure 8.1: Experimental fission cross sections of 40Ca + 144Sm (blue circles) compared to
calculated cross sections using FRESCO (gold triangles) without coupling to open transfer
channels.

104

sity will produce high intensity neutron-rich RIBs which will enable the AT-TPC to measure

the fusion excitation functions of reactions with high neutron excess. The transition from

ReA3 to ReA6 and from ReA6 to ReA12 will enable the exploration of these fusion reactions

at higher energies and will also allow the use of ancillary detectors upstream of the AT-TPC

that can assist in beam identification.

The fusion-fission experiments utilizing the AT-TPC, 46K,19F + 208Pb, were the initial

assessment of this detector for use of future fusion-fission and fusion-evaporation measure-

ments using both solid and gas targets. The AT-TPC has been found to be ideal for highly

efficient anisotropy and fusion excitation function measurements. With more systematic

studies of detector conditions and data analysis, Z identification of fission fragments will

be possible and lead to the measurement of Z-distributions and quasi-fission studies. The

present experiments also led to the creation of a new analysis method for AT-TPC data that

will be a guide for future experiments measuring fusion-fission reactions.

Since the AT-TPC can measure total excitation functions when using a gas target, cap-

ture excitation function measurements can be expedited using the AT-TPC with a gaseous

heavy target. Future work using the AT-TPC detector can focus on heavy ion fusion-fission

reactions using a heavy gas target with neutron excess beam such as 54Ca or 53K, with in-
tensities of ∼102 pps, to explore fusion excitation functions at the limit of stability. Possible

heavy gas targets include high Z noble gases including 40Ar, 84Kr, 129,131,132Xe, and more

speculatively organometallic compounds such as tetraethyl- and tetramethyl-lead.

105

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