Development of (p,p′γ) detection capabilities at

iThemba LABS through the study of low-lying

E1 strength in 58Ni

by

Refilwe Emil Molaeng

A dissertation submitted to the Faculty of Science, University of

the Witwatersrand, Johannesburg, in fulfilment of the

requirements for the degree of Master of Science.

April, 2022



Declaration of authorship

I, Refilwe Emil Molaeng, hereby declare that this thesis titled Development

of (p,p′γ) detection capabilities at iThemba LABS through the study of

low-lying E1 strength in 58Ni is my own original work. It is being submitted

for the Degree of Master of Science to the University of the Witwatersrand, Jo-

hannesburg. It has not been submitted previously for any degree or examination

to any other university.

Signature:

Refilwe Emil Molaeng

Date: April 25, 2022

i



This work is dedicated to my loving parents, Goitsemang and Onkokile

Molaeng.

“Mmatla kgomo ya gaabo kodumela o etse mhata sediba”

A Tswana proverb

ii



Abstract

The principal aim of this study was to explore the (p,p′γ) detection capabilities at

0◦ at the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS)

in South Africa. This was done through the study of the low-lying dipole strength

of 58Ni with a proton beam of Ep = 80 MeV. The inelastically scattered protons

were measured with the K600 magnetic spectrometer positioned at 0◦, while the

subsequent γ decay was measured with the Ball of hyper-pure Germanium and

Lanthanum bromide detectors (BaGeL) at backward angles at distances ranging

from 17-20 cm away from the target.

Low-lying dipole strength, commonly known as the Pygmy Dipole Resonance

(PDR), appears in nuclei with neutron excess and can be pictured macroscopically

to result from oscillations of these excess neutrons against an inert core with

N ' Z. By its nature, the PDR may elucidate the formation of the neutron skin

in nuclei.

Proton inelastic scattering experiments at very small angles including 0◦ favour

electric dipole excitations allowing for the extraction of the full low-lying E1

strength. Detecting these protons in coincidence with the subsequent γ-ray decay

further improves the selectivity to very low spin transfer, allowing for resolved

excited states between 3 and 10 MeV and multipolarity identification. Moreover,

the high-energy resolution high-purity germanium detectors used in decay stud-

ies allow for an improvement of the standard energy resolutions obtainable with

magnetic spectrometers.

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The coincidence matrix obtained for this study indicated a decay to the ground

state and the first excited state. Since this experiment was an initial test of

the (p,p′γ) detection capabilities at 0◦, the beam time was limited and so, the

statistics obtained are low. As a result, the p-γ angular correlations and hence,

the spins and parities of the excited states, could not be determined. However,

a total of 19 excited states were identified in this work and were found to be in

agreement with those from the National Nuclear Data Center. Only two of these

states were identified to have Jπ = 1−. The results of this study were compared

with previous (α, α′γ) and (γ, γ′) studies and yielded good agreements overall.

iv



Acknowledgement

I would like to extend my gratitude to the National Research Foundation (NRF)

and the Marie Sklodowska-Curie Fellowship Programme (MSCFP) by the Inter-

national Atomic Energy Agency (IAEA) for providing me with funding for the

duration of my MSc. I am grateful to iThemba LABS for welcoming me into

their student community and for providing me with all the resources I needed to

successfully complete my project.

To my supervisors: Dr Lindsay Donaldson, Dr Luna Pellegri and Prof Iyabo Us-

man, thank you so much for adopting me as your academic child. Thank you for

your support and guidance. You have been the best teachers and amazing role

models. I would also like to thank the iThemba LABS K600 magnetic spectrome-

ter group members for always helping out. It was always comforting to know that

I am a part of this amazing and supportive team.

To my fellow students at Wits and iThemba LABS, thank you for always lending

a helping hand and for always pitching up for all the friendly get-togethers. The

friendships forged in these years will be forever cherished.

A million thank yous to my parents. To my father, thank you for being superman

every time my world needed saving. To my mother, thank you for being the

greatest teacher of love, compassion and fearlessness without even trying. To the

rest of my family and friends, thank you for being my cheerleaders. Your love and

support means a lot to me.

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Contents

Declaration i

Acknowledgement ii

Abstract iii

List of Figures ix

List of Tables xiv

1 Introduction 1

2 Literature review 6

2.1 Pygmy dipole resonance . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Techniques for excitation of the pygmy dipole resonance . . . . . 9

2.2.1 Nuclear Resonance Fluorescence (NRF) . . . . . . . . . . . 12

2.2.2 Hadronic probes . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Previous studies on the low-lying E1 strength in 58Ni . . . . . . . 19

2.3.1 58Ni(α, α′γ) with a NaI(TI) detector and the QMG/2 spec-

trograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.2 58Ni(α, α′γ) with HPGe detectors and the Big-Byte Spec-

trometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Experimental details and techniques 22

vi



3.1 iThemba LABS SSC laboratory . . . . . . . . . . . . . . . . . . . 23

3.2 K600 magnetic spectrometer . . . . . . . . . . . . . . . . . . . . . 25

3.2.1 Focal-plane detectors . . . . . . . . . . . . . . . . . . . . . 27

3.2.2 0◦ mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2.3 Dispersion matching . . . . . . . . . . . . . . . . . . . . . 33

3.2.4 Target ladder information . . . . . . . . . . . . . . . . . . 34

3.3 BaGeL detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4 Data acquisition system (DAQ) . . . . . . . . . . . . . . . . . . . 38

3.5 Estimation of the experiment runnning time . . . . . . . . . . . . 41

4 Data extraction and analysis 42

4.1 Data extraction and analysis of the K600 detection system . . . . 42

4.1.1 Particle identification . . . . . . . . . . . . . . . . . . . . . 42

4.1.2 Data extraction from the focal-plane detectors . . . . . . . 48

4.1.3 Energy calibration of the focal-plane detectors . . . . . . . 57

4.1.4 Background subtraction . . . . . . . . . . . . . . . . . . . 63

4.1.5 Energy resolution of the K600 magnetic spectrometer . . . 67

4.2 Data extraction and analysis of the BaGeL detection system. . . . 67

4.2.1 Energy calibration of the clover detectors . . . . . . . . . . 67

4.2.2 Gamma-ray time . . . . . . . . . . . . . . . . . . . . . . . 69

4.2.3 Addback procedure . . . . . . . . . . . . . . . . . . . . . . 71

5 Results and discussions 75

5.1 Description of the measured (p,p’γ) results . . . . . . . . . . . . . 75

5.1.1 The coincidence matrix . . . . . . . . . . . . . . . . . . . 75

5.2 Excitation-energy spectrum: Extraction of the PDR . . . . . . . . 82

5.3 Comparison with previous experiments . . . . . . . . . . . . . . . 83

5.3.1 Comparison with (α,α’γ) experiments . . . . . . . . . . . . 83

5.3.2 Comparison with a (γ,γ) experiments . . . . . . . . . . . . 86

vii



6 Conclusions and outlook 88

Bibliography 89

viii



List of Figures

2.1 Schematic distribution of E1 strength in an atomic nucleus showing

the splitting of the E1 strength into the Pygmy Dipole Resonance

(PDR) and the Giant Dipole Resonance (GDR) [19]. . . . . . . . 7

2.2 Comparison of transition densities of the low-lying E1 state for 56Ni

and 68Ni [32]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Schematic representation of the main experimental methods used

in the study of low-lying dipole strength and its decay modes [32]. 12

2.4 Two-dimensional matrix of the γ-ray decay energy versus the exci-

tation energy in 58Ni for θ= 135◦ [7]. . . . . . . . . . . . . . . . . 20

2.5 Two-dimensional matrix of the γ-ray decay energy versus the exci-

tation energy in 58Ni for θ= 135◦ [8]. . . . . . . . . . . . . . . . . 21

3.1 The layout of the iThemba LABS SSC laboratory [3]. . . . . . . . 24

3.2 Schematic representation of the K600 magnetic spectrometer posi-

tioned in the 0◦ mode [3]. It should be noted that the collimator

carousel has been replaced by a collimator ladder. . . . . . . . . . 26

3.3 An illustration of the collimator ladder and three collimators as-

sembled on the ladder [56]. . . . . . . . . . . . . . . . . . . . . . . 27

3.4 A schematic diagram of the K600 VDC focal-plane detectors [15]. 31

3.5 The focal-plane detector package of the K600 magnetic spectrom-

eter [60]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.6 Image of the viewer (ZnS) on the target ladder. . . . . . . . . . . 35

ix



3.7 The BaGeL frame in the K600 vault showing how the BaGeL struc-

ture opens and closes around the scattering chamber and how the

γ-ray detectors are arranged on the frame [12]. . . . . . . . . . . . 37

3.8 A schematic layout of the K600 trigger electronics [65]. . . . . . . 40

3.9 A schematic representation of the data acquisition system for the

BaGeL detectors [66]. . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1 A two-dimensional plot of the change in energy of the particles

in scintillator 1 as a function of their time-of-flight for an empty

target (top) and 24Mg (bottom). The CUTscint1vsTOF software

gate selecting the events of interest is shown with a solid black line. 45

4.2 A two-dimensional plot of the change in energy of the particles in

scintillator 2 as a function of their time-of-flight before the CUTscint1vsTOF

software gate was applied (top) and after it was applied (bottom).

The creation of another software gate (CUTscint2vsTOF) selecting

the events of interest is shown with a solid black line. . . . . . . . 46

4.3 A two-dimensional plot of the change in energy of the particles in

scintillator 1 vs their change in energy in scintillator 2 before the

TOF-related software gates were applied (top) and after they were

applied (bottom). An additional software gate further isolating the

protons of interest was created and is shown with a solid black line. 47

4.4 Comparison of the position spectra before (black) and after (blue)

the particle identification gates are applied. The peaks represents

the excited states of 24Mg. . . . . . . . . . . . . . . . . . . . . . . 48

4.5 TDC channel vs time histograms showing how the TDC channels

fail to align before (top) the application of cable-length offsets and

how the TDC channels align after (bottom) the offsets were imple-

mented. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

x



4.6 A comparison of the two-dimensional resolution spectra of the X1

(left) and U1 (right) wireplanes before (top) and after (bottom) the

LUT offsets were implemented. The y-axis represents the difference

of the slopes of the drift distances in the first and last wires of the

plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.7 A prominent excited state in the TOF vs focal-plane position scat-

ter plot for 24Mg with no lineshape correction applied (top), a third-

order polynomial fit on selected points along the lineshape shown

in the panel above (middle) and a straighter line with improved

resolution after the correction has been implemented (bottom). . . 55

4.8 Comparison of the focal-plane position spectrum without (top) and

with (bottom) lineshape correction. . . . . . . . . . . . . . . . . . 56

4.9 Comparison of the focal-plane position spectrum of the chained

runs before (top) and after (bottom) position offsets were imple-

mented. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.10 Focal-plane position spectra for 12C (top) and 24Mg (bottom). . . 59

4.11 A plot ofQBρ values against the K600 focal-plane position values of

24Mg and the second-degree polynomial fitted to the data is shown

in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.12 A representation of the reaction 1 + 2 → 3 + 4 in the laboratory

reference frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.13 The aquired excitation-energy spectrum for the 24Mg target (top)

and the 58Ni target (bottom). . . . . . . . . . . . . . . . . . . . . 63

4.14 Top: Y1 focal-plane projection. Bottom: A two dimensional plot

of the Y1 vs X1 focal-plane position. In both spectra, the black

region outlines the events of interest while the region in pink shows

the background that was subtracted to produce a background-free

excitation-energy spectrum. . . . . . . . . . . . . . . . . . . . . . 65

xi



4.15 The top panel shows the two background contributions in red and

green. The raw data are displayed in blue and the total background

which is subtracted from the raw data is displayed in blue. The

bottom panel shows the comparison of the background subtracted

spectrum (black) with the raw data (bue). . . . . . . . . . . . . . 66

4.16 The GammaRawADC spectrum for 24Mg. Top right: GammaRawADC

gated on the 6.432 MeV excitation energy of the K600 for one in-

dividual segment of the clover detectors. . . . . . . . . . . . . . . 68

4.17 The calibrated γ-energy spectra of 24Mg. Top right: γ energy gated

on the 6.432 MeV excitation energy of the K600. . . . . . . . . . . 69

4.18 Comparison of two Gammatime spectra of two different clover de-

tector segments before the offsets table was implemented (top) and

after the offsets table was implemented (bottom). . . . . . . . . . 70

4.19 The aligned Gammatime spectra of all 12 clover detectors with the

prompt peak identified for the addback procedure. The Full Width

at Half Maximum (FWHM) of the prompt peak is 37 ns. . . . . . 72

4.20 The comparison of gamma-energy spectra of the clover detectors

before (blue) and after (red) the addback procedure is implemented.

As can be observed in the zoomed in spectrum (top), the addback

procedure increased the photo efficiency. . . . . . . . . . . . . . . 74

5.1 A comparison of the coincidence matrix of the detected γ rays and

the measured excitation energy in 58Ni when gated on the prompt

peak (top) and random peak (bottom) of the Gammatime spectrum. 78

5.2 A comparison of the 0+ ground state γ energy spectrum when gated

on the prompt peaks and when gated on a random peak. The figure

shows that the coincidence events are indeed found at the prompt

peak of the Gammatime spectrum. . . . . . . . . . . . . . . . . . 79

xii



5.3 The excitation-energy spectra of the 58Ni(p,p’) and 58Ni(p,p’γ) re-

actions at θ = 0◦. The spectrum on top shows how the background

contribution is greatly reduced when the excitation energy is gated

on the γ detectors. . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.4 The excitation energy (left) and γ decay (right) spectra for 58Ni.

The plot also shows the corresponding peak of the excitation and

γ energies when gated on decay to the 0+ ground state and the 2+

first excited state. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.5 PDR region of 58Ni showing the two identified states with Jπ = 1−. 82

5.6 Comparison of the K600 (p,p’γ) and the KVI (α,α’) and (α,α’γ)

excitation-energy spectra [7]. . . . . . . . . . . . . . . . . . . . . . 84

5.7 Comparison of the K600 (p,p’γ) and the second KVI (α,α’γ) γ

decay spectra [8]. The arrows on the (p,p’γ) spectrum gives an

indication of where the peaks on the (α,α’γ) spectrum could be

found. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

xiii



List of Tables

3.1 The configuration of the BaGeL detectors. . . . . . . . . . . . . . 36

4.1 A summary of the 24Mg peak positions and sigma values before and

after the lineshape correction was implemented. . . . . . . . . . . 53

4.2 A summary of the 24Mg peak positions and sigma values before and

after the X1 position offsets were implemented. . . . . . . . . . . 54

4.3 The focal-plane position peak centroids and their assigned energies

from the NNDC [70] for the calibration targets, 12C and 24Mg. . . 58

4.4 A comparison of the excitation-energy values obtained for the focal-

plane spectra from the K600 magnetic spectrometer and those from

the NNDC [70] for 24Mg. . . . . . . . . . . . . . . . . . . . . . . . 62

4.5 A summary of the centroid, σEx and energy resolution,Eres, ob-

tained for each of the two most prominent 24Mg and 58Ni excitation-

energy peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.6 A summary of the addback efficiency of 58Ni after the addback

procedure. The spectrum was gated on decay to ground state and

first excited state. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.1 Transitions observed for decay to the ground state and the 2+
1 state.

A comparison to NNDC values [70] for 58Ni is also provided. . . . 77

5.2 A comparison of the excitation energy of the K600 magnetic spec-

trometer (p,p’γ) with the NNDC values [70] for 58Ni. . . . . . . . 83

5.3 Comparison of the K600 (p,p’γ) with (γ, γ) experiments [9, 10]. . . 87

xiv



Chapter 1

Introduction

The iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) is a

multidisciplinary research facility that focuses on the development, operation and

use of particle accelerators and related research equipment [1]. Experimental

nuclear structure and different reaction mechanisms at moderate-to-high excita-

tion energy and angular momentum have been studied extensively at this facility

for over 40 years. Light-ion scattering experiments are measured with the K600

magnetic spectrometer, while γ-ray spectroscopy has been largely performed with

the AFRican Omnipurpose Detector for Innovative Techniques and Experiments

(AFRODITE) γ-ray array. The K600 magnetic spectrometer is one of the only

two facilities in the world (the other being the Grand Raiden magnetic spectrom-

eter at the Research Center for Nuclear Physics (RCNP) in Japan) that is capable

of measuring inelastic reactions at extreme forward angles including 0◦ with high

energy-resolution (≤100 keV) at medium beam energies [2]. Such measurements

have the advantage of providing selectivity to low angular momentum transfer

excitations. This selectivity can be further improved by coupling the magnetic

spectrometers with γ-ray detectors, allowing for the detection of the subsequent γ-

ray decay. Studies of γ-ray emission provide direct and precise information about

the location and properties of the excited states, and so, this type of experimen-

1



tal set-up allows for the characterisation of the decay path for low multipolarity

excited states [3]. Measuring the subsequent γ decay in coincidence with the in-

elastically scattered probe allows for the effective separation of nearby excitations,

the determination of branching ratios, the assignment of multipolarities and the

investigation of the isospin character in nuclei of interest. γ-ray spectroscopy can

be performed with high-resolution semiconductor detectors such as High-Purity

Germanium (HPGe) detectors and high-efficiency scintillators such as LaBr3 de-

tectors.

The iThemba LABS facility has been developed constantly to improve the selec-

tivity of 0◦ measurements and include particle and γ-decay coincidence measure-

ments. In December 2012, an experimental test was conducted at the iThemba

LABS. Two HPGe detectors from the AFRODITE array were successfully coupled

with the K600 magnetic spectrometer for the detection of an (α, α′γ) reaction on

24Mg at 160 MeV. This experiment allowed for the separation of the excitation-

energy peaks of interest and the determination of branching ratios [4]. In 2016,

the spectrometer was coupled with 8 HPGe detectors from the AFRODITE array

to perform an (α, α’γ) reaction on deformed 154Sm at 120 MeV [5]. The results

showed that a detailed spectroscopy of E1 excitations below the particle threshold

was achievable [6].

In the present study, the iThemba LABS K600 magnetic spectrometer was coupled

with a ball of 12 high-resolution HPGe detectors from the AFRODITE array and

5 high-efficiency Cerium-Doped LaBr3 (LaBr3:Ce) detectors. This combination

of detectors is commonly referred to as the Ball of Germanium and Lanthanum

bromide detectors (BaGeL). The aim of the present study was to investigate the

(p,p’γ) detection capabilities at 0◦ at iThemba LABS using a beam with Ep=80

MeV. Since this set-up favours low-spin transfer, the study was conducted through

the investigation of low-lying E1 strength in 58Ni. This region of interest has been

studied previously in 58Ni using different techniques and probes [7–10], meaning

2



that the experimental results from the present study could be compared to these

pre-existing data.

The low-lying E1 nuclei response referred to above is commonly known as the

Pygmy Dipole Resonance (PDR). It is described as an out-of-phase oscillation of

the neutron skin and an N = Z core. It is attributed to a concentration of Jπ =

1− states located around the particle threshold in both stable and unstable nuclei.

This resonance lies well below the Giant Dipole Resonance (GDR), but it is some-

times challenging to distinguish them from each other owing to fragmentation and

fine structure [11]. Although theoretical and experimental evidence for this low-

lying strength has been established, a comprehensive picture of its systematics still

needs to be drawn. Therefore, continuous development of different experimental

techniques, such as the one developed in this study, is important to provide addi-

tional information for a better understanding of the properties and nature of the

PDR. The most important challenge in the interpretation of the PDR states is the

establishment of the characteristic transition densities and isospin character [12].

Using hadronic probes such as protons and alpha particles at energies of 80 MeV

and 120 MeV, respectively, can provide this information [12]. Furthermore, the

(p,p’γ) reaction is well suited for the study of nuclei with high neutron thresholds

such as 58Ni [13]. It also has improved sensitivity to the inner transition den-

sity in comparison with the (α, α′γ) reaction. This means that complementary

information to that obtained from α-particle inelastic scattering and electromag-

netic excitation can be obtained from the present study for the case of 58Ni if the

(p,p’γ) detection capabilities of the K600-plus-γ-array system are adequate at 0◦

at iThemba LABS.

As mentioned earlier, this study seeks to test and develop the (p,p’γ) detection

capabilities of the K600 magnetic spectrometer coupled to a Ball of HPGe LaBr3

detectors (BaGeL) at iThemba LABS. This was done through an investigation into

the low-lying E1 strength of 58Ni using proton inelastic scattering at Ep = 80 MeV.

3



To achieve the aim of this research, the following specific objectives were carried

out:

• A background-free (p,p’γ) excitation energy spectra for the 58Ni isotope

from the K600 magnetic spectrometer was acquired at zero degrees.

• A coincident γ-decay spectra of 58Ni was acquired from the γ detectors. In

this study, only the γ events from the HPGe detectors were analysed.

• A 2-dimensional matrix between the γ decay and the excitation energy was

constructed and decays to the ground state and the first excited state were

identified.

• The identified excited states were compared to those from the National

Nuclear Data Center (NNDC) and previous experiments, thus assigning

some to the PDR.

The layout of this dissertation is as follows:

Chapter 2 provides a detailed overview of the PDR. A brief discussion of various

experimental techniques and probes used to excite the PDR is provided. Previous

studies on the low-lying E1 strength in 58Ni are also presented.

Chapter 3 presents a detailed description of the experimental tools used and

procedures followed for the successful running of this experiment. This includes

all procedures from beam production to the detection of the inelastically scattered

protons and γ decay following de-excitation of the target. The data acquisition

system of the experiment is also described.

Chapter 4 gives the details of the offline extraction of the relevant experimental

information from the data files provided by the data acquisition system. Further

offline analysis steps taken to optimise the data are also presented.

4



Chapter 5 presents and discusses the analysed data. The coincidence matrix and

the corresponding excitation and γ-decay energies are presented. Comparisons to

previous studies that use α particles and γ rays as probes are also discussed.

Chapter 6 presents a summary of the results and their implications. Recom-

mendations for future experiments are also given.

5



Chapter 2

Literature review

The atomic nucleus (and the behaviour of its constituents) has attracted a lot of

interest from experimental and theoretical physicists since its discovery by Ernest

Rutherford in 1911. To study how the protons and neutrons comprising a nu-

cleus behave, the nucleus should be subjected to an external perturbation and

its response should be examined [14]. Many theories have been put forward to

explain the different observed phenomena and, in some cases, to predict certain

behaviours of the nucleus. For example, several resonance-like structures can be

observed when nuclei interact with photons, electrons, or hadrons [11]. These

resonances can be grouped into different categories of multipoles depending on

how the nucleus responds to the perturbation. One of the ways in which these

multipoles are categorised is by the angular momentum transfer (L). For example,

L = 0, 1 and 2 correspond to the monopole, dipole and quadrupole resonances, re-

spectively. A multipole pattern also exhibits isoscalar and/or isovector properties

depending on the isospin (T ) changes of the nucleus [15]. This chapter gives an

overview of the phenomenon of interest in this study, which is the PDR (Pygmy

Dipole Resonance), and the different techniques that are used to study it. Two

previous studies conducted on the PDR of 58Ni are also presented and discussed

in this chapter.

6



2.1 Pygmy dipole resonance

Experimental studies of resonances started more than 75 years ago when W. Bothe

and W. Gentner [16] observed an enhanced photo-dissociation cross section in

certain nuclei. A reasonable estimation of the resonance energy and cross section

was given by A. Migdal in a seminal work [17], where he explained the enhanced

cross section as a dipole oscillation of the protons against the neutrons in a nucleus.

Not long after that, G.C. Baldwin and G.S. Klaiber [18] managed to measure

photofission cross sections using Bremsstrahlung from a betatron and, for the first

time, the near-Lorentzian shape of the resonance referred to as the GDR (Giant

Dipole Resonace) was established. The observed cross section in the energy range

of the GDR exhausted nearly 100% of the sum rule for isovector electric dipole

transitions [11]. It was concluded that the remaining dipole strength had to be

small, which finally led to the idea of the lower-energy dipole strength commonly

known as the PDR. Figure 2.1 shows how the E1 strength splits into the PDR

and the GDR.

Figure 2.1: Schematic distribution of E1 strength in an atomic nucleus showing
the splitting of the E1 strength into the Pygmy Dipole Resonance (PDR) and the
Giant Dipole Resonance (GDR) [19].

A basic description of the electric dipole excitation is given by the three-fluid

7



hydrodynamical model. Within this model, two independent electric dipole res-

onances are naturally found, one originating from the out-of-phase oscillation of

all protons and neutrons (i.e. the GDR) and the other originating from the out-of

phase oscillation of the neutron skin and an N = Z core (i.e. the PDR) [20].

The PDR in particular is attributed to a concentration of Jπ = 1− states located

around the particle threshold in both stable and unstable nuclei [19,21]. PDR-like

excitations are expected to be enhanced in neutron-rich, unstable isotopes since

they have a larger neutron excess [19].

First investigations into the N = 82 isotones using (α, α′γ) reactions have indi-

cated, in comparison to photon scattering experiments, a splitting of the low-lying

dipole strength [22]. The strength separates into two groups: the lower-lying part,

which is excited by both isoscalar and isovector probes, and the high-energy part,

which is excited only by electromagnetic probes [23]. It has been proposed that

only the lower-lying part should be attributed to the PDR, i.e. an excitation mode

that is clearly distinct from the GDR in contrast to the higher-lying E1 strength

with transition densities on the way to the GDR. However, the amount of low-

lying dipole strength that should be assigned to the PDR in order to calculate

the total strength of this excitation mode is not yet known [22].

Like other multipole excitations, the electric dipole response of the atomic nuclei

is partly directly linked to certain properties of the underlying nuclear force [11].

Some theoretical studies of the PDR predict a relationship to the symmetry term

of the nuclear binding energy and the nuclear equation of state [24, 25]. The

PDR also has implications for neutron capture rates in astrophysical processes,

since the Jπ=1− states of the PDR act as doorway states in the neutron capture

process [26]. The process, commonly known as the r-process, is responsible for the

synthesis of about 50% of the elements that are heavier than iron. The equilibrium

properties of neutron stars can be modelled through the information carried by the

E1 strength distribution [27]. The nuclear dipole polarisability, αD, is suggested

8



by the studies of Energy Density Functionals (EDFs) using Skyrme forces [28] or

a relativistic framework [29] to be a possible observable that has implications on

both the neutron skin and symmetry energy. This polarisability can be described

as [30]:

αD =
h̄c

2π2e2

∫
σabs

ω2
dω (2.1)

where σabs is the photoabsorption cross section and ω is the photon energy. From

this expression, it is clear that the energy dependence of αD is inverse and thus αD

depends on the E1 strength at low energies. Furthermore, there are existing ad-

vanced theoretical methods that can give a realistic description of the E1 strength

distributions [31] and, therefore, different experimental techniques should also be

developed in order to confirm the predictions of those theoretical methods.

2.2 Techniques for excitation of the pygmy dipole

resonance

The N = Z core that oscillates against a neutron skin in a PDR mode can be

perceived as having an isospin symmetric core. As a result, the PDR should be

investigated using different isovector and isoscalar probes that are sensitive to the

isospin character of the nucleus [32]. The nature of the response of the states in

the PDR region can be obtained by studying the shape of the transition densities.

Transition densities give a reflection of the contribution of protons and neutrons to

a particular excitation. They can be used to theoretically calculate the oscillation

spatial distribution of vibrational states such as the E1 excitations, showcasing

the notion of isoscalar and isovector excitations. The isovector excitations are

associated with the relative out-of-phase motion of the neutrons versus protons

which results in a change of isospin (∆T = 1). The isoscalar excitations on

the other hand are illustrated by the neutron and proton transition densities of

the same sign, resulting in no change of isospin (∆T = 0). These microscopic

9



transition densities can be obtained from the wave function and the X and Y

amplitudes derived from Hartree-Fock (HF) plus Random-Phase Approximation

(RPA) calculations [32].

By observing the transition densities, it has been shown that, in low-lying regions,

nuclei with N = Z have no significant strength of the isovector component, while

for all other isotopes there is a significant isoscalar component. As a result,

depending on the N to Z ratio, the states belonging to the low-lying region will

have different contributions of the isovector and isoscalar components for different

isotopes. As an example, the different nature of these states in 56Ni and 68Ni are

illustrated in Fig. 2.2. Here, the proton and neutron, and isovector (IV) and

isoscalar (IS) transition densities for the low-lying dipole states of 56Ni and 68Ni

are compared. At E = 12.10 MeV, the proton and neutron transition densities of

56Ni are completely in phase both inside the nucleus and on the surface, while the

IS is clearly dominating over the IV transition. The right panel (E = 10.41 MeV)

of 68Ni depicts the typical behaviour of the PDR where the protons and neutrons

are oscillating in phase inside the nucleus but out of phase on the surface. The

IS and IV transition densities have the same magnitude on the surface, while on

the inside of the nucleus, although in phase, the IS has the major contribution.

This illustration further proves that in order to extract the full strength of the

PDR, probes with relative contributions of the IS and IV components should be

used. As such, protons with their Coulomb component and different mixtures

of isovector and isoscalar nuclear components are good candidates to probe the

PDR.

10



Figure 2.2: Comparison of transition densities of the low-lying E1 state for 56Ni
and 68Ni [32].

This section gives an overview of some of the major experimental techniques and

probes that are used in the study of the PDR. The most important aspects of these

different techniques along with their advantages and limitations are discussed. A

summary of different excitation mechanisms using different techniques as well as

the subsequent decay modes are provided in Fig. 2.3.

11



Figure 2.3: Schematic representation of the main experimental methods used in
the study of low-lying dipole strength and its decay modes [32].

2.2.1 Nuclear Resonance Fluorescence (NRF)

Low-lying E1 states are commonly studied through different Nuclear Resonance

Fluorescence (NRF) techniques using real-photon sources with endpoint energies

up to the particle thresholds [11]. Unlike in other inelastic scattering experiments,

photons are always fully absorbed in the excitation energy resulting in the for-

mation of a resonance state with high selectivity to multipolarity 1 [11]. The

excitation mechanism in this technique is well known. Therefore, extracting in-

trinsic properties like parity, spin or transition densities in a model-independent

way from the measured quantities such as the angular distribution and cross sec-

tion is possible. This subsection gives a brief description of four different NRF

techniques used to excite the PDR.

12



2.2.1.1 NRF with Bremsstrahlung

The Bremsstrahlung beam used in these experiments (Fig. 2.3(a)) is produced by

impinging an electron beam on a radiator target such as niobium. At ELBE [33]

and S-DALINAC [34], the maximum electron beam energy reached for NRF ex-

periments is 13.2 and 10 MeV, respectively. The maximum γ-ray energies that

can be reached depend on the energy of the electron beam. With Bremsstrahlung,

there is a continuous energy spectrum, which means that a large excitation-energy

region can be studied during one experimental setting. Even though the photon

spectrum is calibrated, this continuity also means that the exact energy of the

incident photon is not known and so, the energy of each event cannot be ex-

tracted [32]. However, the assumption is always that the detector measures the

decay of the populated states to the ground state since the photon is fully ab-

sorbed (i.e. the photon energy is directly equal to the excitation energy). This

assumption neglects the feeding from higher-lying states because the measured

quantity is the product of the photo-absorption cross section and the branching

ratio of the γ decay to the ground state. Statistical decay simulations may be

employed to correct branching ratios and the feeding scheme so that the photo-

absorption spectrum is reconstructed [32]. The most recent studies of the PDR

using Bremsstrahlung were conducted at ELBE [33] and the S-DALINAC [34]. In

both setups, a high photon flux and large-volume HPGe detectors were combined.

Excellent sensitivity for the energy of the PDR was provided through the addition

of active Compton suppression and massive shielding. NRF with Bremsstrahlung

beam has been used extensively to study the dipole strength distribution in stable

N = 82 isotones [35–38]. The finalised systematic survey on the PDR of these

isotones were conducted for a semimagic nucleus 136Xe [36]. For all these isotones,

a resonance-like fragmentation around the E1 was observed in the energy region

between 5 and 8 MeV. The analysis showed that this fragmetation decreased with

N , while the overall low-lying E1 increased. This was an indication that the total

13



strength is dependent on the N to Z ratio.

2.2.1.2 NRF with tagged photons

Improvements for the Bremsstrahlung experiments mentioned above can be devel-

oped using tagged photons (Fig. 2.3(b)). Tagged-photon beams are also produced

via Bremsstrahlung, but, in this case, one photon per electron is produced through

a sufficiently thin radiator target [32]. The energy of these tagged photons is mea-

sured from the coincidence between the scattered Bremsstrahlung electron and the

γ rays emitted by the nucleus of the radiator target. The detectors for the scat-

tered electrons are placed at 0◦ behind the radiator target. The following equation

is used to determine the remaining energy of the scattered electron Ee′

Eγ = E0 − Ee′ (2.2)

where Eγ is the energy of the produced photon and E0 is the energy of the electron

beam. From this equation, it is evident that the energy of the tagged photons also

shows characteristics of continuity but, because of the coincidence measurements,

the energy of the individual photons is known. The downside of this method is

that the rate at which electrons are detected behind the radiator is limited, which

means that the tagged-photon flux measured also becomes limited. Consequently,

the achievable reaction rate becomes small.

2.2.1.3 NRF with laser Compton backward scattering

The Laser Compton backward Scattering (LCS) photon beam is produced through

the collision of low-energy laser photons with highly relativistic electron beams. As

opposed to the previous NRF experiments discussed, LCS provides an adjustable

narrow-energy-range photon beam with mono-energies. The back-scattered pho-

14



tons (at 180◦) have the maximum energy given by approximately;

Eγ′ = 4γ2Elaser (2.3)

where γ is the relativistic Lorentz factor for the electrons and Elaser is the energy

of the initial laser photon. The polarisation of the laser beam is maintained in the

scattering process, which allows for the produced photon beam to be polarised

close to 100%. A polarised beam is advantageous for identifying the spin and

parity of the resonance state. This advantage has been exploited to establish the

E1 character of the PDR [39–41]. Currently, two operating facilities that use this

method are the Teras storage ring [42] and HIγS at Duke University [40,41,43]. At

the latter institution, the electrons drive a free electron laser, while at the former,

an external laser is used to provide photons. For the provision of high electron flux

for efficient Compton scattering, the electrons are stored in a ring in both facilities.

At HIγS, the rewards of this quasi-monoenergetic photon beam are utilised in a

γ3 setup (Fig. 2.3(c)) [44]. In this particular setup, cascade decays are measured

for the data where the photon beam energy is not the same as the detector γ-

ray energy. The investigation is typically aimed at the decay of several low-lying

states to the ground state. In some cases, γ−γ coincidence measurements may be

taken. In [40], a decay of the low-lying 2+ state to the ground state on 138Ba has

been observed. This means that this first excited state could have been populated

by the decay of a primary state at Ei = Eγ. However, those primary transitions

were not observed. It was concluded that it is possible that the majority of the

low-lying 2+ states could be as a result of inelastic cascades decay from the 1−

states. Thus the intensiy of decay of the 2+ could be used to extract the cross

sections for the 1− contribtions.

15



2.2.1.4 Self-absorption NRF

The first self-absorption experiment was performed using Bremsstrahlung photons

at the S-DALINAC to investigate the decay pattern of low-lying dipole states of

140Ce [45]. As opposed to the NRF techniques mentioned above where the decay

of the excited states to the ground state is measured, this technique measures

an absorption spectrum when a photon beam is bombarded on a thick absorber

(shown in Fig. 2.3(d)). The measured spectrum shows absorption lines at the

resonance energy of the target. A direct measurement of the ground-state transi-

tion width is evident for pronounced absorption lines. Furthermore, the intensity

of the transmitted spectrum is reduced with respect to the original one because

of the attenuation effects of the atoms.

2.2.2 Hadronic probes

NRF experiments are much more selective to low spin transfer but they do not

provide full access to the strength of the PDR in both stable and unstable nu-

clei [11]. Therefore, it becomes imperative to use different techniques to probe

different components of the nucleus. Alpha particles, owing to their isoscalar

internal structure, are appropriate for probing the isoscalar component of the nu-

cleus, while intermediate-energy protons will excite the Coulomb component and

different mixtures of isovector and isoscalar nuclear components. This makes these

hadronic probes, at intermediate energies of 80 MeV and 120 MeV, respectively,

a valuable complementary tool to populate the states of interest and make it easy

to distinguish between excitations belonging to the GDR and the PDR since the

PDR lies well below the GDR [11,32, 46] and the GDR above the PDR is a pure

isovector excitation. Selectivity to low-spin excitation using hadronic probes can

be achieved through particle-γ decay coincidence measurement. This method will

be further explained in Sec. 2.2.2.2.

16



2.2.2.1 Coulomb interactions with protons at 0◦

Relationships between cross sections and transition strength can be applied more

appropriately for cross sections measured at 0◦ than at larger angles, where cross

sections are extrapolated. Coulomb excitations at angles very close to zero (Fig.

2.3(e)) dominate the total cross sections of electric dipole states, while at angles

a little larger than 0◦, this cross section is dominated by nuclear excitation [32].

Through Coulomb excitations via proton inelastic scattering at intermediate en-

ergies, the resulting cross sections are well described by a one-step reaction with

DWBA calculations [12, 32]. Since the cross section is dominated by Coloumb

scattering at 0◦, it is possible to extract the E1 strength in a model-dependent

way. Protons at relativistic energy excite the nuclei via a virtual photon, thereby

allowing for investigation of the isovector component of the excitation. This pow-

erful technique was first performed successfully in 1991 at the Research Center

for Nuclear Physics, Osaka University [47], and is also widely used at iThemba

LABS [3]. Unlike NRF experiments or (γ, xn) reactions, protons probe the full

excitation strength for all the decay channels. At RCNP, a proton beam of 295

(392) MeV can produce a measured excitation-energy spectrum that goes from

≈ 5 (7) MeV to ≈ 23 (32) MeV. This implies that the measured cross section spans

excitation energies across the particle separation energy up to the high-energy tail

of the GDR. (p,p’) reactions at zero degrees have been constantly developed to

further increase sensitivity to low-spin excitations and reduce background contri-

butions significantly. As is the case in this study and for other hadronic probes

mentioned in Sec. 2.2.2 above, this can done by measuring the subsequent gamma

decay of the excited states in coincidence with the scattered protons.

2.2.2.2 Particle-γ coincidence

In this experimental technique, depicted in Fig. 2.3(f), a magnetic spectrometer

is used to analyse the scattered particles while γ-ray detectors are used to detect

17



the γ-ray decay in coincidence. This technique allows the experimentalist to

measure the energy loss of the inelastically scattered particles (which translates

to the excitation energy) and the subsequent γ decay of the excited nucleus.

The coincidence data can be sorted into a matrix where one axis represents the

energy loss of the probing particle during the scattering process, and the other

axis represents the energy of the γ rays measured in coincidence. The high energy-

resolution of the HPGe detectors used in this type of experiment is exploited to

determine the spin and parity of the excited states, while the known transitions

obtained by NRF measurements are used as complementary information. Possible

background contributions and cascade decays are excluded by selecting decays to

the ground state only. This is done by imposing the condition Ex ' Eγ.

The first study to perform coincidence measurements in order to overcome the

disadvantages introduced by hadronic probes was by T.D. Poelhekken et al. at

KVI Groningen [7]. In that experiment, a 120 MeV alpha beam was bombarded

on a 58Ni, 208Pb, 40Ca and 90Zr target. The inelastically scattered alpha particles

were measured with the QMG/2 spectrograph, while the subsequent γ decay was

measured with a NaI(TI) detector. The coincidence condition between the alpha

particles and γ rays favoured low-spin states and the scattering cross section for

discrete Jπ= 1− levels in the above-mentioned four nuclei could be determined.

The α − γ angular correlation could also be analysed. The 58Ni results of this

study along with those of a more recent study will be presented and discussed in

Sec. 2.3.1 and 2.3.2, respectively.

Another approach of studying the dipole strength distribution through particle-γ

coincidence was developed at the University of Oslo, Norway. In their experiments,

reactions such as (3He,αγ) and (3He,3He’γ) at beam energies between 30-45 MeV

are used to excite the low-lying strength. The scattered particles are measured

with Si telescopes while the subsequent γ decay is measured with NaI detectors

[48]. The Oslo method enables the experimentalist to simultaneously extract

18



the γ strength function and the level density from excitation-energy-tagged γ-ray

spectra [49,50]. The γ strength functions extracted using this method are strongly

affected by the E1 dipole response up to the to the neutron separation energy. The

states are excited through nuclear reactions, either transfer or inelastic scattering

at low energies. The coincidence matrix between the γ decay and the excitation

energy is constructed and the γ-ray strength function is determined through a

statistical decay model [48]. This γ-ray strength is interpreted as a representation

of the transition strength between the states with fixed multipolarity (usually

E1) [32]. The corresponding nuclear level density is calculated theoretically as an

additional fitting function.

2.3 Previous studies on the low-lying E1 strength

in 58Ni

The studies discussed in this section both employed coincidence techniques through

coupling of a magnetic spectrometer with γ detectors in order to explore the low-

lying strength in 58Ni. The identification of the isospin structure in the PDR,

especially the isoscalar contributions, is one of the most important pieces of infor-

mation that is needed to form a coherent picture of the PDR. Hence, in these two

studies, a beam of alpha particles (isoscalar probe) was used to probe the PDR.

In Sec. 5.3.1 of Chapter 5, the results of the current study will be compared with

those presented in this section.

2.3.1 58Ni(α, α′γ) with a NaI(TI) detector and the QMG/2

spectrograph

As mentioned in Sec. 2.2.2.2, an experiment was conducted by T.D. Poelhekken

et al. in 1992 to study the low-energy isoscalar E1 strength in 58Ni, 208Pb, 40Ca

and 90Zr. This study aimed to improve the selectivity to low-spin excitation

19



while giving access to the full isoscalar part of the PDR. The diagonal loci on the

two dimensional matrix of γ energy versus excitation energy shown in Fig. 2.4

illustrates a decay to the 0+ ground state and the 2+ first excited state of 58Ni.

This means that this study did not only favour excitations with low spin transfer

but it also allowed for individual decay channels to be studied by applying a gate

on the diagonal loci. The multipolarities of the excited states could be determined

from the established α-γ correlations. A total of 6 states between 6 MeV and 10

MeV were recorded and denoted as the Isoscalar Low Energy Dipole Resonance

(ISLEDR). As can be observed from the two-dimensional matrix, the diagonal loci

are relatively thick, indicating the poor energy resolution of the NaI detectors. As

a result, this setup could not be used where nuclei with high level densities were

of interest.

Figure 2.4: Two-dimensional matrix of the γ-ray decay energy versus the exci-
tation energy in 58Ni for θ= 135◦ [7].

20



2.3.2 58Ni(α, α′γ) with HPGe detectors and the Big-Byte

Spectrometer

In 2002 Harakeh, Wörtche, and Zilges proposed that the KVI Groningen Big-Byte

Spectrometer (BBS) be coupled with HPGe detectors [52]. A series of experiments

commenced from October 2002 using a larger array of high-volume HPGe detec-

tors after a successful feasibility test using two small-volume HPGe detectors. In

2006, Savran et al. [8] used the newly developed coincidence setup at the KVI

Groningen Big-Byte Spectrometer to perform an (α,α’γ) experiment at 136 MeV

on 58Ni. As can be seen from Fig. 2.5, the diagonal lines on the two-dimensional

matrix are relatively thin, indicating the improved energy resolutions of the HPGe

detectors. In addition, the detection of γ decay after proton/neutron emission has

been observed, which means that the decay of excitations above particle thresh-

old could be studied successfully. The results were found to be consistent with

those of Poelhekken et al. The same selectivity to low-spin transfer states can be

observed from the dominating transitions to the 0+ ground state and the 2+ first

excited state of 58Ni. The strong, isolated Jπ = 1− state at Ex=6.023 MeV has

been observed in both studies.

Figure 2.5: Two-dimensional matrix of the γ-ray decay energy versus the exci-
tation energy in 58Ni for θ= 135◦ [8].

21



Chapter 3

Experimental details and

techniques

A (p,p’γ) reaction was measured for the first time at iThemba LABS using the

K600 magnetic spectrometer coupled with BaGeL (an array of HPGe and LaBr

detectors). Over the years, (p,p’) reactions such as the one studied in [3] have been

used extensively at iThemba LABS to extract the excitation-energy spectrum of

various isotopes. However, these measurements did not provide any information

with regards to the decay of the excited states. In this study, the coincidence

condition between the K600 magnetic spectrometer and the γ-ray detectors al-

lowed for the simultaneous detection of the (p,p’) reaction and the subsequent γ

decay of the excited states. This chapter gives a description of the equipment and

techniques used in the experiment. The first section of this chapter (Sec. 3.1)

presents an overview of the iThemba LABS Separated Sector Cyclotron (SSC)

facility along with the injector cyclotrons used at iThemba LABS. Section 3.2

reports on the K600 magnetic spectrometer and the details related to the set-up

of the spectrometer (such as the 0◦ mode) that were critical for the successful

running of the experiment. Described in Sec. 3.3 is BaGeL and the specifica-

tions in relation to its configuration. The last section (Sec. 3.4) presents the

22



data acquisition system, which includes the electronics involved in obtaining the

experimental data files and the software used in the process.

3.1 iThemba LABS SSC laboratory

The K=200 SSC at iThemba LABS is a variable-energy machine that is capable of

accelerating protons to a maximum energy of 200 MeV. It provides ion beams to

the subatomic physics, radioisotope production and radiation biophysics research

groups. There are two main facilities that are used to perform subatomic physics

research, namely, the K600 magnetic spectrometer, which is the backbone of the

present study, and the γ-ray spectroscopy facility, which consists of a selection of γ-

ray detectors that can be arranged in different configurations. In this experiment,

an 80-MeV proton beam was extracted from the SSC and delivered to the K600

magnetic spectrometer through a high-resolution double monochromator system

that consists of the X, P1, P2 and S beamlines. A schematic representation of

the iThemba LABS SSC laboratory is given in Fig. 3.1. The K600 magnetic

spectrometer with its components will be explained in detail in Sec. 3.2.

The SSC consists of four identical C-shape sector magnets, each with a sector

angle of 34◦ [53]. The injection radius is 0.952 m and the extraction radius is

4.156 m. The pre-accelerated beam that is injected into the SSC is supplied

by one of two injector cyclotrons, namely, a K8 Solid Pole Cyclotron 1 (SPC1)

and a K11 Solid Pole Cyclotron 2 (SPC2). Both the pre-accelerators have four

magnetic sectors, two 90◦ dees (hollow semicircular structures) and an extraction

radius of 0.476 m [54]. As their names suggest, the K8 SPC1 and K11 SPC2 were

designed to accelerate protons to a maximum beam energy of 8 MeV and 11 MeV,

respectively. SPC1 has an internal Penning ionisation gauge ion source, while the

SPC2, which was used for the present experiment, uses either of the two available

ion sources, which are the Electron Cyclotron Resonance (ECR) ion source and

23



the polarised proton ion source. The beams are injected axially into the SPC2

with a spiral inflector. Three interchangeable inflectors are available to cover the

range of energies and species. A proton beam of 80 MeV was provided by the SSC

facility for the duration of this experiment. This specific beam energy is widely

regarded as an intermidiate energy in nuclear structure studies and was chosen

looking at the fact that at intermidiate energies, protons excite the Coulomb

and different mixtures of isovector and isoscalar nuclear components [11, 32, 46]

wheras protons at higher energies will mostly excite the isovector component of

the nucleus. Therefore at this intermidiate proton beam energy, we can get a

better picture on the region of the PDR since different mixtures of the nuclear

components will be accessed.

Figure 3.1: The layout of the iThemba LABS SSC laboratory [3].

24



3.2 K600 magnetic spectrometer

The K600 magnetic spectrometer of iThemba LABS is a large tracking system

that consists of magnets and position-sensitive detectors. A schematic represen-

tation of this spectrometer is provided in Fig. 3.2 and illustrates all the major

components involved in the detection process. It is composed of five main ele-

ments, namely, a quadrupole magnet, two dipole magnets (D1 and D2) and two

trim coils (K and H). The quadrupole is positioned at the entrance of the spec-

trometer and its purpose is to focus the beam vertically at the focal plane. It acts

as a converging ion-optical lens in one direction and a diverging ion-optical lens

in the perpendicular direction; that is, it focuses the beam in one direction and

defocuses it in the other.

Following the quadrupole magnet are the two dipoles. The function of these

dipole magnets is to allow the momentum dispersion of the charged particles at

the focal plane to be varied. This is done by changing the ratio of the magnetic

field of the two dipole magnets. In terms of ion-optical relations [55], a dipole

separates particles with different energies similar to how white light separates

into its components when it passes through a glass prism. The H-coil and the K-

coil are located inside D1 and D2, respectively, and they are used to fine tune the

horizontal focus at the focal plane. The different shapes of these coils gives rise

to different inherent magnetic characteristics. The shape of the K-coil results in

a dipole and a quadrupole component and is used to correct first-order kinematic

variations of momentum with the horizontal scattering angle θ (described by the

ion-optical variable (x | θ)). The shape of the H-coil gives rise to a dipole as well

as a hexapole component, and is used to correct second-order kinematic variations

(x | θ2).

At the turning axis of the spectrometer lies the scattering chamber. This is where

target materials are enclosed during experiments for collision with the beam from

25



the accelerator facility. The scattering chamber contains the target ladder with six

target positions. The inelastically scattered protons from the scattering chamber

are collimated by selecting one of the different collimator holders in the collimator

ladder, which is positioned at the entrance of the quadrupole magnet where the

collimator carousel used to be. A schematic representation of the collimator ladder

is shown in Fig. 3.3. In the absence of a collimator, the angular spread of the

proton beam would increase and result in scattering off other materials inside

the spectrometer. Consequently, a significant amount of background would be

observed in the focal-plane spectra.

Figure 3.2: Schematic representation of the K600 magnetic spectrometer posi-
tioned in the 0◦ mode [3]. It should be noted that the collimator carousel has
been replaced by a collimator ladder.

26



Figure 3.3: An illustration of the collimator ladder and three collimators assem-
bled on the ladder [56].

3.2.1 Focal-plane detectors

In ion-optical instruments, the plane where particles that are scattered at direct

angles originating from the same excited nucleus converge is called a focal plane.

A focal-plane detector is positioned in this region to detect ions across the fo-

cal plane in one or two dimensions [57]. The scattered ions can be detected in

any of the three available focal planes: high-dispersion, medium-dispersion or

low-dispersion. These different dispersion modes can be exploited depending on

the required conditions of different experiments such as the momentum range re-

quired. The momentum range of each focal plane is equivalent to the horizontal

size of the focal plane (x) divided by the dispersion (D). The high-dispersion

mode has access to a limited energy range but with a very high energy-resolution

(∼ 25 - 50 keV for (p,p’)). It is good for separation of the beam from the low-

est measurable excitation energy Ex, and it also allows access to lower excitation

energies (∼ 3.2 MeV) in 0◦ mode than would be achievable with the other dis-

persion modes [3]. The medium-dispersion mode has a fair range of accessible

27



momentum as well as good energy-resolution capabilities. In this mode, a larger

momentum range where pmax/pmin = 1.097 is covered when compared to the

high-dispersion mode where pmax/pmin = 1.063. This, as a result, allows for the

investigation of a broad excitation-energy region when the spectrometer is oper-

ated in medium-dispersion mode. The low-dispersion mode is suitable for use if

the experimentalist is interested in a large momentum range; however, this mode

gives the worst energy resolution among the three options. The high-dispersion

mode used in this experiment resulted in an accessible excitation-energy range of

approximately 3.5 - 10.5 MeV.

The two types of detectors that are responsible for the detection of the scattered

particles at the focal plane of the K600 magnetic spectrometer are MultiWire

Drift Chambers (MWDCs) and plastic scintillators.

3.2.1.1 Multiwire Drift Chambers

The operation of an MWDC is based on the ionisation of gas molecules by radi-

ation. When an energetic nuclear particle enters the hollow gas-filled chamber of

the detector, it ionises the medium gas and forms electron-ion pairs. An electric

field is applied to drive the electrons towards the electrode that is situated along

the center of the chamber while the positive ions are driven to the conductive

walls of the chamber. A load resistor is also connected to complete the circuit.

A potential drop across the load resistor is measured by a pulse height analyser

and is amplified. The measured electronic signal is proportional to the applied

voltage and the energy of the radiation, and depends on the type and pressure of

the gas medium [58].

The three original drift chambers, developed and built at iThemba LABS (1989-

1993) have two different geometrical configurations that correspond to the drift

direction of the electrons [59]. The first two drift chambers have the main drift

direction of electrons perpendicular to the signal-wire plane and are, therefore,

28



called the Vertical Drift Chambers (VDCs). In the third drift chamber, the elec-

trons drift in the plane of the signal wires and it is, therefore, called the Horizontal

Drift Chamber (HDC). The two VDCs are used to take measurements of the po-

sition along the length of the focal plane as well as the angle at which a charged

particle crosses the focal plane. The HDC is used to measure particle position in

the vertical direction of the focal plane.

Between 2006 and 2009, iThemba LABS manufactured two new VDCs because

of the very limited vertical-position detection capabilities of the HDC [59]. Each

new VDC, shown schematically in Fig. 3.4 and photographically in Fig. 3.5, has

two wire planes in an XU configuration. The X signal wires are perpendicular to

the scattering plane, while the U signal wires are angled at 50◦ with respect to

the scattering plane. This configuration is important for determining the particle

rigidity and the scattering angle accurately, especially for 0◦ measurements. The

X wire plane of the VDCs is made up of 198 gold-plated tungsten signal wires,

while the U wire plane is only made up of 143 similar signal wires. The wires are

20 µm in diameter, and they are placed 4 mm away from one another. Since the

applied electric field is inversely proportional to the square of distance to the wire,

this means that the smaller the diameter the more the charge multiplication will

take place very close to the wire. Furthermore, 199 and 144 field-shaping wires, 50

µm in diameter, also made of gold-plated tungsten are found interspaced at equal

distances between the X and U signal wires, respectively. One extra guard wire is

found at both ends of the two wire planes. They are 125 µm in diameter and are

composed of 80% Ni and 20% Cr. The guard wires reduce current leakage and

spontaneous discharge by reducing the electric field at the ends of the VDC. In

this experiment, a negative voltage of 3400 V was applied across the field-shaping

wires. Three cathode planes, which are 16 mm apart and consist of 20-µm thick

aluminium foil, sandwich the wire planes. The inside of the VDCs is isolated

from the atmosphere with two 25-µm-thick Mylar planes. The operation of these

29



detectors is based on the ionisation of a mixture of 90% Ar and 10% CO2 between

the two mylar planes. To determine the position of the events at the focal plane,

information on drift time and drift distances of the electrons in the VDC is used.

In each cell, drift time is measured from the region where primary ionisation

occurs to the region where avalanche occurs. These times are measured relative

to the time a pulse is recorded from the scintillator that is situated behind the

VDC. To obtain the drift distance, which is the distance travelled by the electron

from the signal wire to the position where it first passes through the drift cell, a

conversion has to be done from the drift times. This conversion is achieved by a

look-up table (discussed in Sec. 4.1.2.2). It is only after accurate drift distances

are obtained that accurate focal-plane position coordinates can be determined.

In this study, only one VDC was used instead of two. This was done to ensure

that the protons do not lose most of their energy in the VDCs before they reach

the plastic scintillators since the proton-beam energy was just 80 MeV which falls

within the intermediate energy range.

30



Figure 3.4: A schematic diagram of the K600 VDC focal-plane detectors [15].

Figure 3.5: The focal-plane detector package of the K600 magnetic spectrometer
[60].

31



3.2.1.2 Plastic scintillator detectors

The two plastic scintillator detectors, wrapped in sheets of aluminised mylar, are

positioned just downstream from the drift chambers (also shown in Fig. 3.5) and

are very close to the focal plane of the K600 magnetic spectrometer. Scintillator

detectors are made up of scintillating materials that can interact with an ener-

getic particle and convert its kinetic energy into detectable light. The scintillation

medium should be of good optical quality and transparent for light with wave-

lengths of its own emission [58]. When an energetic nuclear particle enters the

detector, it excites the molecules of the scintillating materials. De-excitation of

these molecules results in the emission of visible photons. These photons are then

focused to a photo-cathode where they can eject electrons through the photoelec-

tric effect. The ejected electrons are directed to a photo-multiplier tube within the

photo-cathode and they are multiplied by changing the applied electric field. The

electrons are collected and, thereafter, form an electronic signal that is linearly

proportional to the energy that was deposited into the detector.

The plastic scintillatodddfr detectors of the K600 magnetic spectrometer are con-

nected to photo-multiplier tubes via 90◦ twisted pair adiabatic lightguides to both

ends of each of the scintillators. These plastic scintillators provide event trigger

signals and aid in particle identification through ∆E −∆E particle-identification

spectra.

3.2.2 0◦ mode

The combination of an 80-MeV beam with scattering measurements at 0◦ was

chosen for this experiment so that selectivity to excitations with low angular-

momentum transfer can be achieved, thus exciting the PDR. Even though, in this

mode, both the unscattered beam and the scattered particles pass through the

spectrometer very close to each other due to the small difference in their magnetic

rigidity, the spectrometer provides a means by which they can be separated to

32



achieve a high energy-resolution measurement. The detectors are placed in the

high-dispersion focal plane so that the beam can be separated from the lowest

measurable excitation energy [3]. Situated inside the concrete wall of the spec-

trometer vault, after the focal-plane detectors, is a Faraday cup that acts as the

0◦ beamdump. The unscattered beam from the spectrometer is transported there

via the 0◦ beamline (shown in Fig. 3.5).

3.2.3 Dispersion matching

The momentum spread of the beam affects the obtainable energy resolution with

a magnetic spectrometer. As the momentum of the beam from the accelerator

increases, the momentum spread also increases linearly. The use of collimators,

therefore, ensures that the momentum dispersion is limited. This spread can be

further limited by implementing dispersion matching techniques, thereby improv-

ing the energy resolution of the spectrometer. During experiments, the beam is

set up such that the position and angle of the proton that interacts with the

target is independent of the momentum of the proton before the interaction. As

a result, the position and angle of the inelastically scattered proton that reaches

the focal plane is dependent on the initial beam energy spread thus limiting the

energy resolution of the spectrometer [61]. To overcome this challenge, the beam-

line optics are adjusted so that the beam characteristics match the requirements

of the magnetic spectrometer. This is done by separating the protons according

to their momentum in such a way that the protons with high momentum will

take a longer path in the spectrometer, while the ones with low momentum will

take a shorter path, thus achieving an achromatic focus at the focal plane of the

spectrometer [62, 63].

When the spectrometer is operated at 0◦, the faint beam dispersion matching

technique is applied. This is done by placing three beam attenuation meshes

between the ECR ion source and SPC2. This results in the reduction of the

33



number of protons in the beam without distorting the beam profile. The magnet

elements in the spectrometer are also scaled such that the faint beam passes

directly through the focal-plane detectors. The matching conditions of the beam

can then be analysed from the properties of the beam at the focal plane, and the

energy resolution can be optimised.

3.2.4 Target ladder information

For this experiment, five targets, ZnS (used as the viewer), 24Mg (used for cali-

bration of the focal plane), 12C (also used for calibration), 58Ni (isotope of interest

in this experiment) and an empty target, were mounted at different positions on

the target ladder during the experiment. The areal densities of the 24Mg, 12C and

58Ni targets were 0.7 mg/cm2, 1.053 mg/cm2 and 5 mg/cm2, respectively. ZnS

is a luminescent material that is used as a viewer during K600 experiments at

iThemba LABS to check the beam position. The position is adjusted periodically

to suit the requirements of the experiment. Figure 3.6 shows the viewer in posi-

tion on the target ladder. Empty targets are used to determine the background

contribution to the acquired spectra (as can be seen in Sec. 4.1.1). 24Mg and 12C

have prominent and well-known states, hence they were chosen for calibrating the

focal plane. The physics target, 58Ni, was chosen because the target material can

be rolled easily and it is not prone to oxidation. Furthermore, as mentioned in

the introduction, there are already existing studies of the low-lying strength in

58Ni using different probes [7–10] which can be used for comparison with the data

from the present study.

34



Figure 3.6: Image of the viewer (ZnS) on the target ladder.

3.3 BaGeL detectors

The subsequent γ decay following the excitation of the target was measured with

BaGeL, an array of 12 High-Purity Germanium (HPGe) and 5 Cerium-Doped

Lanthanum Bromide (LaBr3:Ce) scintillation detectors. The BaGeL frame, dis-

played in Fig. 3.7, is aptly named since it resembles two bagel halves that enclose

the scattering chamber during coincidence measurements.

Each HPGe detector is made up of four individual crystals referred to in this work

as segments. The detectors take the shape of a clover, hence they are named clover

detectors. They are solid state detectors made up of semiconductor material, and

their functioning relies on the intermediate band gap between the valence and the

conduction band of the material [58]. A semiconductor detector is made up of a

p-n junction diode. The positive (p) side and a negative (n) side of a diode are

created by adding impurities to a semiconductor material. In between the two

sides of the diode, there is a neutral region called the depletion region. It is this

depletion region that behaves as a charged-particle or photon detector. A reverse

bias voltage is supplied to the p-n junction diode to create a large depletion region

and minimise the amount of current in the circuit such that the only significant

35



measured current is due to the interaction of charged particles and photons [58].

In this experiment, each of the 12 HPGe detectors were fully depleted by a reverse

bias voltage of 3000 V. When an energetic nuclear particle enters the depletion

region of the detector, it then forms electron-hole pairs. These electrons move

through the circuit and lead to a potential drop across a load resister, and a

current pulse is detected. The LaBr3:Ce detectors are scintillation detectors and

their operation was discussed in Sec. 3.2.1.2. A configuration summary of the

BaGeL detectors is given in Table 3.1. Six clover detectors were mounted on the

left arm of the BaGeL structure and the other six were mounted on the right arm.

Three LaBr3:Ce detectors were mounted on the scattering chamber and the other

two were mounted on the right side of the BaGeL frame. θ and φ are spherical

coordinates from the beam plane.

Table 3.1: The configuration of the BaGeL detectors.

Position Detector label Detector model ref. Dist. from target (cm) θ φ

L1 Canberra 39 19.5 90◦ 30◦

L2 Ortec 2 18.5 90◦ 0◦

Left L3 Canberra 38 19.5 90◦ 330◦

clovers L4 Canberra 63 18.5 120◦ 25◦

L5 Canberra 61 19.5 120◦ 335◦

L6 Ortec 3 18.5 155◦ 0◦

R1 Canberra 35 17.5 90◦ 149◦

R2 Ortec 1 17.0 90◦ 1800◦

Right R3 Canberra 36 18.0 90◦ 211◦

clovers R4 Canberra 37 18.0 120◦ 155◦

R5 Canberra 40 17.5 120◦ 205◦

R6 Ortec 4 18.5 155◦ 180◦

LaBr3 1 - #51 20 45◦ 159◦

LaBr3 2 - #52 20 45◦ 205◦

LaBr3:Ce LaBr3 3 - #48 13.2 90◦ 0.◦

LaBr3 4 - #49 20 135◦ 90.0◦

LaBr3 5 - #50 20 135◦ 270◦

The coupling of the K600 magnetic spectrometer with HPGe clover detectors and

LaBr3:Ce detectors allows for the significant reduction of the background con-

tributions to the spectra, further improves the selectivity to low-spin excitations

36



and, most importantly, allows for the identification of different decay paths when

a gate is applied on the two-dimensional p-γ coincidence matrix.

Figure 3.7: The BaGeL frame in the K600 vault showing how the BaGeL struc-
ture opens and closes around the scattering chamber and how the γ-ray detectors
are arranged on the frame [12].

37



3.4 Data acquisition system (DAQ)

During detection at the focal plane of the K600 magnetic spectrometer, the trigger

signal is produced by a set of electronics that adhere to the Nuclear Instrumenta-

tion Module (NIM) standards. The VDC drift time, the time-of-flight (TOF), the

measurement of accumulated charge in the scintillator detectors, as well as the

accumulated scaler signals are digitised by hardware modules that comply with

Versa Modula Europa (VME) standards.

The triggered signals from the wire planes are pre-amplified and discriminated

by 16-channel electronic cards located on the VDC Plastic Circuit (PC) board.

The signals are transported through 16-channel twisted-pair ribbon cables to the

CAEN V1190A Time-to-Digital Converters (TDCs). The TDCs can achieve a

resolution of 100 ps. Attached to the scintillator detectors of the K600 are pho-

tomultiplier tubes. Signals from these tubes are digitised by a 12-bit current-

integrating CAEN V792 charge-to-digital converter. The coincidence of the two

scintillator detectors, assumed to have an efficiency of 100% for the detection of

energetic charged particles whose mass is one atomic mass unit or greater, forms

the trigger signal for the Maximum Integrated Data Acquisition System (MI-

DAS) [15], which is a data acquisition package that is extensively used in nuclear

and particle physics. Once the trigger signal is produced for MIDAS, the rela-

tive time that elapses between the cyclotron Radio-Frequency (RF) signal and a

coincident scintillator-detector signal, referred to as the particle’s TOF is estab-

lished. It should be noted that the TOF is also the time the proton takes to reach

the focal plane from the scattering chamber. This time is important for particle

identification purposes as will be discussed in Sec. 4.1.1.

Beam current signals at the beamstop inside the scattering chamber were mea-

sured with a Brookhaven Instruments Corporation Model 1000C Current Inte-

grator (CI). The generated output pulse from the CI is discriminated and sent

38



to the VME scaler module. Together, the known full-scale setting of the CI and

the scaler module is used to calculate the integrated current. A pulser and two

scalar modules, uninhibited and inhibited, are used to measure the deadtime of

the DAQ system. The deadtime per event is approximately 6 µs. Figure 3.8 shows

an overview of the K600 trigger electronics for the VME DAQ system.

The γ rays interacting with the clover detectors generate time and energy signals

that are pre-amplified within the clovers. The pre-amplified signals are anal-

ysed by three Mesytec Ampliflier+CFD (MSCF-16Ch) modules from which the

obtained energy and time signals can be fed into the VME DAQ system. The

energy output signal from the amplifier is proportional to the amount of energy

deposited in the clover detector, while the squared time signal obtained contains

the information of the time of the interaction. The amplified energy and time

signals are transported by 16-channel ribbon cables to the CAEN Analogue-to-

Digital Converter (ADC) and CAEN TDC, respectively. The time and energy

signals from the LaBr3:Ce detectors are amplified and discriminated in the LaBr

PRO, a custom-made NIM module developed by the INFN-Milan group (Italy),

and are then further transported via 16-channel ribbon cables for digitisation at

the CAEN ADC and TDC. A schematic representation of the BaGeL electronic

system is shown in Fig. 3.9. It is important to note that the data from the

LaBr3:Ce detectors were not analysed as part of this work, but their analysis

forms part of the future developments and outlook of this study.

The γ-p coincidence measurement is K600-trigger based as explained before.

When there there is an event at the focal plane that triggers the acquisition

system, the γ events in the BaGeL detectors that fall within an appropriately

delayed window are recorded and represent the coincidence data. Offline analysis

of the data was performed using ROOT, an object-oriented program and library

developed by CERN [64].

39



Figure 3.8: A schematic layout of the K600 trigger electronics [65].

40



Figure 3.9: A schematic representation of the data acquisition system for the
BaGeL detectors [66].

3.5 Estimation of the experiment runnning time

To estimate the running time of this experiment, the following factors were taken

into consideration: Firstly, for an A = 58 nucleus, the single scattering yield is

Y(p,p’γ) = 124 events/hour when the beam current is 0.5 nA, the target thickness

is 4 mg/cm2 , the K600 magnetic spectrometer solid angle is 3.5 msr with 0.85

efficiency. Secondly, for 6 HPGe and 6 LaBr3 detectors at 17 cm from the target,

the γ detection efficiency is 1.4 % at 6 MeV with 100% branching ratio to the

ground state and the γ-ray coincidence yield is Y(p,p’γ) = 2 events/hour. In the

proposal submitted to the Program Advisory Committee (PAC) of iThemba LABS

[12], it was estimated that five days of continuous beamtime will be required. Two

days of this time would be dedicated to beam setup, tuning and calibration and

the last three days would be used to run the experiment. However the PAC

believed that the experiment should be regarded only as a commissioning run and

therefore only provided two days of continuous beamtime. About 36.5 hours of

that time was used for beam setup, tuning and calibrations. The remaining 11.5

hours was used to take measurements of the data analysed in this thesis.

41



Chapter 4

Data extraction and analysis

Raw data in the form of event files for each run were obtained using MIDAS. A

C++ code developed at iThemba LABS was used to convert the MIDAS data

files to ROOT files offline. Before the extraction of useful information from the

ROOT data files, e.g., the excitation-energy spectrum or the γ-decay spectrum,

specialised scripts developed at iThemba LABS were used offline on ROOT to

perform all the necessary data-optimisation procedures as well as for the calibra-

tion of the detectors used during the experiment. This chapter is divided into two

sections, where the first will cover the data extraction and analysis of the K600

detection system, and the second will cover that of the BaGeL detection system.

4.1 Data extraction and analysis of the K600 de-

tection system

4.1.1 Particle identification

A particle leaves characteristic information behind as it passes through the focal-

plane detection system. Different techniques and methods can be used to interpret

this information and thus reveal the identity of the particles. The identification

42



of a charged particle relies on its position in the focal plane, its energy loss in

the plastic scintillators, and the time it takes to reach the focal plane from the

scattering chamber (the particle’s time-of-flight (TOF)). The two methods used

for particle identification (PID) in the present study are TOF selection and the

∆E correlation technique, which uses the information related to the energy loss

of the particle through the scintillators.

4.1.1.1 Time-of-flight selection

Determining the TOF of a particle is very useful in particle identification because

although different types of particles may have similar rigidities, their different

momenta will always be related to different TOFs. Software gates were used to

isolate the events related to the reaction of interest from beam-halo events. This

was done by plotting a histogram of the energy loss of the particles in scintillator 1

as a function of their TOF for an empty frame and for the 24Mg target. By com-

paring how the energy was lost in the scintillator detector through the 24Mg target

and the empty frame, as shown in Fig. 4.1, the inelastically scattered protons of

interest could be identified and separated. A software gate as illustrated by the

solid black line in Fig. 4.1 (referred to as CUTscint1vsTOF in the figure captions)

was applied. To further reduce the background contributions, an additional gate

was created from a plot of the energy loss in scintillator 2 versus TOF (Fig. 4.2)

referred to as CUTscint2vsTOF in the caption. It should be noted that another

gate, CUTTOFvsX1, was created from TOF versus focal-plane position, but at

this stage, the background was already significantly reduced by the first two gates

and the effects of this new gate were almost redundant.

4.1.1.2 ∆E correlation technique

A fourth gate was created from the energy change correlations of the protons as

they move through the two scintillator detectors. This PID selection is based on

43



the fact that the type of particle and its associated kinetic energy will determines

how it loses energy as it interacts with the detector material. Therefore, the way in

which the energy of the protons changes as they travel through the two scintillator

detectors (∆E−∆E) is used to identify the inelastically scattered protons. Figure

4.3 shows how this PID gate was created from a two-dimensional plot of the energy

changes in the two scintillators. It should be noted that the CUTscint1vsTOF,

CUTscint2vsTOF and CUTTOFvsX1 software gates were collectively applied on

the bottom spectrum of Fig. 4.3.

The effects of these software gates can be observed in Fig. 4.4. The black posi-

tion spectrum is plotted without any PID software gates and it, therefore, sits

on top of a lot of background events. The PID software gates were applied

on the blue spectrum where the majority of the beam-halo-related background

has been removed. As can be seen in the top panel of Fig. 4.1, there are still

some instrumental-background related events as well as some low-energy protons

(caused by scattering off the target foil followed by rescattering off any exposed

part inside the spectrometer) that fall in our region of interest. Further back-

ground subtraction is, therefore, required to remove these remaining background

events. This will be discussed in Sec. 4.1.4.

44



Figure 4.1: A two-dimensional plot of the change in energy of the particles
in scintillator 1 as a function of their time-of-flight for an empty target (top)
and 24Mg (bottom). The CUTscint1vsTOF software gate selecting the events of
interest is shown with a solid black line.

45



Figure 4.2: A two-dimensional plot of the change in energy of the particles
in scintillator 2 as a function of their time-of-flight before the CUTscint1vsTOF
software gate was applied (top) and after it was applied (bottom). The creation of
another software gate (CUTscint2vsTOF) selecting the events of interest is shown
with a solid black line.

46



Figure 4.3: A two-dimensional plot of the change in energy of the particles in
scintillator 1 vs their change in energy in scintillator 2 before the TOF-related
software gates were applied (top) and after they were applied (bottom). An
additional software gate further isolating the protons of interest was created and
is shown with a solid black line.

47



Figure 4.4: Comparison of the position spectra before (black) and after (blue)
the particle identification gates are applied. The peaks represents the excited
states of 24Mg.

4.1.2 Data extraction from the focal-plane detectors

The K600 analyser uses a ray-tracing algorithm to convert drift distances to focal-

plane position coordinates. Before this can be done, however, the measured drift

times in the VDC’s drift cells must be converted to drift distances using a Look-Up

Table (LUT). It is important to note that there is only one LUT per wireplane,

which means that one must ensure that the drift times for all the wires in each

wireplane fall in a similar time range. One of the factors that cause variations in

the measured drift times is the difference in the ribbon-cable lengths that connect

the preamplifier output to the TDC. Cable-length offsets are, therefore, applied to

correct for these variations first and hence ensure accurate drift-time values. Once

this is done, the LUTs can be created and implemented. This section describes

how the cable-length offsets were determined and implemented and, thereafter,

how the LUTs were created.

48



4.1.2.1 Cable-length offsets

Cable-length offsets were calculated using a script developed by a K600 collabora-

tor together with a statistically significant white-tune dataset, which is produced

by illuminating the whole focal plane uniformly. Since the experiment was part

of a larger experimental campaign, the information extracted from a previously

analysed white spectrum was used because all of the targets used in the current

experiment have strong structures. This process helps with identifying misaligned

and/or dead TDC channels. It is important to ensure only events of the particle of

interest are selected in order to create a good offset table. This selection was done

by implementing the gates created around the protons of interest in the previous

section. After the offsets were generated, the runs were re-analysed to verify that

the TDC channel vs time histograms were aligned. The results of applying the

cable-length offsets are depicted in Fig. 4.5.

4.1.2.2 Look-up-table creation and look-up-table offsets

Once the drift-time characteristics of the VDC are established and corrected, the

LUT is created. In this procedure, a specialised script is used to convert the VDC

drift times to drift distances for each wire plane. This conversion is obtained from

the following equation:

y(t) =

(
dN

dy

)−1 ∫ t

t0

(
dN

dt′

)
dt′ (4.1)

where y(t) is the drift distance, dN
dt′

is the drift-time distribution and dN
dy

is a

measure of the spatial distributions of events in the drift cell. The limits of

integration t0 and t are the times of the arrival of the particle in the drift cell

and the time at which the pulse appears at the anode, respectively [69]. Since

factors such as voltage, gas mixture, the energy and charge state of the ionisation-

inducing particles, and the physical condition of the chamber may differ for every

49



experiment, LUTs should be created for each experiment (and each wire plane).

It may happen that the LUTs also need to be corrected to ensure accurate mapping

of the drift times to drift distances. The need for LUT offsets can be assessed

using the two-dimensional resolution (Res2D) spectrum shown in Fig. 4.6. If the

central regions of these spectra are misaligned, a LUT offset is required. As can be

observed in Fig. 4.6 (top), although very subtle, the Res2D spectra only indicate

the need for a small offset for the X1 LUT. It should be noted that U1 and X1

refer to the U and X wire planes of the VDC used in this experiment, respectively.

Figure 4.5: TDC channel vs time histograms showing how the TDC channels
fail to align before (top) the application of cable-length offsets and how the TDC
channels align after (bottom) the offsets were implemented.

50



Figure 4.6: A comparison of the two-dimensional resolution spectra of the X1
(left) and U1 (right) wireplanes before (top) and after (bottom) the LUT offsets
were implemented. The y-axis represents the difference of the slopes of the drift
distances in the first and last wires of the plane.

4.1.2.3 Lineshape corrections

Lineshape correction is an offline procedure to remove the effect of the aberration

induced by the spectrometer fields. The momentum distribution of the particles

that reach the focal plane can vary, some bending more than others, resulting in

different TOFs. This means that certain correction parameters should be deter-

mined to account for the TOF dependence of the focal-plane position. The need

for these correction parameters is indicated by poorly-resolved slanted states such

as the one shown in Fig. 4.7 (top). A well-resolved state gives rise to a straight

thinner line. To obtain the lineshape correction parameters, gi, a polynomial of

third order (Fig. 4.7 (middle)) was fitted to regular interval points along the

51



prominent state in Fig 4.7 (top) as:

Xcorr = g0 + g1(TOF − TOFoffset) + g2(TOF − TOFoffset)
2

+g3(TOF − TOFoffset)
3.

(4.2)

Using the parameters obtained from the fit, the X1 position was corrected to be

XCi = Xfp −Xcorr (4.3)

where Xfp is the original X1 focal-plane position. The effect of this lineshape

correction is shown in Fig. 4.7 (bottom). As can be seen, the state is now much

straighter. There is a slight over correction between 2242 and 2248 on the TOF

axis, but this has only a minor effect on the overall energy resolution of the state.

While there will be kinematic differences between the 24Mg(p,p’) and 58Ni(p,p’)

reactions, the effect of these differences with regard to the lineshape correction is

small for scattering angles at and close to zero degrees. To confirm this, relativistic

reaction calculations were performed using JRelkin [71] to determine the energy of

the particles detected in the focal plane for the 24Mg(p,p’) and 58Ni(p,p’) reactions

for the 0 - 2◦ angular acceptance with Ep = 80 MeV. As an example, at 0◦, the

values obtained for the 24Mg and 58Ni reactions at an excitation energy of 6

MeV were 73.989 MeV and 73.960 MeV, respectively. At 2◦ deg, these values

were 73.985 MeV and 73.958 MeV, respectively. Therefore, the kinetic energy

differences over the angular acceptance of the K600 are 4 keV and 2 keV for the

24Mg(p,p’) and 58Ni(p,p’) reactions, respectively. The correction parameters for

24Mg were, therefore, also used for the 58Ni runs.

The effects of the lineshape correction can be seen again in the comparison of the

spectra in Fig. 4.8. The bottom spectrum is lineshape corrected and evidently

has better resolved peaks. The peak centroids and the standard deviation, σpos,

52



values of the two most prominent peaks of the 24Mg spectrum before and after the

lineshape correction is implemented are summarised in Table 4.1. The improved

resolution can be seen by comparing the values of sigma for each peak before and

after the correction.

Table 4.1: A summary of the 24Mg peak positions and sigma values before and
after the lineshape correction was implemented.

X1-position peak centroid (mm) σpos (mm)

Before 452.43 2.45
619.81 2.59

After 452.19 0.81
618.42 0.93

4.1.2.4 Data offsets and chaining

Drifts in the SSC fields (due to factors such as day/night temperature changes)

and Radio Frequency (RF) changes (due to optimisation of the beam by operators)

may affect the TOF and focal-plane positions of the inelastically scattered protons

by the time they reach the focal plane. This means that the TOF and focal-plane

position have to be adjusted to ensure that all the experimental runs of the same

isotope can be chained together, and the results of the particle identification

procedure performed on one run can be implemented on all the other runs.

The difference between the centroids of the TOF spectra of each of the 24Mg, 12C

and 58Ni runs relative to a reference run was determined, and a table of offsets was

produced and implemented. The well-defined peaks of the position spectrum of

the 24Mg calibration runs were used to determine shifts in the focal-plane position

spectra over time. The position of the same prominent peak in each 24Mg run

was determined, and the difference relative to the position of the corresponding

peak in the reference 24Mg run was established. The 24Mg position offsets were

assigned to 58Ni and 12C runs based on their proximity in time to each 24Mg

run. In addition to TOF and X1-position offsets, Y1-position offsets had to be

53



determined to correct for beam fluctuations present in the vertical plane. The Y1-

position spectrum for each of the runs was used to calculate the offsets relative

to the reference calibration run.

Once the data offsets were applied, the data runs were chained together so as

to increase the statistics for further analysis procedures. To check whether the

offsets were applied correctly, peak centroids as well as the sigma values of the

chained runs (for TOF, Y1 and X1-position) were obtained and compared to those

of single runs. Table 4.2 shows such values for the X1-position spectrum. From

the table, it can be seen that the position of the peak centroids of the single 4041

and 4044 runs before the offsets were applied differ noticeably from that of the

4034 run. However, this difference was reduced after the offsets were applied,

and the value for the chained runs agreed well with that of the reference run.

Furthermore, the sigma values for the chained runs after the implementation of

the offsets improved compared to that before the offsets were applied. In Fig.

4.9, the focal-plane position spectrum of the chained runs before the offsets were

implemented is compared to that after the offsets were implemented. The well-

resolved peaks in the bottom spectrum indicate that the offsets were implemented

successfully.

Table 4.2: A summary of the 24Mg peak positions and sigma values before and
after the X1 position offsets were implemented.

Run no: X1-position peak centroid (mm) σpos (mm)

Before 4034 452.21 0.78
4041 453.40 0.76
4044 453.50 0.88
chained runs 452.85 1.09

After 4034 452.21 0.78
4041 452.22 0.74
4044 452.21 0.87
chained runs 452.20 0.83

54



Figure 4.7: A prominent excited state in the TOF vs focal-plane position scatter
plot for 24Mg with no lineshape correction applied (top), a third-order polynomial
fit on selected points along the lineshape shown in the panel above (middle) and a
straighter line with improved resolution after the correction has been implemented
(bottom).

55



Figure 4.8: Comparison of the focal-plane position spectrum without (top) and
with (bottom) lineshape correction.

56



Figure 4.9: Comparison of the focal-plane position spectrum of the chained runs
before (top) and after (bottom) position offsets were implemented.

4.1.3 Energy calibration of the focal-plane detectors

Energy calibration of the focal-plane detectors is crucial for converting positions

(in mm) on the focal plane to excitation energies (MeV). This process is made

up of two subroutines: the first being position-to-momentum calibration through

magnetic rigidity and the second being a momentum-to-energy calibration.

57



4.1.3.1 Position-to-momentum calibration

The 12C position spectrum (shown in Fig. 4.10 (top)) has two well-defined peaks

which correspond to the well-known 7.654 MeV and 4.439 MeV states. These val-

ues were used to establish a rough relationship between the excitation energy and

the focal-plane position of the K600 magnetic spectrometer. This means that a

rough MeV per mm value for the focal-plane was obtained so that the focal-plane

position peaks in 24Mg (shown in Fig. 4.10 (bottom)) could be matched to excita-

tion energies from the National Nuclear Data Center (NNDC) [70] with improved

accuracy for energy calibration purposes. This position-to-energy relationship was

established using the following equation:

FPV − SPV
FPC − SPC

(MeV/mm) (4.4)

where FPV and SPV are the first and second peak values for the excitation ener-

gies and FPC and SPC are the first and second peak’s centroids (right to left) in

the 12C spectrum. Several X1-position peak centroids and their assigned energies

from the NNDC for the calibration targets are presented in Table 4.3.

Table 4.3: The focal-plane position peak centroids and their assigned energies
from the NNDC [70] for the calibration targets, 12C and 24Mg.

Calibration target X1-position peak centroid (mm) Assigned NNDC Ex (MeV)
12C 359.36 7.6540

603.03 4.4390
24Mg 196.75 9.8281

236.04 9.3011
306.96 8.3579
452.17 6.4323
483.70 6.0108
618.45 4.2382

58



Figure 4.10: Focal-plane position spectra for 12C (top) and 24Mg (bottom).

The calibration subroutine described here involves obtaining the momentum of

the protons from their position on the focal plane through magnetic rigidity. The

magnetic rigidity, R of a particle with charge Q and momentum p moving through

a magnetic field B, with a radius of curvature r is given by

R = Br =
p

Q
(4.5)

59



p = QBr (4.6)

and the momentum and rigidity are related as follows:

p

[
MeV

c

]
=

c

1× 109
QBρ[e.kG.cm]. (4.7)

JRelkin [71] was used to calculate the QBρ of the inelastically scattered protons

for selected states. Inputs such as the scattering angle, the thickness of the target

and the approximate excitation energy corresponding to the focal-plane position

of each excited state in the 24Mg spectrum were required in the programme. The

obtained QBρ values were plotted against the K600 focal-plane position values,

xfp, as shown in Fig. 4.11. A second-degree polynomial of the form:

P = c1x
2
fp + c2xfp + c3. (4.8)

was fitted through the data points and the obtained calibration parameters, cn,

were included in the configuration file used in the analyser to calculate the K600

momentum.

Figure 4.11: A plot of QBρ values against the K600 focal-plane position values
of 24Mg and the second-degree polynomial fitted to the data is shown in