Study on the influence of Nuclear Deformation on the Pygmy Dipole Resonance in Samarium isotopes Harshna Jivan A thesis submitted to the Faculty of Science,University of the Witwatersrand, in fulfillment of the requirements for the Degree of Doctor of Philosophy Supervisor Dr. Luna Pellegri Co-Supervisor Prof. Elias Sideras-Haddad Johannesburg, 2023 Declaration I, Harshna Jivan, hereby declare that this Thesis is my own, unaided work. It is being submitted for the Degree of Doctor of Philosophy in Physics at the University of the Wit- watersrand, Johannesburg. It has not been submitted before for any degree or examination at any other University. Harshna Jivan 28 day of September 2023 in Johannesburg, South Africa. i For Her, The one who carried her even before she carried me, Who fed my heart and showed me that I could play with carefree glee, My sweet and precious Aji. . For Her, The one that nurtured me, Who fed my wild imagination and grew my curiosity, My dear darling Mummy. . For Her, The one that always stood beside me, Who held my hand and lead the way between dreaming to possibility, My inspiring Sis, Rupli. ii Acknowledgements I am extremely grateful to my advisors, Dr Pelegri and Prof Haddad for their guidance, advice, patience and continuous support over the course of my PhD study. Thank you both for believing in my capabilities and not letting me give up despite my personal challenges. To Luna, you’re mentorship has been invaluable in introducing me to the niche of PDR studies as well as in helping me navigate through the intricacies that analyzing these data- sets entailed. Thank you for your commitment to me and this project. I would not have reached the finish line without your guidance or support. From the very first day that I arrived at iThemba LABS, you welcomed me with open arms and took me under your wing. I truly appreciate the bond that we have built, the life lessons shared and all the opportunities I got to experience along this journey. To Prof Haddad, thank you for steering me towards joining the Wits Nuclear Structure Group, encouraging me to take on this endeavor and providing the opportunity for me to spend time based at iThemba LABS. I am grateful for your insight and perspectives shared with me about life, physics and everything in-between. Thank you for your genuine care and fatherly advice in helping me navigate through my personal challenges. A big hearty Thank You to the iThemba LABS Beam staff and all the BaGeL campaign collaborators for all their efforts during the setting up of equipment and for dedicating their time to taking shifts and ensuring a successful experimental run. A special mention goes to Dr Retief Neveling, Dr Ricky Smit, Dr Paul Papka, Dr Lindsay Donaldson, Dr Phil Adsley, Dr Vicente Pesudo and Dr Daniel Marin Lambarri. I have had the fortunate pleasure to work alongside each of you and have gained so much as a result. Thank you to Dr Ntombi Kheswa for making the targets needed for the experiments. iii To Retief and Phil, thank you for showing me the ropes behind the K600 analyser, assisting me in the integration of the gamma analysis codes and for teaching me so many nifty coding tips and tricks. Thank you both for sharing your insights and opinions in the analysis and also for your willingness to troubleshoot through the various challenges encountered along the way. Thank you to Dr Edoardo Lanza for performing the semi-classical model calculations in order to extract the theoretical cross-sections needed to interpret the experimental data. Thank you for taking the time to explain each step of the calculation in detail, aiding in my understanding of the theoretical description of the PDR and for making my time in Catania so memorable. Thank you also to Dr Elena Litvinova and Dr Kenichi Yoshida for providing the transition density calculations required for the semi-classical model calculations for the 144Sm and 154Sm cases respectively. The financial assistance of the National Research Foundation (NRF) towards this research is hereby acknowledged. Opinions expressed and conclusions arrived at, are those of the author and are not necessarily to be attributed to the NRF. I also wish to thank thé L’Oréal-UNESCO ForWomen in Science Sub-Saharan Africa Programme for the endowment awarded to me towards my PhD research. And finally, to my family and friends, I truly appreciate all the support and care each of you have given me. To my three pillars of support, Mum, Rupal and Nish, no words could suffice to express the gratitude I have for everything you all have been for me over these last few years. Thank you for believing in me so fiercely, for supporting my choices and decisions, for accepting my weird eccentricities and loving me for who I am. No matter how big any challenge presents, I know that I can get through it as long as I have you three on my team. From the top of my head to the bottom of my toes, out of every bit of me, appreciation flows! iv v Abstract The past decade has seen an increase in studies dedicated to understanding the low-lying electric dipole (E1) response, commonly referred to as the Pygmy Dipole Resonance (PDR). These studies revealed that the PDR has a mixed isospin nature, and that the use of complimentary probes is needed to fully understand this response. Since majority of studies on the PDR focused on spherical nuclei, the influence that deformation has on the PDR response is yet to be understood. Preliminary relativistic proton scattering studies on 154Sm performed at RCNP (Japan), showed potential evidence for a splitting in the PDR response similar to that of the Giant Dipole Resonance with deformation. A tentative interpretation suggested that this splitting could be connected to the splitting of the resonance structure with respect to the K quantum number. Theoretical studies considering the deformed HFB+QRPA model however, suggest that this splitting is connected to the isospin mixed character of these states as observed in spherical nuclei. The isoscalar responses of the spherical 144Sm and axially deformed 154Sm isotopes were investigated for the first time using the inelastic scattering of alpha particles at 120 MeV. The comparative experiments were performed at iThemba LABS in South Africa, coupling together for the first time, the K600 magnetic spectrometer in zero-degree mode with the BaGeL (Ball of Germanium and LaBr3:Ce detectors) array. The particle-gamma coincidence measurement was used to obtain the cross section for the population of the pygmy states. In both nuclei, the region of the PDR was excited and the E1 multipolarity of the transitions was supported by the angular correlation between the α-particles and the co-incident γ-rays measured. The total exclusive cross section measured for 144Sm amounted to 24.3 ± 3.8 mb/sr while for 154Sm to 18.8 ± 2mb/sr. The experimental results were compared with the prediction vi of the RQTBA and the deformed HFB+QRPA theories, respectively. The theoretical cross sections were extracted within a semiclassical coupled-channel approach. The fragmentation observed in the experiment for the 144Sm was underestimated by the calculations, although good agreement with the total cross section measured was found. In the case of the deformed 154Sm however, the experimental cross section accounted for only 52% of the predicted cross section in the same excitation region. The isoscalar response extracted in this thesis was compared with the isovector strength obtain from an experiment performed at RCNP using the relativistic proton scattering at forward angles. The double hump observed in the isovector channel was not found in the case of the isoscalar strength. This implies that the difference obtained between these two experiments is related to the “isospin splitting” of the PDR rather than a splitting of the strength connected with the K quantum number. vii Table of Contents 1 Introduction 1 2 Review of the PDR 5 2.1 Macroscopic description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Microscopic description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Experimental studies of the PDR . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 The PDR with deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Theoretical considerations 16 3.1 Cross-section calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Angular Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4 Experimental Techniques and Equipment 23 4.1 iThemba LABS accelerator facilities . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 The K600 magnetic spectrometer . . . . . . . . . . . . . . . . . . . . . . . . 26 4.3 The Focal Plane detector system . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3.1 Multiwire Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3.2 Paddle detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.4 The BaGeL array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5 Signal Processing and DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.5.1 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.5.2 DAQ system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5 Data Analysis 36 5.1 K600 Focal-Plane Data reduction . . . . . . . . . . . . . . . . . . . . . . . . 36 5.1.1 Particle identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.1.2 VDC position tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.1.3 VDC efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.1.4 Line-shaping procedures . . . . . . . . . . . . . . . . . . . . . . . . . 48 viii 5.1.5 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.2 BaGeL - Clover Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.2.1 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.2.2 Gamma Time Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2.3 Addback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2.4 Clover Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.3 The Coincidence matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.4 Background subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.5 Contaminant Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.6 Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.7 Multipolarity assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6 Results and Discussion 76 6.1 Co-incidence matrix and extracted decay spectra . . . . . . . . . . . . . . . . 77 6.2 144Sm vs 154Sm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.3 Theoretical Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.3.1 144Sm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.3.2 154Sm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.4 (α, α′γ) vs (γ, γ′) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.5 (α, α′γ) vs (p, p′) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7 Conclusions 91 TABLE OF CONTENTS ix List of Figures 1.1 An illustrative depiction of the Electric dipole (E1) excitations typically ob- served for spherical nuclei. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1 The isovector and isoscalar dipole strength distribution obtained from HF plus QRPA with SGII interaction model calculations [21] for isotopes of Ca, Ni, Zr and Sn as presented in ref.[18]. The results are smoothed using a Lorentzian of width 1-2 MeV. The electromagnetic responses are shown in the upper panels in red and the isoscalar responses are shown in blue. . . . . 8 2.2 QPM calculations of the reduced transition probabilities B(E1) for 136Xe comparing different phonon coupling configurations taken from ref.[22]. Panel (a) shows the results for when only one-phonon states are taken into account, (b) when coupling up to two-phonons are included and (c) when coupling up to three-phonons are included. . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Results of the dipole response obtained in a HF+RPA calculation with a SGII interaction for the 68Ni nucleus. In the left part, the isovector (top frame) and isoscalar (bottom frame) (multiplied by −1) strength functions calculated by convoluting the corresponding reduced transition probability with a Lorenzian of 1 MeV width are shown. The regions for the PDR, IVGDR and ISGDR excitation modes is indicated. In the left part, the proton and neutron transition densities (upper frames) and isoscalar and isovector transition densities (lower frames) are shown, for the dipole states at energies 10.8 MeV (PDR), 15.6 MeV (IVGDR) and 31.6 MeV (ISGDR). Images adapted from [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 x 2.4 Average cross sections measured in 128Te and 130Te with quasi-monochromatic photons. Panels (a) and (b) depict the total elastic cross section (blue squares) highlighting the contribution of the strength in peaks with green open squares. Panels (c) and (d) shows the photoabsorption cross sections dividing the contributions into total elastic (blue squares), inelastic (red tri- angles) component. The total cross section below particle emission threshold is shown with black circles and the one obtained from (γ, n) measurement is shown with green diamonds. Images obtained from [25]. . . . . . . . . . . . . 13 3.1 Deflection function for the system α+144Sm at Eα = 120 MeV. The horizontal lines indicate the experimental α-scattering angle range. . . . . . . . . . . . 19 3.2 Deflection function for the system α+154Sm at Eα = 120 MeV. The horizontal lines indicate the experimental α-scattering angle range. . . . . . . . . . . . 20 3.3 Angular correlations obtained from ANGCOR after averaging over the open- ing angle of the K600 spectrometer for 144Sm, 154Sm, 24Mg and 16O. Green, pink and blue correspond to dipole, quadrupole and octapole modes respectively 22 4.1 Photograph of the experimental set-up in the K600 vault at iThemba LABS 23 4.2 A schematic layout of the accelerator and ancillary facilities at iThemba LABS [0]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3 Schematic layout of the K600 magnetic spectrometer. Scattered particles enter the spectrometer via the scattering chamber and are focused by the magnets on the high dispersion focal plane where they are measured by the Focal Plane Detection System (FPDS). . . . . . . . . . . . . . . . . . . . . . 26 4.4 Photograph of the UX type MWDC as mounted near the focal plane (left) and the U-type wireplane (right) where the wires are inclined at 50◦. . . . . 28 4.5 Example of the drift lines associated with a typical particle track travelling through the VDC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.6 Photograph of a set of paddle detectors with the scintillators wrapped in foil. The PMT’s are not mounted here. . . . . . . . . . . . . . . . . . . . . . . . . 30 4.7 Photographs of BaGeL taken during experiments on 144Sm. The detectors positioned to the left and right of the incoming beam are shown in the left and right panels respectively. The beam direction is indicated with yellow arrows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.8 A schematic diagram of the electronics for the K600 focal plane detector system. 33 4.9 A schematic diagram of the BaGeL electronics in Exp1. . . . . . . . . . . . . 34 LIST OF FIGURES xi 4.10 A schematic diagram of the BaGeL electronics in Exp2. . . . . . . . . . . . . 35 5.1 Variation in Focal plane X position with run entries before and after offset implementation for chained 24Mg data in Exp2. . . . . . . . . . . . . . . . . 38 5.2 PID spectra shown for 24Mg, 144Sm and 154Sm in the top, middle and bottom panels respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.3 TDC reference times for the various TDC channels of the VDC wires for Exp2, showing the effect of implementing the cable offset to align the trailing edge of the drift time distributions . . . . . . . . . . . . . . . . . . . . . . . 42 5.4 The Look-up table (LUT) for the X wireplane used in Exp2 . . . . . . . . . 43 5.5 Schematic diagram of a typical trajectory associated with a charged particle passing through a wire-plane, resulting in a V type structure. . . . . . . . . . 44 5.6 Schematic diagram of an event track triggering a "W" type structure . . . . 44 5.7 Schematic diagram of an event track triggering a "Z" type structure . . . . . 45 5.8 Logic flow in the ray-tracing procedure for determining which drift distance is allocated when multi-hits are fired for a triggered wire. . . . . . . . . . . . 46 5.9 Relative particle Time of Flight vs Focal plane position zoomed in on the 250mm (left) and 615 mm (right) 24Mg target peaks highlighting the slanting in peaks that affect the position resolution. . . . . . . . . . . . . . . . . . . . 48 5.10 Line-shaping correction parameter extraction as implemented on the 6.432 MeV state around 615 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.11 ToF vs Focal plane position after implementing the line-shaping correction. . 49 5.12 Schematic of the kinematics of a nuclear reaction . . . . . . . . . . . . . . . 50 5.13 Focal Plane X position for 24Mg data indicating the peaks used in the calib- ration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.14 Rigidity calibration curves fitted with a 3rd order polynomial function for each experiment as indicated . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.15 Calibrated Excitation energy spectra for 24Mg targets of (a) 0.7mg/cm3 and (b) 3.3 mg/cm3 thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.16 Decay scheme for the 6.432 MeV excited state in 24Mg. The relative intensities for the gamma decays are indicated in the brackets below the corresponding gamma energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.17 Calibrated gamma decay spectrum for all clovers summed with a selection on the 6.432 MeV excited state in 24Mg. . . . . . . . . . . . . . . . . . . . . 56 5.18 The time spectrum for an individual HPGe detector from each experiment, measured relative to the radio frequency (RF) of the SSC . . . . . . . . . . . 58 LIST OF FIGURES xii 5.19 Matrix of Gamma Time for each Clover detector segment during Exp2. . . . 59 5.20 Matrix showing the variation in Gamma time for full Clover array with run entries in the chained 24Mg data from Exp2. . . . . . . . . . . . . . . . . . . 59 5.21 Comparison of the Clover Addback mode vs singles mode γ-decay spectra from the 6.432 MeV excited state in 24Mg. . . . . . . . . . . . . . . . . . . . 60 5.22 The α-γ coincidence matrix obtained for 24Mg data measured in Exp1. A good correlation between the α excitation energies (Ex) measured by the K600 focal plane detectors and their corresponding γ-decay (Eγ) measured by the BageL Clover detectors can be observed. The black diagonal band indicates γ-decays to the ground state, while the magenta band indicates decays to the 1st excited state at 1.368 MeV. . . . . . . . . . . . . . . . . . . 63 5.23 Projections of the γ-ray spectra (left panel) and excitation-energy spectra (right panel) from the 24Mg(α, α′γ) data, without any gating condition (top), gated on ground state transitions (middle) and gated on transitions to the 1st excited state (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.24 The α-γ coincidence matrix obtained for 144Sm data measured in Exp2. The α excitation energies (Ex) measured by the K600 focal plane detectors are shown on the x-axis and their corresponding γ-decay (Eγ) measured by the BageL Clover detectors are shown on the y-axis. The black diagonal band indicates γ-decays to the ground state, while the magenta band indicates decays to the 1st excited state at 1.66 MeV. . . . . . . . . . . . . . . . . . . . 65 5.25 The α-γ coincidence matrix obtained for 154Sm data measured in Exp2. The α excitation energies (Ex) measured by the K600 focal plane detectors are shown on the x-axis and their corresponding γ-decay (Eγ) measured by the BageL Clover detectors are shown on the y-axis. The black diagonal band indicates γ-decays to the ground state, while the magenta band indicates decays to the 1st excited state at 81.98 keV. . . . . . . . . . . . . . . . . . . 65 5.26 Plot of the time at which measured γ-particles arrived at the clover detectors with respect to the RF of the SSC . The selected off-prompt used for gener- ating the random co-incidence background matrix is indicated by the black dashed lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.27 Background matrix with the gated band region indicated in black dashed lines 67 5.28 144Sm ground state decay counts spectra with background. . . . . . . . . . . 68 5.29 154Sm ground state decay counts spectra with background. . . . . . . . . . . 68 5.30 Comparison of counts corrected with efficiencies for detectors at θ = 90◦ and θ = 135◦ in Exp1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 LIST OF FIGURES xiii 5.31 Comparison of counts corrected with efficiencies for detectors at θ = 90◦ and θ = 155◦ in Exp2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.32 Multipolarity assessment for individual states in 144Sm . . . . . . . . . . . . 72 5.33 Multipolarity assessment for the broad range of states in 144Sm . . . . . . . . 73 5.34 Multipolarity assessment for the broad range of states in 154Sm . . . . . . . . 73 5.35 Multipolarity assessment for states identified in 24Mg . . . . . . . . . . . . . 74 5.36 Multipolarity assessment of contaminant peaks . . . . . . . . . . . . . . . . . 75 6.1 144Sm co-incidence matrix and direct decay projection . . . . . . . . . . . . . 77 6.2 154Sm co-incidence matrix and direct decay projection . . . . . . . . . . . . . 78 6.3 144Sm Vs 154Sm Cross-sections . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.4 RQTBA predicted proton and neutron transition densities for the dipole state at 6.88 MeV in 144Sm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.5 Comparison between measured and calculated cross sections for 144Sm . . . . 82 6.6 Comparison between the experimental extracted and theoretical calculated summed cross-sections for 144Sm. . . . . . . . . . . . . . . . . . . . . . . . . 83 6.7 Deformed HFB+QRPA predicted proton and neutron transition densities for the K=0 and K=1 dipole states at 7.49 MeV and 7.33 MeV respectively in 154Sm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.8 Comparison between measured and calculated cross sections for 154Sm . . . . 85 6.9 Comparison between the experimental extracted and theoretical calculated summed cross-sections for 154Sm . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.10 Comparison of PDR states observed 144Sm measured using the (α, α′γ) re- action channel in this study vs the (γ, γ′) reaction channel measured in [56] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.11 Electric dipole cross-section obtained in 154Sm(p,p’) experiments at RCNP [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 LIST OF FIGURES xiv List of Tables 4.1 Table summarising technical details of BaGeL for 154Sm experiments . . . . 31 4.2 Table summarising technical details of BaGeL for 144Sm experiments . . . . 32 5.1 Summary of parameters used for the rigidity calibration in Exp1 . . . . . . . 53 5.2 Summary of parameters used for the rigidity calibration in Exp2 . . . . . . . 53 xv Chapter 1 Introduction The atomic nucleus is a fascinatingly complex system. Whilst one would expect such a system with many degrees of freedom to behave in a chaotic and disorderly manner when subjected to an external stress, instead it is able to self organise into simple modes of collective motion. The modes of collective motion that manifest in the form of vibrations are of particular interest to the field of nuclear structure physics as studying their properties can provide better insight into the bulk properties and the non-equilibrium dynamics of nuclei. In this thesis, particular attention is drawn to the Electric dipole (E1) response observed in atomic nuclei. The E1 strength is almost entirely exhausted by the Giant Dipole Resonance (GDR), located in the energy range of 10-20 MeV. A small contribution to the strength however, comes from a number of low-lying 1− states concentrated around the neutron- separation threshold. These states are frequently denoted as the Pygmy Dipole Resonance (PDR). The typical E1 dipole response observed for spherical nuclei is illustrated in Fig.1.1. Within the hydrodynamic model, the PDR has been interpreted as an oscillation of excess neutrons against a proton-neutron saturated core [1, 2]. Its connection to the neutron skin, therefore, makes investigations of the PDR particularly important. The neutron-skin thickness has been linked to several parameters that influence the Equation of State (EOS), including the nuclear polarizability [3, 4] as well as the symmetry energy [5]. In addition, since the PDR falls in the region of the neutron separation energy, it has an influence on the r-process particularly in the synthesis of heavier nuclei [6] and also has an impact on the 1 Figure 1.1: An illustrative depiction of the Electric dipole (E1) excitations typically observed for spherical nuclei. gamma strength function at the particle threshold [7]. Studies that contribute to an accurate understanding of the PDR strength and which aid towards building a microscopic picture of the underlying structure behind this low-lying strength are therefore highly desirable. The PDR has been studied over a range of nuclei, spanning several mass regions across the nuclear chart. Complementary studies comparing the use of hadronic probes such as α- particles and 17O with that of γ-ray probes, revealed a structural splitting of the PDR. These findings imply that a higher-lying subset of states (populated better with γ-ray probes) display more isovector (IV) characteristics, while the lower-lying states (populated by both probe types) have a strong isoscalar (IS) component. Although previous studies have provided a wealth of information on the PDR, they have been mostly concentrated on spherical nuclei and only very recently have studies turned focus to deformed nuclei. In the case of the GDR, the role of deformation has been studied in Sm and Nd isotope chains using both γ-ray and α-particle probes. These studies revealed a splitting in the response whereby a lower-energy component of the GDR became more prominent with increasing deformation, giving the appearance of a double-hump structure [8, 9, 10]. This splitting has been attributed to the different contributions arising from the K=0 and K=1 quantum numbers as defined along and perpendicular to the nuclear deformation axis. Introduction 2 Preliminary (p,p’) studies on 154Sm performed at the Research Center for Nuclear Physics (RCNP) [11, 12], showed potential evidence for a splitting in the PDR response similar to the K-splitting observed in the GDR. This conclusion however, was drawn based on the consideration that the energy difference between the two peaks found is compatible with the deformation of the nucleus ground state. Theoretical studies considering relativistic quasiparticle random phase approximation calcu- lations based on a deformed Hatree-Fock-Bogoliubov (HFB) model suggests a predominance of K=0 strength in the lower part of the response rather than being equally distributed, while the higher-energy part of the strength shows both K=0 and K=1 components [13]. Additionally these calculations predict an isovector and isoscalar response where the isospin mixed character of these states show a suppressed response in the isoscalar channel at high energies, similar to that observed in spherical nuclei. This thesis sets out to investigate the isoscalar PDR response in deformed nuclei for the first time. Comparative experiments were performed at iThemba LABS in South Africa, on the spherical 144Sm and prolate deformed 154Sm using the (α, α′γ) reaction channel. 144Sm and 154Sm occur on opposing extremes in the chain of isotopes that undergo a transition in shape-phase from vibrators to rotors, characterized by a soft potential in the beta degree of freedom [14]. These experiments were the first to couple together the K600 magnetic spectrometer in the zero-degree mode with the BaGeL (Ball of Germanium and LaBr3:Ce detectors) array. The layout of the thesis is as follows: Chapter 2 provides a brief review of theoretical and experimental studies dedicated to the PDR, highlighting the well established properties and open questions regarding this dipole mode. A focus is placed on details pertaining to the PDR in deformed nuclei. Chapter 3 provides a description of the theoretical considerations necessary to interpret the reactions investigated in this thesis. The cross sections based on theoretical models are shown. Introduction 3 In Chapter 4, the reader is introduced to the experimental techniques and equipment used to perform the (αα′γ) scattering measurements at iThemba LABS. Chapter 5 contains a descriptive detailing of the various data reduction processes used to extract the experimental cross-sections. A multipolarity assessment to confirm the E1 nature of the measured states in terms of the particle-gamma angular correlations is also shown. In Chapter 6, the cross-section results obtained from the experiment for the isoscalar com- ponent of the PDR in the two Sm isotopes is presented. The results are discussed in comparison with the theoretical predictions shown in Chapter 3, as well as in comparison to data obtained from other studies which utilised complementary probes to investigate the PDR region of these Sm isotopes. The thesis draws to a close in Chapter 7, where conclusions from the present study and future plans are discussed. Introduction 4 Chapter 2 Review of the PDR A large effort toward studying the PDR both experimentally and theoretically has taken place since the first signature of this low lying dipole strength was observed. From the theoretical perspective, the PDR has been investigated using both macroscopic models and microscopic model representations. The review papers of Refs [15, 16] give a comprehensive description of the various models that have been used, including describing their successes, shortcomings and limitations. Experimentally, the PDR has been studied within several mass regions of the nuclear chart. A predominant portion of these studies probed the PDR region using the (γ, γ′) reaction channel, however the multi-messenger approach utilizing complimentary probes became well established in the last decade. An extensive review of the experimental effort towards studying the PDR is given in refs. [17, 18]. In this chapter, the main properties of the PDR inferred from the reviews are highlighted, while particular attention is given to the PDR in deformed nuclei. 2.1 Macroscopic description One of the first macroscopic interpretations by Mohan et al. [1], modelled the PDR states within a hydrodynamic approach similar to the Steinwedel and Jensen [19] model that showed success in interpreting the GDR for heavy mass nuclei. In these models, the nucleus is described as a liquid drop consisting of compressible proton and neutron fluids which can undergo collective density fluctuations about their equilibrium density. For oscillations where the protons and neutrons move in phase, the mode is described as isoscalar (IS), 5 whilst for out-of-phase motion the mode is called isovector (IV). The oscillatory motion can be described by considering the effect of bulk properties such as polarisation, pressure and flow velocity, with the condition imposed that the total density should remain constant within the nuclear radius. In the case of the IVGDR, the result is a compressional density oscillation of the proton fluid against the neutron fluid. For describing the PDR, a 3-fluid model was first considered which described the protons, neutrons occupying the same orbitals in a core and excess neutrons each as individual compressible fluids. In this model, two independent dipole modes arise, which for the case of 208Pb results in a dipole resonance at 13.3 MeV and one at 4.4 MeV. These coincide with the GDR and PDR regions respectively. In order to reduce the complexities of describing the restoring force when considering 3 fluids, instead another 2 fluid model was suggested which treated the combination of protons and neutrons occupying the same levels as a core fluid oscillating out-of-phase with a fluid of excess neutrons. This has been the most commonly used for describing the PDR from a macroscopic viewpoint. A similar macroscopic model by Bastrukov et al. [20], model the PDR excitation as an elastodynamic excitation whereby the nucleus, considered to be a sphere containing an elastic continuous medium consists of a core with uniformly distributed nuclear and electric charge densities surrounded by a layer. The PDR excitation in this case arises from the oscillation of the layer against the core which is induced by the elastic restoring force. The total electromagnetic strength, estimated from the squared dipole moment of the charge- current density, as well as the estimated energy for the dipole mode showed fairly reasonable agreement with experimental data. However the nature of the dipole mode being only of isoscalar character is inherently implied with this model. 2.2 Microscopic description While macroscopic models give physical insight into the gross features and bulk properties of the various nuclear excitation modes, a much more accurate and in-depth understand- ing of these phenomena can be obtained when considering how the microscopic nature Review of the PDR 6 of the nucleus gives rise to these behaviours. These models are based on the mean field and energy-density functional theories and have been able to successfully predict import- ant characteristics of the giant resonances such as their energy, strength and the damping mechanisms responsible for their measured widths. They have also been successful at re- producing the low-lying PDR strength and its increase in relation to increasing the neutron excess. Examples of microscopic models which have been able to successfully reproduce the PDR strength include the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme or Gogny ef- fective nuclear interactions in spherical and closed shell nuclei, the HFB plus Quasi-particle RPA (QRPA) in open shell spherical and deformed nuclei, relativistic mean-field models like relativistic RPA and Quasi-particle RPA. Figure 2.1 shows predictions of the isovector and isoscalar dipole strength distributions obtained for the electromagnetic and isoscalar responses in several isotopes of Ca, Ni, Zr and Sn from ref [18]. These calculations were obtained using a discrete self-consistent Hartree-Fock plus RPA code with an SGII skyrme interaction [21]. This figure highlights the development of the low lying PDR strength with increasing neutron number in both the isoscalar and isovector channels for nuclei spanning different mass regions. The main principle behind these models is to construct a self consistent mean field describing the potential generated by all the nucleons in a nucleus to form a basis for the ground state wave equations. Excitations can then be built up from elementary 1p-1h (or quasi particle) configurations which correspond to as an example, the promotion of a particle above the fermi surface leaving a resulting hole in the level below. From the residual interaction, state mixing of all p-h configurations occurs. States of the same angular momentum which add coherently, give rise to a collective state. In some models, coupling to more complex configurations like 2p-2h, 3p-3h are included which reproduce certain features observed in experiments better. Other theoretical approaches based on the particle-vibration coupling model take into ac- count the strong coupling of nucleons to nuclear surface oscillations associated with the collective excitation. In the quasi particle-phonon model (QPM), phonons are constructed Review of the PDR 7 Figure 2.1: The isovector and isoscalar dipole strength distribution obtained from HF plus QRPA with SGII interaction model calculations [21] for isotopes of Ca, Ni, Zr and Sn as presented in ref.[18]. The results are smoothed using a Lorentzian of width 1-2 MeV. The electromagnetic responses are shown in the upper panels in red and the isoscalar responses are shown in blue. from the solutions of the QRPA and the coupling to up to three phonons are included. In the Relativistic Quasi-particle Time-Blocking Approximations (RQTBA), the quasi particle- phonon coupling is also taken into account. These models have been the most successful at reproducing the fragmentation of the low lying dipole states observed in experiments due to their inclusion of 1 phonon states coupling to higher configurations. The effect of including higher order couplings to QPM predictions, calculated in ref [22] for 136Xe, is shown in Fig.2.2. The results show more fragmentation when the coupling with up to two-phonon (middle panel), and up to three-phonon (bottom panel) configurations are included. Although the centroid shifts to lower energies, the overall strength summed over the fragmented region is almost unchanged. One of the main features which define the microscopic interpretation of the PDR, arise from observing the shape and relative displacement of the proton and neutron transition Review of the PDR 8 Figure 2.2: QPM calculations of the reduced transition probabilities B(E1) for 136Xe com- paring different phonon coupling configurations taken from ref.[22]. Panel (a) shows the results for when only one-phonon states are taken into account, (b) when coupling up to two-phonons are included and (c) when coupling up to three-phonons are included. densities, which significantly differ from those of the IVGDR and ISGDR. The transition densities are fundamental in describing the excitation process for a given state. For states in the IVGDR, the proton and neutron transition densities are out of phase, resulting in an almost pure isovector mode that is in agreement with the macroscopic picture predicted for this mode. For states in the ISGDR, the proton and neutron transition densities are in phase both inside the nucleus and at the nuclear surface, resulting in an isoscalar mode which reflects the behaviour of a bulk compressional mode. In the case of the PDR state however, the proton and neutron transition densities are in phase on the inside of the nucleus whilst at the surface, neutrons provide the predominant contribution. This results in a very Review of the PDR 9 mixed isospin character, where the isoscalar and isovector transition densities resemble the same shape and strength at the surface. An example of these features is shown in Fig.2.3 for the the dipole response in 68Ni. The transition densities were calculated in ref [16] using a HF+RPA with a SGII Skyrme inter- action [23, 24]. The strength functions were calculated using a convolution of the corres- ponding reduced transition probability with a Lorenzian of 1 MeV width. In the left part of the figure, the isoscalar and isovector strength functions for 68Ni are shown, with the three regions corresponding to the PDR, IVGDR and ISGDR modes highlighted. On the right part of the figure, the transition densities calculated for three states belonging to each of the highlighted modes is shown. The upper panels (a-c) show the proton and neutron transition densities while the resulting isoscalar and isovector transition densities are shown on the bottom panels (d-f). The transition densities for states from the IVGDR and ISGDR regions clearly show distinct isovector and isoscalar behaviour respectively. The state for the PDR region however shows isospin mixed behaviour. While the various model calculations differ in certain aspects like the strength distribution, fragmentation or collectivity of the PDR, they all predict this same characteristic shape of the transition densities for this low lying dipole mode. 2.3 Experimental studies of the PDR On the experimental front, first experiments for investigating the PDR utilized the photon scattering method of Nuclear Resonance Fluorescence (NRF) to great effect and make up the bulk of available PDR data spanning nuclei over the whole mass region. The mixed isospin nature of the states enabled the use of both electromagnetic and hadronic probes to investigate these states. Experiments utilizing α probes in coincidence with γ decay later showcased an unexpected result regarding the isospin characteristics of the PDR. This sparked the necessity to use complimentary probes in further investigations and the multi- messenger approach came to be. Comparative investigations with further hadronic probes like protons and 17O were soon performed. An extensive review of the experimental effort Review of the PDR 10 Figure 2.3: Results of the dipole response obtained in a HF+RPA calculation with a SGII interaction for the 68Ni nucleus. In the left part, the isovector (top frame) and isoscalar (bottom frame) (multiplied by −1) strength functions calculated by convoluting the corres- ponding reduced transition probability with a Lorenzian of 1 MeV width are shown. The regions for the PDR, IVGDR and ISGDR excitation modes is indicated. In the left part, the proton and neutron transition densities (upper frames) and isoscalar and isovector trans- ition densities (lower frames) are shown, for the dipole states at energies 10.8 MeV (PDR), 15.6 MeV (IVGDR) and 31.6 MeV (ISGDR). Images adapted from [16]. towards studying the PDR is given in refs. [17, 18]. For the purpose of this thesis, the main properties of the PDR established from these studies are summarised below. Thus far, the PDR has been identified as a collection of dipole states lying at an energy well below the IVGDR, exhausting a small percent of the Energy Weighted Sum Rule. They can be found in both stable and unstable nuclei containing a neutron excess at energies surrounding the neutron emission threshold. They can be excited by both isoscalar and isovector probes due to their strong isospin mixed behavior. Below the neutron separation energy, the PDR states are separated in two parts, a low energy component of dipole states which are excited by both electromagnetic and nuclear probes and a higher energy com- ponent populated only by the isovector interaction. This characteristic, referred to as PDR Review of the PDR 11 (or isospin) splitting has been observed in all nuclei investigated using the multimessenger approach. There are still uncertainties regarding the interplay between the isoscalar and isovector responses, especially in the region above the neutron separation threshold where an entangling with the IVGDR tail contributes. In earlier studies of the PDR, it was assumed that these dipole states predominantly de- excited via direct decay to the ground state. However, recent studies conducted with the High Intensity γ-ray Source (HIγS) at the Duke Free Electron Laser Laboratory at Duke University revealed that these assumptions may not hold true. In these experiments, high intensity quasi-monoenergetic photon beams obtained using Laser Compton Backscattering (LCB) are used to excite dipole states. With the LCB method, low-energy laser photons are Compton scattered off electrons accelerated to ultra-relativistic energies within storage rings, thereby producing fully polarised photon beams with an energy spread of 3-5%. The coincident γ-decays are then measured using the high-resolution and high-efficiency γ3 setup. The photo-absorption cross section is indirectly measured from the contribution of transitions depopulating the excited state by direct decays as well as by cascade decays via the first low-lying states. The strength for transitions that decay via high-lying states can not be detected although statistical calculations predict that these account for a small percentage of the total cross-section. The photoabsorption cross-sections obtained with HIγS experiments on Te isotopes [25] are shown in Fig. 2.4. The two top panels show the contribution to the total elastic cross section derived from unresolved transitions. This fraction is related to the fragmentation of the E1 strength where coupling to complex configurations becomes more relevant. In general, an increasing trend with the excitation energy is found. Furthermore, the contribution from cascade decays also increases with excitation energy, as seen in the lower panels of Fig. 2.4. The higher energy states in the PDR region appear to have a more complex nature and as a result, the branching ratio to the ground state appears to be decreasing in favour of higher lying "doorway states". Review of the PDR 12 Figure 2.4: Average cross sections measured in 128Te and 130Te with quasi-monochromatic photons. Panels (a) and (b) depict the total elastic cross section (blue squares) highlighting the contribution of the strength in peaks with green open squares. Panels (c) and (d) shows the photoabsorption cross sections dividing the contributions into total elastic (blue squares), inelastic (red triangles) component. The total cross section below particle emission threshold is shown with black circles and the one obtained from (γ, n) measurement is shown with green diamonds. Images obtained from [25]. 2.4 The PDR with deformation Experimental studies of the PDR in strongly deformed nuclei are only recently starting to be performed and a clear picture of the role that deformation plays on this low lying dipole Review of the PDR 13 mode is yet to be established. In the IVGDR, a splitting of the response into a double- humped structure is observed for most deformed nuclei. The splitting has been linked to the different frequencies of the longitudinal (K = 0) and transversal (K = 1) vibrations with respect to the symmetry axis. The response of the deformed nucleus 76Se above 4 MeV was studied using a quasi-monochromatic gamma beam at the HIγγS facility [26]. The E1 strength obtained did not show any clear evidence of a splitting distribution in this nucleus. However, from the theoretical interpret- ations obtained using a Time Dependent Hartree Fock (TDHF) model, the picture of the PDR as the isospin saturated core vibrating against the neutron skin, was not validated. This is likely to be related to the lack of neutron excess in this nucleus. A strong remark was made by the authors highlighting the importance to account for the contribution of the branching to low lying excited states in the estimation of the total dipole strength. In another study, the summed B(E1) measured between 6 and 8 MeV for the Xe and Mo isotopic chains [27] was measured by trying to correlate the strength with the neutron excess ratios and the quadrupole deformation parameter β2. The general trend observed is an increase of the strength withN/Z ratio for both Mo and Xe isotopes while a decrease with deformation is seen in the Xe chain. Overall in this study it appeared that the deformation did not have any considerable effect on the total strength found in these neutron-rich nuclei. A different method that can be used to identify the K-quantum number associated with a transition is to use the predictions of the Alaga rules [28] for which the decay branching ratios of excited states to the ground state band depends on the K-quantum numbers of the excited states Ratio = B(E1; 1− −→ 2+ 1 ) B(E1; 1− −→ 0+ 1 ) = {0.5forK=1 2.0forK=0 (2.1) Although this rule has proved to be useful for low-energy states, it still has to be determine whether it holds at higher excitation regions. It may provide a plausible way in which to deduce information on the K-spitting. Measuring the ratio between the branching to the ground state and to the first excited state for the pygmy states is challenging due to the close proximity of the first 2+ state to the ground state for strongly deformed nuclei. For Review of the PDR 14 instance, in the case of studying the PDR in 164Dy [29], it was difficult to distinguish the decay to the ground state from the decay to the 2+ 1 state due to their close energies. Thus, an estimation of the branching ratio was obtained using the mean azimuthal asymmetries of the transitions. The PDR region showed a reduction from the expected value, indicating a mixing between the decays to the 2+ 1 state and the ground state. This suggests that no evidence for a splitting of the PDR built on the ground-state band was visible in 164Dy. Another rare-earth nucleus, 156Gd [30], also showed similar results. Even though some attempts were made to gain information on deformation in the PDR, the results extracted from these experiments are unfortunately inconclusive regarding the role that deformation plays. These studies emphasize the need for a smaller energy spread of the photon beam to achieve a clean separation of the decays to the ground state and the first excited state. A future LCB facility under construction in Romania, the Extreme Light Infrastructure- Nuclear Physics (ELI-NP) is anticipated to provide extremely intense monoenergetic photon beams where an energy spread of less than 1% is possible. Review of the PDR 15 Chapter 3 Theoretical considerations In this Chapter, the theoretical considerations necessary to interpret the reactions investig- ated in this thesis are presented. The cross sections calculated for 144Sm and 154Sm based on theoretical models are shown. In addition, calculations for the α− γ angular correlation resulting from the inelastic scattering reaction is presented. The angular correlation pattern is required for extracting the experimental cross-section and for assessing the multipolarities of the extracted states. 3.1 Cross-section calculations The use of methods such as the Distorted Wave Born Approximation (DWBA) or Coupled- channels (CC) in the description of nuclear scattering is well established in direct reaction theory [31]. In conjunction with these full quantal calculations, the use of semiclassical approximations provide a nice way to calculate the cross-sections for inelastic α scattering as it allows for a description of the nuclear reaction process where the most important ingredients can be easily identified. The model makes the assumption that colliding nuclei move along a classical trajectory defined by the real part of the optical potential, whilst the internal degrees of freedom are described quantum mechanically. The excitation of one of the partners of the collision is then due to the mean field of the other. The following descriptions for the semiclassical model calculations are summarised from [16]. 16 For the inelastic scattering of a pair of nuclei a and A, considering only target excitations, the Hamiltonian can be written as HA = H0 A +W (t), (3.1) where H0 A is the internal hamiltonian of the target and the external field W describes the excitation of nucleus A due to the mean field Ua of nucleus a, whose matrix elements depend on time through the relative co-ordinate R(t): W (t) = ∑ ij 〈i|Ua(R(t))|j〉a†iaj + h.c. (3.2) The sums over the single particle states, denoted by i and j , run over both the particle and hole states. By solving the Schrodinger equation in the space spanned by the eigenstates of the internal Hamiltonian |Φα〉, the final population for each of the states can be calculated non-perturbatively. The time-dependent state, |Ψ(t)〉, of the target nucleus can be expressed as |Ψ(t)〉 = ∑ α Xα(t)e−iEαt|Φα〉, (3.3) where the ground state is included in the sum as the term α = 0. By substituting |Ψ(t)〉 in the Schrodinger equation, coupled-channel equations for the amplitude Xα(t) is obtained. Ẋα(t) = − ∑ α′ei(Eα−Eα′ )t〈Φα|W (t)|Φα′〉Xα′(t) (3.4) These semiclassical coupled channel equations are equivalent to the Schrodinger equation and their solution for each excited state α gives the amplitudes Xα(b, t). The dependence on the impact parameter b arises due to the fact that the classical trajectories have to be solved for each impact parameter. From their solutions, the probability of exciting the internal state |Φα′〉 can be constructed as Pα(b) = |Xα(t = +∞)|2 (3.5) Theoretical considerations 17 for each impact parameter b. Finally, by integrating Pα over the range of impact parameters corresponding to the experimental scattering angle range, the total cross section is obtained. σα = 2π ∫ bmax bmin Pα(b)T (b)bdb (3.6) The transmission coefficient T (b) takes into account processes not explicitly included in the model space which take flux away from the elastic channel. It is usually taken as a depletion factor that falls to zero as the overlap between the two nuclei increases. A standard practice is to construct it from an integral along the classical trajectory as T (b) = exp { −2 h̄ ∫ +∞ −∞ VI(R(t′))dt′ } , (3.7) where VI is the imaginary part of the optical potential associated to the studied reaction. When the imaginary part is not available from the experimental data, it is assumed as half the magnitude of the real part. The range of impact parameters over which the Pα is integrated is determined from the deflection function for the reaction system as measured in the experiment. For these studies, this was done for α+144Sm at Eα = 120MeV and α+154Sm at Eα = 120MeV , and the solid opening angle of 0− 2◦ was considered. The deflections functions for the two reactions are shown in the Fig.3.1 and Fig.3.2. The real part of the optical potential, which together with the Coulomb interaction determ- ines the classical trajectory, is constructed with the double-folding procedure [32]. The same procedure has been adopted to compute the radial form factor which are the fundamental part of the transition matrix elements 〈Φα|W (t)|Φα′〉. They are obtained by double-folding of the transition densities obtained from microscopic model calculations performed for the two Samarium isotopes. For both folding procedures, the nucleon-nucleon interaction M3Y- Reid type[30] was used. For 144Sm, transition densities were obtained using the Relativistic Quasiparticle Time Theoretical considerations 18 0 10 20 30 40 50 60 b (fm) -5 0 5 10 θ cm (d eg re es ) α + 144Sm @ 120 MeV 8.23 fm 8.32 fm Figure 3.1: Deflection function for the system α+144Sm at Eα = 120 MeV. The horizontal lines indicate the experimental α-scattering angle range. Blocking Approximation (RQTBA) [33], while for 154Sm, transition densities were obtained using a deformed Hartree-Fock Bogoliobov coupled to quasiparticle random-phase approx- imation (HFB+QRPA)[13]. The results for the cross-sections are shown in Chapter 6, where they are compared to the measured cross-sections investigated in this thesis. 3.2 Angular Correlations In order to determine the singles cross-section from coincidence experiments, one needs to have a prediction of the angular correlation W (Ωγ) between the inelastically scattered α- particle and the coincident decaying γ-particle. The relation between the double-differential cross-section and the single α-scattering cross section is given by dσ dΩα = 4π Γ Γf 1 W (Ωγ) d2σ dΩαdΩγ (3.8) Theoretical considerations 19 0 10 20 30 40 50 60 b (fm) -5 0 5 10 θ cm (d eg re es ) α + 154Sm @ 120 MeV 8.555 fm 8.66 fm Figure 3.2: Deflection function for the system α+154Sm at Eα = 120 MeV. The horizontal lines indicate the experimental α-scattering angle range. where the Γ Γf is the branching ratio to the final state and W (Ωγ) is the α − γ angular correlation. The angular distribution of the emitted γ-rays results from the polarization of the nucleus in the nuclear reaction, which in turn depends on the scattering angle of the α-particle. W (Ωγ) is therefore also dependent on the α scattering angle, and is in general non-isotropic. For the excitation of an even-even nucleus by α-particles to a state with angular momentum J, followed by γ-decay to a 0+ state, the angular correlation can be calculated from the m-state population amplitudes [34] P J m W (θ, φ) = ∑ σ ∣∣∣∣∣∑ m (−1)mP J me −imφdJmσ(θ) ∣∣∣∣∣ 2 , (3.9) where dJmσ(θ) is a rotation matrix. The polar (θ) and azimuthal (φ) angles are defined Theoretical considerations 20 relative to the x-axis in the direction of the beam and the quantization axis perpendicular to the reaction plane. The m-state amplitudes can be obtained in DWBA by P J m = T Jmα′α√∑ m |T Jmα′α |2 ≈ T Jmα′α√ ( dσ dΣ)J (3.10) To calculate the angular correlation, the program code ANGCOR [35, 36] was used. In the code, one needs to define the dynamics of the reaction used to populate the state of interest, the spin and parity involved as well as the mode by which it decays. The form of the decay is calculated from the initial spin substate (m-state) distribution. For α-γ correlations, the calculation is done following the formulation described by Rybicki et al. [37], which follows the phase conventions of Rose and Brink [38]. To obtain the m-state distribution, the DWBA calculation using the coupled-channels code CHUCK3 [39] was used. The optical model parameters needed by CHUCK3 to describe the scattering reaction were taken using the global parameterization of Nolte [40] . CHUCK3 includes only a first-order approximation of the isoscalar form factor to describe collective excitation. In the case of dipole transitions, this corresponds to centre-of-mass motion and thus higher order terms of the form factors are needed. The form factors as defined by Harakeh and Dieperink [41] were calculated as inputs for CHUCK3 using the code FORMF available at [36]. Due to the strong dependence of the angular correlations on the solid angles of the detectors, the respective geometries have to be accounted for. In the case of the HPGe detectors, ANGCOR directly incorporates this factor as calculated from the geometrical attenuation coefficients specified in the input which were determined according to the descriptions in ref. [42]. The solid angle of the K600 was then accounted for by averaging the angular distributions obtained from ANGCOR over the K600 angular acceptance of ±2◦. The procedure summarised above and the necessary input files for each step is described in full detail in [43]. The final averaged angular correlations obtained for 144Sm, 154Sm, 24Mg and 16O using this method are shown in Fig.3.3. The dipole, quadrupole and octapole angu- lar correlations are shown in green, pink and blue respectively. The use of these calculated Theoretical considerations 21 angular correlation patterns in the extraction of the double differential cross-section and for confirming the dipole character of the PDR states under study will be revisited in Chapter 5. Figure 3.3: Angular correlations obtained from ANGCOR after averaging over the opening angle of the K600 spectrometer for 144Sm, 154Sm, 24Mg and 16O. Green, pink and blue correspond to dipole, quadrupole and octapole modes respectively Theoretical considerations 22 Chapter 4 Experimental Techniques and Equip- ment The (α, α′γ) experiments on 154Sm and 144Sm were performed at iThemba Laboratory for Accelerator Based Sciences (iThemba LABS), in South Africa over individual experimental campaigns for each isotope. In both experiments, the Seperated Sector Cyclotron (SSC) provided a beam of alpha particles accelerated between 117 and 120 MeV. The K600 mag- netic spectrometer and its focal plane detection systems were used for the α-particle de- tection whilst the BaGeL array (Ball of Germanium and LaBr detectors) was used for the subsequent γ-rays. In this chapter, an overview of the experimental equipment and tech- niques used are provided. Figure 4.1: Photograph of the experimental set-up in the K600 vault at iThemba LABS 23 4.1 iThemba LABS accelerator facilities The Separated Sector Cyclotron (SSC) is the primary accelerator at iThemba LABS used along with other ancillary facilities to conduct nuclear research. The SSC consists of four C-shaped sector magnets each with a sector angle of 34◦. A layout of the accelerator infrastructure and beamlines is shown in Fig. 4.2. The facility has two injector cyclotrons where beams are produced and pre-accelerated to sufficient energies before entering the SSC. The K=8 Light-ion Solid-Pole Injector Cyclotron 1 (SPC1) has an internal Penning Ionisation Gauge (PIG) ion source and can accelerate particles from protons to heavy ions with a mass-to-charge ration of 0.25. The K=10 Light- ion Solid-Pole Injector Cyclotron 2 (SPC2) has 3 possible external sources; a polarised ion source and two electron cyclotron resonance (ECR) ion sources. Beams from the ex- ternal sources are transported to SPC2 via a transfer beamline and axially injected using a spiral reflector. The accelerated beams from both SPC1 and SPC2 are extracted using an Electrostatic Extraction Channel (EEC) and two magnetic extraction Channels (MEC1 and MEC2). The ECR source and SPC2 were used for the experiments conducted for this thesis. After extraction from SPC2 and further acceleration in the SSC, a pulsed beam with energies of 117.88 MeV and 120.6 MeV were achieved in the experiments for 154Sm and 144Sm data taking respectively. The radio-frequency(RF) of the cyclotron in each case was 33.5 MHz and 33.9 MHz, resulting in a time difference of ˜30 ns between consecutive beam bunches. The beam was then guided through the high-energy beamlines (X, P and S lines) which are equipped with sets of quadrupole and dipole magnets and slits for optimisation, to the K600 Magnetic Spectrometer. In order to optimise the energy resolution of the spectrometer, the beam was dispersion matched to the focusing conditions of the spectrometer. Due to the positioning of the 0◦-beamdump, regular dispersion matching would be tedious to perform and a faint beam technique was used instead [45]. In this technique, the initial beam from the ion source is attenuated using copper meshes, resulting in a reduction of intensity by a factor of up to Experimental Techniques and Equipment 24 Figure 4.2: A schematic layout of the accelerator and ancillary facilities at iThemba LABS [0]. 106 without affecting the profile of the beam. The magnet settings of the spectrometer are then scaled such that the beam passes through the focal plane detectors where the degree of dispersion can be assessed. The beamline elements can then be optimised in order to minimise the size of the beam image observed and thus achieve lateral dispersion matching. Experimental Techniques and Equipment 25 4.2 The K600 magnetic spectrometer The K600 Magnetic Spectrometer is a Quadrupole-Dipole-Dipole (QDD) type spectrometer that was used to detect the scattered α-particles. Figure 4.3 shows a schematic layout of the spectrometer. A quadrupole magnet (Q) at the entrance of the spectrometer enables vertical focusing at the focal plane. The two horizontally-bending dipole magnets (D1 and D2) allow the momentum dispersion to be adjusted by varying the ratio of the two dipole magnets. Figure 4.3: Schematic layout of the K600 magnetic spectrometer. Scattered particles enter the spectrometer via the scattering chamber and are focused by the magnets on the high dis- persion focal plane where they are measured by the Focal Plane Detection System (FPDS). Within each dipole, there is a pole-face current winding coil, the K and H trim coils respect- ively. The K-coil (in D2) has a dipole and quadrupole focusing component, and is used to adjust for first-order kinematic variations of momentum with the horizontal scattering angle (x|θ). The H-coil (in D1) has a dipole and hexapole component, and is used to correct for second-order (x|θ2) aberrations. The terms (x|θ) and (x|θ2) represent the sensitivity of the focal plane position (xfp) to the scattering angle (θscat) of the reaction products [46]. Experimental Techniques and Equipment 26 The particle beam delivered from the accelerator enters the scattering chamber which con- tains a target ladder capable of holding up to six targets. The inelastically scattered particles which are scattered off the target enter the spectrometer and are collimated by one of the collimators installed in front of the quadrupole magnet. The diameter of the collimator thus defines the solid angle acceptance of the spectrometer. The particles are then focused on the high dispersion focal plane of the spectrometer, where a position sensitive detector system is positioned. The unscattered beam is transported through the 0◦-beamline to the 0◦-beamstop embedded in the concrete wall of the experimental area. 4.3 The Focal Plane detector system At the focal plane, a focal plane detector system (FPDS) is in place to determine the energy and scattering angle of the incident particles. The FPDS can accommodate for two multi- wire drift chambers and two plastic scintillation (paddle) detectors. In the experiments conducted, one vertical drift chamber (VDC) with a UX type wire configuration and a single paddle detector were used at the high dispersion focal plane. 4.3.1 Multiwire Drift Chamber The UX type VDC was designed in order to provide a more accurate position discrimination particularly for 0◦ measurements. The chamber contains a set of wire planes; the X signal- wires positioned perpendicular to and the U signal-wires angled at 50◦ to the scattering plane respectively. The wire-planes are sandwiched between three cathode planes composed of 20 µm thick aluminium foil, with an 8 mm spacing between each adjacent wire and cathode plane. The wire-planes consist of alternating signal wires and field shaping wires, spaced 4 mm apart which are composed of gold-plated tungsten. The signal-wires are 20 µm in diameter while the field shaping wires are 50 µm in diameter. In the X wire-plane, there are 199 field shaping wires and 198 signal wires. In the U wire-plane, there are 144 field shaping wires and 143 signal wires. At the ends of both wire-planes are guard wires made from Ni-Cr Experimental Techniques and Equipment 27 (80%/20%) with a diameter of 125µm. For each wire-plane, the signal and field wires are soldered onto a circuit board. Figure 4.4: Photograph of the UX type MWDC as mounted near the focal plane (left) and the U-type wireplane (right) where the wires are inclined at 50◦. Flanking the outer cathode planes, are two Mylar planes of 25 µm thickness which isolate the inner chamber from atmosphere. The chamber is filled with a gas mixture containing Ar (90%) and CO2 (10%) and sealed. A high voltage of − 3.5 kV was applied to the cathode planes, while − 500 V was applied to the field shaping wires. As an α particle passes through the VDC, it ionizes a track along its path. Since the VDC is positioned perpendicular to the spectrometers bending plane, its trajectory will traverse several adjacent drift cells before exiting the VDC. An example of such an event is shown in figure 4.5. The free electrons produced from the ionization drift along the field lines to the closest anode wire where charge multiplication takes place and the signal is registered. The drift time between the primary point of ionization and the point where this charge cascade occurs for a given drift cell is then measured. Since the electric fields are set such that the drift velocity is constant, the corresponding drift distance can be determined [47]. A ray-tracing procedure is thus implemented in which the wire “hits” corresponding to a particular event and their relevant drift distances are determined in order to accurately gauge the intersection point and angle of the particles trajectory with the wire plane. A description of the ray-tracing procedure is given in section 5.1.2. Experimental Techniques and Equipment 28 Field shaping wires (-500 V) Signal wires (Ground) Cathode (-3500 V) Cathode (-3500 V) Figure 4.5: Example of the drift lines associated with a typical particle track travelling through the VDC. 4.3.2 Paddle detector The paddle detector consists of a Bicron BC408 plastic scintillator ( 122 cm x 10.2 cm) connected on either ends to 90◦ twisted pair adiabatic lightguides which are read out by Hamamatsu R329-02 Photomultiplier tubes. The paddle detector serves primarily to provide a fast timing trigger signal for the Data Aquisition (DAQ) system and is also used for particle identification. 4.4 The BaGeL array The BaGeL array (Ball of Germanium and LaBr:Ce3 detectors) was used to measure the γ-rays resulting from the de-excitation of the states populated by the inelastic scattering reaction. The array was designed for the first experiments ever performed at iThemba Experimental Techniques and Equipment 29 Figure 4.6: Photograph of a set of paddle detectors with the scintillators wrapped in foil. The PMT’s are not mounted here. LABS which coupled a gamma detector array with the K600 magnetic spectrometer. In the 154Sm experiments (Exp1), 8 High Purity Germanium detectors (HPGe) and 2 Large volume LaBr:Ce3 detectors (borrowed from Oslo University) were used. In the 144Sm experiments (Exp2), BaGeL was comprised of 12 HPGe and 5 LaBr:Ce3 detectors, obtained as part of the African LaBr:Ce3 array (ALBA) project of iThemba LABS. The detectors were mounted on an oyster-clamp type structure and positioned at backward scattering angles as close to the target chamber as possible. An oyster-clamp mounting structure was used so that the gamma detectors could be moved away from the scattering chamber during beam tuning and moved back in place during data taking without com- promising their positions. This was necessary in order to prevent damage from the large amount of background induced by the beam when impinging on the viewer used for tuning. The oyster-clamp also accommodated for the cooling system of the HPGe and the required pipes and wiring in an orderly manner so that mishaps could be avoided when opening and closing the structure. On the incident faces of the HPGe detectors, thin lead and copper absorbers were placed to shield them against low-energy γ and X rays (̃ 3-5 mm total shielding thickness). In Exp1, Experimental Techniques and Equipment 30 the absorbers were taped on, whilst in Exp2, fitted covers housing the absorbers were 3-D printed to clip onto the HPGe detectors. A photograph of BaGeL mounted around an open scattering chamber during the 144Sm experiment is shown in figure 4.7. Technical details and position information for each detector are summarised in table 4.1 and 4.2 for each experiment respectively. Figure 4.7: Photographs of BaGeL taken during experiments on 144Sm. The detectors positioned to the left and right of the incoming beam are shown in the left and right panels respectively. The beam direction is indicated with yellow arrows. Table 4.1: Table summarising technical details of BaGeL for 154Sm experiments Detector Label Detector Model ref. Distance from target (cm) θ φ L1 Canberra 41 16.3 125.3◦ 45◦ L2 Canberra 39 16.6 135◦ 0◦ L3 Canberra 38 16.7 90◦ 0◦ L4 Canberra 36 16.9 90◦ 35◦ R1 Canberra 63 16.6 90◦ 180◦ R2 Canberra 37 15.9 135◦ 180◦ R3 Canberra 40 16.6 125.3◦ 135◦ R4 Canberra 35 16.5 90◦ 145◦ Experimental Techniques and Equipment 31 Table 4.2: Table summarising technical details of BaGeL for 144Sm experiments Detector Label Detector Model ref. Distance from target (cm) θ φ L1 Canberra 39 18.5 90◦ 300◦ L2 Ortec 2 18.5 90◦ 0◦ L3 Canberra 38 18.5 90◦ 330◦ L4 Canberra 63 18.5 120◦ 25◦ L5 Canberra 61 18.5 120◦ 335◦ L6 Ortec 3 18.0 155◦ 0◦ R1 Canberra 35 18.5 90◦ 149◦ R2 Ortec 1 18.5 90◦ 180◦ R3 Canberra 36 18.5 90◦ 211◦ R4 Canberra 37 18.5 120◦ 155◦ R5 Canberra 40 18.5 120◦ 205◦ R6 Ortec 4 18.0 155◦ 180◦ 4.5 Signal Processing and DAQ 4.5.1 Electronics All the electronics modules used within the experiments comply to NIM and VME standards. A schematic diagram of the electronics for the K600 FPDS is shown in Fig. 4.8. For the VDC’s at the K600 focal plane, 16 channel P-TM 005 cards obtained from Technoland pre- amplify and discriminate the drift time signals from the wire-planes which were read out by CAEN V1190 Time to digital converters (TDC). The signals from the PMT’s at the paddle detector were read out by CAEN V792 charge to digital converters (QDC). In addition, logic outputs from a constant fraction discriminator (CFD) were used to create the trigger signal for the DAQ. A schematic diagram of the electronics for BaGeL is shown in Fig. 4.9 for Exp1 and Fig. 4.10 for Exp2. Each segment of the HPGe Clover detectors were connected to a charge- sensitive pre-amplifier which converts the collected charge deposited within a crystal to a voltage signal corresponding in proportionality to the deposited energy from an incident particle. Two outputs were generated from the pre-amplifier in order to record both an energy and a timing pulse. For the energy, the signal was digitized using a 32 Channel analogue to digital converter (ADC). In the first set of experiments on 154Sm, CAEN V792 Experimental Techniques and Equipment 32 A D C g at e A D C b u s y Figure 4.8: A schematic diagram of the electronics for the K600 focal plane detector system. Experimental Techniques and Equipment 33 ADC’s and CAEN V1190 TDC’s were used. In the second experimental campaign (144Sm data taking), the Mesytec MSCF-16 modules were used which have both the signal timing and voltage signal digitization capabilities. Clover 1 PA 16 ch CAEN Amplifier N568 Clover 2 PA Clover 3 PA Clover 4 PA CAEN ADC V792 4x D elay 50ns F IF O 4 F IF O 3 F IF O 2 4x D elay 50ns 4x D elay 50ns 4x D elay 50ns Ribbon to LEMO CFD QUAD 934 CFD QUAD 934 CFD QUAD 934 CFD QUAD 934 LEMO to Ribbon CAEN TDC V1190 Clover 5PA 16 ch CAEN Amplifier N568 Clover 6PA Clover 7PA Clover 8PA CAEN ADC V792 F IF O 8 F IF O 7 F IF O 5 Ribbon to LEMO CFD QUAD 934 CFD QUAD 934 CFD QUAD 934 CFD QUAD 934 LEMO to Ribbon CAEN TDC V1190 4x D elay 50ns 4x D elay 50ns 4x D elay 50ns 4x D elay 50ns BaGeL Left BaGeL Right Figure 4.9: A schematic diagram of the BaGeL electronics in Exp1. 4.5.2 DAQ system The K600 Data Acquisition System incorporates the Maximum Integrated Data Acquisition System (MIDAS) [48] software to process and store the data digitized by the VME electronics described above. The data is acquired on an event-by-event basis. The MIDAS software features allow for transport of data between multiple computers, thus online analysis and system monitoring are made more convenient. Experimental Techniques and Equipment 34 Clover 1 PA Clover 2 PA Clover 3 PA Clover 4 PA CAEN ADC V792 CAEN TDC V1190 16 ch Mesytec 1 MSCF-16 Amplifier with CFD Clover 5 PA Clover 6 PA Clover 7 PA Clover 8 PA CAEN ADC V792 CAEN TDC V1190 16 ch Mesytec 2 MSCF-16 Amplifier with CFD Clover 9 PA Clover 10 PA Clover 11 PA Clover 12 PA CAEN ADC V792 CAEN TDC V1190 16 ch Mesytec 3 MSCF-16 Amplifier with CFD BaGeL Left BaGeL Right Figure 4.10: A schematic diagram of the BaGeL electronics in Exp2. Experimental Techniques and Equipment 35 Chapter 5 Data Analysis In this Chapter, the data analysis procedures for extracting the experimental cross-sections are presented. During the experiments, data was collected for runs alternating between the 24Mg calibration target with the 154Sm or 144Sm targets for each respective experiment. The raw data for each run is stored in an event-by-event format in a midas file created by the MIDAS Data Acquisition system. These files were then analysed offline using the K600analyser C++ code [49] developed at iThemba LABS. The code translates the raw MIDAS files into ROOT [50] files, with various subroutines to treat the different variables that are then stored as "branches" within a type of relational database called a "TTree". In the first part of the chapter, the offline analysis pertaining to the data collected from the K600 focal-plane detectors is discussed. Thereafter, the data analysis of the gamma ray decay data measured with BaGeL is presented. As in Chapter 4, the experimental period pertaining to the 154Sm data acquisition will be referred to as Exp1 whilst that pertaining to the 144Sm data acquisition will be referred to as Exp2. 5.1 K600 Focal-Plane Data reduction The main components for the reduction of the focal-plane data entail: 1. Selecting the events of interest through performing particle identification. 2. Creating a look-up table which correlates the drift-distances to drift-times in the VDC 36 which are used to accurately determine the position that the α-particle passes through at the focal plane. 3. Implementing a line-shaping correction to further adjust the kinematic aberrations and to improve on the resolution of the measured peaks. 4. Calibrating the position spectrum to excitation energy. In addition to the above mentioned steps, offset corrections are implemented for variations in the particle time-of-flight (TOF), X-position, Y-position and paddle pulse height signals that occur between runs in order to ensure that a common cut selection can be implemen- ted across all the data. Variations in the TOF occur when adjustments to the SSC RF are implemented in order to keep the beam intensity optimized over the duration of data collec- tion. The beam intensity is affected when environmental factors like temperature changes cause the SSC magnets to drift over time. Fluctuations in the beam energy as well as minor adjustments to the magnet settings result in slight variations to the focal plane position for a given excitation peak, while small changes in the paddle signals can be influenced by the performance of the PMT’s over time. The offsets for the above mentioned variables were computed for each run of 24Mg, in which the level density between peaks is much smaller and thus distinct peaks can be identified. The offsets of the closest 24Mg runs were then matched to the corresponding Sm runs. Figure 5.1 shows the variation in focal plane X-position with experiment entries for the chained run data set of 24Mg during the full beam period in Exp2 before and after imple- menting the offsets. Each bin corresponds to 100 000 entries, with the average 30 minute data run containing around 750 000 entries. The variations in 5.1a are caused by minor changes to the K600 magnetic fields when beam tuning was required in order to compensate for issues such as the beam buncher tripping, a power failure and the amplifier to the ion source tripping to name a few examples. As seen in 5.1b, applying the offsets accounts for these variations, and along with the line-shaping corrections described in section 5.1.4, vastly improves the resolution. This also ensures that a common rigidity calibration can be applied to calculate the excitation energy. Data Analysis 37 (a) Before offset implementation (b) After offset implementation Figure 5.1: Variation in Focal plane X position with run entries before and after offset implementation for chained 24Mg data in Exp2. Data Analysis 38 5.1.1 Particle identification The excited nucleus resulting from the nuclear reaction may decay via several decay mech- anisms. In order to select only the events corresponding to the inelastically scattered αs, particle identification is performed by assessing the interaction of the particle as it passes through the detector system. A particle of charge q, mass m and velocity ~v, is subjected to a Lorent’z force exerted by the magnetic field ~B of the spectrometer, described in equation 5.1. The magnetic rigidity gives a measure of the "bending" effect to the particles motion as a result of this magnetic field ~B. It is defined non-relativistically in equation 5.2, where ρ is the radius of curvature of the particle through the spectrometer and p is its corresponding momentum. A particle with higher momentum or smaller charge will thus have a larger resistance to being deflected by a given B field. d~v dt = q γm x~B (5.1) R = Bρ = p q (5.2) The magnetic rigidity thereby influences the position at which the particle passes through the focal plane, as well as the distance d that it travels along its path from the scattering chamber to the focal plane detectors. The time-of-flight correlating to this pathway, ToF = d v , is measured in the experiment as the relative time elapsed between a coincident paddle signal and the RF signal of the SSC. The TOF of the particle, the amount of energy it deposits in the scintillator of the paddle detector and its position at the focal plane can therefore be used to identify it. PID spectra for the 24Mg, 144Sm and 154Sm run data, as well as empty target runs for each experiment are shown in figure 5.2. Data Analysis 39 Figure 5.2: PID spectra shown for 24Mg, 144Sm and 154Sm in the top, middle and bottom panels respectively. The left panels show the paddle detector response as a function of relative TOF from which the various particle contributions are identified. A clear distinction between the α and proton loci can be observed. The beam halo sits just to the top right of the α region of interest. In some runs, the beam halo drifted into this Data Analysis 40 region resulting in a larger background corresponding to the low energy side of the focal plane (̃ 650-780 mm). The right panels show the paddle detector response as a function of the Focal-plane X- position (with the PID cut to the left already implemented). A further graphical cut is applied, as indicated by the red line, in order to further optimise the data selection. 5.1.2 VDC position tracking As described in Section 4.3.1, the position at which a particle passes through the focal plane can be determined using the drift-time characteristics of the detector. The drift distance y, between the signal wire and the point along the particles track at which it crossed a particular drift-cell, can be calculated from: y(t) = ( dN dt )−1 ∫ t t0 dN dt′ dt′ (5.3) where dN dt is the spatial distribution of drift-times, t0 is the time at which the particle arrives in the drift-cell, and t is the time at which the pulse registers at the anode [47]. In order to obtain the characteristic distribution dN dt , a "white spectrum" is used, whereby the focal plane is homogeneously illuminated with particles resulting in uniformly distributed particle tracks. The average timing response of each signal wire is thus measured. Since the drift-time distribution is proportional to the drift velocity ω(t), a look-up table (LUT) is generated which correlates drift-times to drift-distances using equation 5.4. y(t) = ∫ t t0 ω(t′) dt′ ∝ ∫ t t0 dN dt′ dt′ (5.4) A white-spectrum is generally obtained by adjusting the K600 magnets so that particles in the beam continuum can be used to homogeneously illuminate the focal plane. In the case of 0◦ measurements however, this is not as straightforward to do without causing extremely high rates in the focal plane detectors. Data Analysis 41 Instead, one can use scattered particles from the samarium targets to sufficiently illumin- ate the focal plane homogeneously, owing to the high level density of excited Sm states. Thus a Sm data run gated for α particle selection was used to generate the LUTs for each experiment. Since the LUT generated is a global parameter that applies to a full wire plane in general, time delays that vary between the different signal wires must be accounted for before gen- erating the LUT. These delays predominantly arise due to the varying lengths in the cables between the pre-amplifiers and the TDC module. Thus, cable length offsets are implemen- ted such that the trailing edge of the drift time signals for each wire channel are aligned. Figure 5.3 shows the effect of implementing these cable offsets. (a) Before offset implementation (b) After offset implementation Figure 5.3: TDC reference times for the various TDC channels of the VDC wires for Exp2, showing the effect of implementing the cable offset to align the trailing edge of the drift time distributions Figure 5.4 shows the LUT generated for the X wire-plane used in Exp2. Within the experi- ment, the drift times for each wire plane are measured relative to the trigger signal received from the paddle detector. Hence, in the LUT, the shorter drift time correlates to a longer drift distance. Data Analysis 42 Figure 5.4: The Look-up table (LUT) for the X wireplane used in Exp2 Once the drift lengths for all the associated wire cells triggered by a particle traversing a wire-plane are determined, a ray-tracing subroutine is implemented to reconstruct its trajectory and determine the precise point at which the particle crossed the wire-plane. A schematic of a particle traversing through a wire-plane and depositing energy across various drift cells along its track is shown in the upper part of figure 5.5. The separation distance s between each signal wire is indicated, as well as the drift length ywire# between the point of energy deposition and the respective signal wire for each triggered cell. The lower part of figure 5.5 shows the corresponding drift length vs drift cell number spectrum for the set of triggered signal wires. This spectrum ideally should exhibit a "V" type structure due to the inability to deduce information on which side of the wire was actually triggered from drift time alone. Occasionally, "W" and "Z" type structures, as shown in figure 5.6 and figure 5.7, may also occur. Whether these arise due to spurious electronic behaviour or actual physical events is still under question. Part of the ray-tracing procedure therefore functions to remove the uncorrelated events in these "W" and "Z" type structures, in order to reconstruct "V" type event tracks. Data Analysis 43 1 2 3 4 5 6 7 8 Signal wire Guard wire Drift cell Energy deposition region s y 1 y 2 y 3 y 5 y 6 Signal wire drift cell # Signal wire drift cell # 1 2 3 4 5 6 7 8 D rif t Le ng th Figure 5.5: Schematic diagram of a typical trajectory associated with a charged particle passing through a wire-plane, resulting in a V type structure. 1 2 3 4 5 6 7 8 Signal wire Guard wire Drift cell Energy deposition region y 1 y 2 y 3 y 5 y 6 Signal wire drift cell # Signal wire drift cell # 1 2 3 4 5 6 7 8 D rif t Le ng th y 7 y 8 Figure 5.6: Schematic diagram of an event track triggering a "W" type structure Data Analysis 44 Signal wire drift cell # 1 2 3 4 5 6 7 8 Signal wire Guard wire Drift cell Energy deposition region y 1 y 2 y 3 y 5 y 6 Signal wire drift cell # 1 2 3 4 5 6 7 8 D rif t Le ng th y 7 y 8 Figure 5.7: Schematic diagram of an event track triggering a "Z" type structure The ray-tracing subroutines work as follows: (1) It identifies the first and last wires for the set of adjacent triggered wires corresponding to a "V" type track. It further identifies the wire with the shortest drift distance in order to gauge the point of inversion. (2) In the instance where multi-hits occur in a particular drift cell, a logic flow following the conditions highlighted in figure 5.8 is followed in order to choose the drift-distance most likely to correlate to the true particle track. This wire is then excluded from the fitting procedure described later, as for the case where a particle travels very close to the signal wire, the energy cascade resulting from the ionisation does not accurately reflect the true drift distance. This has been observed to affect the fitting procedure such that a poorer position resolution is obtained when included. It is assumed that the trajectory is a straight line within the VDC and thus the slope of Data Analysis 45 If multi-hits: Hits with a drift distance >7.9 All hits with drift distance <7.9 If outer wire Not outer wire Reject shorter drift distance Reject drift distance >7.9 Reject shorter drift distance Figure 5.8: Logic flow in the ray-tracing procedure for determining which drift distance is allocated when multi-hits are fired for a triggered wire. the track is constant. The slope S of the track can be calculated using the drift distances ywire# for any of the adjacent wire pairs that have been "hit" using: Si,i+1 = yi+1 − yi s (5.5) A linear least squares fit over the various slopes computed is then used to interpolate where the particle track intersects with the focal plane. In the case of the U-wire plane, the inclination of the wires at 50º allows to obtain both horizontal and vertical focal plane positions. Assuming a constant slope, the difference in slopes D = S1,2− Si,i+1, for wire hits on either side of the track should ideally be 0. However, statistical fluctuations lead to a distribution centered about 0. The standard deviation σD of this distribution is then be used to estimate the intrinsic cell accuracy σc for the VDC and the cell position accuracy σx as derived in [45] by: σx = σc√ n = σD 2 √ n (5.6) where n is the number of wires used to determine the position at which the track intersects the focal plane. Data Analysis 46 5.1.3 VDC efficiency The operational efficiency (ε) of the VDCs gives an indication to its ability to detect charged particles. It is described by: ε = εg · εi (5.7) where εg is the geometric efficiency and εi is the intrinsic efficiency. The geometric efficiency is assumed to be 100%, since a previous measurement taken at iThemba LABS using a horizontal drift chamber (HDC) indicated that particles of a selected rigidity are well-focused in the vertical focal plane position. The intrinsic efficiency is defined by εi = Naccepted Ntotal (5.8) where Ntotal is the total number of events recorded at the focal plane, for a selected rigidity, and Naccepted is the number of valid events recorded. An event is considered valid based on if it meets the following criteria: • the TOF and paddle signals should fall within gated regions • the number of wires "hit" for an event should be between 3-6 • the reduced chi squared (χ2) of the least squares fit should be less than 1 • and, the drift time should fall within the gated region. The operational efficiency of the combined XU type VDC is then taken as the product of the efficiencies for each individual wire-plane. εUX = εU .εX (5.9) For the 154Sm data runs, εUX was 76% and for the 144Sm data runs, εUX was 94%. Exper- imental factors that affect the efficiency of the VDC include the condition of the gas and the amount of high voltage applied to the respective wire-planes. Data Analysis 47 5.1.4 Line-shaping procedures The position resolution for a given excitation of the residual nucleus, particularly for the 0◦ mode in which the angular acceptance for the spectrometer is ±2◦, is mainly affected by two things. Particles emitted from the target at different reaction angles for the same excitation energy have different momenta and therefore arrive at the focal plane over a more spread out region. Secondly, optical aberrations in the beam profile also have an effect. While the K and H trim coils are used to minimise these effects, the residual effects can be corrected for by using a line-shaping procedure. The effect mentioned above can be observed when looking at the TOF vs Focal-plane po- sition for 24Mg data, where discrete states appear as slanted lines. Figure 5.9 shows the TOF vs X position for peaks around 250 mm (left) and 615 mm (right) which correspond to energies of ˜14 MeV and the 6.4323 MeV 0+ state in 24Mg respectively. The influence of the kinematics is evident as states at lower energy (and hence at the higher focal-plane position) appear more slanted than those at higher energies. Figure 5.9: Relative particle Time of Flight vs Focal plane position zoomed in on the 250mm (left) and 615 mm (right) 24Mg target peaks highlighting the slanting in peaks that affect the position resolution. The line-shaping correction is implemented by correcting the X-position with a 5th order polynomial function dependent on the TOF. This polynomial function is determined from Data Analysis 48 fitting the distribution of the X position about a mean X position for the 6.4323 MeV state, as a function of the ToF distribution about a mean ToF value. This is shown in figure 5.10. Furthermore, the correction is implemented in a linear manner such that the position at 250 mm has a 0 factor correction, while the position at 615 mm has a 1 factor correction. The line-shape corrected spectra are shown in figure 5.11. Figure 5.10: Line-shaping correction parameter extraction as implemented on the 6.432 MeV state around 615 mm. Figure 5.11: ToF vs Focal plane position after implementing the line-shaping correction. Data Analysis 49 5.1.5 Energy Calibration Since the excitation level densities for the Samarium targets are so high, identifying specific excited states to use towards a direct energy calibration can not be performed. Therefore, the focal plane position spectrum was first calibrated with the particles rigidity using the product QBρ for known transitions in 24Mg. The corresponding excitation energy was then calculated for the relevant targets, using the 2-body kinematics equations detailed below: Figure 5.12: Schematic of the kinematics of a nuclear reaction Energy conservation law: E1 + E2 = E3 + E4 + Ex (5.10) Momentum conservation law: p1 = p3 cos θ + p4 cosφ 0 = p3 sin θ − p4 sinφ (5.11) note: E = T +mc2, E2 = p2c2 +m2c4 and Q = (m1 +m2 −m3 −m4)c2. Taking the square of equations 5.11 (p1 − p3 cos θ)2 = p2 4 cos2 φ p2 3 sin2 θ = p2 4 sin2 φ Data Analysis 50 and summing them, result in: p2 1 − 2p1p3 cos θ + p2 3 cos2 θ + p2 3 sin2 θ = p2 4(sin2 φ+ cos2 φ) p2 1 + p2 3 − 2p1p3 cos θ = p2 4 (5.12) From equation 5.10 T1 +m1c 2 +m2c 2 = T3 +m3c 2 + T4 +m4c 2 + Ex (5.13) Ex = T1 − T3 − T4 +m1c 2 +m2c 2 −m3c 2 −m4c 2 Ex = T1 − T3 − T4 +Q (5.14) T1 = Tbeam T3 = √ p2 3c 2 +m2 3c 4 −m3c 2 T4 = √ p2 4c 2 +m2 4c 4 −m4c 2 (5.15) using equation 5.12 T4 = √ p2 1c 2 + p2 3c 2 − 2p1p3c2 cos θ +m2 4c 4 −m4c 2 (5.16) Ex = T1 − √ p2 3c 2 +m2 3c 4 +m3c 2 − √ p2 1c 2 + p2 3c 2 − 2p1p3c2 cos θ +m2 4c 4 +m4c 2 +Q (5.17) For the inelastic scatting case Q = 0, using natural units where c=1: Ex = T1 − √ p2 3 +m2 3 +m3 − √ p2 1 + p2 3 − 2p1p3 cos θ +m2 4 +m4 (5.18) The excitation peaks used for the calibration are identified in the final position spectrum for 24Mg targets shown in figure 5.13 for Exp1 - 154Sm data taking (top) and Exp2 - 144Sm data taking (bottom). In Exp1, a thin 0.7 mg/cm3 24Mg target was used while in Exp2 the 24Mg target was 3.307 mg/cm3. Data Analysis 51 (a) (b) Figure 5.13: Focal Plane X position for 24Mg data indicating the peaks used in the calibra- tion. Data Analysis 52 For the thicker target, the chance for a reaction projectile to interact with the target and undergo small energy losses increases. As result, each excitation peak gets distributed over a wider spread in energy. Hence, the peaks observed for the thin Mg target in Exp1 appear more distinct compared to those in Exp2. In addition, the collimator between the target chamber and spectrometer entrance in Exp2 was placed incorrectly, resulting in approximately 0.3 mm of its metal lip being positioned within the beam stream and hence causing some additional energy losses. As a result, these peaks have a low energy tail. The calibration peaks in Exp1 were fitted with a Gaussian function, while the peaks in Exp2 were fitted with a Gaussian + Exponential function in order to determine the centroid position. The program JRelKin [51] was used to calculate the QBρ values corresponding to the excitation peaks used. The corresponding values for the two experiments are summarised in tables 5.1 and 5.2. The calibration points were then fitted with a 3rd order polynomial function. The calibration curves for the two experiments are shown in figure 5.14 Table 5.1: Summary of parameters used for the rigidity calibration in Exp1 No. E(peak)[MeV ] Jπ X position [mm] QBρ [ekGcm] 1 11.8649 1- 357.303 2985 2 11.7281 0+ 364.002 2987 3 9.3054 0+ 487.669 3022 4 8.4373 1- 532.096 3034 5 8.3580 3- 536.261 3035 6 6.4323 0+ 634.878 3062 Table 5.2: Summary of parameters used for the rigidity calibration in Exp2 No. E(peak)[MeV ] Jπ X position [mm] QBρ [ekGcm] 2 11.7281 0+ 346.2 3023 3 9.3054 0+ 466.6 3057 4 7.6165 3- 550.6 3081 5 7.3490 2+ 563.5 3085 6 6.4323 0+ 609.3 3098 The calibrated excitation energy spectra are shown in figure 5.15. In Exp1, a resolution of 68 keV @ 6.43 MeV was achieved for the 0.7 mg/cm3 24Mg target. While in Exp2, a resolution of 102 keV @ 6.43 MeV was achieved for the 3.3 mg/cm3 24Mg target. Data Analysis 53 Figure 5.14: Rigidity calibration curves fitted with a 3rd order polynomial function for each experiment as indicated (a) (b) Figure 5.15: Calibrated Excitation energy spectra for 24Mg targets of (a) 0.7mg/cm3 and (b) 3.3 mg/cm3 thickness. Data Analysis 54 5.2 BaGeL - Clover Data reduction The main components in the data reduction of the HPGe Clover detectors entail: 1. Calibrating the ADC channels to energy. 2. Selecting the events arriving in the prompt time peak. 3. Implementing an addback procedure between the four crystal segments. 4.