The World Ends Tomorrow and YOU MAY DIE! Well, no, probably not. . . but whatever you do, just keep reading! Cover page illustration by: Karin Rönmark The theory of everything Konstfack University College of Arts, Crafts and Design spring exibition 2009. http://www.karinronmark.se/ List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I P.-A. Söderström, et al. Spectroscopy of Neutron-Rich 168,170Dy: Yrast Band Evolution Close to the NpNn Valence Maximum. Physical Review C, 81:034310, 2010

II G. M. Tveten, P.-A. Söderström, et al. The neutron rich isotopes 167,168,169Ho studied in multi-nucleon transfer reactions. In manuscript.

III P.-A. Söderström, et al. Interaction Position Resolution Simulations and In-beam Measurements of the AGATA HPGe detectors. Nuclear Instruments and Methods in Physics Research, A638:96, 2011.

IV P.-A. Söderström, J. Nyberg, and R. Wolters. Digital pulse-shape discrimination of fast neutrons and γ rays. Nuclear Instruments and Methods in Physics Research, A594:79, 2008.

V E. Ronchi, P.-A. Söderström, J. Nyberg, E. Andersson Sundén, S. Conroy, G. Ericsson, C. Hellesen, M. Gatu Johnson, M. Weiszflog. An artificial neural network based neutron-gamma discrimination and pile-up rejection framework for the BC-501 liquid scintillation detector. Nuclear Instruments and Methods in Physics Research, A610:534, 2009.

Reprints were made with permission from the publishers. Major publications not included in this thesis.

1. K. Straub, et al. Decay of drip-line nuclei near 100Sn. Submitted to the GSI Scientific Report 2010.

2. A. Pipidis, et al. The Genesis of NEDA (NEutron Detector Array): Characterizing its Prototypes. Submitted to the LNL Annual Report 2010.

3. F. C. L. Crespi, et al. Measurement of 15 MeV γ rays with the AGATA cluster detectors. Submitted to the LNL Annual Report 2010.

4. M. ¸Senyigit,˘ et al. AGATA Demonstrator Test with a 252Cf Source: Neutron-Gamma Discrimination. Submitted to the LNL Annual Report 2010.

5. D. D. DiJulio, et al. Electromagnetic properties of vibrational bands in 170Er. Eur. Phys. J., A47:25, 2011.

6. S. Hirayama, et al. Production of protons, deuterons, and tritons from carbon bombarded by 175 MeV quasi mono-energetic neutrons Prog. Nucl. Sci. Tech., 1:69, 2011.

7. B. Cederwall, et al. New spin-aligned pairing phase in atomic nuclei inferred from the structure of 92Pd. Nature, 469:68, 2011.

8. T. S. Brock, et al. Observation of a new high-spin isomer in 94Pd. Phys. Rev. C, 82:061309, 2010.

9. A. Blazhev, et al. High-energy excited states in 98Cd. J. Phys. Conf. Ser., 205:012035, 2010.

10. R. Wadsworth, et al. The northwest frontier: Spectroscopy of N ∼ Z nuclei below mass 100. Acta Phys. Polon., B40:611, 2009.

11. P.-A. Söderström, et al. AGATA: Gamma-ray tracking in seg- mented HPGe detectors. In Proceedings of the 17th International Workshop on Vertex detectors, PoS (VERTEX 2008), page 040. Sissa, 2009.

12. U. Tippawan, et al. Studies of neutron-induced light-ion production with the MEDLEY facility. In O. Bersillon, et al. (editors), Proceedings of the International Conference on Nuclear Data for Science and Technology 2007, page 1347. EDP Sciences, 2008. 13. M. Hayashi, et al. Measurement of light-ion production at the new Uppsala neutron beam facility. In O. Bersillon, et al. (editors), Proceedings of the International Conference on Nuclear Data for Science and Technology 2007, page 1091. EDP Sciences, 2008.

14. M. Hayashi, et al. Neutron-induced proton production from carbon at 175 MeV. In T. Hazama and T. Fukahori (editors), Proceedings of the 2007 Symposium on Nuclear Data November 29-30, 2007, Ricotti, Tokai, Japan, volume JAEA-Conf 2008-008, page 62. Japan Atomic Energy Agency, Tokai-mura, Japan, 2008.

15. P.-A. Söderström. Detection of fast neutrons and digital pulse shape discrimination between neutrons and γ rays. In A. Covello, et al. (editors), Proceedings of the International School of Physics ’Enrico Fermi’, volume 169 Nuclear Structure far from Stability: new Physics and new Technology, page 551. SIF, Bologna and IOS Press, Amsterdam, 2008.

16. M. Hayashi, et al. Effect of nuclear interaction loss of protons in the response of CsI(Tl) scintillator. Engineering Sciences Reports, Kyushu University, 29:374, 2008.

Contents

1 Background ...... 1 1.1 Nuclear structure ...... 3 1.1.1 The nuclear landscape ...... 3 1.1.2 Spin and energy ...... 5 1.2 Nuclear astrophysics ...... 6 1.2.1 S-process ...... 8 1.2.2 R-process ...... 8 1.2.3 P-process ...... 9 1.2.4 Rp-process ...... 9 1.2.5 νp-process ...... 9 1.3 Radioactive ion beam facilities ...... 10

Part I: Physics 2 Theory of deformed nuclei ...... 13 2.1 Nuclear deformation ...... 13 2.1.1 Nilsson model ...... 15 2.1.2 Particle plus triaxial rotor model ...... 17 2.1.3 Cranking model ...... 19 2.1.4 Variable moment of inertia model ...... 20 2.2 Nuclear deformations in the r process ...... 21 2.3 Heavy-ion induced nuclear reactions ...... 24 3 PRISMA and CLARA experiment ...... 27 3.1 LNL accelerator complex ...... 29 3.2 PRISMA ...... 29 3.2.1 MCP ...... 30 3.2.2 Quadrupole and dipole magnets ...... 32 3.2.3 MWPPAC ...... 33 3.2.4 Ionization chambers ...... 33 3.2.5 Mass determination ...... 35 3.3 CLARA ...... 38 3.4 Dysprosium isotopes ...... 40 3.5 Holmium isotopes ...... 42 4 Evolution of collectivity ...... 45 4.1 Variable moment of inertia ...... 45 4.2 Deformations in odd-A nuclei ...... 47 4.3 Rigidity and backbending ...... 49 Part II: Technology 5 The AGATA HPGe spectrometer ...... 55 5.1 HPGe crystals ...... 56 5.2 Electronics ...... 56 5.3 Pulse-shape analysis ...... 58 5.4 Tracking of γ rays ...... 59 5.5 Data acquisition ...... 60 5.6 Position resolution ...... 61 5.6.1 Reaction selection and simulations ...... 63 5.6.2 Experiment ...... 65 5.7 Neutrons in AGATA ...... 67 6 Neutron detector NEDA ...... 71 6.1 SPIRAL2 ...... 71 6.2 The Neutron Wall ...... 72 6.3 The neutron detector array NEDA ...... 72 6.3.1 The BC-501A and BC-537 liquid scintillators ...... 73 6.3.2 Geometry ...... 74 6.3.3 Detection of scintillation light ...... 74 6.3.4 Electronics ...... 75 6.4 Digital pulse shape analysis ...... 76 6.4.1 Charge comparison and zero cross-over ...... 76 6.4.2 Artificial neural networks ...... 80 6.4.3 Time resolution ...... 80

Part III: Discussion 7 Outlook ...... 87 7.1 AGATAatLNL...... 87 7.2 AGATAatGSI...... 89 7.3 AGATA at SPIRAL2 ...... 90 8 Concluding remarks ...... 93 9 Kollektiv kärnstruktur hos neutronrika sällsynta jordartsmetaller och nya instrument för gammaspektroskopi ...... 95 10 Acknowledgements ...... 99 Bibliography ...... 103 Contribution to the papers ...... 121 List of Acronyms

ACTAR Active Targets

ADC analog-to-digital converter

AGATA Advanced Gamma Tracking Array

AGAVA AGATA VME Adapter

ALICE A Large Ion Collider Experiment

ANN artificial neural network

APD avalanche photodiode

ATC AGATA triple-cluster

BCS Bardeen, Cooper and Schrieffer

BGO bismuth germanate

B2FH Burbidge, Burbidge, Fowler and Hoyle

CARMEN Cells Arrangement Relative to the Measurement of Neutrons

CERN Organisation Européenne pour la Recherche Nucléaire

CIME Cyclotron pour Ions de Moyenne Energie

CLARA Clover Detector Array

CNO carbon, nitrogen and oxygen

CPU central processing unit

DANTE Detector Array for multi-Nucleon Transfer Ejectiles

DAQ data aquisition system

DESCANT Deuterated Scintillator Array for Neutron Tagging

DESIR Désintégration, Excitation et Stockage des Ions Radioactifs

DSP digital signal processor ESS European Spallation Source FAIR Facility for Antiproton and Ion Research FAZIA Four pi A and Z Identification Array FET field-effect transistor FOM figure-of-merit FPGA field programmable gate array FRS fragment separator FWHM full width at half maximum GANIL Grand Accelerateur National d’Ions Lourds GASPARD Gamma Spectroscopy and Particle Detection GDR giant dipole resonance GRETA Gamma Ray Energy Tracking Array GSI Gesellschaft für Schwerionenforschung mbH GTS global trigger and synchronization GUI graphical user interface HELIOS Helical Orbit Spectrometer HPGe high-purity germanium IBFM interacting boson-fermion model IBM interacting boson model IC ionization chamber ILL Institut Laue-Langevin IReS Institut de Recherches Subatomiques de Strasbourg ISAC Isotope Separator and Accelerator ISOL isotope separation on-line LHC Large Hadron Collider LINAC linear accelerator LNL Laboratori Nazionali di Legnaro LYCCA Lund-York-Cologne Calorimeter MCP micro-channel-plate MS/s megasamples per second MSU Michigan State University MWPPAC multi-wire parallel-plate avalanche counter NARVAL Nouvelle Acquitision temps-Reel Version. 1.6 Avec Linux NEDA Neutron Detector Array NFS Neutrons for Science NIM Nuclear Instrumentation Module PARIS Photon Array for studies with Radioactive Ion and Stable beams PC personal computer PMT photomultiplier tube PSA pulse-shape analysis PSD pulse-shape discrimination QCD quantum chromodynamics RHIC Relativistic Heavy Ion Collider RIB radioactive ion beam RIKEN Rikagaku Kenkyusho¯ RISING Rare Isotope Spectroscopic Investigation at GSI S3 Super Separator Spectrometer SPIRAL Système de Production d’Ions Radioactifs en Ligne TOF time-of-flight TRIM Transport of Ions in Matter TRS total Routhian surface VME Versa Module Europe VMI variable moment of inertia WMAP Wilkinson Microwave Anisotropy Probe ZCO zero cross-over

List of Figures

1.1 Illustration of the particles of the standard model and their tree-level interactions ...... 2 1.2 Selection of nuclear structure topics in the nuclear chart and in the E − J plane ...... 4 1.3 Periodic table from an astronomer’s point of view and a geol- ogist’s point of view ...... 7

2.1 Collective excitations of an atomic nucleus ...... 14 2.2 Nilsson diagram for protons, 50 ≤ Z ≤ 82...... 17 2.3 Solar r-process abundances, contours of constant neutron sep- aration energy and constant β-decay rates ...... 22

3.1 The region of interest, for this work, in the Segré chart ...... 28 3.2 The PRISMA and CLARA set-up ...... 28 3.3 Sketch of the PRISMA spectrometer ...... 31 3.4 Positions of the reaction fragments as measured by the MCP . 31 3.5 The positions and time-of-flight in the MWPPAC ...... 34 3.6 Partial energy loss and range of the fragments with respect to the total energy loss of the fragments in the IC ...... 36 3.7 Relative mass of the fragments with respect to their position in the MWPPAC and the bending radius with respect to the energy used to obtain the absolute mass ...... 36 3.8 Mass spectrum from PRISMA of target-like fragments gated on krypton ...... 38 3.9 The CLARA HPGe detector array ...... 39 3.10 Doppler-corrected spectra from beam-like and target-like fragments as recorded by CLARA ...... 40 3.11 Time-of-flight with respect to γ-ray energy for a selection on 168Dy...... 41 3.12 Spectrum of γ-ray energies from target like fragments gated on 168Dy ...... 42 3.13 Spectrum of γ-ray energies from targetlike fragments gated on 170Dy...... 43 3.14 Ground state rotational bands for dysprosium isotopes with N = 94 − 104...... 43 3.15 Ground state rotational bands for 167Ho and 169Ho and the level scheme for 168Ho...... 44

4.1 Quadrupole deformation parameters β2 for even-even nuclei according to the Möller and Nix calculations and experimen- tally measured β2 deformations ...... 46 4.2 Experimentally measured β2 values and Harris parameters for a selection of even-even nuclei ...... 46 4.3 Projections of the particle plus triaxial rotor parameter space for 100 000 random points ...... 48 4.4 Total Routhian Surface calculations of Dy isotopes with 160 ≤ A ≤ 170...... 50 4.5 Total Routhian Surface calculations of Ho isotopes with 161 ≤ A ≤ 171...... 51

5.1 The AGATA HPGe crystals ...... 57 5.2 Signals from the core, the segment with the primary hit, and from the mirror charges for a γ-ray interaction in a six fold segmented HPGe detector ...... 57 5.3 Simulated interaction points of 30 γ rays of energy Eγ = 1.33 MeV in the (θ,φ sinθ) plane of an ideal germanium shell ...... 59 5.4 Effects of the position resolution when determining the angle used to correct for the Doppler shifts of the γ rays ...... 62 5.5 The difference between the calculated interaction position res- olutions and the mgt smearing parameter ...... 66 5.6 The AGATA detector in position for the first commissioning experiment ...... 67 5.7 Gamma-ray spectrum measured using the 30Si +12 C reaction with the AGATA triple cluster detector ...... 68 5.8 Interaction position resolution as a function of γ-ray energy . . 69 5.9 The AGATA and HELENA detectors in position for the neu- tron experiment...... 69

6.1 Pulse shapes from a BC-501 liquid scintillator from a γ ray and a neutron interaction ...... 74 6.2 Possible geometry of the NEDA detector array ...... 75 6.3 Weighting function for digital and analogue charge compari- sonPSD...... 77 6.4 Difference between the integrated rise time of a γ-ray and a neutron pulse ...... 78 6.5 FOM and R for the ZCO and charge comparison based meth- ods as a function of energy, bit resolution and sampling fre- quency ...... 79 6.6 Fraction of incorrectly identified γ-ray and neutron events as a function of the deposited energy for the artificial neural network 81 6.7 Sampling of a Gaussian function with a time between sam- pling points equal to the σ of the Gaussian function ...... 82 6.8 The measured times, T, as a function of T1 and the time dis- tributions due to the finite sampling frequency ...... 83 6.9 Time distributions folded with a typical Gaussian time resolu- tion of a liquid scintillator detector plus PMT ...... 84

7.1 Grazing calculations of production cross-sections for dyspro- sium isotopes ...... 88 7.2 Calculated production cross-sections of the Dy isotopic chain intheFRS...... 90

1. Background

“Thence come the maidens mighty in wisdom, Three from the dwelling down ’neath the tree; Urðr is one named, Verðandi the next, On the wood they scored, and Skuld the third. Laws they made there, and life allotted To the sons of men, and set their fates.” – Prophecy of the Völva

Since the dawn of time women and men have thought about the world, why it looks the way it does and what it is actually made of. In order to understand nature, observations have been made and based on these (and a fair amount of imagination to fill in the blanks) conclusions have been drawn about the universe. One example of the early beliefs about the world is from the Nordic countries, where the three norns Urðr, Verðandi and Skuld weaved the fabric of reality at the roots of the world tree Yggdrasill. Nothing could be found outside of this weave, since it contained the entire cosmos [1]. These days, the number of observations is much larger and the scientific method has been developed. Thus, our understanding of the universe is much more accurate today than during the days of the Vikings. There are still, how- ever, many blanks to fill. In order to fill some of these blanks, the present front-line of theoretical physics considers another weave. Using a mathemat- ical formulation of the most fundamental constituents of matter as tiny multi- dimensional Planck scale threads making up space-time itself, the reality can be modelled through these threads different vibration patterns. This theory is known as the supersymmetric string theory, or simply superstring theory [2]. However, even if this theory aims at describing the universe from first princi- ples it is very much under development and still far from being experimentally testable. So at the moment, the most fundamental description of the world is instead given by an effective theory called the standard model [3–5]. The standard model describes the universe in terms of the electromagnetic, the weak and the strong nuclear interactions that govern the dynamics between the fundamental particles: quarks1 and leptons that make up the matter and bosons to mediate the interactions between these. Furthermore, the standard model contains an additional boson, the Higgs boson [8, 9], that generates

1The name quark was given by Murray Gell-Mann and is a actually nonsense word from the book Finnegan’s Wake, by James Joyce, where the sentence “Three quarks for Muster Mark” is sung by a chorus of sea birds [6, 7].

1 Figure 1.1: Illustration of the particles of the standard model and their tree-level inter- actions. The leptons in the standard model are the electron (e), the muon (μ), the tauon (τ) and their corresponding neutrinos (νe,νμ ,ντ ). The quarks of the standard model are the up (u), down (d), charm (c), strange (s), top (t) and bottom (b) quarks. The quark-gluon structures of the proton (uud) and neutron (udd) are also shown. Figure from [10]. mass to some of the particles. The Higgs boson is the only particle of the standard model yet to be discovered. See figure 1.1 for an illustration of the particles of the standard model and their respective interactions. All matter that we encounter in everyday live is made up of atoms. The atoms in turn are composed of an atomic nucleus, with a specific number of protons [11, 12] and neutrons [13] (together commonly referenced as nucleons), surrounded by a cloud of electrons. Nuclear matter is governed by the interaction between the fundamental standard model particles quarks and gluons. This part of the standard model is known as the quantum chromodynamics (QCD) [14] and could in principle be used to calculate any feature of the nuclear matter, although this is a very complicated task. As of today, lattice QCD has successfully been used to calculate the mass of the proton2 [16]. Even if this is a great achievement it is still a long way to go before QCD can be used to understand the complex dynamics of a many-body nuclear system. To reduce the complexity of these calculations one can construct effective nucleon-nucleon interactions from QCD or experiments. Using these it is pos- sible to calculate the properties of any nuclear system from the first principles, ab initio, of this effective theory. For practical reasons one is, however, limited

2There is, however, some controversy about this statement. Since the calculations are carried out for heavier quarks masses the results must be scaled down to the physical masses through chiral extrapolation [15].

2 to few-body systems. When the system becomes too large, also the ab initio calculations become unfeasible. The largest system that so far has been stud- ied ab initio using an importance-truncated no-core shell model is 40Ca [17]. To study heavier nuclear systems, but also to simplify the study of lighter sys- tems, different models based on phenomenological observations of the nuclear matter are introduced. Some of these models will be presented in further detail in chapter 2.

1.1 Nuclear structure As mentioned earlier, each atomic nucleus is made of a specific number of protons and neutrons. The nucleus is usually denoted AXx, where Xx is the element label and A is the number of nucleons in the nucleus. For lighter nuclei the number of protons and neutrons are approximately the same, while heavier nuclei consist of more neutrons than protons. The chart of nuclides, or the Segré chart, is a plot of the number of protons versus the number of neutrons, see figure 1.2. As seen in the Segré chart, the number of stable nuclei are very few. Arranged in a bent line called the line of β stability, there are only about 250 of them. Many more nuclei can, however, be constructed either in laboratories on earth or in violent astrophysical events like supernovae explosions. About 3000 elements have up to now been created and observed in laboratories, but theorists predict that more than 6000 bound nuclei can exist between the neu- tron and proton drip-lines, which are defined as the limits of nuclear existence. The physics of these very exotic nuclides is to a large extent unknown and many surprises probably await in this terra incognita.

1.1.1 The nuclear landscape One of the most notable features in figure 1.2, the line of β stability, roughly follows a pattern of lines with certain values of the number of protons and neutrons. These numbers, called the magic numbers, represent the nuclei in nature that are most tightly bound and form closed shells where the main structure properties comes from the behaviour of the nucleons outside these shells. The shell model of spherical nuclei is one of the most fundamental of nuclear physics and is well described in many standard references [18–24]. Some calculations also suggest the existence of new magic numbers larger than has been observed so far. These new magic numbers could cause an “Is- land of Stability” of superheavy elements where completely new long-lived chemical elements would appear. For further details regarding the discovery of super-heavy elements see reference [25] and references therein. To test the nuclear shell model it is of much interest to explore the proton- rich side of the line of β stability. The proton-rich region around 100Sn is,

3 Nuclear Structure nuclear masses, superheavy half-lives & radii elements Far From Stability: 298X ?? 114 184 Current Topics 126 proton-neutron 310Z ?? pairing 126 184 114 XIXII I X II IX III VIII IV VII VI V ground-state 184 proton emitters

82 Vp superallowed 150Sn ] -3 decay p n

"skins" [fm

N=Z 14 + 468 O 0 2 50 r [fm] A=120 isobars: Nd to Sr + V 126 ud evolution of shell structure 126 14 + A=1 N 0 b E 82 20 50 28 82 neutron number stable nuclide 20 50 r-process +/EC decay - decay 8 decay 20 2 p emitter 28 spontaneous 11 ''halo" Li extreme shapes fission protons nuclei (n, ) (n, ) predicted neutrons nuclide

©1998 Margareta Hellström, LU - Based on an idea by Brad Sherrill, MSU.

band termination high-K isomers pairing collapse? 60 =

collective 0 PNP = behavior collapse p n p h n -ray ion energy

t hyper- a

t n deformation tio ma perdefor exci su 149Gd, 148Eu chaos aggering t S

shape e Gamma-ray energy lin I=2 vibrations st yra staggering

j j energy { 192Hg 194Hg gap R M1 0+ even- M1 odd A even-even M1 identical bands even odd-Z odd-N odd-odd rigid body 158 pair gap Er

Sm Gd Er Yb "shears" bands Dy Hf small W h Nd Os back- angular momentum moments bending of inertia

©1998 Margareta Hellström, LU - Based on an idea by Mark Riley, FSU.

Figure 1.2: Selection of nuclear structure topics in the nuclear chart, with proton num- ber versus neutron number, (top) and in the excitation energy versus angular momen- tum plane (bottom). By M. Hellström, based on ideas by M. Riley and B. Sherrill.

4 for example, an ideal testing ground for another important aspect of nuclear structure physics, the proton-proton, neutron-neutron and proton-neutron pair- ing [26]. The nucleus 100Sn is the heaviest self-conjugate doubly-magic nu- cleus that is expected to be bound, first discovered by two independent experi- ments [27, 28] and recently studied using the fragment separator (FRS) at GSI [29, 30]. On the neutron rich side of the Segré chart, the only area where the drip- line has been reached is the area containing the light neutron-rich nuclei. The first time this area was explored the results showed that some neutron-rich nuclei, in particular 11Li, had an abnormally large size. In fact, 11Li has the same size as 208Pb despite the much fewer number of nucleons. This was interpreted as 11Li being a so called Borromean3 halo nucleus consisting of a 9Li core surrounded by a halo of two neutrons, a picture that was confirmed by further measurements on 11Li [31, 32]. Future efficient and precise neutron detectors, see chapter. 6, can provide an opportunity to further understand the structure, radii, masses and reaction probabilities of neutron-rich exotic nuclei. Such understanding is crucial for the knowledge of how the chemical elements we are made of are created through a process called the r-process, further discussed in section 1.2.

1.1.2 Spin and energy The study of the structure of nuclei often involves measuring the characteristic energies and angular distributions of particles (for example electrons, neutrons or α particles) or γ rays emitted from these nuclei. In order for particles or γ rays to be emitted from a nucleus it must be provided with some excess en- ergy. For closed shell nuclei this excess energy can be understood in terms of rearrangement of the nucleons within the shell structure. For collective sys- tems like a rigid, deformed nucleus excitation energy could for example go into nuclear rotation, increasing the angular momentum, or spin, of the nu- cleus. When all excess energy goes into angular momentum and no energy into other excitation modes, for example shape vibration, the nucleus is said to be in an yrast4 state. The yrast line is illustrated in figure 1.2, together with some phenomena that can occur when providing the nucleus with excitation energy. Even if the collective properties give a good description of the nucleus at low spin and excitation energy, the properties of high spin states will show that the nucleus cannot simply be described by only collective motion, but that the

3This name comes from the Borromean family crest which is made of three rings entwined such that if one is removed the entire system falls apart. In the same way the Borromean halo nuclei consist of a nucleus and a halo of two neutrons, while neither system of the specific nucleus and one neutron halo nor the system of two neutrons are bound. 4The name yrast originates from a Swedish play with words. Literally it translates to “most dizzy”, which you of course become if you spin as fast as you can.

5 properties of the individual nucleons are also very important. One example of this is when the nucleon-nucleon pairs break and the angular momentum is reduced with increasing excitation energy, an effect called backbending that was first discovered in 1971 [33]. The influence of single particles on the collective behaviour of nuclei also gives rise to other effects. One of these being when the single particles of the broken pairs have a large spin along the axis of nuclear symmetry, giving rise to long lived excited states called high-K isomers [34]. These high-K isomeric states close to the yrast line results from the nuclear system being well ordered with clear rules for how it can decay. At higher excitation energies the nuclear system is fully chaotic. This region of order-to-chaos transition is another example of where the nuclear many-body system is yet to be fully understood [35, 36]. But not all high energy excitations show this chaotic behaviour. At high ex- citation energies with small angular momentum other kinds of collective be- haviour can be observed where the nucleus can be interpreted as separated into proton and neutron fluids and, for example, oscillate against each other [37] or have rotational oscillations with opposite phase around a common axis [38]. This kind of collective behaviour is usually referred to as giant resonances, and will be briefly discussed in section 5.7. This is just a small selection of the different phenomena shown in figure 1.2, which in turn is just a small selection of the different phenomena that occur in the atomic nuclei. It should, however, be clear that nuclear many-body systems are very complex and that there is a long way before its phenomenology can be explained from the first principles of QCD.

1.2 Nuclear astrophysics To answer the question where matter, as we know it, originates from we should go back to the beginning of the universe. The current model of the universe says that it originated from a singularity that expanded into its current size. This model is referred to as the Big Bang, based on an idea of Lemaître [39] that was first confirmed by Hubble [40] and have been confirmed many more times after that, most recent by the Wilkinson Microwave Anisotropy Probe (WMAP) measurement of the cosmic microwave background [41] to test the cosmic inflation theory. The very first moment is currently beyond our physical understanding and would require a theory that combines quantum field theory with gravity, for example the previously mentioned superstring theory [2]. However, the uni- verse expanded and about 10−12 s after the Big Bang the four forces took their current form. The universe then consisted of hot quark-gluon plasma. This is the first point in the time line of the universe where nuclear physics, although at very high energies, plays an important role in our understanding of nature. The study of the quark-gluon plasma is a task that has been undertaken at the

6 H He

CNO Ne

Mg Si S

Fe

H

LiBe BCNOF

Na Mg Al Si P S Cl

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br

RbSrY ZrNbMo RuRhPdAgCdInSnSbTeI

Cs Ba La1 Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi

Ac2

Figure 1.3: Periodic table from an astronomer’s point of view (top) and a geologist’s point of view (bottom). The size of the box is proportional to the element abundance. From reference [45].

Relativistic Heavy Ion Collider (RHIC) [42] and that will be further studied by ALICE at the Large Hadron Collider (LHC) [43]. As the universe expanded and cooled further, neutrons and protons formed and together fused into the light elements. A first attempt to describe this early nucleosynthesis was made by Alpher, Bethe and Gamow [44]. After the Big Bang nucleosynthesis, the universe consisted of about 75 % hydrogen, 25 % helium and some traces of heavier elements. This is approximately true also today from an astronomical point of view, apart from a small amount of heavier elements, see figure 1.3. From a geological point of view, however, the picture is very different. If we look around us we see many elements other than hydrogen and helium. The distribution of elements in the earth’s crust is illustrated in figure 1.3. These elements must have been created somewhere else than in the Big Bang, for example in the fusion processes of a star. In the beginning of a stars life it burns with the same process as in the Big Bang nucleosynthesis, that is proton- proton fusion into deuterium and further into helium [46] or, if these elements exist, a thermonuclear cycle involving carbon, nitrogen and oxygen (CNO) [46, 47]. When the core of the star has run out of hydrogen it will instead

7 start to burn helium, creating 12C5. The carbon can then be further used as a starting point to synthesise heavier elements through reactions such as 12C + 4He, 16O+ 4He, 12C+ 12C, 16O+ 16O and similar. For details, see for example reference [48]. There is, however, still a problem with this model. The nuclei that are most tightly bound are the nuclei around iron, thus the star cannot gain energy by fusing heavier nuclei. A solution to this problem came with the breakthrough paper by Burbidge, Burbidge, Fowler and Hoyle (B2FH) [49]. In that paper, three different processes to synthesise heavier nuclei were proposed, called the s-process, the r-process and the p-process.

1.2.1 S-process The first process that was proposed in the B2FH paper was the slow neutron- capture process, or s-process. This is a process that occurs at locations with a low density of neutrons and an intermediate temperature, for example in a type of red giant stars called asymptotic giant branch stars. It starts with a seed nucleus from the iron area, the endpoint of the charged particle reactions. These stable nuclei capture neutrons, turning them into radioactive isotopes of the same element. The half life of this radioactive isotope is then determining the probability for the nucleus to capture another neutron, or decay. When the neutron capture probability becomes so small that the average time for neutron capture is larger than the half life, it will β decay to the next heavier element, turning one neutron into a proton and an electron. In this way, the line of β stability is followed closely up to 209Bi, the heaviest stable element. Since this process involves stable and close-to-stable nuclei most of them are accessible for detailed measurements of neutron capture cross sections and β decay half-lives.

1.2.2 R-process As the s-process can only create nuclei up to 209Bi it cannot explain the exis- tence of the heavier naturally occurring elements like 232Th, 235U and 238U. Furthermore, the s-process does not reach stable neutron-rich intermediate- mass nuclei further away from the line of β stability. The process suggested in the B2FH paper for the creation of these elements was instead the rapid neutron-capture process, or r-process. While the s-process occurs at areas in the universe with a low density of neutrons so that the average time for neu- tron capture in general is smaller than the half life of the radioactive isotope, there are other areas of so high neutron densities that the half life of the ra- dioactive isotope is negligible. These very high neutron density areas can be found in core-collapse supernovas like the famous supernova SN1987A in the Large Magellanic Cloud [50, 51]. In these areas the neutron capture rapidly

5As 8Be is unbound, three helium nuclei are required in this process.

8 creates very neutron rich nuclei that, when the process stops, either β decays or fissions back to β stability. Since this process occurs close to the neutron drip-line in the terra incognita, very little is known of the exotic nuclei par- ticipating in this process. As discussed in section 1.1 many surprises prob- ably awaits there, some of which will be discovered at the radioactive ion beam (RIB) facilities discussed in section 1.3.

1.2.3 P-process The third process proposed in the B2FH paper was the proton-capture process, or p-process, to explain the heavy proton-rich nuclei that cannot be produced by the s- or r-process, for example 190Pt or 168Yb. It occurs in similar areas as the r-process, core-collapse supernovas, but instead of neutron-capture the γ rays in this high temperature environment removes neutrons from the nuclei and thus increases the proton ratio of the resulting nucleus. It is not actually so much of a proton-capture process, but more of a neutron-removal process.

1.2.4 Rp-process The rapid proton-capture process, or rp-process [52], is not one of the original B2FH processes, but the process in which the lighter proton-rich nuclei are created. Although the end point of the rp-process is not precisely known it is estimated to be located in the area around nuclei with 100 nucleons and at least less than tellurium [53]. To establish this endpoint is one of many motivations for the study of atomic nuclei around 100Sn [29]. The rp-process takes place right after the thermonuclear explosion of a binary system consisting of a neutron star that is accreting hydrogen and helium from another star. This explosion causes a very hot and proton rich environment where consecutive proton captures can occur.

1.2.5 νp-process A quite recently suggested astrophysical process to complement the four clas- sical processes is the νp-process [54, 55] that have emerged from advances in core-collapse supernova simulations. When a core-collapse supernova occurs the γ radiation and proton-rich matter is accompanied also by a large neutrino, ν, and antineutrino, ν¯ , emission [51]. This emission can cause the total dis- integration of heavy nuclei into protons and neutrons. When these recombine into nuclei in the hot environment after the explosion, similar as the fusion processes in stars, elements up to iron are recreated. However, antineutrino capture in these nuclei will result in protons transforming into neutrons, al- lowing the process to flow past iron creating intermediate-mass proton-rich nuclei.

9 1.3 Radioactive ion beam facilities To study the physics described in previous sections specific tools and methods are needed. The very first use of an ion beam for studies of nuclear reactions was done by Rutherford when he used a collimated 226Ra source of α parti- cles together with a nitrogen gas [56]. This work was followed by Cockcroft and Walton who designed a machine that, instead of using radioactive decay as a source for particles, used electric fields to accelerate ions to study nuclear reactions [57]. Around the same time the neutron was discovered [13] and in 1942 the first artificial nuclear reactor was built under the stands of a football stadium at the University of Chicago6 [60]. After this, the fission of uranium made it possible for a large number of neutron-rich radioactive isotopes to be produced and studied. For example, by bombarding a uranium target with a particle beam it was possible to produce radioactive noble-gas isotopes and study them in an electromagnetic isotope separator [61], a method that is now called isotope separation on-line (ISOL). The ISOL method was further re- fined in Louvain-la-Neuve where the isotope separator was connected to the existing accelerator complex, creating an accelerated beam of radioactive ions [62]. Another method, developed at Oak Ridge National Laboratory, to separate fission fragments of different types from each other is to use magnetic fields that give a mass separation of the fragments when they are emitted in-flight from a thin target [63]. This in-flight fragmentation technique has now been developed so that instead of using the fission energy to give the fragments the necessary kinetic energy, a heavy-ion beam is accelerated to high energies, typically to about 50% of the speed of light. To produce the RIB, one lets the primary heavy ion beam hit a light target like beryllium after which it will either fragment or fission into a cocktail of reaction products. The reaction products are then separated by a system of dipole magnets, quadrupole mag- nets and energy degraders. This technique is implemented at, for example, the FRS at GSI [64]. Many modern facilities for RIB production have recently been built or will be built in the future. For example the RIB factory at RIKEN [65], the new RIB facility at Michigan State University (MSU) [66], the upgrade to ISAC- III [67] at TRIUMF, the upgrade to HIE-ISOLDE at CERN, the upgrade to SPIRAL2 [68] and the future EURISOL at GANIL, the upgrade to the Super- FRS at FAIR and the new RIB facility SPES [69] at Laboratori Nazionali di Legnaro (LNL). These new facilities will require powerful experimental set- ups, two of which that are discussed in chapter 5 and chapter 6 of this thesis.

6This reactor was also the starting point of the era when nuclear physics entered world politics through the infamous bombings of Hiroshima and Nagasaki [58, 59].

10 Part I: Physics

2. Theory of deformed nuclei

“Non-Euclidean calculus and quantum physics are enough to stretch any brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional real- ity behind the ghoulish hints of the Gothic tales and the wild-whispers of the chimney corner, one can hardly expect to be wholly free from mental tension.” – H. P. Lovecraft, The Dreams in the Witch House

As mentioned in section 1.1, one of the most successful descriptions of the structure of nuclei is the nuclear shell model, further discussed in sec- tion 2.1.1. However, as also mentioned in section 1.1, it quickly becomes more difficult to make accurate predictions using the shell model when mov- ing away from the closed shells. Instead, it is the interplay between the macro- scopic shape degrees of freedom and the microscopic nature of the underlying single-particle structure of the shell-model orbitals that offers an explanation for the nuclear behaviour. As this work focuses on the collective structure of nuclei, a couple of macroscopic descriptions, and their interplay with the nuclear shell model, will be introduced in the following sections.

2.1 Nuclear deformation The surface of an atomic nucleus can be described in terms of spherical har- monics, Yμλ, of order μλ, by the equation ∞ μ R(θ,φ)=Rα 1 + ∑ ∑ αμλYμλ(θ,φ) , (2.1) μ=1 λ=−μ where (R,θ,φ) are the parameters of a standard spherical coordinate system and Rα is related to the radius of a sphere with the same volume as the nucleus to be described [24]. If all coefficients αμλ = 0 the nuclear surface becomes spherical. The only collective excitation of a spherical nucleus is the vibra- tions around this spherical shape. As each vibration quanta carries the same energy, this will result in an excitation spectrum with equal distance between

13 4 2 0 4 2 10

8

2 2 6

4

2 0 0 0 Figure 2.1: Collective excitations of an atomic nucleus. From left to right is the spher- ical vibrator, the γ-soft vibrator and the rigid rotor.

the energy levels where all magnetic substates to an energy level will be en- ergy degenerate. If the nucleus is not spherical but stretched in one direction, α20 = 0, the vibrations can occur both along the symmetry axis, so called β vibrations, and perpendicular to it, so called γ vibrations. See below for a dis- cussion about β and γ. Furthermore, a deformed nucleus can also rotate with a rotational energy, E ∝ J(J + 1), where J is the spin of the rigid rotating nu- cleus. The schematic excitation energy spectra for a spherical vibrator, a γ-soft vibrator and a rigid rotor are shown in figure 2.1. The coefficients αμλ are, however, not in general a convenient way to de- scribe nuclear shapes. Instead one usually defines the shape in terms of Euler angles. Assuming axial symmetry for all deformations of higher order than μ = 2, the most important Euler angles, βμ and γ = γ2, of the nucleus can be defined as

a20 = β2 cosγ, (2.2) a22 = β2 sinγ = a2−2, (2.3) a40 = β4, (2.4) a60 = β6. (2.5)

Unfortunately, different conventions exist and are frequently used regarding the notation of the deformation parameters. Two of these notations will be used in this work, βμ and εμ . For moderate deformations (−0.2  β2  0.4 and −0.05  β4  0.15) βμ and εμ are approximately related as ε ≈ . β − . β 2 + . β β − . β 2, 2 0 944 2 0 122 2 0 154 2 4 0 199 4 (2.6) ε ≈− . β + . β 2 + . β β + . β 2. 4 0 852 4 0 141 4 0 122 2 4 0 295 2 (2.7)

14 For further discussions on the relation between βμ and εμ , see reference [70]. Different conventions also exist for the definition of βμ and γ, but in this work ◦ the Lund convention will be used, where β2 > 0 and γ = 0 corresponds to an axially symmetric prolate nucleus.

2.1.1 Nilsson model To describe the deformed shell model, or the Nilsson model, we first need to return to the spherical shell model. As is evident from a large number of experimental observables, for example the binding energies, some nuclei with certain number of protons and neutrons, the so called magic numbers, are more strongly bound than other nuclei. This is an effect of the mean field nuclear potential. A model of the nuclear potential can be made very complex to reproduce all subtle effects of the mean field, but also simplified potentials are known to give good agreement with experimental data. The most common of these simplified potentials are the square well potential, the Woods-Saxon potential and the harmonic oscillator potential. For a quantum mechanical harmonic oscillator potential with frequency ω, the Hamiltonian of a particle with mass m moving in this potential can be written pˆ2 mω2xˆ2 H = + . (2.8) 2m 2 The energy eigenstates, with the principal quantum number n, of the particle is 3 E = h¯ω n + , (2.9) 2 with degeneracy (n + 1)(n + 2). It is easy to see that already this crude ap- proach reproduce the first three magic numbers (N,Z = 2,8,20). For a more realistic nuclear potential that becomes flat in the center and at large distances an orbital angular momentum term, ˆ2, can be added to the potential. The angular momentum of the orbital is usually denoted using the spectroscopic notation from atomic physics, where = 0,1,2,3,4,5,6,... correspond to the s, p, d, f, g, h, i, ... symbols. The ˆ2 term has two effects, to lower the en- ergy of the high lying states with high angular momentum and to break the (n+1)(n+2) degeneracy so that states with different is no longer energy de- generate. Finally, by introducing a coupling between the intrinsic spin and the orbital angular momentum, as introduced by Goeppert-Meyer [18], ˆ·sˆ, where states with parallel and s are favoured, also the orbital angular momentum degeneracy breaks and the magic numbers are completely reproduced. The full modified oscillator potential is now pˆ2 mω2xˆ2 H = + −Cˆ· sˆ− D(ˆ2 −ˆ2). (2.10) 2m 2

15 Returning to the deformed shell model, instead of the spherical shell model potential the modified oscillator potential can be written [71] pˆ2 m(ω2xˆ2 + ω2yˆ2 + ω2zˆ2) H = + x y z −Cˆ· sˆ− D(ˆ2 −ˆ2), (2.11) 2m 2 where the oscillator frequencies are 2 2π ωx = ω0(ε2,γ) 1 − ε2 cos γ + , (2.12) 3 3 2 2π ωy = ω0(ε2,γ) 1 − ε2 cos γ − , (2.13) 3 3 2 ω = ω (ε ,γ) 1 − ε cosγ . (2.14) z 0 2 3 2

Here ε2 determines the strength of the quadrupole deformation and γ the devi- ation from axial symmetry. Higher order terms, like the hexadecapole defor- mation ε4, can also be included in the model. The relation between ε2,4 and the deformation parameters β2,4 are discussed in section 2.1. The deforma- tion of the nuclear potential will further break the degeneracy of the spherical shell model. In the prolate deformed potential, equatorial orbitals (with angu- lar momentum vector parallel to the z axis) will require a higher energy due to the steeper potential relative to the polar orbitals, due to the softer potential. In figure 2.2, the energy levels for protons, 50 ≤ Z ≤ 82 is shown as a func- tion of the deformation parameter, ε2, in a so called Nilsson diagram. When there is no deformation, ε2 = 0, the orbitals become energy degenerate and the spherical shell model gaps are reproduced. The different orbitals are labelled π according to the Nilsson labels, K [nnzΛ], where K is the projection of the to- tal angular momentum on the z axis, π is the parity of the orbital, n is the total number of nodes in the wave function, nz is the number of these nodes in the z direction and Λ = K ±1/2 is the component of the orbital angular momentum along z. For example, the 7/2−[523] orbital with spin and parity Kπ = 7/2−, where the spin momentum is anti-aligned with the angular momentum, orig- inate from the n = 5 harmonic oscillator shell. It has nz = 2 nodes in the z direction and an orbital angular momentum of Λ = 3 along z, giving a total angular momentum of = 5. The two nodes in the z direction, nz = 2, together with the projection of the total angular momentum on the z axis K = 7/2gives a total spin of 11/2 for the orbital. Thus, this correspond to the negative par- −1 7/2 ≈ . ◦ ity h11/2 orbital with an orbital plane at an angle of sin 11/2 39 5 with respect to the z axis.

16 [72]. iue2.2: Figure n falohrpie ulos h aitna sfrsc oe a be can model a such for is Hamiltonian consist- core The a nucleons. outside paired explicitly other treated all is of nucleon treat ing odd To single paired. only a are where 2.1, model nucleons section all in where described nuclei odd-A model, even-even collective vibrator to or apply rotor model deformed rotor basic triaxial The plus Particle 2.1.2 E (h ) s.p. ulitemdlnest emdfid n a od hsi ocet a create to is this do to way One modified. be to needs model the nuclei

3/2[431] 11/2[615]

3/2[411] 5/2[422] 1/2[301] 3/2[541] 7/2[514] 7/2[503]

iso iga o rtn,50 protons, for diagram Nilsson 13/2[606] 11/2[505]

5/2[532] 9/2[505]

7/2[413] 3/2[402] 1/2[550]

7/2[404] 1/2[420] 3/2[422]

7/2[523] 1/2[411]

5/2[413] 1/2[431] 1/2[440]

9/2[514] 2d 3s 1/2 5/2 50 82 1h 1g 1g 2d

11/2

9/2 7/2 3/2

3/2[431]

3/2[422] 5/2[422] 1/2[400] 9/2[404]

11/2[505]

1/2[431]

7/2[413] 3/2[532] 1/2[420] 1/2[660] 9/2[514]

≤ 5/2[402]

3/2[651] Z 1/2[550]

1/2[301] 3/2[541] 7/2[404]

≤ 5/2[303]

7/2[523]

1/2[411]

2(ε 82

1/2[660] 3/2[651]

3/2[411]

3/2[301] 5/2[413] 4 5/2[642]

= 1/2[400] 5/2[523]

3/2[521] 3/2[402] ε

2

2

) erne from Reprinted /6). 7/2[633]

1/2[530] 5/2[532]

1/2[301]

1/2[550] 5/2[642] 1/2[541]

1/2[411] 3/2[761]

3/2[541]

1/2[660] 3/2[301] 7/2[633] 3/2[642]

1/2[651] 5/2[402] 1/2[770] 1/2[640] 7/2[404] 5/2[532] 1/2[541] 5/2[303] 1/2[301] 3/2[651] 3/2[411] 17 written as H = Hcore + Hsp + Hint, (2.15) where Hcore is the Hamiltonian of the even-even core, Hsp is the Hamiltonian of the single particle and Hint is the interaction between the core and the single particle. The requirements of the core is that it is collective and that polarization effects are negligible or included in Hint. If this is fulfilled, the core can in principle be chosen as any physical collective system; for example a vibrator, an axially symmetric rotor [23, 73], a triaxial rotor [23, 73–75] or be described in terms of the interacting boson model (IBM) which gives the interacting boson-fermion model (IBFM) [76]. Note that, in general, one is restricted to a fixed core shape used as input and that the model cannot predict the deformation parameters of this input. The particle plus triaxial rotor model describes an odd particle outside an even-even rigid triaxial rotor. This means that one can use the deformed shell model Hamiltonian, similar to the Nilsson treatment, as a core. The first step is the creation of, and diagonalization of, the deformed shell model Hamiltonian with the desired parameterization of the mean field, most commonly a Woods- Saxon potential or modified oscillator potential [70, 77, 78]. The particle-hole interaction is included in Hsp and Hint together. Once the deformed shell model orbitals has been constructed, the particle-particle pairing interaction is included using the Bardeen, Cooper and Schrieffer (BCS) method [19, 23, 79] by transforming the system to quasiparticles and creating the corresponding creation and destruction operators. To obtain a BCS vacuum giving the correct particle number of the one quasiparticle intrinsic state of the odd nucleus, the average of the two neighbouring even-even nuclei is used. Finally, we will have a Hamiltonian that acts on the system as a whole, the intrinsic one quasiparticle state alone as well as a Coriolis term that couple the intrinsic and rotational motions.

2.1.2.1 Coriolis attenuation parameter A well known problem in the particle plus triaxial rotor calculations is that the mixing between intrinsic states due to the Coriolis term is too large compared to experimental data, especially for high- orbitals. To take care of this an ad hoc attenuation parameter, 0 < ζ < 1, has been introduced that multiplies the Coriolis matrix elements. The parameter ζ is known to go down as far as ζ = 0.5 in some nuclei. A number of possible explanations for the Coriolis attenuation have been proposed. Some of these are that it is a finite particle number effect [80], a Pauli principle effect manifested as the boson-fermion exchange term in the IBFM [81], that a better treatment of pairing without the BCS method is needed [82] or that it origin from neglected octupole couplings [82]. However, there is no clear consensus of the interpretation.

18 2.1.3 Cranking model A complementary model to the particle plus triaxial rotor is the cranking model [83, 84]. This model treats all the nucleons equivalently as particles moving in a rotating mean field and makes no distinction between core and valence particles, thus allowing for multi-quasiparticle states. This is impor- tant to describe high spin effects such as, for example, backbending. Further- more, the cranking model calculates the deformation parameters instead of using them as an input to the model. The model does, however, not do so well for low-spin and non-yrast states or for estimation of the electromagnetic properties of the nucleus [82]. In the cranking model, the total energy, Etot,n,ofan-quasiparticle config- uration is given by the contribution from the macroscopic properties of the nucleus, Emacr, as well as the microscopic properties of the nucleus, Emicr,n,as

Etot,n(Z,N;ˆx)=Emacr(Z,N;ˆx)+Emicr,n(Z,N;ˆx). (2.16)

The macroscopic part varies smoothly with particle number and is usually taken from the liquid drop model. In this simple approach to the binding en- ergy the semi-empirical mass formula developed by von Weizsäcker [85], 2 ( − )2 2/3 Z N Z EB = avA − asA − aC − ai + δ(A), (2.17) A1/3 A is used as a starting point. The terms in eq. (2.17) are related to the volume of the nucleus (av), the surface energy (as), the Coulomb repulsion of the protons (aC), the proton-neutron symmetry (ai) and the nuclear pairing energy (δ(A)). Already this expression reproduces the bulk behaviour of the relatively heavy nuclei very well1, but for detailed variations of masses and deformations, mi- croscopic effects needs to be included. The proton-neutron symmetry term can be modified according to reference [86] and the pairing energy can be calcu- lated using the Lipkin-Nogami approach of the BCS method [87]. The main difference between the Lipkin-Nogami approach and the regular BCS approx- imation is that the role of particle-number violating terms is minimized. Usu- ally the Strutinsky shell correction [88, 89] method is applied to obtain Emicr,n, where the microscopic total energy is calculated, for example using the Nils- son method, and added to the liquid drop energy Emacr. When the system is defined, it is rotated by a frequency, h¯ω. The effects on the single-particle orbitals in the rotating potential are calculated. In the rotat- ing frame the inertial forces will influence these orbitals. Due to this treatment some things are worth pointing out. The eigenstates of the Hamiltonian will

1Actually this semi-empirical formula gives very good prediction. For example one can, if one adds a gravitational term to the eq. (2.17), within reasonable limits predict the critical mass of a neutron star. It is very impressive that the fitted values still are quite valid after an extrapolation from 1 < A < 250 to A ≈ 5 · 1055, over 53 orders of magnitude. See Box 7a in reference [20].

19 not be the energies in the lab system, but energies in the rotating frame referred to as Routhians. Neither will the total angular momentum or the angular mo- mentum projection on the symmetry axis be good quantum numbers any more. The only good quantum numbers remaining in the cranking Hamiltonian are the parity and signature (π,α). The total energy in the lab frame is calculated as the sum of the single particle contributions and the spin is the projection of the total angular momentum on the rotation axis. After each calculation, the results are renormalized to the liquid drop model. These calculations are performed on a grid in the deformation space, (β2,γ,β4), creating an energy surface, or a total Routhian surface (TRS). The equilibrium deformation is obtained by minimizing the Routhian in the used deformation space. As the calculations are made at a specified rotational frequency, not at a specified spin, and the energies calculated are the Routhians, not the lab frame energy. The spin and lab frame energy can vary across the TRS deformation space grid, so one should be careful when transforming the TRS into a physical energy and spin surface.

2.1.4 Variable moment of inertia model A model that is closely related to the cranking model is the variable moment of inertia (VMI) model. The VMI model does not have any predictive powers about the structure of the nucleus under study, but it can serve as a useful tool to extract physics from the energy spectrum of the nucleus, a reference for high spin states, and highlight deformation systematics [90]. In the VMI model, the energy of a deformed nucleus is written as I(I + 1) I˜2 E(xˆ,I˜)= +V(xˆ)= +V(xˆ), (2.18) 2J (xˆ) 2J (xˆ) wherex ˆ is the intrinsic configuration of the nucleus, I˜= I(I + 1) is the spin, J is the moment if inertia and V is the intrinsic energy. When the system is rotated with frequency ω, the Routhian can be written as 1 R(xˆ,ω)=V(xˆ) − J (xˆ)ω2. (2.19) 2 If we are interested in describing the yrast states of the nucleus the first deriva- tive of the Routhian with respect tox ˆ must be zero, and if we are interested in the equilibrium state the first derivative of the intrinsic state energy with respect tox ˆ must also be zero. This makes it possible to write the spin of the system as 2 I˜ = ω(J0 + ω J1), (2.20)

20 and the energy of the system as 1 3 E = ω2 J + ω2J . (2.21) 2 0 2 1

For a full derivation, see reference [90]. The ground-state rotational band can thus be represented by the two constants [J0,J1] called the Harris parameters [91, 92]. These parameters are defined as

J0 = J (xˆ) − xJ (xˆ), (2.22) and J (xˆ)2 J = , (2.23) 1 2V (xˆ) where 1 J (xˆ) x = ω2. (2.24) 2 V (xˆ)

These expressions give a very good representation of the first members of the ground state band in deformed even-even nuclei [93, 94]. For odd nuclei, how- ever, one needs to add a non-collective spin component, i, to equation (2.20) and a bandhead energy, E0, to equation (2.21) [90]. Besides creating a reference for studies of the structure of deformed nuclei, the parameters [J0,J1] have some interesting physical meanings. For example, J0 is directly related to the moment of inertia of the system, and thus also the deformation of the nucleus. For rotational nuclei, J0 can per definition not become negative so a negative J0 either imply that the nucleus is becoming vibrational [94] or that higher order expansions of I˜ and E in terms of ω are needed. The parameter J1 is related to the rigidity of the system. The small- est values of J1 occur when the deformed prolate minimum in the potential- energy surface is most pronounced [90].

2.2 Nuclear deformations in the r process One example of where the theory of deformed nuclei outlined in this chapter can be applied is the astrophysical r-process. As described in section 1.2.2, the r-process occur in high neutron density areas in the universe, where the average time for neutron capture is smaller than the half life of the radioactive isotope, and a (n,γ)–(γ,n) equilibrium between neutron capture and photo- disintegration has established itself. After this so called steady phase of the r-process, the free neutrons disappear and the nuclei β decay back to stabil- ity, a process called freeze out. The most dominant features of the abundance distribution of elements created during the steady phase and freeze out are

21 Figure 2.3: Calculated (line) and measured (crosses) solar r-process abundances (top). Contours of constant neutron separation energy in MeV (solid lines) and constant β-decay rates in s−1 (dashed lines). The inset is a schematic of two such contours with the arrows depicting the flow of nuclei into the region containing the separation- energy kink (bottom). Reprinted with permission from [95] (top) and [96] (bottom). Copyright by the American Physical Society.

the large peaks at A ≈ 80, A ≈ 130 and A ≈ 195 that are due to the r-process flow through closed shells. The second most pronounced feature is the peak at A ≈ 160 in the rare-earth region. See figure 2.3 for a selection of the r-process abundance distribution.

22 While the closed shell peaks are well understood to be formed during the steady phase [49], it has been argued that the A ≈ 160 peak is due to the deformation in the nuclei created after the steady phase freeze out [96]. An explanation that has been proposed is that nuclei deform when deformation increases stability. As the deformation maximum is reached the nucleus can- not deform more so the next heavier nucleus will be less stable, an effect that can mimic closed shells. However, the process proposed to explain the abundance peak is slightly different from the process behind the closed shell peaks. As long as the sys- tem is in (n,γ)–(γ,n) equilibrium the r-process path will follow a contour of constant separation energy, / 2 3 2 ρNAYn 2πh¯ Sn(Z,Nmax)=−kT ln . (2.25) 2 mnkT

In this equation kT is the temperature, ρ the density, NA Avogadro’s number and Yn the free neutron abundance per nucleon. If the temperature and den- sity does not change dramatically, the r-process stays in (n,γ)–(γ,n) equilib- rium even after steady phase is over. Thus, the path will continue to lie along contours of constant neutron separation energy as it moves towards stability. See figure 2.3 for an example of some r-process paths during freeze out. It is during this time that the peak in the rare-earth nuclei is formed. Besides the large kinks at the closed neutron shells, a kink in the separation energies at N ≈ 104 is clearly seen, corresponding to the deformation maximum in the calculations. This kink causes the peak to form in two ways. One way is similar to the closed shell isotopes, that the kink produces a concentration of populated iso- topes close together. The other way is due to the effect that the free neutron abundance per nucleon falls much more rapidly than the temperature and den- sity as the path moves towards stability by β decay, and that the contours of constant β decay rate does not coincide with the contour of constant separa- tion energy in this region, see figure 2.3. Below the kink the nuclei along the contour are farther from stability and decay faster than average. So a β decay followed by a neutron capture will cause their value of A to increase. The nu- clei above the kink, however, decay slower than average, allowing them time to photodisintegrate and thus decrease their value of A. As seen in figure 2.3, this reproduces the peak quite well. However, one can note that there is a small overestimation of the nuclei with higher mass num- bers and a small underestimation of the nuclei with lower mass numbers. This could be related to the assumption of N = 104 as the deformation maximum all the way down to Z = 50. A better understanding of the evolution of nuclear deformations in this region might improve the agreement between calculated and observed abundances.

23 2.3 Heavy-ion induced nuclear reactions Nuclear reactions can be classified in many different ways, for example ac- cording to the time during which the reaction occur, the energies involved in the reaction or the so called impact parameter that determine how close the nuclei are during the reaction. For example, in Coulomb excitation reactions, which are not actually nuclear reactions as such, the Coulomb field from the interacting nuclei is used to excite both the beam and the target. Coulomb excitation experiments are usually carried out at low beam energies, but can as well be carried out at relativistic beam velocities. Since the nuclei in this reaction do not come into direct contact, the impact parameter will be large. See, for example, the recent experiment carried out at LNL to search for two- phonon excitations in 170Er [97]. The opposite reaction to Coulomb excitation, in terms of the impact param- eter, is the fusion reactions where the two nuclei fuses together and de-excite through γ-ray emission or by particle evaporation. These types of reactions usually involve head-on collisions between the nuclei at relatively low en- ergies, but above the Coulomb barrier, and with long enough reaction times so the compound nucleus has time to form. Since most angular momentum goes into the spin of the compound nucleus, the fusion-evaporation reactions are well suited to study high-spin states. Together with a good neutron de- tector array for evaporated particles it is also a valuable tool for experiments aiming at studies of proton-rich nuclei. See for example reference [26] where a fusion-evaporation reaction was used together with the Neutron Wall, de- scribed in section 6.2. Fusion-evaporation reactions were also used in the first commissioning run with the AGATA array, see chapter 5. At the other extreme, regarding the energies involved, are the fragmentation reactions. In this case heavy nuclei at relativistic velocities are fragmented by letting them hit a light nucleus. The nuclear fragments can then be studied by themselves, see for example refs. [98, 99] for some recent results, or via secondary reactions like Coulomb excitation. In between these reactions are the deep inelastic collisions, or multi-nucleon transfer reactions. These are fast nuclear reactions at intermediate energies, where the surfaces of the nuclei come into contact at a grazing distance, al- lowing for a fast redistribution of neutrons and protons among the nuclei. Thus, nucleons are transferred between the beam and the target, but the frag- ments produced in the reaction keeps resemblance to the original beam and target nuclei. The primary fragments de-excite through evaporation of neu- trons, protons and α particles, and emission of γ rays. Heavier fragments can also fission. These collisions can be used to populate neutron rich parts of the Segré chart not reachable by fusion-evaporation reactions. Angular momen- tum is transferred from the relative orbital motion to intrinsic spin through three different relative motions, sliding, rolling and sticking. The sliding pro- cess is the simplest of these as the nuclei slide with respect to each other and,

24 thus, does not transfer any angular momentum. The rolling mode is when the beam nucleus is rolling on the target nucleus and, thus, by a strong frictional force deposits some of its angular momentum to the target nucleus, causing it to rotate in the opposite direction. The sticking mode is when the nuclei stick together and begins to rotate around a common centre of gravity, while each fragment has the same rotational velocity around their own centre. The maximum of the angular distribution of the binary cross-section when the dis- tance between the two nuclei is equal to the sum of their radii is known as the grazing angle of the reaction. For more details on experimental and theoretical aspects of deep inelastic collisions see for example refs. [100–102].

25

3. PRISMA and CLARA experiment

“You do research now? Want a cappuccino and a pack of cigarettes to go with it?” – Buffy, the Vampire Slayer

As discussed in chapter 2, one important approach to the nuclear many- body problem is the macroscopic approach, based on the collective properties of nuclei. The regions in the Segré chart where quadrupole collectivity is most prominent are around the doubly mid-shell nuclei, with many valence parti- cles and far away from closed shells. The distance from the closed shells is sometimes quantified in terms of the product of valence nucleons NpNn [103], which is equal to the number of neutron-proton interactions outside the shell. Neglecting any potential sub-shell closures, the nucleus with A < 208 that has 170 the largest number of valence particles is 66 Dy104. Accordingly, it should be one of the most collective of all nuclei in its ground state [104]. However, sub-shell closures, such as those at Z = 64 [105, 106], and at Z = 76 [107] as well as microscopic effects complicates the simple NpNn relationship and it is not clear where the maximum of collectivity is located. The amount of collectivity has been shown to have a smooth dependence on both the energy of the first excited state, E(2+), and the reduced transition probability from the first state to the ground state, B(E2:2+ → 0+), as well as the energy ratio of the first excited 4+ and 2+ states, E(4+)/E(2+) [105, 107–109]. Furthermore, it has been suggested that 170Dy could be the single best case in the entire Segré chart for the empirical realization of the SU(3) dynamical symmetry of the IBM [110]. Although many deformed nuclei show some of the predicted signatures of the SU(3) IBM symmetry, to date, no nucleus has been demonstrated to show them all. Previous experimental work in this region has been limited due to a lack of suitable conventional nuclear reactions able to populate such exotic neutron- rich nuclei. The only experiment that has reported production of 170Dy, before this work, was using fragmentation of a 1 GeV per nucleon 208Pb beam at GSI [111]. The use of deep inelastic transfer reactions have been successful in populating 168Dy as described in this chapter and reference [112, I], 169Ho [113, 114], 172Er [115], 174Er [116] and 178Yb [117]. The location of 170Dy in the region of interest in the Segré chart is shown in figure 3.1. In this chapter, an experiment aiming to study the structure of 170Dy, and the neighbouring nuclei 168Dy, 167Ho, 168Ho and 169Ho will be described. The experiment was carried out at the PRISMA and CLARA set-up, shown

27 166Yb 167Yb 168Yb 169Yb 170Yb 171Yb 172Yb 173Yb 174Yb 175Yb 176Yb 177Yb 178Yb 179Yb 180Yb 181Yb 182Yb

165Tm 166Tm 167Tm 168Tm 169Tm 170Tm 171Tm 172Tm 173Tm 174Tm 175Tm 176Tm 177Tm 178Tm 179Tm 180Tm 181Tm

164Er 165Er 166Er 167Er 168Er 169Er 170Er 171Er 172Er 173Er 174Er 175Er 176Er 177Er 178Er 179Er 180Er

163Ho 164Ho 165Ho 166Ho 167Ho 168Ho 169Ho 170Ho 171Ho 172Ho 173Ho 174Ho 175Ho 176Ho 177Ho 178Ho 179Ho

162Dy 163Dy 164Dy 165Dy 166Dy 167Dy 168Dy 169Dy 170Dy 171Dy 172Dy 173Dy 174Dy 175Dy 176Dy 177Dy 178Dy

161Tb 162Tb 163Tb 164Tb 165Tb 166Tb 167Tb 168Tb 169Tb 170Tb 171Tb 172Tb 173Tb 174Tb 175Tb 176Tb 177Tb

160Gd 161Gd 162Gd 163Gd 164Gd 165Gd 166Gd 167Gd 168Gd 169Gd 170Gd 171Gd 172Gd 173Gd 174Gd 175Gd 176Gd

159Eu 160Eu 161Eu 162Eu 163Eu 164Eu 165Eu 166Eu 167Eu 168Eu 169Eu 170Eu 171Eu 172Eu 173Eu 174Eu 175Eu

158Sm 159Sm 160Sm 161Sm 162Sm 163Sm 164Sm 165Sm 166Sm 167Sm 168Sm 169Sm 170Sm 171Sm 172Sm 173Sm 174Sm Z64666870 N 98 100 102 104 106 108 110 112 Figure 3.1: The region of interest, for this work, in the Segré chart. Light grey boxes represent short lived nuclei and dark grey boxes represent stable nuclei. White boxes with black text represent nuclei where no previous information of excited stated were known before this work, and with grey text nuclei that have not been observed at all.

Figure 3.2: The PRISMA and CLARA set-up. Photo from reference [118].

in figure 3.2, at the XTU Tandem-ALPI-PIAVE accelerator complex at LNL using multi-nucleon transfer reactions between 82Se and 170Er. The beam was 82Se at an energy of 460 MeV and an intensity of ∼25 enA (∼2 pnA) for effectively ∼ 3.5 days. This beam was incident on a 500 μg/cm2 thick self-supporting 170Er target. Beam-like fragments were identified using the PRISMA magnetic spectrometer, placed at the grazing angle of 52◦. The γ-

28 ray energies from both the beam-like and target-like fragments were measured using the CLARA array, in this experiment consisting of 23 Compton sup- pressed clover detectors.

3.1 LNL accelerator complex The main accelerator complex for nuclear physics at LNL consists of three machines that accelerate the ions delivered by an electron cyclotron reso- nance ion source [119]. The Tandem XTU accelerator, that was used in this experiment, has been in operation since 1982 and nominally runs at a ter- minal voltage of 18 MV. The charge stripping is usually obtained using a 5 μg/cm2 carbon foil. Together with the XTU accelerator there is also a su- perconducting resonant cavity post-accelerator, ALPI [120], for heavy ions. ALPI can provide ion beams up to uranium with energies between 5–20 MeV per nucleon. Instead of the Tandem XTU, there is also the option to use PI- AVE [121], which is an injector for ALPI based on superconducting radio frequency quadrupoles and quarter wave resonance structures. For this exper- iment, only the XTU tandem and the ALPI post-accelerator was used.

3.2 PRISMA As no experimental information about the structure of 170Dy was known be- fore this experiment it was not possible to identify the reactions leading to 170Dy from its emission of γ rays. Instead, 170Dy had to be identified from the reaction products of the 170Er(82Se,82 Kr)170Dy reaction. The identification of the reaction products was also an important tool for the other nuclei stud- ied in this experiment, such as 168Dy where the 4+ → 2+ and the 2+ → 0+ transitions had been previously observed [122], as a means of reducing the background from other, more strongly populated, reaction channels. To identify the beam-like reaction fragment the large-acceptance magnetic spectrometer PRISMA [123–125] was used. PRISMA is designed to iden- tify nuclei populated in heavy-ion binary reactions at kinetic energies of 5– 10 MeV/A. It covers a solid angle of 80 msr, has a momentum acceptance of Δp/p = ±10 %, a dispersion of ∼ 4 cm per percent in momentum and a counting rate capability of 50–100 kHz. The total flight distance from the start detector to the focal plane is ≈ 6.5 m. It can be positioned at angles between −20◦ to 130◦ relative to beam line. The spectrometer consists of two large magnets, one 50 cm length and 32 cm diameter quadrupole mag- net and one dipole magnet with 1.2 m radius of curvature in a 60◦ bending angle for the central trajectory. Together with the magnets a set of start and focal plane detectors was also used. The start detector is a micro-channel- plate (MCP) located right after the target chamber. The focal plane detectors

29 consist of a multi-wire parallel-plate avalanche counter (MWPPAC) for (x,y) position measurements of the fragments exiting the dipole and an ionization chamber (IC) grid for total kinetic energy, E, and partial kinetic energy, ΔE, measurements of the fragments. The atomic number (Z) resolution in this ex- periment was Z/ΔZ ≈ 65 and the mass resolution (A)wasA/ΔA ≈ 200 for elastic scattering of 82Se. The set-up of PRISMA is illustrated in figure 3.3.

3.2.1 MCP The first detector in PRISMA, 25 cm after the reaction chamber, is a rectan- gular MCP with a size of 80 × 100 mm2 mounted in Chevron (or ’V’ shaped) configuration. It is located in a stainless steel box, tilted 45◦ with respect to the optical axis, with two transparent windows. At the exit window there is a20μg/cm2 carbon foil with a voltage of −2300 V. The MCP detects the (x,y) positions, with an accuracy of 1 mm, of the secondary electrons pro- duced when the beam-like fragments passes the carbon foil before entering the quadrupole magnet. The MCP also registers the time when the fragment enters PRISMA with an accuracy of 400 ps, which is later used together with the MWPPAC to extract the time-of-flight (TOF) of the fragment through the spectrometer. The efficiency of the MCP is 100% in typical experiments. For more details, see reference [126]. It can be calibrated in x and y using a thin cross of wires and two nails located downstream in PRISMA, see fig- ure 3.4.

3.2.1.1 Calibration of the MCP Since the calibration of the MCP is the most critical part of the data sorting procedure and was done in a non-standard way it will be described here in some more detail, following the matrix method in reference [127]. As seen in figure 3.4, a reference cross with four flags is placed on the carbon foil. The reference cross is slightly deformed due to the magnetic field that accel- erate the secondary electrons from the carbon foil to the MCP. Furthermore, the mask is rotated by 2–3◦, as seen on the projection of two nails in the quadrupole magnet. Due to this, a linear calibration containing both the x and y parameter is used as

x = ax + bxx + cxy, (3.1)

y = ay + byx + cyy, (3.2) where (x ,y ) is the calibrated position in mm and (x,y) is the uncalibrated position. A coefficient matrix, A, containing the positions of the reference

30 MWPPAC

Dipole

3279 mm 720 mm IC

540 mm Quadrupole MCP 250 mm

Figure 3.3: Sketch of the PRISMA spectrometer. y (ch)

3000

2000

1000 1000 2000 3000 x (ch) Figure 3.4: Positions of the reaction fragments accepted by the PRISMA spectrometer as measured by the MCP, before calibration. The reference cross for calibration and the projection of two nails in the quadrupole magnet is clearly visible.

31 points can thus be defined as ⎛ ⎞ 1 x y ⎜ 1 1 ⎟ ⎜ ⎟ ⎜ 1 x2 y2 ⎟ ⎜ ⎟ A = ⎜ 1 x y ⎟. (3.3) ⎜ 3 3 ⎟ ⎝ 1 x4 y4 ⎠ 1 x5 y5

The covariance matrix, V, of the fitting parameter vector, θˆ T =(a,b,c), can be calculated from the matrix expression ⎛ ⎞ Vaa Vab Vac − ⎜ ⎟ (θˆ)= T 1 = , V A A ⎝ Vba Vbb Vbc ⎠ (3.4) Vca Vcb Vcc this gives the parameters ⎛ ⎞ ax T ⎜ ⎟ θˆx = V(θˆx)A x¯ = ⎝ bx ⎠. (3.5) cx

Similarly for y, ⎛ ⎞ ay T ⎜ ⎟ θˆy = V(θˆy)A y¯ = ⎝ by ⎠. (3.6) cy

3.2.2 Quadrupole and dipole magnets The PRISMA quadrupole magnet is located 54 cm from the target. It has an aperture diameter of 32 cm and an effective length of 50 cm, giving length- over-diameter ratio of ≈ 1.5 which is on the limit for the fringing field to be small enough with respect to the inner field. The purpose of the quadrupole magnet is to focus the fragments along the y axis to increase the acceptance of PRISMA. At the same time the fragments are defocused along the x axis, due to the properties of the quadrupole field. The maximum field strength of the quadrupole is BQ = 0.848 T. In this experiment, the field strength was BQ = 0.645 T. The main component of PRISMA is the large dipole magnet that sepa- rates fragment trajectories with respect to their magnetic rigidity. It is located 160 cm from the target, 60 cm from the quadrupole, and has a curvature ra- dius of 1.2 m. It has a pole gap of 20 cm height and 1 m width with a maxi-

32 mum magnetic rigidity of BDρ = 1.2 Tm. The field strength of the dipole was BD = 0.707 T in this experiment.

3.2.3 MWPPAC At the focal plane of PRISMA, the first detector is a 1 m wide MWPPAC located 327.9 cm from the dipole. The MWPPAC is divided into three elec- trodes with a total active focal plane area of 100 × 13 cm2, mounted in a stainless steel vacuum vessel filled with isobuthane, C6H10, in this experi- ment at a pressure of 6.5 mbar. On each side of the vacuum vessel along the optical axis is a 1.5 μm thick Mylar window, located 3 mm from the anode wire planes, supported by 100 μm thick stainless steel wires with a distance of 3.5 mm between them. Both the central cathode and the x-position wire plane are divided into ten independent sections each, while the y-position wire plane covers the entire width of the MWPPAC. Each x-position anode has 100 gold- plated tungsten wires of thickness 20 μm, giving a spacing of 1 mm. Each cathode has 330 gold-plated tungsten wires, giving a spacing of 0.3 mm. The y-position anode has 136 gold-plated tungsten wires giving a spacing of 1 mm. From the electrodes, the xleft and xright signal in the focal plane is read out, as well as the stop signal for the TOF measurement and the amplitude of the cathode signal. The yup and ydown signals are also read out and used mainly for beam positioning. From the difference in xleft and xright the x position of the fragment at the focal plane, xFP, can thus be extracted. The x positions in the MWPPAC and the TOF between the MWPPAC and the MCP are shown in figure 3.5.

3.2.4 Ionization chambers The last detector in the focal plane of PRISMA is the IC array located 72 cm after the MWPPAC. The IC array consists of four segments (z-direction) of 100(x)×20(y)×250(z) mm3 in ten sections (x-direction), see figure 3.3. This segmentation makes it possible to use ΔE − E techniques to resolve the dif- ferent atomic numbers of the fragments. Furthermore, there are two more out- ermost sections used as veto detectors for fragments that leave the chamber without depositing all their energy in the active volume. Each section is read out by a common cathode and a common Frisch grid but every segment has its individual anode. The Frisch grid is made of 1200 gold-plated tungsten wires of thickness 100 μm and the entrance window is made of a 1.5 μm thick My- lar foil supported by 1000 stainless steel wires of thickness 100 μm with a distance of 1 mm between them. To provide a high drift velocity and, thus, a good energy resolution the IC array is filled with methane gas, CH4, in this experiment at a pressure of 62 mbar.

33 (a) (b) 4000 (ch) ounts left C x 60000 3000

40000 2000

1000 20000

0 0 0 1000 2000 3000 4000 0 200 400 600 800 1000 xright (ch) xfp (mm)

(c) (d) 500

5

Counts 10

TOF (ns) 400 104

300 103

2 10 200

10 100 100 200 300 400 500 0 200 400 600 800 1000 TOF (ns) xfp (mm)

Figure 3.5: The right versus left position in the MWPPAC (a) and the xFP position at the focal plane (b). The time-of-flight between the MCP and the MWPPAC (c) and the time-of-flight versus the xfp position at the focal plane (d).

The energy loss of the fragment in the IC detectors is governed by the Bethe-Bloch equation, dE(z) MZ2 ∝ , (3.7) dz E(z) where z is the distance along the beam trajectory, M is the mass of the frag- ment, Z the atomic number of the fragment and E the energy at a given mo- ment. This means that the energy loss of different fragment species in the different segments of the IC array will vary. The Z can be obtained by com- paring the energy deposited in the first two layers of the IC, ΔE, to the total energy, E. This is illustrated in figure 3.6. In a similar way, the range, r of

34 the fragment in the IC will also depend on the energy loss as − E dE 1 r(E)= − dE, (3.8) 0 dz where E is the total energy of the fragment when entering the IC. The range and energy is also compared in figure 3.6. In the analysis in this work, r–E is the quantity that was used as it made it possible to resolve Z down to lower incident energies.

3.2.5 Mass determination One of the most important features of the PRISMA spectrometer is its abil- ity to separate fragments of different mass by reconstructing their trajectory through the magnets, following the procedure of references [128, 129]. The (x,y) position where a fragment with charge q enters the quadrupole is ob- tained from the MCP. The forces, F, acting on the fragment when it is passing through the quadrupole are

Fx = qvbx, (3.9) Fy = −qvby, (3.10) where v is the, so far unknown, velocity of the fragments and b is the magnetic field gradient. The equations of motion will thus be d2x = k2x, (3.11) dz2 d2y = k2y, (3.12) dz2 where qb k2 = , (3.13) Mv

dx = dy = for a fragment of unknown mass, M. Denoting dz x and dz y , the solu- tions to equations (3.11)–(3.12) are x(z)=Asinh(kz)+Bcosh(kz), (3.14) y(z)=C sin(kz)+Dcos(kz), (3.15)

x (z)=Akcosh(kz)+Bksinh(kz), (3.16)

y (z)=Ckcos(kz) − Dksin(kz), (3.17) where the boundary conditions causes the coefficients A, B, C and D to depend on the position and velocity vector of the fragment entering the quadrupole magnet, as measured by the MCP. Thus, using equations (3.14)–(3.17), the

35 (a) (b) 5500 2800 2600 r (a.u) E (a.u.) 5000 2400 2200 4500 2000 Z=36 4000 1800 Z=34 1600 3500 1400 1200 Z=35 3000 1000 800 2500 1000 1500 2000 2500 500 1000 1500 2000 2500 E (a.u.) E (a.u.)

Figure 3.6: Partial energy loss (a) and range of the fragments (b) with respect to the total energy loss of the fragments in the IC. The selection used for selenium (Z = 34), bromine (Z = 35) and krypton (Z = 36) isotopes are also shown in panel (b).

(a) (b) 460 2800 440

Rv (a.u) 2600 + + M/q (a.u.) 420 + 24 25 2400 23 + 400 26 + 2200 27 380 360 2000 340 1800 + 320 1600 + +24 20 + 23 21+ 22 300 1400 280 1200 0 200 400 600 800 1000 1000 1500 2000 2500 xfp (mm) E (a.u.)

Figure 3.7: Relative mass, M/q, of the fragments with respect to their position in the MWPPAC (a) and the bending radius, Rv, with respect to the energy (b) used to obtain the absolute mass, M, of the fragments. The different charge states for selenium (Z = 34) is shown in panel (b).

36 position and velocity vector of the fragment entering the dipole magnet can be calculated. The radius, R of the trajectory of the fragment in the dipole can in principle be calculated from the Lorentz force, Mv2 = qvB , (3.18) R D but as the mass, M, and the atomic charge, q, are not yet known the value of R needs to be guessed. By default, the first guess is R = 1200 mm. Using this guess and equations (3.14)–(3.18), the position where the fragment hits the MWPPAC can be calculated. The velocity, v, is obtained from the TOF information and the total length of the guessed track. The calculated position in the MWPPAC is compared to the measured position in the MWPPAC and the guessing procedure is iterated until the difference is less than 1 mm and, thus, the correct values of R, v and M/q have been obtained. The M/q ratio for the selenium (Z = 34) isotopes is shown in figure 3.7. To obtain the absolute mass of the fragment its charge state also needs to be known. This can be achieved from the relation 1 E = mv2, (3.19) 2 which together with eq. (3.18) gives E ∝ qRv. (3.20)

A plot of E together with Rv that separates different q is shown in figure 3.7. The absolute identification of each charge state is obtained by comparing the intensities in figure 3.7 with the transmission calculations from the reaction code available at LNL. By selecting each charge state, q, and multiplying this with M/q, a mass spectrum of the detected fragments can be obtained. Such a spectrum is shown in figure 3.8 for krypton (Z = 36) isotopes. However, the fragments of interest in this experiment were not the beam- like fragments, but the target-like fragments. Unfortunately, the target-like fragments were too heavy to be resolved by the PRISMA spectrometer. The A and Z of the target-like fragments can be calculated directly assuming a binary reaction without any particle evaporation. The velocity vectors of the target-like fragments, which are important for the Doppler correction, can be calculated using standard two-body kinematics, again assuming a binary reac- tion. The mass limits on the target-like fragments are also shown in figure 3.8.

37 1600 1400 A 167 Counts 1200 A 168 A 166 1000 800 A 165 600 A 169 400 A 164 A 170 200

0 81 82 83 84 85 86 87 88 89 Kr mass Figure 3.8: Mass spectrum from PRISMA of target-like fragments gated on krypton (Z = 36). The masses (A) of the corresponding dysprosium isotopes are also shown. Reprinted from reference [130].

3.3 CLARA To measure the γ rays emitted by the fragments, the CLARA [131] high-purity germanium (HPGe) array was used. CLARA is an arrangement consisting of the clover detectors from the EUROBALL III and EUROBALL IV arrays1 [133]. Each Clover detector is composed of four HPGe crystals, mounted in a single cryostat, with a diameter of 50 mm and surrounded by a bismuth germanate (BGO) shield to suppress Compton scattering out from the detector and increase the peak-to-total ratio. In its full configuration, CLARA consist of 25 Clover detectors closely packed in a hemisphere around the target posi- tion of PRISMA, at angles between 104–256◦ with respect to the entrance of the spectrometer. A photo of the CLARA array is shown in figure 3.9. In the full configuration, the total photopeak efficiency of CLARA is 3.3 % for single 1 MeV photons and the peak-to-total ratio is 48 %. In this exper- iment 23 Clover detectors were mounted. Doppler correction was performed event-by-event using the velocity vectors measured by PRISMA. This gave an energy resolution of 4.4 keV (0.7 %) at 655 keV for the beam-like fragments and 5.8 keV (1.1 %) at 542 keV for the target-like fragments reconstructed ac-

1The EUROBALL Cluster detectors are now assembled into the RISING array at GSI [132] and the EUROBALL Phase I detectors are used in the JuroGam array at the University of Jyväskylä physics laboratory. At the time of writing, the University of Jyväskylä also has the Clover detector as CLARA has been decommissioned and replaced with the AGATA Demonstrator array, see chapter 5

38 Figure 3.9: The CLARA HPGe detector array. Photo from reference [118].

cording to the procedure in section 3.2.5. Doppler-corrected spectra for beam- like and target-like fragments are shown in figure 3.10. The γ-ray spectra obtained from CLARA were then analysed using both in singles mode and using the γγ-coincidence technique.

39 Beam like

5 Counts 10

104 Se

103 Br

102 Kr

0 100 200 300 400 500 600 700 800 900 1000 E (keV)

Target like

5 Counts 10

104 Er

103 Ho

102 Dy

0 100 200 300 400 500 600 700 800 900 1000 E (keV)

Figure 3.10: Doppler-corrected spectra from beam-like and target-like fragments as recorded by CLARA. The spectra shows all isotopes for each Z without any mass gate.

3.4 Dysprosium isotopes As mentioned in section 3.2.5, the analysis of the target-like fragments was carried out using the assumption of binary reactions, that no particles were evaporated neither in the beam-like fragments nor in the target-like fragments. This is not true, however, since the experiment was carried out on nuclei far in the neutron-rich region and, thus, neutron-evaporation channels all the way up to four neutrons are strongly populated. At the CLARA and PRISMA set- up it was not possible to identify the evaporated neutrons or in any other way identify evaporated particles event-by-event. One way to solve this is to com- pare neighbouring selections on A and Z and, by looking at which peaks that appear and disappear depending on the cuts, conclude which γ-ray peaks that belong to which isotope.

40 280

270 TOF (ns) 260

250

240

230

220130 140 150 160 170 180 190 200 210 220 230 E (keV) Figure 3.11: Time-of-flight with respect to γ-ray energy for a selection on 168Dy as- suming a binary reaction. The two-neutron evaporation peak is seen at 243 ns and the four-neutron evaporation peak is seen at 250 ns. The continuous band at 181 keV is corresponding to random background events from the target, 170Er.

For example, by making a selection on 170Dy (82Kr) one would expect to see also 168Dy from two-neutron evaporation and 166Dy from four-neutron evap- oration. Making a selection on 168Dy (84Kr) would make the 170Dy γ rays disappear, but would show 166Dy from two-neutron evaporation and 164Dy from four-neutron evaporation. Another way is to use the TOF, corresponding to the total kinetic energy, of the fragments through PRISMA. For the four iso- topes 164Dy, 166Dy, 168Dy and 170Dy the two-neutron separation energies are, S2n = 13.93 MeV, S2n = 12.76 MeV, S2n = 12.12 MeV and S2n = 11.24 MeV, respectively [134–137]. The neutron evaporation cannot take place unless this amount of energy is transferred from the kinetic energy of the fragments which means that the TOF is increased ≈ 2.7% for two-neutron evaporation channels and ≈ 5.5% for four-neutron evaporation channels. As the TOF of the kryp- ton isotopes in this experiment is ≈ 237 ns, this would correspond to a mini- mum TOF of 243 ns for the two-neutron evaporation channels and a minimum TOF of 250 ns for the four-neutron evaporation channels. The γ-ray energy is shown against the TOF in figure 3.11, for a gate on 168Dy (84Kr) where three distinct peaks is clearly visible, corresponding to binary reactions (173 keV), two-neutron evaporation reactions (177 keV) and four-neutron evaporation reactions (169 keV). A continuous band at 181 keV is also seen, correspond- ing to random background events from the 4+ → 2+ transition in the target, 170Er. The γ-ray spectrum for 168Dy, with a TOF gate to suppress neutron evaporation events, is shown in figure 3.12 where a rotational band is clearly seen. This rotational band was verified by the γγ coincidence technique, see reference [112, I] for details. The same was also done for 170Dy. However, in this case the high back- ground from the very strong γ-rays from the target made it not possible to

41 70 60 50 40 30 Counts/1 keV 20 10

00 50 100 150 200 250 300 350 400 450 500 Energy (keV) Figure 3.12: Spectrum of γ-ray energies from target like fragments gated on the beam- like fragments 84Kr plus a short time of flight. The transitions identified as the rota- tional band in 168 Dy are marked with solid lines. Reprinted from reference [112, I].

unambiguously identify the 4+ → 2+ transition in 170Dy and as no excited states were known, the traditional γγ coincidence technique could not be em- ployed. Instead, a gate on the 777 keV γ-ray in the binary partner, 82Kr [138], was used to reduce the background. This made it possible to do a tentative identification of the 4+ → 2+ transition at 163 keV. The results are shown in figure 3.13. The yrast bands of the dysprosium isotopes with N = 94−104 are shown in figure 3.14.

3.5 Holmium isotopes The analysis of the 167Ho and 169Ho isotopes was carried out in the same way as for the dysprosium isotopes. Even if the cross sections were higher for production of the Ho nuclei, the many excited states with similar energies and the Z resolution of PRISMA made it more difficult to produce clean γ-ray spectra. The details of the analysis are presented in reference [114, II] and the level schemes from the analysis are shown in figure 3.15. A number of γ rays was also observed in 168Ho. The level scheme from reference [143] has been revised and is shown in figure 3.15. An interesting result from the analysis in this experiment is the observation of the previously known 143 keV γ-ray that in reference [143] was assigned to the (1)− → 3+ transition with a half life longer than 4 μs. This lifetime is not compatible with the observation of the transition in this work. Furthermore, the previously ob-

42 0 rm[3,15 3–4]adtecretwr o 6 for work current the and 139–141] 135, [134, from emlk fragments beam-like oi ie erne rmrfrne[1,I]. [112, reference from Reprinted line. solid eeec [142] reference iue3.14: Figure 3.13: Figure iefragments like 2 hw fildhsorm.Tebcgon ae r bu 0tmstewdho the of width the times 20 tentative about the are also on gates is gates background gates The adjacent using histogram). background (filled the shown of estimation An (bottom). fragments like 10 4 8 2 6 + 160 rniinin transition 462 297 386 197 10 12 14 16

87 Counts/3 keV Counts/1 keV Dy 0 2 3 4 0 2 4 6 8 1 94 0101020203030404050 450 400 350 300 250 200 150 100 50 0 1429 284 967 γ 581 87 a soitdwt h rs 4 yrast the with associated ray 0 pcrmof Spectrum rudsaerttoa ad o ypoimiooe with isotopes dysprosium for bands rotational state Ground γ rypasadnraie eaiet h ieo h ekgts The gates. peak the of size the to relative normalized and peaks -ray 0 82 10 4 2 8 6 170 162 rpu ieo-ih tp.Coincidence (top). time-of-flight plus Kr y h 2 The Dy. 454 283 372 185 Dy 81 82 96 r ieo-ih lsthe plus time-of-flight Kr, 1375 549 266 921 81 γ 163 0 ryeege rmtre-iefamnsgtdo h beam- the on gated fragments target-like from energies -ray 0 + 10 4 2 8 6 164 → 342 259 Ener 418 169 0 Dy 73 + 98 rniinin transition 1261 843 242 501 73 + 0 gy → 0 10 4 8 2 6 166 2

( + 449 273 365 keV 177 Dy 77 rniinin transition γ ryeeg 7 e ntebeam- the in keV 777 energy -ray 100 170 1341 254 527 892 77 + yi rmtecluain in calculations the from is Dy ) 0 –10 (10 0 (4 (2 (8 (6 γ + 168 rysetagtdo the on gated spectra -ray ) ) ) ) ) in 442 170 357 268 173 Dy 75 168 102 yi akdwt a with marked is Dy (1315) (873) (516) (75) (248) yadte4 the and Dy 0 (2 0 (4 N 168 170 170 ) = ) (163) (72) Dy Er Dy 94 104 − (235) + (72) 104 43 → (0 0 ) 21/2 19/2 230 17/2 202 17/2 384 15/2 192 15/2 182 343 167 13/2 483 161 13/2 352 301 11/2 143 11/2 133 1 140 260 122 9/2 143 120 9/2 7/2 98 3 187 193 7/2 217 97 167Ho 168Ho 169Ho Figure 3.15: Ground state rotational bands for 167Ho and 169Ho and the level scheme for 168Ho from this work. served 488 keV γ-ray is observed together with a close lying γ ray of 483 keV. When gating on the γ ray at 488 keV, the 143 keV γ-ray is not seen, while it is seen when gating on the 483 keV γ ray. This is an indication that the ordering of levels is likely different than previously suggested.

44 4. Evolution of collectivity

One of the standard references for nuclear masses, and deformations, is the calculations made by Möller and Nix using the finite range liquid drop model [144]. This reference has for example been used in the calculations in Refs. [95, 96] and, thus, to obtain the results shown in figure 2.3. The β2 deformation parameters from reference [144] are shown in figure 4.1 for even-even nuclei in the region 50 ≤ Z ≤ 82 < and 82 ≤ N ≤ 126. As seen in this figure, the deformations behave smoothly with a maximum in the region around N ≈ 104. In figure 4.1, the evaluated experimental deformations from reference [145] are also shown, but the calculations from reference [144] does not appear to follow the same pattern as the experimental data. Besides the larger absolute variation in deformations for different Z values, the deformation maximum for each Z does not appear to be as stable around N ≈ 104 as in the Möller and Nix calculations. Rather, the deformations seem to peak at lower values of N for lower values of Z. This has been discussed in reference [90] as an effect originating from the contributions to the moment of inertia when the Fermi energy is around the middle of the i13/2 neutron shell, similar to the orbitals shown in figure 2.2. As described in section 2.1.1, the nuclear deformations causes some orbitals to move down relative to the lower lying orbitals in the spherical shell model so that, in this case, the i13/2 neutron shell starts to be filled at lower values of N.

4.1 Variable moment of inertia As the experimental data on nuclear deformation is quite sparse other ways of understanding the evolution of nuclear deformations have to be investi- gated. One other way is to use the excitation energy spectrum together with the VMI model described in section. 2.1.4. The VMI model is based on the Harris parameters [J0,J1] and not the deformations directly. However, J0 can be related to the deformation of the nucleus and J1 can be related to the amount of freezing of the internal structure, that is the rigidity. In this way it is pos- sible to obtain a much richer set of data than when using only experimental deformations directly. The VMI fits have been made according to the proce- dure in reference [90], with the inclusion of the data on 168Dy [112, I] and 170Dy [112, 142]. The experimental data from reference [145] is shown to- gether with the Harris parameters J0 in figure 4.2. Note that the parameters

45 Sn (50) Te (52) 2 2 0.35 0.35 Xe (54) Ba (56) 0.3 0.3 Ce (58) Nd (60) 0.25 0.25 Sm (62) Gd (64) 0.2 0.2 Dy (66) Er (68) 0.15 0.15 Yb (70) 0.1 0.1 Hf (72) Os (74) 0.05 0.05 W (76) Pt (78) 0 0 85 90 95 100105110115120125 85 90 95 100105110115120125 N N

Figure 4.1: Quadrupole deformation parameters β2 for even-even nuclei according to the Möller and Nix calculations [144] (left) and experimentally measured β2 defor- mations [145] (right).

Sm (62) ) 2 50 Gd (64) 0.35 -1 45 Dy (66)

MeV Er (68) 0.3 2 40

( Yb (70) 0 0.25 J 35 Hf (72) 30 Os (74) 0.2 25 W (76) 0.15 20 Pt (78) 15 0.1 10 0.05 5 0 0 90 95 100 105 110 115 120 90 95 100 105 110 115 120 N N

Figure 4.2: Experimentally measured β2 values (left) and J0 Harris parameters (right) for a selection of even-even nuclei.

might differ slightly from reference [90] due to different choices of cut-off and 170 + + that the J0 for Dy is based only on two data points, the tentative 4 → 2 transition from reference [112, I] and the calculated 2+ → 0+ transition from reference [142]. These new data points actually suggest that the apparent shift in the location of the deformation maximum to lower N for lower Z could due to the lack of experimental data in combination with the sub-shell closure at N = 98, and that the N = 104 deformation maximum could be reasonably stable from, at least, Dy to Hf, 66 ≤ Z ≤ 72.

46 4.2 Deformations in odd-A nuclei In figure 4.1, only the deformations of the even-even nuclei are shown for the Möller and Nix calculations, since the only experimental data available in reference [145] is for even-even nuclei. The reason for this is that the defor- mations are usually obtained from measuring the quadrupole moment through the B(E2) values in Coulomb excitation experiments. Coulomb excitation in- vestigations of the odd-A isotopes are more challenging since these nuclei have a high density of low excitation-energy states that are, in most of the cases, connected by low-collectivity transitions. However, recent experiments at REX-ISOLDE have been carried out to study both odd-A [146] and odd- odd [147] nuclei. If the experimental data can be expanded to include also the odd-A nuclei, this would be an important increase in the number of data points available for systematic investigations on the evolution of deformations and collectivity. In reference [114, II] this has been discussed using a minimization proce- dure of the experimental data with the particle plus triaxial rotor model. To evaluate the stability of this fitting procedure a function defining the average difference between the calculated results and the experimental results can be defined as N |E − E | e = ∑ exp PTR . (4.1) i=0 NEexp

Note that the function in equation (4.1) is not the same as the function used in reference [114, II]. This function has been evaluated at 100 000 ran- dom points in the four-dimensional (ε2,γ,ε4,ζ) space. The different two- dimensional projections of this four-dimensional space are shown in figure 4.3 169 for Ho. As is seen in the figure, there is no correlation between γ and ε4 or γ and ε2. The only strong correlation that is seen is between ε2 and ζ, while weaker correlations exist between ε2 and ε4, γ and ζ, and ε4 and ζ. The strong correlation between ε2 and ζ makes it impossible to extract a definite result of the deformation, however, the weak correlations make it possible to put re- strictions on the fit. By restricting γ ≈ 0 and |ε4|  0.05 it is possible to obtain converged values of ε2 and ζ. To restrict the values even further one could use the 1/2−[541] orbital by − π = 1 setting requirements on the energy of the bandhead of the J 2 band. As this orbital has a very strong dependency on ε2 it will limit the fit con- − π = 1 siderably. This, however, requires experimental knowledge of the J 2 bandhead which was not obtained in the experiment in reference [114, II]. Thus, the results are too rough for a systematic comparison along the isotopic chain. One conclusion is, however, that the deformations are smaller than in the neighbouring Z nuclei, which is not unexpected since the presence of a spectator nucleon can modify the deformation parameters, as discussed in ref- erence [90] for odd-A Os isotopes in terms of the VMI model.

47 30 4 0.14 20 0.12 0.1 10 0.08 0.06 0 0.04 -10 0.02 0 -20 -0.02 -0.04 -30 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 2 2

1 4 0.14 0.9 0.12 0.8 0.1 0.7 0.08 0.6 0.06 0.5 0.04 0.4 0.02 0.3 0 0.2 -0.02 0.1 -0.04 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -30 -20 -10 0 10 20 30 2

1 4 0.14 0.9 0.12 0.8 0.1 0.7 0.08 0.6 0.06 0.5 0.04 0.4 0.02 0.3 0 0.2 -0.02 0.1 -0.04 0 -30 -20 -10 0 10 20 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 4.3: Projections of the particle plus triaxial rotor parameter space for 100 000 random points and a requirement that the average error between the experimental and theoretical energy levels are less than e < 1%.

48 4.3 Rigidity and backbending Another important aspect of the collective structure of the nuclei in this region is the rigidity of the nucleus, closely related to the J1 Harris parameter of the VMI model thoroughly discussed in reference [90]. For a very rigid nucleus the moment of inertia is expected to remain unchanged with increasing rota- tional frequency and can also manifest itself through a delayed backbending. The experimental observables, energy and angular momentum, can be translated into the TRS observables through the well known canonical relation between rotational frequency (h¯ω) and angular momentum, ∂H E − E h¯ω = ≈ i f , (4.2) ∂I I˜i − I˜f and the quantum mechanical relation between moment of inertia (J (1)) and angular momentum, ( ) I I˜ + I˜ J 1 = ≈ i f , (4.3) h¯ω 2h¯ω where Ei (Ef) and I˜i (I˜f) are the energy and spin of the initial (final) state, respectively, discussed in more detail in section 2.1.3 and section 2.1.4. Using these relations, the excitation energy spectrum can be compared to the TRS calculations, shown in figure 4.4 for Dy isotopes with 160 ≤ A ≤ 170 (94 ≤ N ≤ 104) and in figure 4.5 for Ho isotopes with 161 ≤ A ≤ 171 (94 ≤ N ≤ 104). As seen in these figures, the backbending region has been reached exper- imentally, for 160Dy, 161Ho and 163Ho. The backbendings in the TRS calcu- lations are, however, clearly occurring at lower rotational frequency than ob- served experimentally. For 162Dy–166Dy and 165Ho, the predicted backbend- ing region has been reached experimentally, but no backbending has yet been observed experimentally, why it is difficult to draw conclusions about how close the TRS calculations are to the experimental backbending for these nu- clei. For the nuclei studied in this thesis, 168Dy, 170Dy, 167Ho and 169Ho, the predicted backbending region was not yet reached experimentally.

49 Dy160 Dy162 ) 100 ) 100 -1 -1 90 90 MeV MeV 2 80 2 80 ( ( (1) 70 (1) 70 J J 60 60 50 50 40 40 30 30 20 20 10 10 0 0 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 (MeV) (MeV)

Dy164 Dy166 ) 100 ) 100 -1 -1 90 90 MeV MeV 2 80 2 80 ( ( (1) 70 (1) 70 J J 60 60 50 50 40 40 30 30 20 20 10 10 0 0 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 (MeV) (MeV)

Dy168 Dy170 ) 100 ) 100 -1 -1 90 90 MeV MeV 2 80 2 80 ( ( (1) 70 (1) 70 J J 60 60 50 50 40 40 30 30 20 20 10 10 0 0 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 (MeV) (MeV)

Figure 4.4: Total Routhian Surface calculations of Dy isotopes with 160 ≤ A ≤ 170 with zero quasiparticles (solid line) compared to available experimental data (circles).

50 Ho161 Ho163 ) 100 ) 100 -1 -1 90 90 MeV MeV 2 80 2 80 ( ( (1) 70 (1) 70 J J 60 60 50 50 40 40 30 30 20 20 10 10 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 (MeV) (MeV)

Ho165 Ho167 ) 100 ) 100 -1 -1 90 90 MeV MeV 2 80 2 80 ( ( (1) 70 (1) 70 J J 60 60 50 50 40 40 30 30 20 20 10 10

0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 (MeV) (MeV)

Ho169 Ho171 ) 100 ) 100 -1 -1 90 90 MeV MeV 2 80 2 80 ( ( (1) 70 (1) 70 J J 60 60 50 50 40 40 30 30 20 20 10 10 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 (MeV) (MeV)

Figure 4.5: Total Routhian Surface calculations of Ho isotopes with 161 ≤ A ≤ 171 (π,α)=(−,− 1 ) with one quasiparticle in the 2 configuration (solid line) and the (π,α)=(−,+ 1 ) 2 configuration (dashed line) compared to available experimental data (π,α)=(−,− 1 ) (π,α)=(−,+ 1 ) with 2 (filled circles) and 2 (open circles).

51

Part II: Technology

5. The AGATA HPGe spectrometer

“It’s the apparent change in the frequency of a wave caused by relative motion between the source of the wave and the observer.” – Sheldon Cooper

As seen in chapter 3, we are currently approaching the limit of what is achievable with stable ion beams and the current detector systems. To reach further out in the terra incognita of the Segré chart new exotic nuclei will be produced at the second generation RIB facilities. These nuclei will be pro- duced with very low cross sections and in a high γ-ray background environ- ment, which makes the weak γ-ray transitions extremely difficult to detect with existing spectrometers. To distinguish these rare events, new instruments with higher efficiency and resolving power are required. The sophisticated high-resolution HPGe arrays, crowned by EUROBALL [133] and GAMMA- SPHERE [148], have given access to very weak signals from high-spin states, unravelling many new nuclear structure phenomena. To increase the detec- tion efficiency in experiments at the first generation RIB facilities and for reactions with low γ-ray multiplicity, HPGe detector arrays like MINIBALL [149] and EXOGAM [150], which are using segmented HPGe detectors to obtain a higher detector granularity, have been built. To increase the detection power even further, the next generation HPGe detector arrays are based on the γ-ray tracking technique, which currently is being developed within the AGATA [151–154] and GRETA [155] projects. One source of background in previous HPGe detector arrays is the true γ rays that are detected, but only deposit parts of their energy in the detec- tor when they are Compton scattered out from the crystal. To suppress this background the detectors can be surrounded with active shields, usually high- efficiency BGO detectors. If a γ ray is Compton scattered the BGO shield will detect it and the event is discarded. This is, however, not a very economic method since it means that the array will cover a smaller solid angle due to the dead space of the BGO shields. Furthermore, the Compton-scattered γ- rays contain information and a method that recover Compton-scattered γ-rays instead of rejecting them would dramatically increase the efficiency. To recover this information the AGATA detector will instead use a method based on γ-ray tracking. By removing the BGO shields and instead deter- mine each interaction position in the crystals it is possible to recreate the γ- ray track and by adding the energy deposition in each interaction point the

55 original γ-ray energy can be obtained. Furthermore, a precise knowledge of the position of the interaction points will increase the precision of the cor- rections for the Doppler effects during in-beam γ-ray spectroscopy and thus also increase the energy resolution. The complete AGATA detector will con- sist of 180 asymmetric hexagonal, tapered and encapsulated HPGe crystals. The HPGe crystals are available in three slightly different shapes that together form an AGATA triple-cluster (ATC) detector [153]. In its full configuration AGATA will forma9cmthick HPGe shell with an 82% solid angle coverage.

5.1 HPGe crystals The AGATA array will consist of tapered closed-end coaxial n-type HPGe crystals, with an impurity concentration of 0.4 · 1010–1.8 · 1010 cm−3, in three slightly different asymmetric shapes. The crystals typically weigh 2 kg each and has a diameter of 80 mm at the rear and a length of 90 mm. The tapering angle is 8◦, creating a hexagonal shape at the front. The bore hole in the crys- tals has a diameter of 10 mm and extends to 13 mm from the front surface. Each crystal is electrically segmented into 36 segments which are read out by 36 outer and one inner (core) contact. There are six angular segments and six segments in the z direction with thicknesses 8, 13, 15, 18, 18 and 18 mm starting at the front face of the detector. The crystals are encapsulated into alu- minium canisters with a 0.8 mm wall thickness. See references [151, 153, 154] and figure 5.1 for a more detailed description of the AGATA HPGe crystals and the ATC.

5.2 Electronics Due to the extreme conditions AGATA will run in, all electronics for the sys- tems have been developed specially for this array. Closest to the crystal are the low-noise silicon field-effect transistor (FET) preamplifiers [156, 157] that op- erates both with a cold part in the detector cryostat and a warm part outside the cryostat. The preamplifiers prepare the signal for the digitizers that contin- uously samples each segment, and the core signal, with a 100 MHz sampling frequency and 14 bit resolution in the analog-to-digital converter (ADC). The signals from all segments are sent to the pre-processing electronics where the energy, time and the digitized leading edge of the traces of all the 36 seg- ments are extracted for the pulse-shape analysis (PSA) (see section 5.3). The core signal is also pre-processed and used as an input into the global trigger and synchronization (GTS) system which provides the system clock and the trigger for the array. The core signal from the GTS system and the interac- tion points obtained from the PSA are then tracked and merged, together with

56 Figure 5.1: The AGATA HPGe crystals. Reprinted from reference [151].

Figure 5.2: Signals from the core, the segment with the primary hit (Seg 4), and from the mirror charges for a γ-ray interaction in a six fold segmented HPGe detector. Figure from [152].

57 data from ancillary detectors that is prepared using a special AGATA VME Adapter (AGAVA) interface, in the event builder.

5.3 Pulse-shape analysis To determine the interaction position in a crystal segment, pulse-shape in- formation from the segment which was hit, the mirror charges in the neigh- bouring segments, and the core signal is used, as illustrated in figure 5.2. The azimuthal position in the crystal segment is obtained by comparing the ampli- tudes of the mirror charges. The radial position is obtained from the shape of the signal of the hit segment. This is done by comparing the sampled pulse-shapes to a database, with more than 30 000 basis sites per crystal, of pulse shapes for different inter- action positions. Each grid point in the PSA basis contains a reference pulse shape with several time steps within the digitizer resolution of 10 ns. For a 2 × 2 × 2mm3 grid with a time step of 1 ns the size of each PSA basis file is roughly 1 GB per crystal. One of the main problems of the PSA algorithms is to obtain the database of pulse shapes. When delivered, the crystals are scanned using radioactive sources [158]. This process gives a very precise database of pulse shapes but it is unfortunately a very slow process. To com- plement the scanned pulse shapes, codes for calculating them are being devel- oped. These calculations are much faster, but the main challenge is to obtain realistic pulse shapes for the complex electric field within the geometry of the AGATA crystal and large uncertainties in the impurity concentration. Further- more, high electric fields and low temperatures will cause the charge carrier drift velocities to become anisotropic with respect to the crystallographic lat- tice orientation [159], which further complicates the situation. The performance of the γ-ray tracking will depend strongly on the qual- ity of the PSA. Accuracy better than 5 mm has to be achieved using algo- rithms fast enough for real-time application. Interaction point coordinates are obtained by comparing the detected pulse shapes to the signal basis. The sim- plest method is the grid search [160] algorithm that works well for experi- ments when there is only one γ ray interaction a time in the same segment. In the grid search algorithm the sum of the squared difference between measured and calculated signals is compared and the interaction point with the best value of this quantity is selected. More sophisticated algorithms have also been de- veloped. Since these algorithms have different advantages and disadvantages a dispatcher code that can distribute the events to the optimal algorithm depend- ing on the event properties is planned within the collaboration. The algorithms evaluated so far are the extensive grid search [161], the particle swarm opti- misation [161], the matrix method [162], genetic algorithms [163], recursive subtraction [164] and neural networks [161].

58 Figure 5.3: Simulated interaction points of 30 γ rays of energy Eγ = 1.33 MeV in the (θ,φ sinθ) plane of an ideal germanium shell with an inner radius of 15 cm and an outer radius of 24 cm. Circles are correctly and squares incorrectly identified clusters. Figure from [152].

5.4 Tracking of γ rays The output from the PSA will contain the energy, time and three-dimensional position of each identified interaction point, located in a, so called, world map for each event. A typical such world map, where the interaction positions are shown in terms of the (θ,φ sinθ) coordinates relative to the center of the ar- ray is shown in figure 5.3. The purpose of the tracking algorithms is to recon- struct the trajectories of the γ rays and disentangle them from their world map. There are two ways to accomplish this, the so called backtracking or forward tracking methods. The backtracking algorithm was developed in Stockholm [165, 166]. This algorithm uses the information that the final, photoelectric, interaction point most probable has an energy deposition between 100 to 250 keV. Starting from this assumed final interaction point, other interaction points are searched for within a distance based on the interaction length in germa- nium for γ rays of that energy. This procedure is repeated until the track is terminated by the source location. In the forward tracking algorithm the interactions caused by a certain γ ray are assumed to be clustered together within a certain angular spread in the (θ,φ sinθ) plane, which depends on the total number of hits registered in the

59 various detectors, see figure 5.3. These clusters are searched for and identified. Initially the source location is labelled to be the zeroth interaction point. The first and second interaction points are chosen randomly and the γ-ray energy after scattering is determined from the measured energy depositions in the cluster. This energy is compared to the energy calculated by the Compton scattering formula Eγ Eγ = , (5.1) + Eγ ( + θ ) 1 2 1 cos γ mec

2 where Eγ is the energy after Compton scattering, mec the electron rest mass and θγ the angle between the incoming and scattered γ ray. The angle θγ is determined from the positions of the three interaction points. A figure-of-merit (FOM) based on the agreement between the two energies is calculated. All possible permutations of interaction points are evaluated and the one with the highest FOM is chosen. This procedure is repeated with the identified first interaction point as a starting point until all interaction points in a cluster have been assigned to the track. An interaction is allowed to be a member of several clusters but only the cluster with the best FOM is accepted. Pair production events are identified if two tracked γ rays each with an energy of 511 keV are found within a cluster. Other types of clustering and tracking have also been considered within the AGATA array. One example it to use fuzzy logic to identify well separated groups in a multidimensional space [167]. The optimal position of the clus- ter centres and the degree of membership of each point is identified using a fuzzy logic algorithm. After the identification, a defuzzification is carried out in which every point is switched from being a member of a certain degree to every cluster to just belonging to one cluster. This is, however, still a work in progress.

5.5 Data acquisition The data aquisition system (DAQ) in AGATA has two functions. The first of these is to process the data flow from the AGATA front end electronics and the ancillary detectors to the local data storage. The local storage is used during the data analysis after which the data is archived at a LHC Grid [168] Tier-1 computing centre in Bologna. The second task is to control and monitor the whole system and the data flow during experimental campaigns. To handle the large data flow in AGATA a well structured DAQ is needed. The DAQ developed for AGATA is called NARVAL [169]. It is written in Ada1, but the actors can load C++ shared libraries. NARVAL is based on

1The Ada language is named after Ada Lovelace, one of the first computer programmers, and was developed for the United States Department of Defence. It was designed for critical sys-

60 an abstract class, called actor, which comes in three types: producers, inter- mediary and consumers. A producer is an actor that collects data from the hardware, such as the VME crates. The intermediary actors performs tasks like PSA, building the event and tracking. The consumers store the data to disk and builds histograms. Finally, there is also the chef d’orchestre actor that handles the state machine and the gestion d’erreurs actor that handles and recovers errors. These actors can be written separately and included in the DAQ so that it is always adapted to the needs of the particular experiment in question. This also means that NARVAL is not a one program DAQ, but more a society of interacting actors that can run on many different computers in parallel. The DAQ chain is controlled by the user through the Cracow graph- ical user interface (GUI) [170], originally developed for RISING. The GUI is not a part of NARVAL, but is an independent program that communicates with NARVAL through web services and can thus be run from any computer connected to the network.

5.6 Position resolution As mentioned in section 5.3, in order to have a high detector peak efficiency a position resolution of  5 mm is required [152]. Previously, two methods have been used to determine the interaction position resolution of segmented HPGe detectors. The first method utilizes imaging techniques with a 60Co source [171]. The second method makes use of the Doppler effect by measuring the energy resolution of peaks in Doppler corrected γ-ray spectra recorded in in- beam experiments in which the γ rays are emitted in-flight by the moving nuclei [172–174]. In the experiments in references [172–174], the position resolution has been obtained by comparing the experimental data with Monte Carlo simulations of the set-up. In this work, and reference [175, III], a Monte Carlo model independent method to obtain the position resolution from an in-beam experiment is presented. The well known Doppler effect is the apparent change in frequency an ob- server experience when a source is moving with respect to the observer [176]. The energy of a Doppler shifted γ ray emitted by a nucleus moving at rela- tivistic velocities is given by the expression (1 − β 2)1/2 Eγ = Eγ . (5.2) 0 (1 − β cosθ) where Eγ is the energy of the emitted electromagnetic radiation, β is the source velocity as a fraction of the speed of light and θ is the angle between tems like avionics, thermonuclear weapon systems and satellites. This is the reason why Ada programs are usually very stable. This is also the reason why the first program one learns to write in Ada is often called “Goodbye, World!”.

61 Ep 4

Ep 3

Ep 2 Wp

z Ep 1

r E d

Figure 5.4: Effects of the position resolution when determining the angle used to correct for the Doppler shifts of the γ rays. Reprinted from [175, III] with permission from Elsevier.

the direction of the source and the direction of the electromagnetic radiation, see illustration in figure 5.4. Here Eγ0 is the energy of the γ ray in the rest frame of the nucleus. The energy resolution of the detected γ rays will thus be given by the expression ∂ 2 ∂ 2 ∂ 2 2 = Eγ0 2 + Eγ0 2 + Eγ0 2, WEγ WEγ Wβ Wθ (5.3) 0 ∂Eγ ∂β ∂θ where WE is the full width at half maximum (FWHM) of the detected energy, Wθ is the angular resolution of the detector, Wβ the spread in velocity of the recoil ions and WEγ the intrinsic resolution in the detector and electronics. The

62 partial derivatives in equation (5.3) are given by ∂ − β θ Eγ0 = 1 cos , / (5.4) ∂Eγ (1 − β 2)1 2 ∂Eγ0 β − cosθ = Eγ , (5.5) ∂β (1 − β 2)3/2 ∂Eγ0 β sinθ = Eγ . (5.6) ∂θ (1 − β 2)1/2

It can be shown [175, 177] that the position resolution, Wp, is given as, −1 2 1 2 2 1 1 W = W , −W , − , (5.7) p 2 Eγ0 c Eγ0 f 2 2 b rc rf where ∂ 2 2 = Eγ0 . b ∂θ (5.8)

The interaction position resolution can, thus, be extracted from equation (5.7) by performing two measurements of WEγ0 at a close (c) and far (f) distance [177].

5.6.1 Reaction selection and simulations A first preliminary survey of reactions possible to use to measure the position resolution experimentally was done using the TALYS code [178], that calcu- late cross sections for reactions with γ rays, neutrons, and light ions up to 4He in the energy range 0.1–200 MeV and a mass range of 12 ≤ A ≤ 339. The contribution of the target thickness to the total FWHM was also studied us- ing the TRIM code [179, 180]. For more details, see reference [181]. A few cases were selected for further simulations using the evapOR code [182, 183], which is a fusion-evaporation code that calculates the fusion cross-section for two arbitrary nuclei, followed by the evaporation of particles from neutrons to 6Li. Furthermore, evapOR generates a Monte Carlo dataset from these cross sections that can be used in further simulations. The requirements on the reactions are discussed in more detail in reference [175, III], but can be summarized in the following points: • minimize the spread of the velocity vector of the residual nuclei (as small Wβ as possible), • enhance the effects of the Doppler broadening due to the γ-ray detection by maximizing β, Eγ0 and sinθ, • select transitions with upper and lower limits on the effective life-time, and • choose a reaction which gives strong and clean peaks in the γ-ray spectra.

63 5.6.1.1 The 2H(81Br,n)82Kr reaction The first selected reaction was 2H(81Br,n)82Kr with a 1044 keV 4+ → 2+ transition in 82Kr. The main advantages of this reaction are the very light target and that only one neutron is evaporated. Due to this, the velocity vector is expected to have a very narrow distribution in both magnitude and direction. There are, however, several long-lived states in 82Kr, for example the yrast ( +) = 8 state has a half life of t1/2 96 ps. Calculations using evapOR show that only < 0.1% of the compound nucleus cross-section feeds states with total angular momentum J ≥ 17/2.

5.6.1.2 The 9Be(136Xe,3n)142Ce reaction The second selected reaction, with 142Ce as the final nucleus, has the advan- tage that the chosen 2+→0+ ground state transition is very strongly populated. The heavy projectile and the relatively light target also gives narrow β and θ distributions of the velocity vector despite the 3n evaporation. A disadvan- tage is that the γ-ray energy is rather low, only 641 keV. The yrast 2+ and 4+ states in 142Ce have lifetimes of 8 ps and 11 ps [184], respectively, which are short enough to fulfil the lifetime criterion. All other states with known life- times are short lived [184] and do not influence the interaction position res- olution determination. However, only states up to spin 6+ are known in this nucleus [184], while in the proposed reaction states of considerably higher spin are populated. Possible long lived ( 15 ps) and strongly populated but so far unobserved high-spin states may therefore influence the measurement.

5.6.1.3 The 12C(82Se,3n)91Zr reaction The third selected reaction has 91Zr as the final nucleus. The 21/2+ state in this nucleus is isomeric with a half life of 4.35 μs [185]. The selected tran- sitions must therefore occur between states above this isomer. For the sim- ulations we chose the (23/2−)→21/2+ transition, which has an energy of 2141 keV [186–188]. A plunger measurement of lifetimes above the isomer was performed using the same inverse kinematic reaction as selected in this work [189]. A state at 5741 keV, which feeds the (23/2−) state at 5308 keV, has a lifetime of 45 ps. The distance travelled by the 91Zr residues during this time is about 1 mm. The selected 2141 keV will, therefore, be slightly influ- enced by the lifetime of the 5741 keV. All other observed states above the 21/2+ isomer had lifetimes and feeding times which were much smaller than 45 ps [189]. Above the 21/2+ isomer there are several other high-energy tran- sitions, which are not fed by the long lived 5741 keV level and which also may be used in the measurement. The relative intensity of the (23/2−)→21/2+ transition in the proposed reaction is not known. We estimate it to be of the order of 10% of the total reaction channel population.

64 5.6.1.4 The 12C(82Se,4n)90Zr and 12C(30Si,np)40K reactions Two reactions, for which experimental results exist on interaction position res- olution measurements, have also been included in the simulations. The first one is the reaction 12C(82Se,4n)90Zr, which was used in a test of a GRETA HPGe crystal [173]. The second reaction is 12C(30Si,np)40K, which was used in the first in-beam commissioning experiment of an asymmetric AGATA triple cluster detector [190, 191], see section 5.6.2.

5.6.1.5 The reference reaction A reference reaction with β = 10.0%, Wβ = 0 and Eγ0 = 50 keV − 5 MeV was also used in the simulations in order to study systematic errors.

5.6.1.6 Results The evapOR data sets were used as input to the AGATA GEANT4 simulation program [154, 192, 193]. This program simulates γ-ray interactions in the AGATA HPGe detectors and produces an output file containing the energy and position of the interaction points within the detectors. The interaction points produced by the GEANT4 program were used as input to the mgt tracking code [194, 195], which is based on the forward tracking algorithm [196]. The results from these simulations, see figure 5.5, show that the proposed method works well. For a more detailed discussion of the results, see reference [175, III].

5.6.2 Experiment The first in-beam commissioning test of the AGATA detectors and infrastruc- ture was performed in March 2009. The proposed reaction to use for the exper- iment was the 12C(82Se,3n)91Zr reaction. Unfortunately, it was not possible to produce a 82Se beam with high enough energy and intensity at the time of the experiment. Therefore the reaction 12C(30Si,np)40K was chosen instead. A 30Si beam with energy of 64 MeV was produced by the Tandem Accelera- tor at LNL, see section 3.1. The γ radiation was detected by the first AGATA ATC [153], see figure 5.6. Data were taken using two distances between the front face of ATC and the target, dc = 55 mm and df = 55 mm [175, III]. The complete front-end electronics and NARVAL DAQ [169] of the AGATA Demonstrator was used in the experiment where dedicated NARVAL actors were performing the on-line PSA and γ-ray tracking in real time. The system included the autofill system, the low-voltage power supply, preamplifiers, the digitizers, the pre-processing electronics, the GTS system, the computer farm for PSA, event building and on-line γ-ray tracking, and the disk storage array. The high-voltage was provided by a standard CAEN SY527 system. As this was the first time in which the full system was running, the processed and tracked spectra were only shown on-line while parts of the digitized pulse shapes were stored to disk for later replay.

65 2 2 2 82 142 1.5 Reference 1.5 Kr 1.5 Ce

- s (mm) 1 - s (mm) 1 - s (mm) 1 p p p

0.5W 0.5W W 0.5 0 0 0 -0.5 -0.5 -0.5

-1 s -1 -1 Wp -1.5 -1.5 -1.5 -2 -2 -2 0246810 0246810 0246810 s (mm) s (mm) s (mm)

2 2 2 91 90 40 1.5 Zr 1.5 Zr 1.5 K - s (mm) 1 - s (mm) 1 - s (mm) 1 p p p W 0.5 0.5W W 0.5 0 0 0 -0.5 -0.5 -0.5 -1 -1 -1 -1.5 -1.5 -1.5 -2 -2 -2 0246810 0246810 0246810 s (mm) s (mm) s (mm)

Figure 5.5: The difference between the calculated interaction position resolutions, Wp, and the mgt smearing parameter, s, (that simulates the position resolution) shown as a function of s for the simulated reactions listed in reference [175, III]. The sys- s tematic error, estimated by a fit of a constant Wp, is shown as a solid line. Reprinted from [175, III] with permission from Elsevier.

The event replay was carried out off-line using the NARVAL emulator run- ning on a dual quad-core Intel E5520 2.27 GHz CPU computer with 24 GB of RAM and a 10 Gbit Ethernet connection to the data storage disk. The pulse- shape analysis running in the NARVALemulator used the adaptive grid-search algorithm [160] with a signal basis grid having a resolution of 2 × 2 × 2mm3 and which was calculated by the ADL code [197–199]. The off-line γ-ray tracking was performed by the mgt program. A tracked γ-ray spectrum mea- sured at the close distance is shown in figure 5.7. The spectrum is Doppler corrected by using the position of the first interaction point and an average value of β = 0.048. As seen in figure 5.7, several γ rays not originating from 40K are also populated. Especially the one-proton evaporation channel (41K) and the one-neutron evaporation channel (40Ca) were found to provide useful data points at low and high energies. The results obtained for the interaction position resolution Wp are listed in table 5.1 and shown in figure 5.8 for the six selected γ rays. As seen, the interaction position resolution varies roughly linearly as a function of γ-ray energy from 8.5 mm at 250 keV to 4 mm at 1.5 MeV, and has an approximately constant value of about 4 mm in the γ-ray energy range from 1.5 MeV to

66 Figure 5.6: The AGATA detector in position for the first commissioning experiment. Reprinted from reference [191].

4 MeV. See reference [175, III] for more detailed discussion on the position resolution results.

5.7 Neutrons in AGATA The experiment in section 5.6.2 measured the position resolution of the AGATA ATC up to about 4 MeV. Although, in some nuclear structure experiments the energies of the γ rays emitted are much higher than this. For example, the γ rays emitted by a giant dipole resonance (GDR) in the rare-earth region will have an energy around 10–15 MeV [200, 201]. Another crucial point for GDR experiments is the possibility to discriminate between neutron and γ rays in AGATA [200]. This is, furthermore, important when doing experiments on neutron-rich nuclei at RIB facilities like FAIR and SPIRAL2. Neutrons can be detected in AGATA either via elastic scattering, Ge(n, n)Ge, inelastic scattering, Ge(n, n γ)Ge, or nuclear reactions [202]. The expected probability of neutrons with energies 1–10 MeV to be detected by AGATA is about 50% [203].

67 106 246 770 1352 18232333 3905 Counts 105

104

41K 40K 40K 103 242 251 760 790 1339 1362

2 10 40K 40K 40Ca

10 1800 1850 2305 2355 3860 3960 0 1000 2000 3000 4000 5000 E 0 (keV) Figure 5.7: Gamma-ray spectrum measured using the 30Si +12 C reaction with the AGATA triple cluster detector placed at the close distance (dc ≈ 55 mm). The spec- trum was created by performing γ-ray tracking using mgt and by applying a Doppler correction based on the position of the first interaction point and an average value of β = 0.048. Expanded views of the six peaks selected for the analysis are also shown in the figure. Reprinted from [175, III] with permission from Elsevier.

A method has recently been developed by Monte Carlo simulations to dis- criminate between neutrons and γ rays in AGATA [204]. In that work, the discrimination was done using the forward tracking algorithm with respect to three parameters: the energy deposited in the first and second interaction points, the incoming direction of the γ ray, and the FOM from the tracking algorithm. Differences in pulse shapes between neutron and γ-ray interactions has also been studied in non-segmented HPGe detectors with negative results [202]. It is, however, not known if this is also true for segmented HPGe detec- tors with much smaller volume per segment than a non-segmented detector. An experiment to check and further develop these methods has been carried out using AGATA, the HELENA array and a 252Cf source, see figure 5.9. 252 The HELENA BaF2 detectors were placed closed to the Cf source with a thick lead shield in-between the source and AGATA to reduce the number γ

68 12 (mm) p

W 10

8

6

4

2

0 1000 2000 3000 4000 5000 E 0 (keV) Figure 5.8: Interaction position resolution as a function of γ-ray energy. The error bars due to statistical errors only. The estimated systematic deviations for the data set are shown as the filled histogram. Reprinted from [175, III] with permission from Elsevier.

Figure 5.9: The AGATA and HELENA detectors in position for the neutron experi- ment.

69 Table 5.1: Experimental values of the interaction position resolution Wp obtained for the six selected γ rays. The columns in the table are the residual nucleus, the energy of the γ ray, the FWHM of the peak at close and far distance, the parameter b and the interaction position resolution. The experimentally determined average interaction distances, needed for the calculation of Wp according to equation 5.7, have the values rc = 100 mm and rf = 270 mm.

Residual Eγ0 WEγ0,c WEγ0,f bWp nucleus (keV) (keV) (keV) (keV) (mm) 41K 246 2.326 ± 0.023 2.148 ± 0.013 11.6 8.6 ± 0.6 40K 770 5.159 ± 0.024 4.732 ± 0.015 36.2 6.10 ± 0.21 40K 1352 7.14 ± 0.04 6.734 ± 0.027 63.5 3.93 ± 0.23 40K 1823 10.31 ± 0.04 9.851 ± 0.025 85.7 3.76 ± 0.18 40K 2333 11.92 ± 0.05 11.365 ± 0.033 110 3.49 ± 0.18 40Ca 3905 19.32 ± 0.14 18.4 ± 0.1 184 3.53 ± 0.32 background in AGATA. The TOF between HELENA and AGATA was used to determine whether a neutron or a γ ray was detected in AGATA. The data from this experiment is still under analysis [205].

70 6. Neutron detector NEDA

6.1 SPIRAL2 One of the new RIB facilities that will be constructed in Europe, as dis- cussed in chapter 1.3, is SPIRAL2 at GANIL. The SPIRAL2 facility will be an ISOL facility based on a high power superconducting driver linear accelerator (LINAC) that will deliver a 40 MeV deuteron beam with a beam current of 5 mA and 14.5 MeV per nucleon heavy-ion beams with a beam current of up to 1 mA. The deuteron beam will be bombarding a UCx target that produces the isotopes for the secondary RIB. The intense stable beams can either be used directly in experiments or for creation of proton-rich RIBs via fusion-evaporation reactions. Two of the experiments that will be located before the uranium target is the Super Separator Spectrometer (S3) and the Neutrons for Science (NFS) project. The S3 is a magnetic spectrometer that will use the high intensity sta- ble ion beams to study, for example, super-heavy nuclei and nuclei beyond the driplines. The NFS facility will be a compliment to other high intensity neu- tron sources, like at Institut Laue-Langevin (ILL) and the European Spallation Source (ESS), to be used for both fundamental and applied neutron research. It will use the protons and deuterons from SPIRAL2 to generate the neutrons. These neutrons will then be used at different experimental setups, for exam- ple CARMEN [206] or the MEDLEY setup previously located in Uppsala [207–209]. After the UCx target and the CIME post-accelerator cyclotron a number of experimental setups will be built for nuclear physics studies using the RIB. Among the planned setups are an experimental area called DESIR, to study exotic nuclei through laser spectroscopy, decay spectroscopy and mass spec- trometry. Furthermore, ACTAR, an active-target detection system, FAZIA, a 4π detector array for isospin studies, GASPARD, an array for reaction studies, PARIS, an array to study giant resonances, shape changes and hyperdeforma- tion, and HELIOS a superconducting solenoidal spectrometer are projected. Finally, the existing HPGe array at GANIL, EXOGAM [150], will be up- graded to EXOGAM2. To further increase the detection efficiency it will be possible to run EXOGAM2 together with the HPGe detector array AGATA, described in chapter 5. A new neutron detector array, NEDA [210], is also projected to replace the existing Neutron Wall [211].

71 6.2 The Neutron Wall The Neutron Wall is the current neutron detector array at GANIL for use in nuclear structure experiments [211]. The Neutron Wall was originally de- signed for experiments together with EUROBALL [133] at LNL and IReS Strasbourg. Since 2005 it is located at GANIL where it is used together with EXOGAM [150], where it in recent experiments [26] has been used together with the charged particle detector array DIAMANT [212, 213]. It consists of 15 hexagonal detectors of two different shapes and one pentagonal detector. The detectors are assembled into a closely packed array covering about 1π of the solid angle. They are filled with the liquid scintillator BC-501A to a total volume of 150 litre. The 16 detectors are in turn divided into 50 segments in total. The hexagonal detectors are subdivided into three individual segments. Each of the segments contain 3.23 litre of scintillation liquid and is read out by a 130 mm Philips XP4512PA photomultiplier tube (PMT). The pentagonal de- tector is subdivided into five individual segments of 1.07 litre each and is read out by a 75 mm Philips XP4312B PMT. The total neutron efficiency of the Neutron Wall is about 25% in symmetrical fusion-evaporation reactions. The pulse-shape discrimination (PSD) in the Neutron Wall is done by NIM elec- tronic units of the type NDE202 [214] based on the zero cross-over (ZCO) discrimination technique.

6.3 The neutron detector array NEDA As mentioned in chapter 6.1, one of the SPIRAL2 instruments being devel- oped is NEDA, that will replace the Neutron Wall. NEDA will be used for nuclear structure studies both on the neutron-rich side and proton-rich side of the line of β stability. In a typical experiment on proton-rich nuclei using a fusion-evaporation reaction, the reaction channel of interest is when two or three neutrons are evaporated. These channels are often very weak compared to the one neutron evaporation channel. This means that high detection effi- ciency is required to separate the reaction channels with two or more neutrons evaporated from one neutron reaction channels. This requires a good way to distinguish multiple-neutron events from one-neutron events that have been misidentified as multiple-neutron events due to scattering between detectors, or neutron cross-talk. Furthermore, an excellent discrimination of neutrons and γ rays is required, especially when using a RIB. It has been shown that even a small amount of γ rays misinterpreted as neutrons dramatically reduce the quality of the cross-talk rejection [215, 216]. The suggested specifications of NEDA, compared to the Neutron Wall, is listed in table. 6.1.

72 Table 6.1: Proposed specifications of NEDA compared to the Neutron Wall. Efficien- cies are estimated for symmetric fusion-evaporation reactions. Parameter NEDA Neutron Wall Type of detector Liquid scintillator Liquid scintillator Type of liquid BC501A or BC537 BC501A Number detectors 150–350 50 Solid angle coverage ∼ 2π 1π Target-detector distance ∼100 cm 50 cm Detector thickness 20 cm 15 cm Scintillation light detector PM, SiPM, APD 5" PM Electronics Fast sampling ADC Analogue NIM units PSA algorithm Digital Analogue 1n efficiency 30–50 % 20–25 % 2n efficiency 3–15 % 1–3 %

6.3.1 The BC-501A and BC-537 liquid scintillators As mentioned in chapter 6.2 and table 6.1, the Neutron Wall uses a liquid scintillator to detect neutrons. The basic processes of scintillation in organic materials are thoroughly described in refs. [217, 218]. A very popular scintil- lator for neutron detection is BC-501A1, based on xylene or dimethylbenzene, C6H4(CH3)2, which is the liquid that is currently used in the Neutron Wall. In DESCANT [219, 220], a neutron detector array project at ISAC similar to NEDA, it is proposed to use a deuterated liquid, BC-537, instead. The liquid BC-501A has a light output that is about 78% of anthracene, a maximum emission wavelength of 425 nm and a hydrogen to carbon ratio of 1.287. It has three decay components with 3.16 ns, 32.3 ns and 270 ns decay times according to reference [221]. An experiment to verify these decay times has been carried out [222] but is still under analysis. Since the relative amount of the slower components compared to the fast component are different for different particle species, see figure 6.1, BC-501A has very good PSD prop- erties. However, practical problems with xylene, like that it is flammable with a flash point (the temperature where it can form an ignitable mixture in air) of 24◦C and can cause neurological damage at high exposures, makes searches for an alternative detection material interesting for future arrays. The liquid BC-537 is made of purified deuterated benzene, C6H6, and has a light output that is about 61% of anthracene, a maximum emission wavelength of 425 nm, a deuterium to carbon ratio of 0.99 and a deuterium to hydrogen

1In older detector arrays a similar liquid called BC-501 was used. These are manufactured by Saint-Gobain Ceramics & Plastics. There is also an equivalent liquid from Nuclear Enterprise known as NE-213

73 1 -ray

10-1 neutron

-2 Amplitude [a.u.] 10

10-3

0 50 100 150 200 250 300 350 400 450 Time [ns]

Figure 6.1: Pulse shapes from a BC501 liquid scintillator from a γ-ray and a neutron interaction. The decay times are 3.16 ns, 32.3 ns and 270 ns. Reprinted from [223, IV] with permission from Elsevier. ratio of 114. Its flash point is −11◦C. BC-537 also have PSD properties and it may give some additional energy resolution and cross-talk rejection prop- erties, which could make it an option to use BC-537 instead of BC-501A in NEDA, despite the lower light output.

6.3.2 Geometry It is very important to carefully study different geometries both to maximize efficiency and to minimize cross talk. The cross talk is due to the effect that neutrons deposit energy mainly by elastic scattering with the protons in the liquid. The energy of the recoil protons can have values from zero up to the incoming neutron energy, depending on the scattering angle. Because of this there exists a probability that the neutron will scatter into a neighbouring de- tector and interact again, causing severe errors in the counting of the num- ber detected neutrons. Several methods attempting to correct for this exist [215, 216]. For example a method based on the TOF difference between the different segments has shown to give good results [216] when the segments are sufficiently far away while neighbouring segments still are problematic. This is important to take into account when designing the geometry of a new array. A suggested geometry is shown in figure 6.2.

6.3.3 Detection of scintillation light One way to improve the efficiency of the neutron detector array is to improve the efficiency of the readout of the scintillation light. The standard way to read out a liquid scintillator is to couple the liquid to a PMT. The PMT typically

74 Figure 6.2: Possible geometry of the NEDA detector array as seen at an angle from the front (left) and from the back (right). consist of a photocathode of a bialkali metal alloy, like Sb-Rb-Cs or Sb-K- Cs [224], a series of dynodes to multiply the photoelectrons and an anode to read out the signal. The bialkali photocathode has a quantum efficiency of maximum ∼ 25% and sensitivity well matched to the most common scintil- lator materials. Another very promising technology is the ultra-pure bialkali photocathode PMTs that have been made available quite recently by Hama- matsu. By using a fine tuned deposition process one could achieve ultra-pure photocathode materials and reach a quantum efficiency of up to 43% [225]. One alternative to a PMT for readout is to use either a regular photodiode or an avalanche photodiode (APD). Today regular photodiodes can be manu- factured up to sizes of about 20 × 20 mm2 while APDs are limited to about 10×10 mm2. The quantum efficiency of the photodiodes can be very high, up to 85% at the peak of maximum sensitivity, but the spectral response of this kind of diodes usually shows a very sharp drop at lower wavelengths. There are, however, also some examples of large-area short-wavelength APDs, like the Hamamatsu S8664 which is planned to be used for the readout for the PANDA¯ electromagnetic calorimeter [226]. Silicon PMTs are another kind of position sensitive readout that has gained popularity in some fields lately [227]. These consist of an array of around 1000 independent APDs per mm2. The quantum efficiency and gain of this kind of readout is quite similar to regular PMTs. The main advantages are good time resolution, no dependency on external magnetic fields and an extremely compact design.

6.3.4 Electronics With the fast development of digital electronics there is an opportunity to use much more sophisticated PSA algorithms than with analogue electron- ics, see chapter 6.4. The term digital electronics means, in this context, that the detector signal is digitized with a fast sampling ADC and then processed using a programmable device like a digital signal processor (DSP), field pro-

75 grammable gate array (FPGA) or even a personal computer (PC). However, digital PSA also has limitations regarding, for example, computing time and signal reconstruction. The influence of the bit resolution and sampling fre- quency of the ADC on the PSD has been investigated in refs. [218, 223].

6.4 Digital pulse shape analysis In both analogue and digital PSA the difference in pulse shape between an in- teracting γ ray and an interacting neutron, see figure 6.1, is used to distinguish between these types of interacting particles. Several sophisticated methods for digital PSD have been developed by var- ious research groups lately. For example, using variable gates in the charge comparison method has been investigated in reference [228]. Another of these methods uses a previously measured standard pulse shape from the detector. By defining a correlation function of a sample pulse shape and the standard pulse shape one can discriminate between neutrons and γ rays [229]. Another method that uses standard pulse shapes has also been developed and is being implemented in a FPGA [230, 231]. In this method the measured pulse shape is fitted with “true” neutron and γ-ray pulse-shapes and the χ2 values of these fits are compared. It has been suggested that one can use fuzzy logic to obtain the true pulse shapes used in these methods [232]. A fourth method that has been developed for digital electronics is the pulse gradient method [233, 234]. In this method two sampling points from the tail of the pulse are selected and the slope between these two points is calculated. All these methods have yielded good results regarding the discrimination of neutrons and γ rays. In reference [223, IV] two methods have been developed to perform digital PSD and to study the effects of the ADC bit resolution and sampling fre- quency on the PSD quality. These methods were developed to be numerically simple, such that the limitations from computing time should be not too large. They were also selected due to their similarity to well studied analogue meth- ods. The two methods were also compared to a standard Neutron Wall NIM electronic unit of the type NDE202 [214] based on the ZCO discrimination technique.

6.4.1 Charge comparison and zero cross-over In the charge comparison method two integration gates are set on the fast and slow decay components of the pulse. By comparing these integrals with each other one will get a separation between neutrons and γ rays. Using digital electronics this method can be generalized to concern evaluating the integral T S = p(t)w(t)dt, (6.1) 0

76 1

10-1 Amplitude [A.U.]

10-2

0 50 100 150 200 250 300 350 400 450 Time [ns]

Figure 6.3: Weighting function w(t) for digital (solid) and analogue (dashed) charge comparison PSD shown together with an average neutron pulse (dotted). Reprinted from [223, IV] with permission from Elsevier.

where T is the time to evaluate the pulse p(t), w(t) is a weighting function and S is a quantity that differs between neutrons and γ rays. To enhance the PSD maximally, the best choice of w(t) has been shown [235] to be n¯(t) − γ¯(t) w(t)= , (6.2) n¯(t)+γ¯(t) wheren ¯(t) and γ¯(t) are the average neutron and γ-ray pulse shapes, respec- tively. See figure 6.3 for an example of how w(t) looks like for the experiment in reference [223, IV]. The other analogue method that has been adapted digitally is the ZCO method. The ZCO method is described in refs. [236, 237]. Integrating the pulse and taking the rise time of the integrated pulse has been shown to be equivalent to shaping and taking the zero-crossing time [238]. In figure 6.4 the principle of the integrated rise-time method is shown. It was found that for the setup in reference [223, IV] the best result was obtained by using the 10–72% rise time. To quantify the results, two different quantities were constructed. The first is the standard FOM (see reference [239]), |Xγ − X | FOM = n , (6.3) Wγ +Wn

77 8

6

4 Integral (a.u.) 2

00 50 100 150 200 Time (ns)

Figure 6.4: Difference between the integrated rise time of a γ-ray (dotted) and a neu- tron (solid) pulse. The points at 10 % and 72 % of the pulse height are indicated by dashed lines. Reprinted from [223, IV] with permission from Elsevier.

where Xγ (Xn) is the centre and Wγ (Wn) is the width of the S distribution for γ rays (neutrons). To complement the FOM a parameter, R, was defined as N R = b , (6.4) Nn − Nb based on the estimated number of γ-ray background counts, Nb, relative to the number of neutron counts, Nn, in the neutron peak. See reference [223, IV] for details on how to calculate R and refs. [218, 223] for a discussion of the advantages and drawbacks of the two quantities. The results from the digital PSD are shown in figure 6.5. As seen, the digital PSD gives at least as good separation as the analogue PSD in the en- tire energy range. The ZCO based PSD method is shown to work better than the charge comparison based. The FOM saturates around 9 bits for the charge comparison based method and at about 10 bits for the ZCO based method2. It should be noted that these values are for the dynamic range of this exper- iment with γ-ray energies between Ee = 15–700 keV and recoil proton ener- gies between Ep = 250–2700 keV. Increasing the bit resolution by one unit would double the dynamic range which implies that a bit resolution of 12 bits would be adequate for most experiments since this allows for PSD up to re- coil proton energies of Ep = 12 MeV. For the low energy pulses the FOM shows no strong dependence of the sampling frequency above 100 megasam-

2However, it is important to remember that the effective number of bits an ADC can use is somewhat smaller than the number of bits in the full range of the ADC.

78 a) b)

1.4 1.2 1

0.8 1 FOM 0.6 R (%) 0.4 0.2 0 10-1 20 30 102 2 102 20 30 102 2 102 E (keV) E (keV)

c) d)

1.4 1.2 1

0.8 1 FOM 0.6 R (%) 0.4 0.2

-1 0 6 8 10 12 14 10 6 8 10 12 14 bit bit

e) f)

1.4 1.2 1

0.8 1 FOM 0.6 R (%) 0.4 0.2

-1 0 100 200 300 10 100 200 300 MS/s MS/s

Figure 6.5: FOM (a, c, e) and R (b, d, f) for the ZCO (circles) and charge compari- son (squares) based methods as a function of energy (a, b), bit resolution (c, d) and sampling frequency (e, f). The solid line (a, b) is from analogue reference data using NDE202 electronics. Filled and empty symbols (c, d, e, f) correspond to an electron (proton) energy gate of Ee = 500–700 keV (Ep = 2200–2700 keV) and Ee = 50– 57 keV (Ep = 500–540 keV) respectively. Reprinted from [223, IV] with permission from Elsevier.

79 ples per second (MS/s). For high energy pulses the FOM increases slowly above 100 MS/s. The R values saturate already around 75 MS/s. The appar- ently odd frequency behaviour for low-energy pulses is due to asymmetries in the distributions of the PSD parameters.

6.4.2 Artificial neural networks To make full use of the information from the digitized pulse shape one can apply a method based on an artificial neural network (ANN) [240], as used in reference [241, V]. An ANN is a computational simulation of the biological neural network that our brains are made of [242–244]. The ANN consist of a number of neurons arranged in layers. The first layer is the input layer, then there are a number of hidden layers and finally an output layer. Each neuron in a layer has its output connected to the input of the neurons in the next layer with a certain weight. By adjusting these weights the network can be trained to generate a desired output pattern for a certain input pattern. Furthermore, each neuron has an internal transfer function that can be used to tune the network for the desired type of application. The most common transfer functions are linear (no modification), a threshold function or a logistic sigmoid function, 1 P(t)= . (6.5) 1 + e−t

The data sets from reference [223, IV] has been analysed using an ANN in reference [241, V] where the simplest type of configuration, the feed forward configuration, was used together with a logistic sigmoid function as transfer function for the neurons. This gave a significant increase in separation quality, especially in the region of small deposited energy, as shown in figure 6.6, which typically contains the majority of the events where the parameter P is defined as = ε2 + ε2, P n γ (6.6)

ε2 ε2 γ where n and γ are the fractions of misidentified neutrons and rays, respec- tively.

6.4.3 Time resolution In a fully digital system the TOF measurement should also be determined by the digitized pulse in the neutron detector relative to a time reference. In ref- erence [223, IV] a test of the influence of the finite sampling frequency on the achievable time resolution was made. Two digitizer channels, each recorded with a sampling frequency of 100 MS/s, were compared and a timing parame- ter Δt21 was defined as the difference between the extracted leading edge times of each of the two channels. The distribution of Δt21 was used as an estimate

80 Figure 6.6: Fraction of incorrectly identified γ-ray and neutron events as a function of the deposited energy for the charge comparison method (open circles), zero-cross over based method (filled circles) and the artificial neural network (crosses). Reprinted from [241, V] with permission from Elsevier.

of the time resolution due to the finite sampling frequency. A FWHM of 1.7 ns was extracted and by comparing this to the achievable intrinsic time reso- lution of a liquid scintillator detector plus PMT, typically FWHM = 1.5 ns or larger, it was concluded that the contribution of the finite sampling frequency to the total FWHM of the time resolution should be almost negligible already at 200 MS/s. To verify this conclusion one can construct an analytical expression for the measured time distribution due to the finite sampling frequency; see figure 6.7 for a definition of the parameters. Using linear interpolation between the sam- pled points for the timing measurements, the time distribution can be shown [218] to be

f (T1) − p0 T = T1 − ΔT , with T0 < T1 < T0 + ΔT, (6.7) f (T1) − f (T1 − ΔT) where f (t) is the pulse shape from the detector. In figure 6.8 two examples of time distributions, using a Gaussian pulse 2 T1 f (T1)=exp − , (6.8) 2σ 2 T1 with p0 = 0.05 and p0 = 0.5 for 100 MS/s, are shown. Assuming that the time between the sampling points and when the pulse passes the threshold is random and uniform one can use equation (6.7) to generate the time response due to the finite sampling frequency. As seen in figure 6.8, the finite sam-

81 1 0.9 0.8 0.7 0.6 0.5 0.4 Amplitude 0.3

0.2 T1 T T0 p 0.1 T1- T 0 0 -2 -1 0 1 2 Time (a.u.) Figure 6.7: Sampling (circles) of a Gaussian function (dashed line) with a time be- tween sampling points, ΔT, equal to the σ of the Gaussian function. The threshold, p0, is crossed at a time T0. The first sampling point above the threshold occur at time T1 and the measured time after sampling is T. Reprinted from reference [218]. pling frequency will result in a non Gaussian time distribution. Folding these time response distributions with a typical intrinsic time resolution of a liq- uid scintillator detector plus PMT of FWHM=1.6 ns, gives the distributions in figure 6.9 for the different sampling frequencies used in reference [223, IV]. As can be seen in the figure, the conclusion in reference [223, IV], that 200 MS/s sampling frequency is enough for a negligible contribution to the time resolution, is verified for a threshold of p0 = 0.5.

82 100 MS/s p =0.05 0 103 0 100

-0.2 1 T 50 T/ Counts

-0.4

0 0 0.5T / 1 0123 1 T1 Time (ns)

100 MS/s p =0.5 0 103 100

0 1 T

T/ 50 Counts

-0.1

0 0 0.5T / 1 0123 1 T1 Time (ns)

Figure 6.8: In the left panels the measured times, T, as a function of T1 are shown for 100 MS/s and thresholds p0 = 0.05 (upper panel) and p0 = 0.5 (lower panel). The times are normalized to σ of the Gaussian pulse. In the right panels the time distributions due to the finite sampling frequency are shown for the parameters used in the corresponding left panels. Reprinted from reference [218].

83 3 p =0.05 10 0 1000

800

600

Counts 400

200

0 -4 -2 0 2 4 6 8 10 12 14 Time (ns)

3 p =0.5 10 0 1000

800

600

Counts 400

200

0 -4 -2 0 2 4 6 8 10 12 14 Time (ns)

Figure 6.9: Time distributions for p0 = 0.05 and p0 = 0.5 folded with a typical Gaus- sian time resolution of a liquid scintillator detector plus PMT with a time resolu- tion of FWHM=1.6 ns. The widths of the distributions are decreasing with increasing sampling frequency. The distributions are for the frequencies 300 MS/s, 200 MS/s, 150 MS/s, 100 MS/s, 75 MS/s, 60 MS/s and 50 MS/s. The widest distributions corre- spond to a sampling frequency of 50 MS/s and the narrowest distributions to a sam- pling frequency of 300 MS/s. Reprinted from reference [218].

84 Part III: Discussion

7. Outlook

“ In the eyes of those who anxiously seek per- fection, a work is never truly completed – a word that for them has no sense – but aban- doned; And this abandonment, of the book to the fire or the public, whether due to weariness or to a need to deliver it for publication is sort of accident,” – Paul Valéry, Au Sujet du Cimetiere Marin

7.1 AGATA at LNL The AGATA Demonstrator, described in chapter 5, is at the moment of writing running at LNL. This is a good opportunity to study the neutron-rich rare-earth region furhter. According to the current time schedule this campaign will con- tinue until the end of 2011, with the AGATA Demonstrator then consisting of 5 ATC detectors. Taking advantage of this new detector technology at LNL and the possibility to use a heavier beam, like 136Xe, both the detection power and production cross-section of the experiment described in chapter 3 could be improved considerably. Thus, it would be possible to extend the systematic studies of collectivity further into the neutron-rich region. Simulations show that at γ-ray energies above a few 100 keV both the Doppler correction capa- bility and photo-peak efficiency of AGATA is much better than of CLARA. At a γ-ray energy of 800 keV GEANT4 simulations give a FWHM of 2.7 keV of the full energy γ-ray peak and a tracked peak efficiency of 7.3% for AGATA at 15 cm, to be compared to 5.2 keV and 4.0%, respectively, for CLARA. The production cross-section of dysprosium isotopes for three different types of ion beams calculated using the grazing code [101, 102] are shown in figure 7.1. Besides the higher production cross-section, the advantage of using a 136Xe beam is the existence of isomers in the binary partners of 168Dy (134Ba) and 170Dy (136Ba) with half-lives of 2.63 μs [245] and 91 ns [246], respectively. By gating on the strongly populated delayed γ rays below the isomers it is possible to identify decays in the binary partners. Using the DANTE [247, 248] detector array and detection of known delayed γ rays in AGATA (isomer tagging) the target-like fragments can be Doppler corrected using their average velocity and by their angle of emission. Since AGATA has no collimators the efficiency to detect delayed γ rays emitted by fragments

87 4

3.5

3 Cross section (mb) 2.5

2

1.5

1

0.5

0 155 160 165 170 175 180 185 A Figure 7.1: Grazing calculations of production cross-sections for dysprosium isotopes using an 170Er target and a 48Ca beam with an energy of 230 MeV (dotted), a 82Se beam with an energy of 460 MeV (dashed) and a 136Xe beam with an energy of 1000 MeV (solid). not located at the target position but at various positions in the target chamber, whose radius is about 10 cm, will be larger than with BGO shielded HPGe arrays. Based on the tentative identification of 170Dy in reference [112, I], the esti- mated number of counts in the 4+ → 2+ and 10+ → 8+ peaks in 170Dy, gated by various conditions, are shown in table 7.1. Efficiencies of 3% for detection of the projectile-like fragments in PRISMA and 30% for detection of target- like fragments in DANTE are assumed. The double and triple coincidence ef- ficiencies used for the estimates in table 7.1, were obtained as the single γ-ray efficiency squared and to the third power, respectively. The relative intensities of the 10+ → 8+ and 4+ → 2+ transitions in 170Dy are assumed to be 0.25, which is the same value as obtained for 168Dy in [112, I]. In the calculations of the number of counts shown in table 7.1 six effective days of beam time and a target thicknes of 0.5 mg/cm2. As seen, the statistics for 170Dy would be increased significantly, and it will also be possible to study nuclei further out in the neutron-rich rare-earth region. Cross sections relative to 170Dy calcu- lated using grazing are: 1/4 for 172Dy, 1/20 for 174Dy, 1/20 for 166Gd and 1/40 for 168Gd.

88 Table 7.1: Number of counts in the γ ray #1 peak for different conditions on the γ-ray and ancillary detectors. The 170Dy 4+ → 2+ transition has been estimated to + + have Eγ ≈ 160 keV. The 170Dy 10 → 8 transition has been estimated to have Eγ ≈ 450 keV. The 136Ba condition correspond to a sum of five gates below the 10+ isomer using isomer tagging. See text for details. Condition γ ray #1 γ ray #2 γ ray #3 Counts γ-PRISMA-TOF 170Dy 4+ → 2+ - - 8300 γγ-PRISMA 170Dy 4+ → 2+ 170Dy 10+ → 8+ - 400 γγγ-DANTE 170Dy 4+ → 2+ 136Ba 136Ba 4100 γγγ-DANTE 170Dy 4+ → 2+ 170Dy 10+ → 8+ 136Ba 500

It is also of interest to study the collective structure and the evolution of nu- clear deformations for nuclei above the Z = 82 shell closure. In particular, the possibility that many superheavy nuclei may have ground state deformations of 0.50 < β2 < 0.60, which is in the superdeformed regime, has been debated in Refs. [249–251]. Even if high-spin spectroscopy of superheavy elements is currently out of experimental reach, an important step toward the understand- ing of these nuclei is the experimental investigations of heavy actinides. The data in this region is very sparse but also very important if one wants to do extrapolations into the superheavy element region. Furthermore, the actinide region is also very interesting in itself as many theoretical predictions have been made [252] but not studied experimentally. The fission of the heavy el- ements also has an important role in the astrophysical r-process, described in section 1.2.2 and section 2.2. Previous experiments using thick targets [253] shows that it is possible to use multi-nucleon transfer reactions for studies of actinides and references [112, 114] show that it is possible to obtain data on target-like fragments by gating on the beam-like fragments identified in a magnetic spectrometer.

7.2 AGATA at GSI Following the physics campaign at LNL, AGATA will move to GSI to be used with relativistic ion beams in the PRESPEC campaign. This campaign is planned for 2012 and 2013 where AGATA will, at the end of the campaign, consist of up to 12 ATC detectors. This campaign can provide a valuable com- plement to the measurements at LNL by the possibility to establish B(E2) val- ues to determine the electric quadrupole moments and the degree of triaxial deformation, and thus the evolution of quadrupole collectivity, for a range of neutron-rich rare-earth nuclei [254]. By using relativistic Coulomb excitation ( + → + ( + → + it would be possible to determine the B E2:0 21 ), the B E2:21 22 ) ( + → + 164 196 and B E2 : 0 22 ) for even-even nuclei between Dy and Os. In such

89 10 1 10-1 10-2 10-3 10-4 Cross section (mb) 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12 10-13 10-14 -15 10 140 150 160 170 180 190 A Figure 7.2: Calculated production cross-sections of the Dy isotopic chain in the FRS for the primary beams 176Yb (solid), 186W (dashed), 197Au (dotted) and 198Pt (dash- dotted). an experiment the secondary beams from the FRS would impinge on a 197Au target at beam energies of ∼ 100 MeV per nucleon using the technique de- scribed in references [132, 255, 256]. After the target, the nuclei could be tagged using the LYCCA [257, 258] spectrometer. In figure 7.2 the production cross-sections, calculated by the LISE++ code [259, 260], for a couple of primary beams with energies of 800 MeV per nu- cleon and projectile fragmentation on a 4 g/cm2 beryllium target are shown. At a recoil energy of ∼ 100 MeV per nucleon and at forward angles, the γ-ray energy resolution should be about 3% [132]. A problem with this kind of mea- surement, however, is the large background from bremsstrahlung radiation for γ-ray energies Eγ  300 keV, why detailed simulations are required.

7.3 AGATA at SPIRAL2 After the construction of SPIRAL2 is completed, AGATA will be moved to GANIL in 2014 and be used together with EXOGAM and NEDA. In this phase it is anticipated that AGATA will consist of up to 20 ATC detectors. The AGATA, EXOGAM and NEDA set-up will be designed to study, for example,

90 the shell structure of nuclei near the proton drip-line using fusion-evaporation reactions [26] and the halo properties of light neutron-rich nuclei [261]. The main requirements of the NEDA array are described in section 6.3. The current focus in the development of NEDA is to decide on a geometry that gives a high efficiency for the physics goals. The neutron-γ discrimina- tion for digital versions of the standard PSD algorithms are described in ref- erence [223]. However, a detailed comparison of the advanced digital PSD algorithms described in section 6.4 would be of interest. Furthermore, a criti- cal parameter in the design of Neutron Detector Array (NEDA) is the rejection quality for neutron cross-talk. A careful study of different methods for cross- talk rejection, for example by applying an artificial neural network would be very valuable for the design of the digital electronics.

91

8. Concluding remarks

I was once attending a series of lectures on nuclear structure given by profes- sor Rick Casten, while he was visiting the University of Surrey. During one of these lectures he told us that when he wrote the first edition of his famous book [21] the publishing company was delaying the publication, which made him afraid that the field would die out before the book was published. When he wrote the second edition of his book, the publishing company was again delaying the publication. But this time it meant that he would have more time to add everything new that was going on. What had happened between the first and second edition of this book? It was the development radioactive ion beam facilities. In recent years the technical developments of the radioactive ion beam facil- ities means that we will soon have access to radioactive ion beams of high in- tensity. In Europe the planned facilities are: NUSTAR/FAIR in Germany, SPI- RAL2 in France, HIE-ISOLDE in Switzerland and SPES in Italy. Experiments performed at these advanced facilities will require new advanced equipment to study the weak signals of exotic nuclei. Two of these instruments under development in Europe are the high-purity germanium spectrometer AGATA and the neutron detector array NEDA. AGATA is a spectrometer based on an entirely new technology called γ- ray tracking. Instead of, as in previous spectrometers, accepting only the γ rays which deposit all their energy into a crystal and to reject any γ rays scat- tered from the crystal, AGATA will have no anti-Compton shields that reject γ-rays that scatter between crystals. By using digital electronics and pulse- shape analysis the position and energy of each γ-ray interaction will be deter- mined. These positions and energies will allow the tracks of the γ rays to be reconstructed. From these tracks, the energies and angles of the individual γ rays can be disentangled, thus dramatically increasing the energy resolution and efficiency of the spectrometer. For this method to work satisfactorily, one must be able to measure the interaction position of the γ rays with an accuracy of at least five millimetres. One part of this thesis has focused on measuring the interaction position resolution of the array using a new method based on how well the detector can correct for the Doppler shift of the γ rays at different distances between the detector and the source. NEDA is a neutron detector project under SPIRAL2 and will be used to- gether with other detector systems at this facility, for example γ-ray spec- trometers like AGATA and EXOGAM2, which is an upgrade of the existing

93 γ-ray spectrometer at GANIL. One of the physics focuses of this set-up is the proton-rich nuclei around the double magic nucleus 100Sn. These nuclei will be studied using fusion reactions between two nuclei, where the compound nucleus subsequently evaporates a certain number of protons, neutrons and α particles. NEDA will detect the evaporated neutrons. One problem with neu- tron detection is that it is difficult differ between neutrons and γ rays in the de- tector. New methods for discriminating between neutrons and γ rays utilizing digital electronics has been one part of this thesis. By moving from analogue to digital electronics, it is possible to use more advanced and efficient algo- rithms for the analysis of the pulse shape from the detector. Digital versions of the more common analogue methods have in this work yielded as good, or better, results as obtained with analogue electronics. A sophisticated digital method, artificial neural networks, has also been applied to the experimental data. It is shown that the neural network can distinguish between neutrons and γ rays even more efficiently. Furthermore, this thesis deals with the evolution of collective structure of neutron-rich nuclei in the rare-earth metals. These are among the most col- lective nuclei that can be found in nature. In particular, the nucleus 170Dy is expected to be the nucleus where the collective structure is maximized. This has important implications for the astrophysical r-process, since it has been suggested that this maximum plays an important role in the abundances of the rare-earth elements that are created in supernova explosions. By performing an experiment at the laboratory LNL in Italy using the magnetic spectrome- ter PRISMA and the γ-ray spectrometer CLARA we have been able to study the structure of the five nuclei 168,170Dy and 167,168,169Ho. These results have been compared to calculations by the variable moment of inertia model, the cranked shell model and the particle plus triaxial rotor model. Furthermore the possibility to use the new radioactive ion-beam facilities to reach further into the neutron-rich area has been discussed.

94 9. Kollektiv kärnstruktur hos neutron- rika sällsynta jordartsmetaller och nya instrument för gammaspektroskopi

Syftet med grundforskning är att förstå världen, hur den fungerar och varför den fungerar som den gör. Detta gäller oavsett vilket forskningsfält det rör sig om: sociologi, psykologi, biologi, kemi eller fysik. Det som skiljer des- sa olika discipliner åt är vilka frihetsgrader man betraktar och vilka effektiva interaktioner man väljer att arbeta med. En effektiv interaktion är ett utmärkt verktyg för att behandla komplexa problem men som samtidigt döljer den un- derliggande dynamik som finns. En sociolog ser, till exempel, den mänskliga interaktionen som grundläggande utan att ta hänsyn till detaljer i de kemiska processer i hjärnan som styr den mänskliga interaktionen i grunden. Inom fy- siken arbetar vi istället med att förstå några av de mest grundläggande interak- tionerna i universum, väl medvetna om att de aldrig i praktiken kan användas för att beskriva effekterna av ett kraschat förhållande eller anledningen till en revolution i Egypten. Däremot hoppas vi att vi så noga som möjligt kunna beskriva var vi kommer ifrån och hur det kommer sig att universum ser ut som det gör. Och historien har visat oss att denna kunskap ofta omdanar det mänskliga samhället även på makroskopiska nivåer. När universum skapades i Big Bang skapades även de lättaste grundäm- nena, det vill säga väte och helium. Efter ett tag började vätet och heliumet klumpa ihop sig och bilda stjärnor, som fortfarande förbränner dessa ämnen till tyngre grundämnen ända upp till järn (26 protoner och 30 neutroner). När stjärnan sedan dör blåser den ut dessa grundämnen i universum, och det är dessa ämnen som vi ser omkring oss. Men om vi tittar runtomkring oss ser vi ju att det finns många tyngre ämnen än järn: koppar, silver, guld, bly och uran bara för att nämna några. Varifrån kommer då de tunga elementen från järn till uran? Tyngre grundämnen än järn bildas när vissa stjärnor på ett våldsamt sätt slutar sitt liv genom supernovaexplosioner. Supernovaexplosioner inne- bär väldigt extrema miljöer med mycket neutroner som driver kärnfysikaliska processer som bildar de tyngre ämnena. Så, vi består alla av stjärndamm från ett par generationer stjärnor som dött en våldsam död. En av de processer, r- processen, som skapar dessa tunga kärnor går nästan helt genom okända och väldigt neutronrika kärnor, ett område som brukar kallas terra incognita. För att förstå detaljerna i denna process är det viktigt att förstå hur dessa neutron- rika atomkärnors struktur ser ut.

95 Inom kärnfysiken säger man att det finns två olika typer av strukturer hos atomkärnorna, dels partikelstruktur och dels kollektiv struktur. De allra lät- taste grundämnena beskrivs till stor del endast av sin partikelstruktur, men när man studerar tyngre grundämnen kommer både kollektiv struktur och par- tikelstruktur att samverka. Eftersom det är kvantmekanikens lagar som styr atomkärnorna ordnar protoner och neutroner (nukleoner) sig i något som bru- kar kallas en skalstruktur, där de fyllda skalen agerar som ett kollektiv och där enskilda nukleoner har mycket liten inverkan på kärnans struktur. Detta gör att enskilda nukleoner utanför dessa slutna skal blir de som bestämmer atomkär- nans egenskaper. För atomkärnor som ligger långt ifrån dessa slutna skal ser situationen helt annorlunda ut. Där är det de kollektiva frihetsgraderna som till stor del bestämmer atomkärnans struktur medan de enskilda partiklarnas inverkan endast kan ses genom subtila effekter i den i övrigt jämna utveck- ling av kärnstruktur mellan olika isotoper som brukar karaktärisera kollektiva kärnor. Atomkärnan är alltså ett tydligt exempel på ett kvantmekaniskt system där både de kollektiva frihetsgraderna och partikelfrihetsgraderna interagerar och måste tas hänsyn till för full förståelse av kärnmaterien. Den här avhandlingen behandlar strukturen hos atomkärnorna i de sällsynta jordartsmetallerna, vilka är bland de mest kollektiva kärnor som man kan hitta i naturen. I synnerhet atomkärnan 170Dy är en kärna som man kan anta ligger precis på, eller i alla fall ganska nära, den plats där den kollektiva struktu- ren är maximerad, precis i mitten mellan två fyllda protonskal och två fyllda neutronskal. Detta är något som bland annat har betydelse för vår förståel- se av den tidigare nämnda r-processen eftersom det har föreslagits att detta maximum spelar en viktig roll i hur mycket av de olika isotoperna av säll- synta jordartsmetaller som bildas i denna. Genom att utföra experiment vid laboratoriet LNL i Italien med två instrument som heter PRISMA, en mag- netisk spektrometer för tunga joner, och CLARA, en germaniumspektrometer för detektion av gammastrålning, har vi kunnat studera strukturen hos de fem atomkärnorna 168,170Dy och 167,168,169Ho. Problemet inför framtiden är att mer neutronrika kärnor ä så är väldigt svå- ra att komma åt med dagens anläggningar. Det finns olika begränsningar för de kärnreaktioner vi har i vår arsenal för att skapa, och studera, dessa exo- tiska, kortlivade kärnor, något som är fundamentalt för att förstå hur tyngre grundämnen bildats och var vi kommer ifrån. Med dessa reaktioner börjar vi närma oss gränsen för hur neutronrika atomkär vi experimentellt kan nå. även om det finns mycket kvar att upptäcka och finjustera i vår förståelse av även kända områden, är det av stor vikt att nå ut i det okända för att öka vår förståelse av kärnmaterien och hur grundämnena bildats. En av de stora be- gränsningarna är att vi bara har ungefär 250 långlivade kärnor att använda i våra experiment. På senare år har den tekniska utvecklingen gått framåt med hög fart, vilket resulterat i att vi snart kommer att ha tillgång till radioaktiva

96 jonstrålar1 av hög intensitet vid nya experimentanläggningar i Europa: FAIR i Tyskland, SPIRAL2 i Frankrike, HIE-ISOLDE i Schweiz och SPES i Italien. Med andra ord kommer arsenalen på ungefär 250 långlivade kärnor uppgrade- ras till tusentals olika kärnor med en livstid från allt från år ner till bråkdelar av en sekund. Helt plötsligt har vi en unik möjlighet att tränga ut i helt okän- da områden. Dessa nya avancerade anläggningar kräver dock ny avancerad utrustning för att vi ska få ut så mycket som möjligt av dem. Två av de instru- ment som är under utveckling i Europa är germaniumspektrometern AGATA och neutrondetektorn NEDA. AGATA är en spektrometer som baseras på en helt ny teknologi som hand- lar om att spåra gammastrålning. Istället för att, som i tidigare germanium- spektrometrar, mäta den strålning som lämnar all sin energi i en kristall och förkasta all strålning som sprids till närliggande detektorer kommer AGATA att även acceptera den strålning som sprids mellan kristallerna. För att kunna mäta strålningen på ett korrekt sätt använder vi digital elektronik och puls- formsanalys för att, genom tidsstrukturen på spänningspulsen från detektorn, ta reda på exakta positioner för gammainteraktionerna. Genom att veta dessa positioner och vilken energi gammastrålningen deponerat på de olika ställena kan man återskapa spåret, eller vilken väg gammastrålningen spridits i detek- torn. Från dessa spår kan man då sortera ut vilka energier gammastrålningen har haft samt vilken vinkel de skickats ut i och därmed dramatiskt öka spekt- rometerns energiupplösning och effektivitet. För att denna metod ska funge- ra tillfredsställande måste man dock kunna mäta interaktionspositionerna för gammastrålningen med en noggrannhet på minst fem millimeter. En del av den här avhandlingen handlar om att undersöka just hur noggrant vi kan mäta interaktionspositionen, det vill säga vilken positionsupplösning detektorn har, genom att använda en ny metod som grundar sig i hur väl detektorn kan kor- rigera för Dopplereffektens inverkan på gammastrålningen vid olika avstånd mellan detektor och stålkälla. NEDA är ett delprojekt under SPIRAL2 och kommer att användas tillsam- mans med andra detektorsystem vid denna anläggning. I första hand är dessa germaniumspektrometrar AGATA och EXOGAM2, som är en uppgradering av den befintliga germaniumspektrometern på GANIL. Ett av de fysikområ- dena som man kommer att fokusera på vid denna uppställning är protonrika kärnor runt den dubbelmagiska kärnan 100Sn. Detta område kommer att stu- deras med hjälp av fusionsreaktioner mellan två kärnor där den sammansatta kärnan evaporerar ett visst antal protoner, neutroner och alfapartiklar. NEDA kommer här att detektera de evaporerade neutronerna. Ett problem med detta är dock att det är svårt att i detektorn se skillnad på vad som är neutronstrål- ning och vad som är gammastrålning, varför nya metoder för att avgöra detta har varit en del av denna avhandling. Genom att övergå från analog till digital elektronik kan man använda mer avancerade och effektiva algoritmer än tidi-

1Till skillnad från den totalt felaktiga och missvisande termen ”radioaktiv strålning” som media använder för att beskriva joniserande strålning, som i verkligheten inte är det minsta radioaktiv.

97 gare för att analysera spänningspulserna från detektorn. Digitala versioner av de vanligaste analoga metoderna har i detta arbete visat sig ge minst lika bra, eller bättre, resultat som den tillgängliga analoga elektroniken. En sofistikerad digital metod, artificiella neurala nätverk, har också applicerats på testdata och det har visats att denna kommer att göra det möjligt att ännu effektivare skilja på neutroner och gammastrålning i neutrondetektorer av den typ man planerar att använda i NEDA-projektet.

98 10. Acknowledgements

First of all, I would like to thank my supervisors, Johan Nyberg and Ay¸seAtaç. You have managed to both steer me in the right direction when needed and at the same time you have given me a lot of scientific freedom and supported me when I wanted to follow my own path and my own ideas. The third person I would like to thank is professor Paddy Regan, who has been a valuable collaborator in many aspects of this work. I would also like to thank Smålands nation and Anna Maria Lundins fund for financing my trip to and participation in the 180Yb experiment at iThemba LABS, Cape Town. For parts of this thesis I have also benefited by the hard work of the un- dergraduate students that have been working in our group. Big thanks to both Ali Al-Adili and Paula Salvador Castiñeira. I would also like to thank all the other collaborators I have worked with to obtain the results presented in this thesis. This, of course, includes everyone in the 170Dy, AGATA and NEDA collaborations but I would like to especially mention the following people: Gry Tveten, a very valuable colleague for the data analysis; Jose Javier Va- liente Dobòn for valuable support in all parts of this thesis and the coordina- tor for the NEDA project; Ryan Kempley for discussions about AGATA data and the movie night at LNL; Grzes´ Jaworski for a good time at many differ- ent places in Europe and James Ollier for all discussions about rigid nuclear structure and sharing the apartment at iThemba LABS. In order for the thesis to be as well written as possible I have also had help from the proofreaders of my manuscript. These people are Henrik Jäderström, Kristofer Jakobsson and Mikael Höök. Great comments from all of you! Furthermore, that I even got started in the field of experimental nuclear physics is much thanks to the MEDLEY crew: Chai Udomrat, Riccardo Bevilacqua, Vasily Simutkin, Stephan Pomp, Masateru Hayashi, Jan “Bumpen” Blomgren, Alexander Prokofiev and Yukinobu Watanabe. I would also like to thank all former and present doctoral candidates, master students, project workers and senior physicists that have worked this depart- ment. I will not mention you all by name, in case I forget someone, but you are all included. A few colleagues have been extra close to me, however, and these I would like to mention: Elias Coniavitis, Oscar Stål, Martin Flechl, So- phie Grape, Erik Thome, Olle Engdegård, Magnus Johnson, Peder Eliasson, Arnaud Ferrari, Camille Bélanger-Champagne, Claus Buszello, Henrik Jäder-

99 ström, Henrik Petrén, Karin Schönning, Mattias Lantz, Bengt Söderbergh and Kristofer Jakobsson. There are also a couple of people who have been a very valuable resource in keeping track of both the univerisy administrative procedures and computer issues, these are Inger Ericsson, Annica Elm, Ib Kôersner and Teresa Kupsc. My time as a doctoral candidate has not, however, only been about research. I have also been lucky enough to have the opportunity to work together with many other people on issues regarding doctoral candidates in every level from the faculty to the European Union. I have had the great opportunity to work together with the following great people in the UUS party: Caroline Erland- son, Johan Gärdebo, Jonas Boström, Klas-Herman Lundgren, Karin Nord- lund, Michel Rowinski, Michael Jonsson, Mathias Johansson, Niclas Karls- son, Kristina Ekholm and many more that I have probably forgot to mention. The PhD Students’ Council of the Faculty of Science and Technology has also done a great job for our local doctoral candidates, especially Marta Kisiel, Adrian Bahne, Kristofer Jakobsson, Riccardo Bevilacqua and Seidon Alsaody. During the year I spent in the doctoral council at the Uppsala Student Union I have also very happy to have gotten to know Marta Axner, Carl Nettelblad and Per Löwdin. Through the Swedish National Union of Students I am also happy to have had the opportunity to collaborate with Odd Runevall, Moa Ekbom, Martin Dackling, Kristina Danilov, Melissa Norström and Lars Abrahamsson. And also the collaboration with the undergraduate representatives Klas-Herman Lundgren, Robin Moberg, Thomas Larsson, Beatrice Högå and Elisabeth Gehrke. Finally I would like to acknowledge the wonderful work done by the people in the European Council of Doctoral Candidates and Junior Researchers, then especially the work by Izabela Stanisławiszyn, Ing-Marie Ahl, Marisa Alonso Núñez and Sverre Lundemo. To Klas-Herman Lundgren and Hanna Victoria Mörck. Your friendship dur- ing this time of trial has been valuable beyond words. Thank you for feeding me at late nights, playing video games with me and putting up with my some- times edgy and emotionally instable state of mind during the period of my thesis writing. There is also other friends that have been very valuable to me. Karin Neil Persson, Jenny Arnberg and Henrik Jäderström have been a great support. Carl Lowisin, Mikael Höök and Caroline Marjoniemi have also been very good friends, both in China and in Sweden. Fredrik Gunnarson and his never-ending enthusiasm for computerized sound. And my great dance teacher Emma Rå- dahl. I would also like to thank my flatmates Tova Dahné and Naomi Reniutz Ursoiu. During these years, I have also had the opportunity to travel the world and meet many people that have influenced my life and inspired me. Unfortu- nately, listing every one of you would just end up as an exercise in futility. But I will go for it anyway: Yao Hailin for showing me the beauty of China;

100 Alma Joensen for introducing me to Faroese-Danish-Icelandic cuisine; Car- mens Dobocan for the dinner and the broccoli at the old castle in Krakow; Diana Zubko for exploring the Institut Français with me; Liliya Ivanova for just being a nice person; Elif Ince for the wonderful boat ride through Istanbul; Madeleine Laurencin for dancing waltz with me in Vienna while the demon- strations were raging outside; Khotso Mokoenya for keeping me company when driving through Lesotho; Amineh Kakabaveh, my favourite mountain partisan and MP and Noriaki Oba for the Japanese-Swedish food crossover experiments involving surströmming and natto¯ fermented soy beans. Sist men inte minst vill jag också tacka Leena Söderström-Blom och Tage Blom.

101

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120 Contribution to the papers

Paper I This paper concerns the identification of the yrast band of 168Dy up to spin 10+ and the tentative identification of the 4+ → 2+ transition in 170Dy. The experiment was carried out with the PRISMA and CLARA set-up at LNL where I participated in the data taking. For this paper I was responsible for the analysis of the experimental data and, together with F. R. Xu and J. Y. Zhu, the interpretation of the data in terms of TRS calculations. I was also responsible for writing the paper.

Paper II The second paper is from the same PRISMA and CLARA experiment as Pa- per I. For this paper, both G. M. Tveten and I were responsible for the data analysis, carried out in parallel to the data analysis in Paper I in order to cross- check the results. The paper concerns the identification of the yrast bands of 167Ho and 169Ho, as well as excited states in 168Ho. The interpretations of the results was made in collaboration between G. M. Tveten and myself, where my main responsibility was the TRS calculations and for writing parts of the paper.

Paper III This paper presents simulations of, and results from, the first commissioning experiment of the AGATA detector array in LNL. The experimental set-up and data taking was carried out by many people from the AGATA collabora- tion. I have been responsible for the simulations of the experiment, together with A. Al-Adili that was a masters student in our group at the time, the data analysis, the interpretation of the results and for writing the paper.

121 Paper IV The fourth paper is about discrimination between neutrons and γ rays in liquid scintillator detectors. The experiment was prepared by R. Wolters when he was an Erasmus student in our group. I have had the main responsibility for data taking, data analysis and interpretation of the results presented in this paper and writing the paper.

Paper V The final paper is an extension of Paper IV, where the data has been reanalysed by E. Ronchi and myself using an artificial neural network. E. Ronchi was at the time a doctoral candidate in applied nuclear physics working with plasma diagnostics for the nuclear fusion group. The analysis was carried out in a collaboration between E. Ronchi and myself, while E. Ronchi was responsible for the model set-up, the interpretation of the results and the writing of the paper.

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