Isomeric yield ratio measurements with JYFLTRAP

Transcription

1 Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1743 Isomeric yield ratio measurements with JYFLTRAP In quest of the angular momentum of the primary fragments VASILEIOS RAKOPOULOS ACTA UNIVERSITATIS UPSALIENSIS UPPSALA 2018 ISSN ISBN urn:nbn:se:uu:diva

2 Dissertation presented at Uppsala University to be publicly examined in 80127, Ångström, Lägerhyddsvägen 1, Uppsala, Thursday, 13 December 2018 at 09:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor José Benlliure (University of Santiago de Compostela, Spain). Abstract Rakopoulos, V Isomeric yield ratio measurements with JYFLTRAP. In quest of the angular momentum of the primary fragments. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology pp. Uppsala: Acta Universitatis Upsaliensis. ISBN In this thesis, isomeric yield ratios of twenty nuclides produced in the fission of nat U and 232 Th by protons at 25-MeV and nat U by high-energy neutrons were studied. The experiments were performed at the IGISOL-JYFLTRAP facility at the University of Jyväskylä. It is the first time that direct ion counting is used for the determination of the intensities of the states of interest, thus avoiding dependency on knowledge of nuclear decay schemes and properties. This was possible due to the superior resolution of a Penning trap which was utilized for this work. Two different techniques were employed, namely the sideband cooling technique and the phaseimaging ion-cyclotron-resonance technique. With the former, a mass resolving power of m/δm = 10 5 can be routinely achieved, while the latter, which was recently implemented at JYFLTRAP, offers an increase in the mass resolving power by a factor of ten. In addition, isomeric yield ratios were also determined by means of γ-ray spectroscopy. From a comparison of the same isomeric pair from two different reactions, a dependency on the fissioning system can be observed. This indicates an effect of the fission mode to the yield ratio. Moreover, the evolution of the odd-a isotopes of Cd and In in the mass range A = exhibit two distinguishably different trends. The ratios for the isotopes of In decrease with increasing mass, while the ratios for the isotopes of Cd are almost constant until mass number A = 125, where an increase can be noticed. The origins of the angular momentum in the fission fragments is one of the long-standing questions regarding the fission process. Surprisingly, fission fragments have been observed to carry a considerable amount of angular momentum, even from fissioning systems with very low (or even zero) angular momentum. So far, the angular momentum can only be inferred from other fission observables, such as the isomeric yield ratios. In this work, a methodology was developed in order to deduce the root-mean-square angular momentum (J rms ) of the primary fragments by employing the nuclear reaction code TALYS. Lower values of J rms for the more spherical nuclei, near the closed-shell neutron configuration at N = 82, and higher ones for fragments with odd proton number have been deduced, in agreement with other studies. Moreover, a correlation between the angular momentum of the primary fragments with the electric quadrupole moments of the products was observed for the isotopes of In. The data can be used to gain insight into scission configuration and as guide for models that propose mechanisms for the generation of the angular momentum. Furthermore, the observed correlation is an indication of the role that the repulsive Coulomb force, together with the shape of the nascent fragment, play in the generation of the fragments angular momentum. Keywords: Nuclear physics, nuclear fission, angular momentum, fission fragments, isomeric yield ratios, fission products, scission, Penning trap. Vasileios Rakopoulos, Department of Physics and Astronomy, Applied Nuclear Physics, Box 516, Uppsala University, SE Uppsala, Sweden. Vasileios Rakopoulos 2018 ISSN ISBN urn:nbn:se:uu:diva (

3 To Katerina and Elias-Sebastian iii

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5 List of papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I II III V. Rakopoulos, M. Lantz, A. Solders, A. Al-Adili, A. Mattera, L. Canete, T. Eronen, D. Gorelov, A. Jokinen, A. Kankainen, V. S. Kolhinen, I. D. Moore, D. A. Nesterenko, H. Penttilä, I. Pohjalainen, S. Rinta-Antila, V. Simutkin, M. Vilén, A. Voss, and S. Pomp. First isomeric yield ratio measurements by direct ion counting and implications for the angular momentum of the primary fission fragments. Physical Review C 98, (2018). DOI: /PhysRevC My Contribution: I wrote the paper, participated in some of the experimental campaigns and performed the analysis of the data. I also developed the methodology for the derivation of the angular momentum and performed the calculations in TALYS. V. Rakopoulos, M. Lantz, S. Pomp, A. Solders, A. Al-Adili, L. Canete, T. Eronen, A. Jokinen, A. Kankainen, A. Mattera, I. D. Moore, D. A. Nesterenko, M. Reponen, S. Rinta-Antila, A. de Roubin, M. Vilén, M. Österlund, and H. Penttilä. Isomeric fission yield ratios for odd-mass Cd and In isotopes using the Phase-Imaging Ion-Cyclotron-Resonance technique. Submitted to Physical Review C - Rapid Communication. My Contribution: I wrote the paper, participated in the experimental campaign and performed the analysis of the data. I also performed the calculations in TALYS. V. Rakopoulos, M. Lantz, A. Al-Adili, D. Gorelov, A. Jokinen, V. Kolhinen, A. Mattera, I. D. Moore, H. Penttilä, A. V. Prokofiev, A. Solders, and S. Pomp. Measurements of isomeric yield ratios of fission products from proton-induced fission on nat U and 232 Th via direct ion counting. EPJ Web of Conferences 146, (2017). DOI: /epjconf/ My Contribution: I wrote the paper, participated in some experiments and performed the analysis of the data. I also performed the calculations in TALYS. v

6 IV V A. Mattera, S. Pomp, M. Lantz, V. Rakopoulos, A. Solders, A. Al-Adili, H. Penttilä, I. D. Moore, S. Rinta-Antila, T. Eronen, A. Kankainen, I. Pohjalainen, D. Gorelov, L. Canete, D. Nesterenko, M. Vilén, and J. Äystö. Production of Sn and Sb isotopes in high-energy neutron-induced fission of nat U. The European Physics Journal A (2018) 54: 33. DOI /epja/i My Contribution: I participated in the preparation of the experimental campaign and the data acquisition. A. Al-Adili, V. Rakopoulos, and A. Solders. Extraction of angular momenta from isomeric yield ratios - assessment of TALYS as a fission fragment de-excitation code. In manuscript (2018). My Contribution: I developed the methodology of the calculations in TALYS for the derivation of the angular momentum and participated in the evaluation of the results. Reprints were made with permission from the publishers. vi

7 Papers not included in this thesis List of papers related to this thesis, but not included in the comprehensive summary, Fission yields at JYFL 1. A. Solders, D. Gorelov, A. Jokinen, V.S. Kolhinen, M. Lantz, A. Mattera, H. Penttilä, S. Pomp, V. Rakopoulos, and S. Rinta-Antila. Accurate fission data for nuclear safety. Nuclear Data Sheets 119, (2014) (ND2013) 2. D. Gorelov, J. Hakala, A. Jokinen, V. Kolhinen, J. Koponen, I. Moore, H. Penttilä, I. Pohjalainen, M. Reponen S. Rinta-Antila, V. Sonnenschein, A. Voss, A. Al-Adili, M. Lantz, A. Mattera, S. Pomp, V. Rakopoulos, V. Simutkin, A. Solders. Isomeric yield ratios of fission products measured with the JYFLTRAP. Acta Physica Polonica B 45, 211 (2014) (Mazurian lakes conference) 3. M. Lantz, A. Al-Adili, D. Gorelov, A. Jokinen, V.S. Kolhinen, A. Mattera, I. Moore, H. Penttilä, S. Pomp, A.V. Prokofiev, V. Rakopoulos, S. Rinta-Antila, and V. Simutkin, A. Solders, and the IGISOL group. Fission yield measurements at IGISOL. EPJ Web of Conferences 122, (2016) (CNR*15) 4. S. Pomp, A. Mattera, V. Rakopoulos, A. Al-Adili, M. Lantz, A. Solders, K. Jansson, A. V. Prokofiev, T. Eronen, D. Gorelov, A. Jokinen, A. Kankainen, I. D. Moore, H. Penttilä, and S. Rinta-Antila. Measurement of fission yields and isomeric yield ratios at IGISOL. EPJ Web of Conferences 169, (2018) (Theory-4) A neutron source for IGISOL-4 5. V. Rakopoulos, M. Lantz, P. Andersson, A. Hjalmarsson, A. Mattera, S. Pomp, A. Solders, J. Valldor-Blücher, D. Gorelov, H. Penttilä, S. Rinta- Antila, R. Bedogni, D. Bortot, A. Esposito, A. Gentile, E. Passoth, A. V. Prokofiev, M.V. Introini, and A. Pola. Target thickness dependence of the Be(p,xn) neutron energy spectrum. EPJ Web of Conferences 66, (2014) (INPC2014) 6. A. Mattera, R. Bedogni, P. Andersson, A. Hjalmarsson, D. Bortot, A. Esposito, A. Gentile, J. M. Gómez-Ros, D. Gorelov, M. Introini, M. Lantz, E. Passoth, H. Penttilä, A. Pola, S. Pomp, A. V. Prokofiev, V. Rakopoulos, S. Rinta-Antila, A. Solders, and J. Valldor-Blücher. Neutron energy spectra from a Be(p,xn) source for fission yield measurements. vii

8 Radiation Protection Dosimetry, Vol. 161, Issue 1-4, 1 October 2014, Pages (2014) (Neudos conference proceedings) 7. A. Mattera, R. Bedogni, V. Rakopoulos, M. Lantz, S. Pomp, A. Solders, A. Al-Adili, P. Andersson, A. Hjalmarsson, J. Valldor-Blücher, A. Prokofiev, E. Passoth, A. Gentile, D. Bortot, A. Esposito, M.V. Introini, A. Pola, H. Penttilä, D. Gorelov, and S. Rinta-Antila. Measurement of the energy spectrum from the neutron source planned for IGISOL. Proceedings of the ERINDA Workshop, CERN, Geneva, Switzerland, 1-3 October 2013, CERN- Proceedings , (2014) 8. A. Mattera, P. Andersson, A. Hjalmarsson, M. Lantz, S. Pomp, V. Rakopoulos, A. Solders, J. Valldor-Blücher, D. Gorelov, H. Penttilä, S. Rinta- Antila, A. V. Prokofiev, E. Passoth, R. Bedogni, A. Gentile, D. Bortot, A. Esposito, M. V. Introini, and A. Pola. Characterization of a Be(p,xn) neutron source for fission yields measurements. Nuclear Data Sheets 119, (2014) (ND2013) 9. M. Lantz, D. Gorelov, A. Jokinen, V. S. Kolhinen, A. Mattera, H. Penttilä, S. Pomp, V. Rakopoulos, S. Rinta-Antila, and A. Solders. Design of a High Intensity Neutron Source for Neutron-Induced Fission Yield Studies. IAEA-F1-TM (2014) 10. D. Gorelov, H. Penttilä, A. Al-Adili, T. Eronen, J. Hakala, A. Jokinen, A. Kankainen, V. S. Kolhinen, J. Koponen, M. Lantz, A. Mattera, I. D. Moore, I. Pohjalainen, S. Pomp, V. Rakopoulos, J. Reinikainen, S. Rinta-Antila, V. Simutkin, A. Solders, A. Voss, and J. Äystö. Developments for neutron-induced fission at IGISOL-4. Nuclear Instruments and Methods in Physics Research B 376, (2016) 11. A. Mattera, S. Pomp, M. Lantz, V. Rakopoulos, A. Solders, A. Al-Adili, E. Passoth, A. V. Prokofiev, P. Andersson, A. Hjalmarsson, R. Bedogni, D. Bortot, A. Esposito, A. Gentile, J. M. Gómez-Ros, M. V. Introini, A. Pola, D. Gorelov, H. Penttilä, I. D. Moore, S. Rinta-Antila, V. S. Kolhinen, and T. Eronen. A neutron source for IGISOL-JYFLTRAP: Design and characterisation The European Physical Journal A 53: 173 (2017) Developments of IGISOL A. Al-Adili, K. Jansson, M. Lantz, A. Solders, D. Gorelov, C. Gustavsson, A. Mattera, I. Moore, A. V. Prokofiev, V. Rakopoulos, H. Penttilä, D. Tarrío, S. Wiberg, M. Österlund, and S. Pomp. Simulations of the fission-product stopping efficiency in IGISOL. The European Physical Journal A, 51: 59 (2015) 13. A. Solders, A. Al-Adili, D. Gorelov, K. Jansson, A. Jokinen, V. Kolhinen, M. Lantz, A. Mattera, I. Moore, N. Nilsson, M. Norlin, H. Penttilä, S. Pomp, A. V. Prokofiev, V. Rakopoulos, S. Rinta-Antila and V. Simutkin. Simulations of the stopping efficiencies of fission ion guides. EPJ Web of Conferences 146, (2017) viii

9 Misc. 14. A. Al-Adili, E. Alhassan, C. Gustavsson, P. Helgesson, K. Jansson, A. Koning, M. Lantz, A. Mattera, A. V. Prokofiev, V. Rakopoulos, H. Sjöstrand, A. Solders, D. Tarrío, M. Österlund, and S. Pomp. Fission activities of the nuclear reactions group in Uppsala. Physics Procedia 64, (2015) 15. A. Al-Adili, D. Tarrío, F.-J. Hambsch, A. Göök, K. Jansson, A. Solders, V. Rakopoulos, C. Gustafsson, M. Lantz, A. Mattera, S. Oberstedt, A. V. Prokofiev, M. Vidali, M. Österlund and S. Pomp. Analysis of prompt fission neutrons in 235 U(n th,f) and fission fragment distributions for the thermal neutron induced fission of 234 U. EPJ Web of Conferences 122, (2016) (CNR*15) 16. A. Mattera, A. Al-Adili, M. Lantz, S. Pomp, V. Rakopoulos, and A. Solders. A methodology for the intercomparison of nuclear fission codes using TALYS. EPJ Web of Conferences 146, (2017) 17. A. Al-Adili, K. Jansson, D. Tarrío, F.-J. Hambsch, A. Göök, S. Oberstedt, M. O. Frégeau, C. Gustavsson, M. Lantz, A. Mattera, A. V. Prokofiev, V. Rakopoulos, A. Solders, M. Vidali, M. Österlund and S. Pomp. Studying fission neutrons with 2E-2v and 2E. EPJ Web of Conferences 169, (2018) 18. A. Mattera, A. Al-Adili, M. Lantz, S. Pomp, V. Rakopoulos, and A. Solders. DElFIN: a TALYS-based tool for the comparison of fission models. In manuscript (2018) ix

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11 Contents 1 Introduction Brief description of the nuclear fission process Chronology of nuclear fission Liquid drop model theory Models to describe fission observables Nuclear shell corrections Multi-Modal Random Neck Rupture model Scission-point configuration model De-excitation of fission fragments Level density models Definition of fission yields Isomeric state: Formation and significance Measurements of isomeric yield ratios Angular Momentum of fission fragments Angular momentum derivation of the fission fragments Experimental facility & techniques Overview of IGISOL-JYLTRAP facility Fission products with the IGISOL technique The JYFLTRAP double Penning trap Isobaric purification with JYFLTRAP Separation of ions with the sideband cooling technique Space charge and pile-up effects Time structure of the sideband cooling technique Phase-Imaging Ion-Cyclotron-Resonance (PI-ICR) technique Separation of ions with the PI-ICR technique Time structure of the PI-ICR technique Analysis of the Penning trap data Measurements of isomeric yield ratios at IGISOL-JYFLTRAP facility Analysis of the data acquired with the sideband cooling technique Time of flight selection Yield determination of the peaks Analysis of the data acquired with PI-ICR technique Time of flight selection xi

12 3.3.2 Yield determination of the peaks Corrections due to radioactive decay losses Sources of uncertainties Comparison of the two techniques γ-ray spectroscopy data Data acquisition procedure Analysis of the data acquired with γ-ray spectroscopy Results & Discussion From purification,...to precision Comparison with experimental data and GEF Comparison of the same isomeric pair for different fissioning systems Studies on isotopes of the same elements n-induced fission at IGISOL Derivation of the angular momentum of the primary fission fragments TALYS for angular momentum of the primary fragments Angular momentum distribution of the primary fragments Excitation energy of the fission fragments Deduced J rms of the primary fission fragments Comparison and discussion of the results J rms of the primary fragments and connection with nuclear structure features Comparison of J rms for different fissioning systems Correlation of J rms with quadrupole moment Q Angular momentum dependence on the excitation energy J rms of fragments from n-igisol Assessment study of the methodology for the derivation of J rms Potential improvements of the applied methodology Summary & Outlook Summary in Swedish - Experimentella mätningar av isomerkvoter References Appendix A: Properties of the studied nuclides Appendix B: Uncertainty of IYR Derivation of the formula Discussion xii

13 List of Tables Table 3.1: Overview of the experimental activities at IGISOL Table 5.1: Results of isomeric yield ratios Table 6.1: Results of the angular momentum of the primary fission fragments Table A.1:Nuclear properties of the measured nuclides xiii

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15 List of Figures Figure 1.1: Representation of the potential energy of a fissioning nucleus as a function of deformation Figure 1.2: Simplistic scheme of the de-excitation of the fission fragments.. 9 Figure 1.3: Decay chain of part of the chart of nuclides Figure 2.1: Schematic overview of IGISOL-JYFLTRAP Figure 2.2: Time structure for the sideband technique Figure 2.3: Time structure for the PI-ICR technique Figure 3.1: Time of flight spectrum for mass A = Figure 3.2: Experimental cyclotron frequency spectrum for mass A = 130, with and without TOF gating Figure 3.3: Experimental quadrupolar cyclotron frequency spectrum for mass A = Figure 3.4: Fitted cyclotron frequency spectrum for mass A = Figure 3.5: Spectrum for mass A = 127 with the PI-ICR technique Figure 3.6: Spectra for mass number A = 125 with and without TOF selection of the ions, as acquired with the PI-ICR technique Figure 3.7: Spectrum for mass A = 125 with the PI-ICR technique Figure 3.8: Spectrum of mass A = 125 converted to polar coordinates Figure 3.9: Experimental spectra of 81 Ge measured with both techniques.. 42 Figure 4.1: Full-energy peak efficiency calibration of the HPGe detector Figure 4.2: γ-ray spectrum for mass A = Figure 5.1: Experimentally determined IYRs Figure 5.2: IYRs of the same pair for different fission reactions Figure 5.3: IYRs for In & Cd Figure 5.4: IYRs for Sn & 130,132 Sb in neutron-induced fission Figure 6.1: Schematic overview of the methodology for the calculations performed with TALYS for the derivation of the angular momentum of the primary fission fragments Figure 6.2: Different level density model calculations for J rms of the primary fission fragments Figure 6.3: Calculations of J rms for 129 Sb with two different level schemes 64 Figure 6.4: Results of the Jrms av of the primary fission fragments as calculated with TALYS Figure 6.5: Derivations of J rms for isomeric yield ratios available in the literature with TALYS Figure 6.6: Odd-even effect in the angular momentum of the primary fission fragments for neutron number N = xv

16 Figure 6.7: Dependency of the angular momentum of the primary fission fragments on the fission reaction Figure 6.8: Correlation of the experimental IYRs, and angular momentum J rms of the primary fragments, with the quadrupole moment Q of the observed products Figure 6.9: Angular momentum dependency on mass number A and excitation energy of the fission fragments Figure 6.10: Calculated J rms for the isotopes of Sn and 130,132 Sb for the neutron-induced fission of 238 U Figure 6.11: Derivation and comparison of J rms of 135 Xe from IYR available in the literature Figure B.I: Relative uncertainties of ratios xvi

17 List of Acronyms BSFGM Back-Shifted Fermi Gas Model. CFY Cumulative Fission Yield. CTFGM Constant Temperature Fermi Gas Model. ENSDF Evaluated Nuclear Structure Data File. FF Fission Fragment. FGM Fermi Gas Model. IFY Independent Fission Yield. IGISOL Ion Guide Isotope Separator On-Line. ISOL Isotope Separator On-Line. IYR Isomeric Yield Ratio. JYFL University of Jyväskylä, Department of Physics (Jyväskylän Yliopisto Fysiikan Laitos). LDM Liquid Drop Model. MCP MutliChannel-Plate. MLDM Microscopic Level Density Model. MM-RNR Multi-Modal Random Neck Rupture. MRP Mass Resolving Power. PI-ICR Phase-Imaging Ion-Cyclotron-Resonance. RFQ Radio Frequency Quadrupole. RIPL Reference Input Parameter Library. SPIG SextuPole Ion Guide. TKE Total Kinetic Energy. TOF Time Of Flight. TXE Total Excitation Energy. xvii

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19 Preface The act of writing requires a constant plunging back into the shadow of the past where time hovers ghostlike. Ralph Ellison Nuclear fission can be considered a complete nuclear physics laboratory, and due to this it is one of the most complex. Thus, there are still many open questions regarding the fission process, one of them being the origins of the angular momentum of the primary fission fragments. By inferring it from other fission observables, such as the isomeric yield ratios, we can achieve a better understanding and, hopefully one day, a complete theoretical description of the whole fission process. Exactly this was one of the main motivations of the present work: to contribute experimental data which eventually can help to illuminate one of the most complicated issues related to fission. One of the means to accomplish this is by studying proton-induced fission. This thesis was developed as part of a broader project with the intention to study fission and to provide nuclear data of high accuracy. The experiments were performed in collaboration with the University of Jyväskylä, at the IGISOL-JYFTRAP facility. Measurements of isomeric yield ratios in fission were accomplished by employing the JYFLTRAP Penning trap for 25- MeV proton-induced fission of nat U and 232 Th. Moreover, isomeric yield ratios were determined by means of γ-spectroscopy for the fission of nat U, induced either by 25-MeV protons or by high-energy neutrons. The first data sets were collected by coupling the IGISOL technique with the superior resolution of a Penning trap. For these measurements we employed the so-called sideband cooling technique, with certain limitations in terms of the mass resolving power. The recently implemented phase-imaging ion-cyclotron-resonance technique at JYFLTRAP provided the opportunity to separate isomeric states at much lower excitation energies, without abolishing the advantages of the sideband cooling technique, i.e., direct ion counting for short-lived nuclides with half-lives below 1 second. Soon after the first measurements, our efforts were focused on the connection of the isomeric yield ratios with the angular momentum of the primary fission fragments and consequently, the scission configuration. Therefore, a methodology was developed to derive the angular momentum of the primary xix

20 fission fragments based on the experimentally determined yield ratios. This method, and all the similar ones that have been proposed in the past, is based on the idea of tracing back, in a sense, to the scission point. This means, that from the last stage of the fission process where the measurements are performed, the time region of the fission products, we go backwards to the point in the process where the compound nucleus snaps (scission). In the methodology presented here, the calculations for the de-excitation of the fission fragments are performed with the nuclear reaction code TALYS. In chapter 1 I will discuss briefly the fission process and some of the models that have been developed over the years in order to describe it. Afterwards, the formation and the significance of the isomeric states and the experimental techniques for measuring isomeric yield ratios are presented. Then, I will give a general overview of some of the hypotheses that currently exist about the generation of the angular momentum of the fission fragments. The chapter closes with a description of the methods that have been used in order to derive the angular momentum of the fragments from experimentally measured fission observables. Chapter 2 includes the description of the experimental facility and techniques, that have been employed in order to determine isomeric yield ratios. This chapter is focused on the experimental techniques that have been used in the JYFLTRAP double Penning trap, since the majority of our experimental data were acquired there. These two techniques are the sideband cooling technique and the phase-imaging ion-cyclotron-resonance technique. In chapter 3, I will present the procedure that was followed in order to analyze the experimental data as acquired from the aforementioned two techniques. Corrections of the yields due to decay losses of the most short-lived nuclides are also discussed in this chapter, while in the last section a comparison of the two techniques is performed. Chapters 2 and 3 are directly related to the measurements of the isomeric yield ratios in [PAPER I & II]. Chapter 4 is related to the data acquired with γ-ray spectroscopy. It starts with a description of the data acquisition procedure and afterwards the data analysis is described. The isomeric yield ratios by means of γ-spectroscopy have earlier been reported for proton-induced fission in [PAPER III] and for neutron-induced fission in [PAPER IV]. In chapter 5 the results of the isomeric yield ratios as acquired with all techniques and for all fission reactions are presented. Moreover, a comparison is performed with data available in the literature and calculations performed with the GEF model. In this chapter I compare isomeric yield ratios of the same nuclide for different fission reactions and investigate the evolution of the isomeric yield ratios for the odd mass isotopes of cadmium (Cd) and indium (In) in the mass range A = Results of isomeric yield ratios have been reported in [PAPER I, II, III, IV]. Chapter 6 is dedicated to the methodology I developed for the derivation of the root-mean-square angular momentum (J rms ) of the primary fission fragxx

21 ments based on the experimentally determined isomeric yield ratios. The chapter starts with a description of the model, by presenting the basic ingredients and the assumptions that have been made. Afterwards, the first results based on this methodology are discussed and an interpretation is attempted. Moreover, the results of J rms for the isomeric yield ratios of the neutron-induced fission reaction are presented. After that, we discuss the benchmark study that has been initiated in order to assess our methodology. This study is described more in detail in [PAPER V]. The chapter closes with a section focused on potential improvements of the model. The deduced values of J rms for the case of proton-induced fission have been reported in [PAPER I, II & III]. xxi

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23 1. Introduction Un peu de théorie éloigne de la pratique. Beaucoup en rapproche. G. Genette Fission fragments are known since long ago to carry a considerable amount of angular momentum [1]. Already in 1972, Wilhelmy et al. deduced an average angular momentum value of 7±2 h for the fragments in the spontaneous fission of 252 Cf [2]. This could sound puzzling, considering that the mother nucleus has 0 + ground state. Isomeric yield ratios (IYR) can provide valuable insights regarding the fission process, since they can serve as a tool in order to deduce the angular momentum of the primary fission fragments. The latter can be of importance towards a better understanding of the scission configuration, and eventually the dynamical evolution of the fissioning nucleus from the saddle point to scission, which is still lacking a complete theoretical description. Thus, it is apparent that although measurements of isomeric yields are performed at a very late stage of the fission process, at the region of the fission products, they may still have implications on earlier stages of this procedure. For these reasons, this chapter starts with a brief description of fission in Sec. 1.1, where the process is described in terms of the liquid drop model. Afterwards, in Sec. 1.2, I will describe a few of the models that have been developed over the years in an attempt to describe the fission observables. At the end of this section, we will take a look at specific models related to scission configuration, considering the connection of the derived angular momentum of the fission fragments with this point. After a brief description of the de-excitation of the fission fragments, a process essential for the calculations of the angular momentum of the fragments based on the experimentally determined isomeric yield ratios, we approach to notions that are more directly related to the title of this work. In Sec. 1.4, I will describe the reasons for the formation of the isomeric states and their significance in various fields of nuclear physics. In Sec. 1.5, the techniques that have been employed for measurements of isomeric yield ratios are presented. Afterwards, in Sec. 1.6, some of the models that encounter the generation of the angular momentum in the primary fragments will be briefly discussed. This topic is still an open question, with a consensus yet to be achieved, as various, and sometimes even competing, theories exist. The list of models presented in this section is far from complete. In the last section of the chapter, Sec. 1.7, I will present different methods to derive the angular momentum based on various experimental techniques. 1

24 1.1 Brief description of the nuclear fission process Chronology of nuclear fission Fission was first observed experimentally at the end of 1938 by Hahn and Strassmann in neutron-induced fission of Uranium, and their results were published in January of 1939 [3]. These results were sent to Meitner and Frisch for interpretation. In February of the same year, Meitner and Frisch published a theoretical interpretation on these experimental findings [4]. In this pioneering paper, for the first time the process was described in terms of a liquid drop which becomes deformed and beyond a critical deformation is breaking apart into two pieces. It was in this paper that the name fission was given to this new type of nuclear reaction. Moreover, Frisch provided the physical evidence for the division of heavy nuclei into parts of comparable size under neutron bombardment [5]. Later the same year (September 1939), Bohr and Wheeler published their prominent work with a theoretical description of the fission process [6]. The authors treated the nucleus as a charged liquid drop, in which two opposing forces, the Coulomb and the nuclear force, control the nuclear stability Liquid drop model theory Nuclear fission is a basic nuclear reaction, but its mechanism is a very complicated process, as a proper description encounters all the difficulties related to the theories describing the atomic nucleus. Thus, despite the fact that fission induced by neutrons in the actinides is perhaps the most studied reaction of nuclear physics, a complete picture of the process is still lacking. The study of fission provides the opportunity to probe the properties of nuclear structure at very large deformations and to investigate the dependency of the nuclear potential energy on the shape of the nucleus [7]. From the perspective of the liquid drop model (LDM) description, a nucleus is assumed to be undeformed at the ground state, as is shown in Fig. 1.1 with the red dashed line. The absorption of an impinging particle, usually neutron or proton, by an actinide target, increases the excitation energy of the formed compound nucleus, resulting in shape deformation and increase of the potential energy. In the landscape of deformation, there is a critical deformation point of no return, which is called the saddle point. Once the nucleus overcomes the fission barrier at the saddle point, it further deforms, and eventually a situation is reached where the neck joining the two nascent fragments is no longer stable but snaps at scission. Thereafter, the two incipient fragments separate, in general with unequal masses. The formation of two fragments (binary fission) is much more likely than the formation of three (ternary fission), which occurs with a low probability of only a few events per 1000 fissions. Therefore, in this work whenever the term fission is used, we will imply binary fission. 2

25 Mass Distribution Potential Energy Liquid drop model saddle point Liquid drop model & shell corrections ground state ground state inner barrier saddle point (outer barrier) scission point Deformation Figure 1.1. The potential energy of a fissioning nucleus as a function of deformation. The red dashed line corresponds to the liquid drop model description, in which a single fission barrier is predicted. The black line corresponds to the liquid drop model with shell corrections, in which a double humped fission barrier is predicted. As has already been mentioned, the concept of the fission barrier has been based on the classical, macroscopic picture of the atomic nucleus as an electrically charged liquid drop, ever since the first attempts of describing fission. The analogy of nuclear behavior to that of a charged liquid drop has been described in the works of von Weiszäcker [8] and Bethe and Bacher [9]. Thus, within this picture the binding energy of a nucleus can be described by the semi-empirical mass formula [10]: E B = E vol + E sur f + E coul + E sym + E pair = α ν A α s A 2/3 α c Z(Z 1)A 1/3 α sym (A 2Z) 2 A 1 + δ (1.1) E vol : the volume term, which is strongly attractive because of the strong force between the nucleons. The linear dependence on A suggests that each nucleon attracts only its closest neighbors. E sur f : the surface energy, which describes the fact that nucleons on the surface have less neighbors to interact with, resulting in a decrease in the binding energy. The surface area of the nucleus is proportional to the square of the mean nuclear radius (R 2 ), with R A 1/3. E coul : the Coulomb term, expresses the repulsive interactions between the protons in the nucleus due to the Coulomb force, and makes the nucleus 3

26 less tightly bound. In cases, like fission, where the nucleus deforms considerably, this term becomes important because the Coulomb repulsion might overcome the short range of the strong nuclear force. E sym : the symmetry term, describes the tendency of the nucleus to be symmetric in protons and neutrons in order to be stable. This term is more important for light nuclei, since for the heavier ones the increase in Coulomb repulsion requires additional neutrons for nuclear stability. E pair : the pairing term, expresses the tendency of nucleons of the same species to couple pairwise in order to form stable configurations. Specifically this term does not contribute when A = odd (odd Z and even N and vice versa), δ = 0. However the relatively high stability of even-even nuclei is taken into account by a positive contribution (+δ) to the total binding energy E B of the nucleus, and the relatively low stability of odd-odd nuclei by a negative contribution ( δ). If the nuclear fluid is assumed to be incompressible, the necessary energy to deform the nucleus can be estimated based on the surface and Coulomb terms. For a nucleus deforming from its original spherical shape, the negative contribution of E sur f will increase, due to a larger surface. Accordingly, the Coulomb energy term E coul is decreased, because of the larger average separation between the charge elements. Bohr and Wheeler introduced a new parameter x, the fissility parameter, which expresses the stability of the nucleus against deformation [6, 11]: x = E 0 coul/2e 0 sur f (1.2) where E 0 coul and E0 sur f are the Coulomb and surface energy, respectively, of a spherical nucleus. A nucleus becomes unstable when x > 1. The simple liquid drop model, with its prediction of a single barrier, was able to describe the general properties of the fission process relatively well. However, it was not successful in quantitive estimation of the heights of the fission barrier [12], and has certain limitations in explaining experimental results. For example, it fails to explain the two distinct modes of symmetric and asymmetric mass division in fission, which was suggested from experiments. Mayer, in her work in 1948, traced the asymmetric fission back to nuclear shell effects, in particular to the stabilizing influence of the 50 proton shell and the 82 neutron shell that coincide in the spherical doubly magic nucleus 132 Sn [13]. 1.2 Models to describe fission observables Nuclear shell corrections In order to explain the fission observables, attempts were made to incorporate the nucleon shell effects into the semi-empirical formula. One of the first works towards this direction was performed by Strutinksy [14], who concentrated on deriving the shell-correction term from actual shell model energy 4

27 levels. Essentially, the shell correction was calculated by summing the energies of occupied single-particle states, and subtracting from this the sum over all occupied states of a uniform distribution of states, i.e. the density of states is smeared out in order to wash-out shell effects. For actinides, the fission barrier becomes double-humped due to the strongly negative shell correction at the deformation that corresponds to the maximum of the LDM potential (saddle point) [12], as can be noticed in Fig. 1.1 with the black line. The addition of the shell effects to the normal liquid drop term resulted in fission barriers of the right order, and also in an oscillatory energy curve with increasing deformation. Moreover, it led to the reproduction of observed ground-state quadrupole moments, where a finite deformation can be noticed instead of a spherical shape. One of the first types of fission that the theory of double-humped barrier provided an explanation for was the occurrence of spontaneously fissioning isomers. The nucleus is lodged at an excited state in the second minimum of the deformation energy curve. It is trapped into retaining its elongated shape since its energy is not sufficient to surmount either barrier. The hypothesis about the spontaneously fissioning isomer was first advanced by Polikanov et al. [15] for the fission of the 14 ms isomeric state of 242 Am. The half-life of the spontaneous fission was appropriate to a state with an excitation energy of several MeV, so its peculiar property was the extraordinary stability against γ-ray decay. The single fission mode considered from the model, based on the potential energy landscape with minimum between the two barriers, provided an important step forward regarding the explanation of the main feature of the mass yield distribution. Nevertheless, this progress was still not sufficient to account for special features of the distribution or average total kinetic energy (T KE) of the fragment pair. A significant improvement towards the explanation of various fission observables was introduced by Brosa, Grossmann and Müller, with the Multi-Modal Random Neck Rupture (MM-RNR) model [16] Multi-Modal Random Neck Rupture model The MM-RNR model, proposed by Brosa [16], is based on the discoveries that many exit channels in spontaneous fission or low-energy induced fission exist, making fission a multichannel reaction. After the nucleus surpasses the outer barrier, there are several paths to disintegrate. Each path suggests a guided evolution of the nucleus through a different fission channel. In the model, instead of one fission barrier, which might well be double-humped, several ones for every nuclide are considered. Moreover, multiple nuclear shapes can be reached at the scission point. At the final stage of scission, and once the shape has been defined, the rupture happens in a random location along a flat neck between the two nascent fragments. 5

28 Four main fission modes are proposed by the model, each one with different characteristics with respect to the mass asymmetry and neck length of the nascent fragments: Standard (S1/S2/S3) mode: Three alternatives exist in this case, with increasing asymmetry. It is a slightly asymmetric mode, with a neck of a standard length. This mode dominates ( 95 %) in near-barrier fission of heavy nuclei of intermediate mass (230 < A < 255). Super-Long (SL) mode: This mode is symmetric, with a longer than average neck. It dominates in near-barrier fission at lower masses (A < 230). It contributes to a mass distribution around half the mass of the compound nucleus (A = A CN/2). The longer distance between the nascent fragments results in lower T KE. Super-Short (SS) mode: This mode is also symmetric, but with a neck length shorter than average. It dominates in near-barrier fission at higher masses (A > 255), and it results higher T KE. Super-Asymmetric (SA) mode: As the name suggests, it is responsible for the masses of the fission products (FP) which are observed at the edges of the distribution. The MM-RNR model is able to reproduce many of the fission observables, such as the mass yield distributions, T KE and neutron multiplicity ν(a). However, this model is now more than 25 years old, and new ideas have emerged in the meantime. Möller introduced calculations of potential landscapes, based on a five-dimensional parametrization of the nuclear shapes [17 20]. In these works, multi-dimensional potential energy landscapes have been calculated for a large selection of nuclei, which later were successfully used for calculations of fission fragment yields, as for example in the random walk model proposed by Randrup and Möller [21] Scission-point configuration model During the fission process, we can observe the evolution of the system from a slightly deformed compound nucleus to two fragments, with various deformations, that move away from each other because of the Coulomb repulsion. As has already been mentioned, two main characteristic points can be noticed in this evolution: the outer saddle point and the scission point. After the critical saddle point, the system continues to deform during the descent of the system from that point to scission. The neck that appears, and which is responsible for joining the two nascent fragments, becomes thinner with increasing deformation, until it breaks and the two fragments arise. The scission point, somewhere between the saddle point and the two separated fragments far apart, is difficult to define unambiguously. As we can read in the work by Bjørnholm et al. [12]: 6

29 By contrast with the region of deformation up to the outer saddle point, this region is a hazy, ill understood area from the overall point of view including the dynamical effect. So far we were concerned with the fission process from the moment of the formation of the compound nucleus, until the two incipient fragments are formed. However, knowledge of isomeric yield ratios can provide important insight regarding the scission configuration just after the neck rupture, but before the neutron emission, as will be explained more in detail in Secs. 1.6 and 1.7. At the scission configuration, the nucleons in the neck region between the nascent fragments may be deemed to be redistributed to the two fragments. At this point, the properties of the fragments, such as the mass, charge and deformation, can be considered determined. Wilkins, Steinberg and Chasman published in 1976 one of the most cited papers with interpretation on the fission process [22], in which they proposed a statistical static scission-point model. In this work, the basic assumption is exactly that the fission fragments distribution can be determined at, or near, the scission point from the relative potential energies of the complementary nascent fragments. These energies were calculated from a system of two coaxial spheroids, separated by a fixed distance and with shapes described by quadrupole deformations. One of the basic ideas behind the model, was that by understanding the influence of the deformed fragment shells, much information of the observed trends and general features of the fission process can be inferred. Thus, a major part of the discussion is dedicated to relate qualitatively the trends of the minima in the potential energy surface, and the regions of deformations associated with them, to the qualitative trends in observed distributions. The model deals with numerous fissioning systems and tries to keep things as simple as possible. As the authors state, the principal aim is to investigate the general validity and applicability of the model, without attempting to achieve optimum fits to the experimental data. In the recent years, some efforts have been made for more contemporary refinements of the model. Lemaître et al. developed a new scission-point model, named SPY [23], which was inspired by the work of Wilkins et al. The major theoretical advances in nuclear structure description that have been made since the late 1970s have been incorporated in the SPY model. By calculating the individual energies of each fragment the model is capable of making predictions for every fissionable nucleus, at moderate computation cost. The aim remains the same as in the Wilkins model: to evaluate how successful such a static, scission-point interpretation can be without further adjustments. At first glance, the MM-RNR model and the scission-point model seem contradictory, especially if we consider that the dominant factor in the latter is the shell effects of the, possibly deformed, fragments, while the former is based on the shell effects of the fissioning nucleus. However, after a careful 7

30 consideration of the two models, one could conclude that they do not confront each other, as the MM-RNR model contains the physics shortly before rupture, while the scission-point model briefly afterwards. As Brosa et al. state in the Homage of their paper [16], their work can be perceived as a continuation to the scission-point model: The prescission shape is not entirely different from the scission-point configuration... And some of the magic numbers of fission are nothing more than the sum of the magic numbers of the fragments plus some nucleons for the neck. These relations are the reason for the considerable success of the scission-point model. If one thinks in such terms of continuation, one may say that the present work is just a tracing back of the scission-point configuration into the internals prior to scission. 1.3 De-excitation of fission fragments To understand the population of isomers in fission we first need to discuss the de-excitation of the fission fragments. Figure 1.2 shows a simplistic sketch of the de-excitation of the fission fragments. The formed fission fragments are highly excited and deformed to a certain degree. They de-excite by emitting neutrons and γ rays. As long as the excitation of the fragments is high the neutron emission prevails, until the excitation energy is reduced around, or below, the neutron separation energy (S n ). After prompt neutron emission the fragments are called secondary or just products. The secondary fragments de-excite first by emitting statistical γ rays. Afterwards, they de-excite by emitting non-statistical γ rays along the yrast line, before they are eventually either trapped in an isomeric state or populate the ground state. The role of the angular momentum during this process is important as it controls the competition between neutrons and photons. Prompt neutrons and statistical γ rays carry away only a small portion of the angular momentum of the fission fragments. Thus, low initial angular momentum produce more neutrons and fewer γ rays, while the opposite occurs for high angular momentum [24] Level density models During the de-excitation of the highly excited fission fragments two regions can be distinguished. The first one corresponds to lower excitation energies where information about the discrete levels of the nucleus exists. For higher excitation energies, where such information are not available or incomplete, statistical models for the nuclear level densities are employed. The distinction between the two regions is rather arbitrary and strongly case dependent as it relies on the available information of discrete energy levels for the specific nucleus. For calculations of nuclear reactions and statistical model calculations, good knowledge of nuclear level schemes is required in order to specify outgoing 8

31 E * Primary Fission Fragments n Secondary Fission Fragments n n γ γ γ n neutron emission }prompt γ-rays E (Yrast) Sn Isomer γ γ γ γ γ γ γ γ }discrete γ-ray emission J Figure 1.2. A simplistic schematic overview of the de-excitation of the fission fragments, first by prompt neutron emission and then by prompt (statistical) γ rays. Afterwards, the emission of non-statistical photons takes place to the region along the yrast line, until either an isomeric or the ground state is populated. reaction channels and calculate partial (isomeric) cross sections. Especially for studies related to population of isomeric states, knowledge of particle and γ-ray decay branchings from each level is important [25]. In this work, the de-excitation of the primary fragments is handled by the nuclear reaction code TALYS [26]. This process is essential for the derivation of the angular momentum of the primary fission fragments based on the experimentally determined isomeric yield ratios. In TALYS, the discrete level scheme is based on the discrete level file of Belgya, as stored in the Reference Input Parameter Library (RIPL-3) database [25]. RIPL-3 contains the known level schemes, electromagnetic and γ-ray decay probabilities which were compiled and available from the Evaluated Nuclear Structure Data File (ENSDF) in October 2007 [27]. TALYS contains six different level density models, three with phenomenological analytical expressions and three with tabulated level densities derived from microscopic models [28]. Fermi gas model and variations The Fermi gas model (FGM) is arguably the most known analytical level density expression and it was first proposed by Bethe in 1937 [29]. The model is based on the assumption that the excited levels of the nucleus are constructed 9

32 by single particles states, which are equally spaced and that collective levels are absent. The Fermi gas level density is [29, 30]: ρ F (E x,j,π) = 1 [ 2J πσ exp (J + 1 ] 2 )2 π 3 2σ 2 12 [ exp 2 ] αu α 1/4 U 5/4 (1.3) where J and Π are the nucleus spin and parity, the first factor 1 2 arises from the assumption of equal positive and negative parity distributions, and σ 2 is the spin cut-off parameter, which represents the Gaussian dispersion of the z- projection of the angular momentum distribution J. The term U is the effective excitation energy and is equal to: U = E x (1.4) where the term E x represents the true excitation energy related to discrete levels, and the energy shift is an empirical parameter equal, or closely related, to the pairing energy. The underlying idea is that accounts for the requirement of break up of nucleons coupled to spin 0, before each component can be excited individually. is an adjustable parameter, and its definition can be different for the various models, as for example for the constant temperature Fermi gas model (CTFGM) and the back-shifted Fermi gas model (BSFGM), which are described later in this section. α is the level density parameter, which in contemporary analytical models is energy-dependent, as is explained below. The total Fermi gas level density, is given by summing Eq. (1.3) over all spins and parities: [ ρf tot (E x ) = 1 π exp 2 ] αu 2πσ 12 α 1/4 U 5/4 (1.5) The level density parameter α Initially α was treated as a nuclide-specific constant value, independent of energy. Ignatyuk [31] recognized the correlation between the parameter α and the shell correction term of the liquid-drop component of the mass formula. Thus, a more realistic level density can be obtained if the expression of α includes energy-dependent shell effects, present at low energy, but disappearing at high energy in a phenomenological manner, as follows: { α(a,z,u) = α 1 + δw(a,z) ( 1 e γu )} (1.6) U where U is the effective excitation energy as defined is Eq. (1.4), δw is the difference between the experimental mass of the nucleus M exp and its mass according to the spherical liquid-drop model mass M LDM. The damping parameter γ determines how rapidly α(a, Z, U) approaches α, and it is defined 10

33 as γ = γ 1 A 1/3, where γ 1 is a global parameter determined to give the best average level density description over a whole range of nuclides. The parameter α is the asymptotic level density value obtained in the absence of any shell effects, and it approximates A/9.4 [28]. The spin cut-off parameter The spin cut-off parameter σ 2 characterizes the angular momentum distribution of the level density. In the continuum, σ 2 can be related to the rigid body moment of inertia of the nucleus I 0 and the temperature t, based on the observation that the collective rotational energy of the nucleus cannot be used for single nucleons excitations [30]. However, and similar to the level density parameter α, the quantity σ 2 /t is not constant, but shows marked shell effects [32]. Thus, according to Refs. [32, 33], the expression for the spin cut-off parameter is with I 0 I0 = σ 2 = σ = σ 2 E F (E x ) = I 0 α α t (1.7) 2 5 m 0 R 2 A ( hc) 2 (1.8) where R = 1.2A 1/3 is the radius, m 0 the neutron mass in amu and A the atomic mass. Phenomenological total densities All phenomenological analytical expressions, such as the CTFGM and the BSFGM, follow a Fermi gas expression at high excitation energies and mainly depend on the level density parameter α. Differences between the models mainly exist on the adjustable parameters and the range of the excitation energy on which the Fermi gas model is applied. Specifically, in the CTFGM, which was first introduced by Gilbert and Cameron [34], the range of the excitation energy is divided in two regions. The low part from 0 MeV up to a matching energy E M, where the constant temperature law applies, and the high part above E M, where the Fermi gas model applies. Consequently, two expressions for the total density functions are defined respectively, with the condition of the continuity of these functions and their first derivatives at the matching energy E M. In this model the energy shift takes into account the even-odd differences of nuclear binding energies. In TALYS this parameter can be altered, although it is not adjustable by default in the model. In the BSFGM [35], the Fermi gas expression is used to describe the level density at all energies. The parameter is treated as an adjustable parameter. The model inherited its name from the negative displacement for odd-odd nuclei. The nuclear level densities in this model are determined by the parameters, α, σ and which are mass and energy dependent. 11

34 Proton Number (Z) Definition of fission yields Measurements of the fission observables such as isomeric yield ratios, mass yield distributions, and so on, are usually performed in the region of the fission products. These products are neutron-rich and usually radioactive, as the emission of prompt radiation is seldom sufficient for the products to reach stability. Thus, they decay through β-decay towards the valley of stability. Neutron emission can also occur if after a β-decay the daughter nucleus is still excited above the neutron separation energy. This kind of decay is called β-delayed neutron emission, in order to differentiate it from the prompt radiation emitted from the primary fragments. Fig. 1.3 shows decay-chains for a part of the chart of the nuclides around mass A 130. The black arrows denote β-decays, while red arrows denote β-delayed neutron emissions. Squares with same color correspond to members of the same isobaric chain Te 131Te 132Te n β Sb 130Sb 131Sb 132Sb Sn 129Sn 130Sn 131Sn 132Sn In 129In 130In 131In 132In Cd 129Cd 130Cd 131Cd 132Cd Neutron Number (N) Figure 1.3. The decay chain of part of the chart of nuclides. The black arrows represent β-decay and the red arrows represent the β-delayed neutron emission. The colors of the squares correspond to nuclides within the same isobaric chain. The determined fission product yields can be categorized based on the time scale of the observation, as the amount of a certain isotope will change with time [36]. Fig. 1.3 can be helpful for an easier understanding of the following product yield definitions: (i) Independent fission yields: a measure of the number of atoms of a specific nuclide produced directly in the fission process before any radioactive decay. 12

35 (ii) Cumulative fission yields: describes the total number of atoms of a specific nuclide produced directly in fission and after the decay of all of its precursors. (iii) Total chain yields: expresses the cumulative yield of the last, either stable or long-lived member of an isobaric chain. (iv) Mass number yields: is the sum of all independent yields of a particular isobaric chain. The difference between the total chain yield and the mass number yield emerges from the contribution of β-delayed neutrons. The former contains the produced nuclides after the β-delayed neutrons, while the latter does not. If there is no emission of delayed neutrons, the two yields concur. Summation of truly independent yields should produce the mass number yields. 1.4 Isomeric state: Formation and significance With the ascertainment that nuclear states in nature are normally short-lived, and this certainly applies to most nuclei and with the question But what makes the metastable nuclear states different? Aprahamian and Sun start their work [37]. One hundred years ago, Soddy hypothesized the existence of states in a single nuclide, with nuclear properties significantly different in terms of stability and mode of breaking up [38]. He was probably the first to imply the term isomer in the nuclear context, in analogy with chemical isomers. The discovery of nuclear isomerism is formally credited to Hahn for his work in 1921 [39]. It took another fifteen years, before von Weizsäcker came up with a theoretical explanation about the metastability of some excited nuclear states [40]. The key aspect was that excited states with a combination of effects, such as large angular momentum and low transition energy, can have a long lifetime for electromagnetic decay. In chemistry, from where the term is borrowed, isomer refers to molecules with different geometrical configurations for the same collection of atoms. Isomeric nuclei are different states of the same numbers of protons and neutrons. In contrast to chemical isomers that have similar energy states, or sometimes identical, nuclear isomers have different energies [41, 42]. Isomers can be characterized as shell-model states, which usually involve one or two, but sometimes even up to ten, unpaired nucleons. For example in an even-even nucleus, the excitation energy can cause the break up of a pair of nucleons. Thus, one or both nucleons are promoted to higher orbits. The remaining even-even core does not contribute neither excitation energy nor angular momentum. Let us assume two broken-pair nucleons (quasiparticles) in different orbits, each one with J π = 11/2 +. The total angular momentum of the nucleus will be the vector sum of the two single components, resulting in a range from 0 + to 11 + [42, 43]. The so-called spin-trap isomers are of 13

36 course not only encountered in even-even nuclei. They can also occur in oddeven and odd-odd nuclei, as for example in the case of odd-odd 180 Ta. The de-excitation of the high-spin created states, requires the emission of highspin and low-energy radiation, resulting in their long half-lives, as mentioned earlier. There is no strict definition of the minimum half-live that an excited state should have in order to qualify as an isomer [41]. From the technical side, any state that has a directly measurable lifetime could me termed as isomer, or in other words metastable [44]. However, a usual rule of thumb is that any state with a lifetime of approximately 1 ns or longer can be considered as isomer [37]. The semantics whether the lifetimes are arbitrarily long or short are not important. The central point is that the lifetimes of these states are unusually long compared to other states, implying a state of a different structure, and especially, an intrinsic state [45]. The nuclear isomers can lose their excess energy by the radioactive decay modes: α,β,γ. Decay by proton or β-delayed neutron emission, or even by nuclear fission, is also possible. The areas where the isomers are traditionally found are in medium-heavy to heavy nuclei, near closed-shells. Closed neutron and proton shells at these regions are met for nuclei with N = 82 and Z = 50 at masses around A 130, with N = 82 and Z = 64 at masses around A 150, and with N = 126 and Z = 82 at masses around A 210. In such nuclei, the nucleons can occupy orbitals with high spins at relatively low excitation energies [44]. As a matter of completeness, and without any intention to enter into details, since this would expand far beyond the aims of the present work, I would like to mention the different types of isomers that have been found to date. As explained by Walker and Dracoulis [41], the nuclear isomers arise in readily distinguishable ways. They are formed because it is difficult for them to change either their shape in order to match the states to which they are decaying ( shape isomers ), or their spin ( spin traps ), or their spin orientation relative to an axis of symmetry ( K-traps ). The mechanisms leading to the different kinds of nuclear isomerism can reinforce each other. The isomers, due to their long lifetime, and as a signature of intrinsic states, can provide an experimental tool that enables high-sensitivity spectroscopy. They can probe many phenomena related to nuclear structure, by exposing not only themselves but also decay paths of the states preceding and following them, which otherwise might be difficult to observe. Thus, studies such as accurate measurement of transition strengths, unambiguous placement of transitions in nuclear level schemes and measurement of nuclear moments [46] can be performed. Knowledge of the population of the isomers, and especially of isomeric yield ratios can be employed for the deduction of mean properties of the angular momentum distribution of the primary fission fragments. Applications of isomers, in the sense that the states populated in isomer decays are the focus of interest, can also be found in many other fields such as in astrophysical 14

37 studies. For example in the rapid-neutron-capture (r-process) nucleosynthesis, fission cycles material back to lower-mass regions. The knowledge of population of the isomeric states can affect the final abundances due to their different β-decay half-lives, as well as β-delayed neutron and neutron-capture probabilities [47]. In addition, determination of direct yield of metastable states in fission can be of interest for energy applications. The β-delayed neutron emission probability of the metastable state, important for calculations of the effect of delayed neutrons in nuclear reactors, can be an order of magnitude different than that of the ground state. Such an example can be found in the case of 98 Y, where the β-delayed neutron emission probabilities are 0.33% and 3.40% for the ground state and the isomer, respectively [48]. Moreover, isomeric yield ratios can be of importance to experiments that study the antineutrino spectra generated by nuclear reactors, which are calculated based on fission yield data and isomeric ratios using the summation method [49]. Lastly, the evolution of isomer production rates as a function of mass number A can be of interest for improving the predictive power of the models on isomeric yield ratios. These estimations are performed through de-excitation calculations of the primary fission fragments, and depend, among others, on the angular momentum and parity of these fragments. The inhibition of decay of the isomers leads to the storage of enormous amount of energies in these states. They could serve as the basis for a nuclear battery, although these energies are much lower than the ones released in fission. However, an efficient way to release on demand the energy stored in the isomers, has yet to be achieved. Thus, a comprehension of the formation of nuclear isomers, through a better understanding of nuclear structure, and the ability to excite and de-excite isomers at will still remain a challenge [37]. 1.5 Measurements of isomeric yield ratios Measurements of isomeric yield ratios have been performed in the past either by applying chemical (selection of Z) [50 62] or physical separation, by using a mass separator (selection of A). After separation, γ-ray spectroscopy is the most employed technique for the determination of the number of fission products. Regarding experiments with mass separation, the Isotope Separator On-Line (ISOL) technique has been employed, where a thick target is irradiated, and the created products are introduced to an ion source, where they are ionized. Afterwards the ions are mass separated by means of magnetic separation, resulting in pure ions beams. Such measurements for the determination of isomeric yield ratios have been performed at the OSIRIS facility of the Studsvik Science Research Laboratory in Sweden, where the ISOL system was directly attached to a nuclear reactor [63, 64]. Determination of isomeric yield ratios have also been performed by utilising the recoil-mass spectrome- 15

38 ter LOHENGRIN at the Institut Laue-Langevin in Grenoble, France [65, 66]. The spectrometer is coupled to the intense neutron flux of a reactor. The selection of the fission products is performed by a combination of electromagnetic separation based on the energy-charge state ratio (E/q) and mass-charge state ratio (A/q). However, all the aforementioned techniques face certain limitations because of the short half-lives of the measured nuclides, the limited mass resolving power (MRP) in the separator, inadequate knowledge of the level schemes and decay properties. Isomeric yield ratios have also been measured with the Ion Guide Isotope Separator On-Line (IGISOL) technique [67, 68], both at the IGISOL- JYFLTRAP facility at the University of Jyväskylä [PAPER III, PAPER IV], and the Tohoku IGISOL facility in Japan [69, 70]. This is a fast and chemically indiscriminate method, in the sense that ions of all chemical elements can be produced, facilitating measurements of short-lived fission products of any element, with half-lives of the order of a few hundred milliseconds. Fission products can be transported and detected at the γ-ray spectroscopy station within milliseconds from their creation, so the half-lives of the measured products remain a constraint for this technique as well. At the University of Jyväskylä, the ion guide technique is coupled with the superior mass resolving power of the double JYFLTRAP Penning trap. A Penning Trap can serve as a high-resolution mass separator, improving significantly the mass resolving power, so that isomeric states separated down to a few hundred kev from the ground state can be measured. With the IGISOL- JYFLTRAP method, a direct ion counting measurement of the relative intensities can be accomplished, without requiring accurate knowledge of the decay level schemes of the products. Thus, this method can overcome most of the difficulties mentioned earlier for the other techniques, although the half-lives of the nuclides still remain a constraining factor. The IGISOL-JYFLTRAP technique has been used for measurements of independent isotopic yields of fission products [71 73], but this thesis consists of the first experimental measurements for determination of isomeric yield ratios. 1.6 Angular Momentum of fission fragments The generation of angular momentum in the fission fragments is still one of the long-standing questions regarding the fission process. The increasing amount of experimental data during the last decades has attracted the attention of the scientists in search of a theory which could explain the angular momentum of the fission fragments. The fact that complementary fragments have comparable but not necessarily equal values of average angular momentum, might seem controversial. Nonetheless, the requirement is that three vectors, the angular momenta of the two fragments and the orbital angular momentum of the system, sum to zero after separation but before neutron emission [2]. Various 16

39 hypotheses have been developed over the years, and in this section I discuss some of them, with the list being far from complete. A vast majority of the experimental and theoretical investigations in the past were related to γ-ray measurements under the assumption that the angular momentum formation is a two step procedure [74 76]. In the first step, the fragments acquire angular momentum at scission due to the excitation of collective transversal degrees of freedom resulting from the interplay between the nuclear and Coulomb forces. In the second stage, angular momentum will be added to the fragments from the mutual Coulomb excitation. Maybe the most widely considered theoretical explanation for the generation of angular momentum in the fission fragments concerns the thermal excitation of collective angular-momentum-bearing scission modes. Nix and Swiatecki first introduced the normal collective modes about the saddle-point configuration [77]. In same spirit, Moretto and collaborators considered a dinuclear system of two touching, equal, rigid spheres and introduced intrinsic degrees of freedom which can bear angular momentum [78,79]. These modes, namely the wriggling, bending, twisting and tilting, are responsible for higher angular momentum of the fragments than what would be expected only from rigid rotation, and also for the misalignment of the fragment spin with respect to the fragment separation axis. They can also induce angular momentum in the fragments, even for a system with zero total angular momentum. The bending mode consists of the rotation of one sphere about an axis perpendicular to the symmetry axis, and the corresponding counterrotation of the other sphere. The twisting mode is similar to the bending mode, only that the spheres rotate about the symmetry axis. In both modes, the angular momentum of the two fragments cancel pairwise. The wriggling mode is more complicated. Both spheres corotate about parallel axes perpendicular to the symmetry axis, while simultaneously counterevolve about each other and about an axis parallel to the rotation axis. In this mode, the angular momenta of the spheres are equal and parallel, and their vector sum is compensated by the orbital angular momentum of the system. Rasmussen et al. proposed a model for calculating the angular momentum distribution of fission fragments [75] at low-energy fission. They considered the special case of one spherical and one deformed nucleus, and later Zieliska-Pfabé and Dietrich generalized the model for both fragments being deformed [76]. In the original model by Rasmussen et al., the interplay between the Coulomb repulsive force and the attractive nuclear force will produce a scission barrier, at which an equilibrium position in the fragmentfragment coordinate is established. Of course this pocket potential, as it is commonly known, is completely hypothetical as there is no experimental or theoretical evidence. However, the essential point is that if this pocket is not too shallow, rotational vibrations like the bending and wriggling mode can carry angular momentum at scission, perpendicularly to the fission axis. Moreover, the role of the Coulomb excitation in altering the angular momentum of 17

40 the fission fragments just after scission was also considered. The idea of the two modes contributing to the angular momentum of the fragments is still employed, as for example in the case of even-even fragments in the cold (neutronless) fission of 252 Cf by Mişicu et al. [80]. Hoffman, already in 1964, investigated the contribution of the Coulomb excitation to the fragments angular momentum [74]. He experimentally determined the anisotropy of prompt γ rays from thermal neutron fission of 233,235 U and 239 Pu. A correlation of the γ-ray intensity with the fragment direction was noticed, which consequently can indicate a relationship between the nuclear spin axis and the direction of fragment motion. In order to decipher the influence of the fission axis to the orientation, and possibly the magnitude, of the angular momentum, calculations of the torque between the electrostatic forces of the fission fragments were performed. Assuming that the fragments retain a fraction of their deformation after scission, he proved that the Coulomb repulsive force will be such that some portion of the Coulomb energy of the fragments will appear as rotational kinetic energy. Therefore, the angular momentum of the fragments can arise from the electrostatic forces between them. Gönnenwein et al. studied the relative population of two isomeric states of 132 Te as a function of total kinetic energy for the neutron-induced fission of the 240 Pu compound nucleus [81]. They exploited the properties of the cold compact and cold deformed fission. All the available energy in the former case goes into the Coulomb energy of repulsion of the fragments, while in the latter, it is exhausted by the deformation energy of the fragments. The term cold in both cases means that there is no intrinsic excitation. The population of the high-spin state was observed to decrease while approaching the extreme of the cold deformed fission and it was interpreted as clear-cut evidence for the thermal excitation of single particle states with high spin. Bonneau et al. investigated the influence of the scission configuration on the fission-fragment spins [82]. They examined microscopically the generation of finite angular momenta in the fragments. The outcome of this study is that the bulk of the fission-fragment spins can be attributed primarily to quantal, rather than to thermal, fluctuations. They made use of a relevant version of the Heisenberg uncertainty principle, applied to systems with somewhat fixed orientation, resulting in a finite average angular momentum. In this sense, it can be claimed that the orientation pumps angular momentum (orientationpumping mechanism) to the system. Relatively recently, the importance of the quantum-mechanical uncertainty of the orbital angular momentum of the fragments, which often is implied to be zero and consequently in conflict with the uncertainty principle, was highlighted by Kadmensky et al. [83, 84]. They assumed that the fluctuation of the orbital angular momentum is the true origin of the angular momentum of the fission fragments and that the latter is compensated by the fragment s spin. 18

41 So far, all the aforementioned models concerned mainly low energy or spontaneous fission. Unfortunately, relevant studies for high energy fission rarely exist. Cuninghame et al. experimentally determined the isomer ratios in Sb and Br fission fragments at high energies [85]. According to the authors, for this case additional contributions are expected to the acquisition of the angular momentum of the fission fragments. Extra unpaired nucleons are expected to exist even at the saddle point of the highly excited fissioning nucleus. In addition, excited collective modes are predicted, in which the two nascent fragments move relative to each other. As can be understood from the above discussion, although the list is far from complete, it is difficult to achieve a quantitative and universally reliable prediction about the angular momentum distribution of the fission fragments, before having a complete picture of the dynamic evolution of the fragments during their descent from saddle to scission point. The question about the stage at which the relevant observables reflect frozen conditions seems still open and subject to interpretation. 1.7 Angular momentum derivation of the fission fragments So far, there is no direct way of measuring the distribution of the angular momentum of the primary fission fragments. Thus, it can only be inferred by measurements of other fission observables. The experimental techniques that can be employed for such derivation comprise measurements of: (i) the angular distribution of prompt γ rays from the fission fragments [74, 86 88]. (ii) energy and multiplicity of prompt γ rays [89 92]. (iii) isomeric yield ratios [50 62]. (iv) the intensities of the cascade transitions to the ground state of the rotational bands [2, 93]. Method (i) has been employed for thermal neutron-induced fission of actinides and spontaneous fission and provide a mass-averaged value for the angular momentum of the fragment. Method (ii) has been used in both low- and medium-energy fission and can give an estimate of the angular momentum of each fragment for a given mass split. However, such methods face challenges to perform a one-to-one correspondence between the secondary γ-ray emission and the scission configuration, considering the de-excitation scheme of the primary fragments, which was mentioned in Sec The issue arise from the competition between the emission of neutron and γ rays around the neutron separation energy. Thus, it is difficult to sort out if the observed γ ray originates from the secondary fragment, i.e. after neutron emission, or from the primary fragment. 19

42 Method (iii) can be employed for estimation of average quantities of the angular momentum distribution of any fragment. As a first step in these approaches, an initial distribution of the angular momentum for each fragment is assumed. The parametrization of this function is performed in a way so that it can take into consideration the moment of inertia and the temperature of the fragment. In fact, these factors appear through the width of the distribution, usually called B 2, which is proportional to the root-mean-square value of the angular momentum distribution (J rms ). This is the quantity which is usually reported in such studies. A combined neutron/γ-ray de-excitation model is employed, similar to the one proposed by Huizenga and Vandenbosch [94,95]. In the last step, a fit of the parameter B 2 is performed in order to have a ratio of the spin population that agrees with the experimentally determined isomeric yield ratio. In our methodology, similar assumptions have been employed, but the de-excitation of the primary fission fragments was handled by the nuclear reaction code TALYS [26], as will be described in detail in chapter 6. Wilhelmy et al., in method (iv), followed a similar approach to the aforementioned one, but replaced the isomeric yield ratios by the experimentally determined intensities of γ-ray transitions in the ground-state bands in eveneven fission products [2]. The behavior of the angular momentum with respect to the mass division is a debatable issue. The results based on the γ-ray multiplicities indicate that the angular momentum exhibit sawtooth behavior as a function of the fragment mass, similar to the pattern of neutron multiplicities [89]. On the other hand the results of the angular momentum, as derived based on measurements of isomeric yield ratios, do not indicate such a dependency [69]. Similarly, a sawtooth structure could not be observed in the work by Wilhelmy et al., who analyzed the γ-ray multiplicity data with the de-excitation code used for the isomer ratios. 20

43 2. Experimental facility & techniques Measure what can be measured, and make measurable what cannot be measured. Galileo Galilei The measurements for the experimental determination of isomeric yield ratios were performed at the IGISOL-JYFLTRAP facility at the Accelerator Laboratory of the University of Jyväskylä (JYFL). An overview of the facility is given in Sec The fission products were produced with the IGISOL technique, presented in Sec Afterwards, the secondary ion beam was transported either to the JYFLTRAP double Penning trap for the determination of the peak intensities with direct ion counting, or at the γ-ray spectroscopy station, where the β-decay products were measured. The ions motion in the Penning trap is presented in Sec In Secs. 2.4 and 2.5, we describe the two techniques that have been employed in JYFTRAP. 2.1 Overview of IGISOL-JYLTRAP facility The Ion Guide Isotope Separator On-Line (IGISOL) facility at the Accelerator Laboratory of the University of Jyväskylä (JYFL) has a long tradition of experiments with radioactive beams of short-lived nuclei, both on neutron-rich fission products, and neutron-deficient nuclei produced in light- and heavyion fusion reactions. Measurements of ground state properties, such as charge radii and masses, and decay spectroscopy have been covered in these experiments [67, 68]. The IGISOL technique based on isobaric mass separation is well suited for experiments to determine fission yields as it is a chemically indiscriminate method, in the sense that an ion beam of any element can be produced. Moreover, as it is a fast technique, measurements of short-lived nuclides can be accomplished [68]. Since 2003, IGISOL is coupled to the double Penning trap JYFLTRAP [96], which offers such a high resolution in mass that isomeric states can be separated. A mass resolving power (MRP) of the order of m/δm = 10 5 has routinely been achieved, which is enough to resolve excited nuclear states, separated from the ground state by a few hundreds of kev. In Fig. 2.1 a schematic overview of the IGISOL-JYFLTRAP facility is shown. The numbers correspond to the most important elements of the facility which will briefly be described in the following sections. 21

44 IGISOL JYFLTRAP Figure 2.1. Schematic overview of the IGISOL-JYFLTRAP experimental facility, at the University of Jyväskylä. The most important elements are enumerated as follows: (1) target position inside a gas filled ion guide, (2) sextupole ion guide (SPIG), (3) dipole magnet, (4) switchyard, (5) β-γ spectroscopy station, (6) radio frequency quadrupole (RFQ) cooler-buncher, (7) beam line to the laser spectroscopy setup, (8) double Penning trap (JYFLTRAP), (9) multichannel-plate (MCP) detector. 2.2 Fission products with the IGISOL technique In June 2010, the IGISOL facility closed down for a major upgrade, in order to be re-commissioned as IGISOL-4 in a new experimental hall. A new 30 MeV cyclotron (MCC30/15) was housed, with the possibility to accelerate protons (18-30 MeV) and deuterons (9-15 MeV) [97]. The MCC30/15 cyclotron is dedicated for use only at the IGISOL-4 beam line. However, in the current measurements the 25-MeV primary proton beam was produced by the K130 cyclotron, which serves the entire JYFL-accelerator laboratory, with currents ranging from 1 up to 10 µa. In fission-related experiments, the charged particle beam, denoted with the blue arrow in Fig. 2.1 impinges on a fissile target, which is mounted in a fission ion guide filled with buffer gas (1). The small thickness of the target, 14 mg/cm 2 and 15 mg/cm 2 for 232 Th and nat U respectively, is one of the key features of the IGISOL technique, as a significant fraction of the products has enough kinetic energy to escape from the target [68, 98, 99]. The highly ionized products stop in the helium buffer gas, while their charge state changes continuously via charge exchange processes with the gas atoms [72,100]. After a rapid lowering of the charge state, a significant fraction of the products remains in the +1 state, due to the high ionization potential of the buffer gas. Eventually, the ions are guided out of the ion guide with the gas flow. The helium gas is removed from the vacuum system by a differential pumping system, and the ions are guided by a sextupole ion guide (SPIG) (2) [101] and electrostatically accelerated to 30q kev (where q is the charge state of the ions, usually q=1) towards a dipole magnet (3). The dipole magnet (MRP 500) is used to separate the isobaric chain of interest based on the mass-to-charge ratio (m/q). The continuous, mass-separated beam is directed either to the β-γ spectroscopy station (5) or the linear quadrupole radio-frequency cooler-buncher 22