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Nuclear Reactions for Nuclear Astrophysics Weak Interactions and Fission in Stellar Nucleosynthesis

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Nuclear Reactions for Nuclear Astrophysics Weak Interactions and Fission in Stellar Nucleosynthesis FACULTY OF SCIENCE UNIVERSITY OF AARHUS Nikolaj Thomas Zinner: Nuclear Reactions for Astrophysics Nuclear Reactions for Nuclear Astrophysics Weak Interactions and Fission in Stellar Nucleosynthesis Dissertation for the degree of Doctor of Philosophy Dissertation 2007 Nikolaj Thomas Zinner Department of Physics and Astronomy October 2007 Nuclear Reactions for Nuclear Astrophysics Weak Interactions and Fission in Stellar Nucleosynthesis Nikolaj Thomas Zinner Department of Physics and Astronomy University of Aarhus Dissertation for the degree of Doctor of Philosophy October 2007 @2007 Nikolaj Thomas Zinner 2nd Edition, October 2007 Department of Physics and Astronomy University of Aarhus Ny Munkegade, Bld. 1520 DK-8000 Aarhus C Denmark Phone: +45 8942 1111 Fax: +45 8612 0740 Email: [email protected] Cover Image: The evolution of the Universe from the Big Bang to the emer- gence of complex chemistry and Life. Printed by Reprocenter, Faculty of Science, University of Aarhus. This dissertation has been submitted to the Faculty of Science at the univer- sity of Aarhus in Denmark, in partial fulfillment of the requirements for the PhD degree in physics. The work presented has been performed under the supervision of Prof. Karlheinz Langanke. The work was mainly carried out at the Department of Physics and Astronomy in Aarhus. Numerous short- term visits to Gesellschaft f¨urSchwerionenforschung (GSI) in Darmstadt, Germany from 2005 to 2007 have been very fruitful toward the comple- tion of the thesis. The European Center for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) in Trento, Italy is also acknowledged for its hospitality during the summer of 2004. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact. Mark Twain (1835 - 1910) Contents Outline vii Acknowledgements viii List of Publications ix 1 Introduction 1 1.1 Children of the Stars . 1 1.2 Stellar Evolution and Supernovae . 2 1.3 Physics of Core-collapse Supernovae . 3 1.4 Nucleosynthesis . 5 1.5 Angle of this Thesis Work . 9 2 Theoretical Nuclear Models 10 2.1 Weak Interactions . 10 2.1.1 Weak Interactions in Nuclei . 12 2.1.2 Cross Sections and Rates . 15 2.2 Nuclear Structure Modeling . 19 2.2.1 Independent Particle Model . 21 2.2.2 Random Phase Approximation . 25 2.2.3 Reduction of Transition Operators . 37 2.2.4 Ground State and Model Space Considerations . 41 2.2.5 Excitation Spectra Examples . 42 2.2.6 Neutrino and Antineutrino Cross Section Comparison 44 2.3 Nuclear Decay Model . 46 2.3.1 Particle Decay Rates and Fission . 47 2.3.2 Fission Fragments . 50 2.3.3 The Dynamical Code ABLA . 52 2.4 Unified Nuclear Model . 53 2.4.1 Energy Mesh . 55 2.4.2 Monte Carlo and Statistics . 56 2.4.3 Neutrino Spectra and Folding . 57 2.4.4 Anisotropy and Exotica . 60 iv 3 Muon Capture 63 3.1 Introduction . 63 3.1.1 Previous Studies . 64 3.2 The Relativistic Muon . 67 3.2.1 The Leptonic Current . 68 3.2.2 The Non-Relativistic Limit . 72 3.2.3 The Relativistic Rate Formula . 74 3.3 Quenching of Multipoles . 87 3.4 The Residual Interaction . 88 3.5 Results and Discussion . 89 3.6 Concluding Remarks . 92 4 Neutrinos and Proton-Rich Ejecta 95 4.1 Introduction . 95 4.2 Neutrino Reactions on Matter . 96 4.3 Hydrodynamical Simulation . 97 4.4 Network and Neutrinos . 99 4.5 νp-process Nucleosynthesis . 101 5 Neutrinos and the r-process 107 5.1 r-process Nucleosynthesis . 107 5.1.1 General Conditions . 107 5.1.2 The Neutrino-driven Wind . 108 5.2 UMP Stars and Neutrino-induced Fission . 111 5.3 Neutrino-induced Fission on r-process Nuclei . 113 5.3.1 Initial Uranium Calculations . 114 5.3.2 r-process Nuclei . 118 5.3.3 Preliminary Conclusions . 125 6 Fission and the r-process 127 6.1 Introduction . 127 6.2 Nuclear Physics Input . 127 6.2.1 β-delayed Fission . 128 6.2.2 Neutron-induced and Spontaneous Fission . 130 6.2.3 Fragment Distributions . 131 6.3 r-process Simulation Model . 133 6.4 Results . 134 6.4.1 The Region and Role of Fission . 134 6.4.2 The N = 184 Shell and Half lives . 138 6.4.3 The N = 82 Shell Closure . 139 6.4.4 Fission and Neutrinos . 141 6.5 Nuclear Data Consistence . 142 6.6 Concluding Remarks . 143 v 7 Summary and Outlook 145 7.1 Outlook - Nuclear Physics . 146 7.2 Outlook - Nuclear Astrophysics . 148 A Formalism and Conventions 150 A.1 Units and Definitions . 150 A.2 Angular Momentum Coupling and Spherical Functions . 151 A.3 Spherical Dirac Equation . 154 B Neutrino Capture Rate Formula 155 C Nucleosynthesis and Entropy 157 Bibliography 159 vi Outline This thesis describes theoretical nuclear physics calculations for the pur- pose of expanding and improving the nuclear data input used in stellar nucleosynthesis modeling. In particular, the neutrino capture and β-decay weak interactions on a broad range of nuclei are considered. The decay of the daughter states resulting from the mentioned reactions are treated in a statistical model. The latter includes both particle emission and fis- sion channels and provides fragments distributions for the fissioning nuclei based on a semi-empirical approach that agrees well with experimental data. These distributions have subsequently been implemented in simulations of the astrophysical r-process which is responsible for producing about half the heavy elements observed in nature. The neutrino capture processes on nuclei are also implemented in astrophysical modeling of ejected material from exploding stars. Here it is found that an entirely new nucleosynthe- sis process operates. It requires the abundances of antineutrinos and can produce many of the rare proton-rich elements whose origin is generally considered unknown. The nuclear physics results presented in the thesis are for reactions where very little experimental information is available. To en- sure that the theoretical model used is not at odds with existing knowledge we have therefore also calculated total muon capture rates within the same framework. The capture rates have been measured in many nuclei across the nuclear chart and therefore provide a good benchmark to test the model against. In chapter one we give an introduction to the Supernova environment which is the likely candidate site for the nucleosynthesis considered in later chapters. Chapter two introduces and describes the nuclear structure and statistical decay models that have been used in the calculations. Muon cap- ture on nuclei is described in chapter three, including novel correction terms for relativistic effects that can influence the capture rate in heavy nuclei. Chapter four discusses the inclusion of neutrino and antineutrino reactions on nucleons and nuclei in nucleosynthesis calculations of early proton-rich ejecta from core-collapse Supernovae. In chapter five we discuss neutrino reactions in the r-process with particular emphasis on the role of neutrino- induced fission and neutron emission. Chapter six presents and discusses results from fully dynamical r-process simulations with all relevant fission channels and realistic fragment distributions included. Conclusions and out- look are given in chapter seven. In the second edition (October 2007) misprints have been corrected and some statements have been clarified. vii Acknowledgements I would like to thank my adviser Karlheinz Langanke for proposing an inter- esting thesis project and for his continuous support and enthusiasm toward it. I am grateful to him for expanding my knowledge of physics, both from the academic point of view but surely also from a human perspective. Al- though most of his advise has proven invaluable there is one subject on which I strayed. Karlheinz once told me that I would never be able to finish a thesis without drinking coffee (as of this time I still do not drink it). I wish to warmly thank Gabriel Mart´ınez-Pinedo for his advise on nu- cleosynthesis issues discussed in this thesis and for providing the network calculations presented. I wish to thank Carla Fr¨ohlich, Darko Mocelj, and F.-K. Thielemann in Basel for making our collaborations both pleasant and fruitful, and for taking care of me during my visit in early 2004. I warmly thank Petr Vogel from the California Institute of Technology for suggestions and discussions on muon capture and for a continued interest in its development. Furthermore, I owe a debt of gratitude to Aleksandra K´elicand K.-H. Schmidt for providing us with the ABLA code and for their help during its implementation. Thanks also goes to Ivan Borzov for various discussion on nuclear structure details. Thanks goes to Hans Fynbo for reading the draft version and correcting a host of trivial and non-trivial mistakes. I wish to thank my friends and colleagues at the university in Aarhus for providing a comfortable and interesting environment to work in. The bar on Friday was always fun. I also give many thanks to TAGEKAMMERET˚ and FC Nordbyen 1993 for providing the needed break from studies whenever necessary. I have many friends outside these places that have also been invaluable during the work, in particular Peter Busch Christiansen always provided comic relief and friendship in Vestervang for most of my life. I hope he will continue to do so in the future. Lastly I want to thank my family for putting up with my dreadful sched- ule and continuous canceling of various events during the past years. You have always provided comfort and support during the brief periods I have actually been away from the university. Thanks to my mother, Inge Zinner, to whom my debt can never be repaid. Always remember that I am, and always was, first and foremost Your son.
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