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  • FACULTY OF SCIENCE

    UNIVERSITY OF AARHUS

    N ikolaj Thom

    as Zinner: N uclear R

    eactions for N uclear A

    strophysics D

    issertation 2007

    October 2007

    Weak Interactions and Fission in Stellar Nucleosynthesis

    Dissertation for the degree of Doctor of Philosophy

    Nikolaj Thomas Zinner Department of Physics and Astronomy

    Nuclear Reactions for Nuclear Astrophysics

  • 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: zinner@phys.au.dk

    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 für Schwerionenforschung (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 se

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