Nuclear Astrophysics A Course of Lectures (cid:1) Graduate students, researchers and amateur readers interested in nuclear astrophysics need fruitful understanding of the basic natural physical processes that occur at the heart of the stellar objects of the cosmos. In this volume the physics involved in various astrophysical processes like the synthesis of light and heavier elements, explosive burning processes, core collapse supernova etc have been critically addressed with minimum mathematical derivations so as to suit all faculties of the readers. For graduate students there are solved problems with exercises at the end of each chapter, for researchers some recent works on the calculation of physical parameters of astrophysical importance like the calculation of S-factors at low energies have been included, and for amateur readers there are lot of history, information and discussion on the astronuclear phenomenon. Dr. Md. A. Khan is Assistant Professor in the Department of Physics, Aliah University, Kolkata. He has received his Ph.D. degree in 2002 from the University of Calcutta. He has over fifteen years of teaching and research experience. His research interests are in the areas of Sub-barrier Fusion in Nuclear Astrophysics and structure of atoms and nuclei. He has published/presented nearly two dozens of papers in international journals and conferences. Nuclear Astrophysics- A Course of Lectures Dr. Md A Khan Department of Physics, Aliah University, New Town, Kolkata CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2018 by Levant Books CRC Press is an imprint of the Taylor & Francis Group, an informa business No claim to original U.S. Government works International Standard Book Number-13: 978-1-138-58816-5 (Hardback) Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. 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CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging in Publication Data A catalog record has been requested Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Preface Nuclear Astrophysics is being taught as a part of the Post Grad- uate Curriculum in Physics in majority of Indian Universities and Institutes. This book is largely based on the lectures delivered to postgraduate students in Physics of the Aliah University for the past few years. The materials are presented in some thirty odd lec- tures and I believe there is much in them for a good one semester course. However this work is intended for both the undergraduate and post graduate students interested in Nuclear Astrophysics, and also for a more general audience since no specific expertise in astronomy, physics and mathematics is required to fruitfully read majority of the text presented in this book. This book contains 11 chapters. The opening Chapter 1 started with a brief introduction to nuclear astrophysics followed by dis- cussion on elementary concepts of nuclear, particle and astro- physics. In chapter 2 nucleosynthesis and its different stages are discussed. Chapter 3 devoted in the description of the reaction cycles starting from hydrogen burning stages to s- and r-neutron processes. In chapter 4 an attempt has been made to explore the opportunities in nuclear astrophysics from both theoretical and experimental points of views. In chapter 5 explosive burning pro- cesses responsible for the nucleosynthesis of chemical elements are discussed. In chapter 6 the core collapse supernovae along with some relevant phenomenon have in explained. In chapter 7 the ba- sic components of r-processes such as - the role of nuclear physics in the r-process, required conditions for r-process, r-process sites, and neutron star mergers are discussed. Phenomenon like nova explosions, X-ray bursts including ideas of black hole and neutron stars are discussed in chapter 8 in the context of nuclear processes in explosive binary star systems. In chapter 9 elementary ideas of the formation of stars and galaxies are introduced. In chapter 10 computational aspects of nuclear astrophysics have been discussed in context of stellar structure and evolution, radiation transfer and some other relevant phenomenon’s. In chapter 11 an account of the major challenges and future prospects of nuclear astrophysics have been discussed. Important bibliographic references for fur- ther studies have been added at the end of each chapter. I am thankful to many of my students who have been attending my lectures and especially to Mahamadun Hassan who constantly insisted me to shape the material presented here. I also acknowl- edge my gratitude to Prof. J. Alam and Dr D N Basu of VECC Kolkata for extending their support by opening avenue for me to do research collaboration in Nuclear Astrophysics. Thanks are due to all my colleagues, friends and staff at the Aliah University for their support and encouragements. Last but not least, I would like to thank my wife, daughters Isra, Sara and son Rayyan for their patience and devotion. Finally I would like to thank the entire team and especially to Mr Millinda Dey of Sarat Book House, Kolkata for their effort to bring the materials in the present form. All suggestions and criticism for the improvement of this edition will be cordially received. May 9, 2016 New Town, Kolkata, India Dr Md Abdul Khan Contents 1 Basics of Nuclear Astrophysics 191 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 1.2 Nuclear Physics . . . . . . . . . . . . . . . . . . . . . . . . . . 1164 1.2.1 Branching of Radioactivity . . . . . . . . . . . . . . . 1175 1.2.2 Binding energy . . . . . . . . . . . . . . . . . . . . . . 1186 1.2.3 Nuclear Reactions . . . . . . . . . . . . . . . . . . . . 1219 1.2.4 Reaction Q-value . . . . . . . . . . . . . . . . . . . . . 2220 1.2.5 α decay . . . . . . . . . . . . . . . . . . . . . . . . . . 2231 1.2.6 β-decay and electron capture . . . . . . . . . . . . . . 2253 1.2.7 γ-decay . . . . . . . . . . . . . . . . . . . . . . . . . . 2275 1.2.8 Nuclear fusion . . . . . . . . . . . . . . . . . . . . . . 2286 1.2.9 The Coulomb barrier . . . . . . . . . . . . . . . . . . . 2298 1.2.10 Reaction rate in a medium . . . . . . . . . . . . . . . 3364 1.2.11 Compound nuclear hypothesis. . . . . . . . . . . . . . 3386 1.2.12 Breit-Wigners one-level formula . . . . . . . . . . . . . 3419 1.2.13 Cross-sections and their derivations . . . . . . . . . . 4420 1.3 Particle physics . . . . . . . . . . . . . . . . . . . . . . . . . . 4475 1.4 Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . 5408 1.5 Scopes of nuclear astrophysics . . . . . . . . . . . . . . . . . . 4519 2 Nucleosynthesis 5691 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5691 2.2 Primordial nucleosynthesis . . . . . . . . . . . . . . . . . . . . 6657 2.3 Stellar nucleosynthesis up to iron (A ≤ 60). . . . . . . . . . . 7713 2.4 Stellar nucleosynthesis beyond iron(A>60) . . . . . . . . . . . 7891 3 Sources of Energy in Stars 9913 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9913 3.2 Hydrogen burning and p-p (proton-proton) chain . . . . . . . 9935 7 8 CONTENTS 3.3 CNO Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9957 3.4 The Hot CNO Cycle and the Rapid Proton Process . . . . . . 19091 3.5 The Early rp–Process and Bottleneck Reactions. . . . . . . . 110023 4 3.6 Helium ( He) Burning . . . . . . . . . . . . . . . . . . . . . . 110035 3.7 The Triple-α Process . . . . . . . . . . . . . . . . . . . . . . . 110035 3.8 Heavier Element α-Burning . . . . . . . . . . . . . . . . . . . 110057 3.8.1 Neutron Production in (α,n) Reactions. . . . . . . . . 110057 3.9 The s and r-Neutron Processes. . . . . . . . . . . . . . . . . . 110057 4 Opportunities in Nuclear Astrophysics 111113 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111113 4.2 Thermonuclear rates and reaction networks . . . . . . . . . . 111124 4.2.1 Thermonuclear Reaction Rates . . . . . . . . . . . . . 111124 4.2.2 Nuclear Reaction Networks . . . . . . . . . . . . . . . 115 117 4.2.3 Burning Processes in Stellar Environments . . . . . . 117 119 4.3 Experimental Techniques in Nuclear Astrophysics . . . . . . . 120 122 4.3.1 Choice of Target . . . . . . . . . . . . . . . . . . . . . 120 123 4.3.2 Choice of detectors . . . . . . . . . . . . . . . . . . . . 121 127 4.3.3 Recoil separators . . . . . . . . . . . . . . . . . . . . . 125 128 4.3.4 Ground State Properties . . . . . . . . . . . . . . . . . 126 128 4.3.5 Resonances Properties . . . . . . . . . . . . . . . . . . 127 131 4.3.6 Transfer Reactions . . . . . . . . . . . . . . . . . . . . 129 4.4 Experimental Nuclear Astrophysics . . . . . . . . . . . . . . . 113302 4.4.1 Energy ranges for measurement of cross-sections . . . 113324 4.4.2 Radioactive Beams . . . . . . . . . . . . . . . . . . . . 113335 4.4.3 In-Flight Separators. . . . . . . . . . . . . . . . . . . . 113368 4.5 Cross Section Predictions and Reaction Rates . . . . . . . . . 113480 4.5.1 Thermonuclear Rates from Statistical Model Calcula- tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114402 4.5.2 Astrophysical S-factors of radiative capture reactions . 115502 4.5.3 Sub-barrierfusionandselectiveresonanttunnelingcross section . . . . . . . . . . . . . . . . . . . . . . . . . . . 115546 4.6 Weak-Interaction Rates . . . . . . . . . . . . . . . . . . . . . 116635 4.6.1 Electron Capture and β-Decay . . . . . . . . . . . . . 116646 4.6.2 Neutrino-Induced Reactions . . . . . . . . . . . . . . . 116679 5 Explosive Burning Processes 117757 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117757 5.2 Explosive H-Burning . . . . . . . . . . . . . . . . . . . . . . . 117779 5.3 Explosive He-Burning . . . . . . . . . . . . . . . . . . . . . . 118813 CONTENTS 9 5.4 Explosive C- and Ne-Burning . . . . . . . . . . . . . . . . . . 118835 5.5 Explosive O-Burning . . . . . . . . . . . . . . . . . . . . . . . 118835 5.6 Explosive Si-Burning . . . . . . . . . . . . . . . . . . . . . . . 118846 5.7 The r-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 118879 6 Core Collapse Supernovae 119913 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119913 6.2 General Scenario . . . . . . . . . . . . . . . . . . . . . . . . . 119968 6.3 Role of weak-Interaction rates in presupernova evolution . . . 129080 6.4 The Role of Electron Capture During Collapse . . . . . . . . 220002 6.5 Neutrino-Induced Processes During a Supernova Collapse . . 220068 6.6 Type II Supernovae Nucleosynthesis . . . . . . . . . . . . . . 220079 7 Basic Components of Astrophysical r-Process 221179 7.1 Role of Nuclear Physics in the r-process . . . . . . . . . . . . 221280 7.2 Parameters controlling the r-process . . . . . . . . . . . . . . 222213 7.3 r-Process Sites . . . . . . . . . . . . . . . . . . . . . . . . . . 222224 7.3.1 Type II Supernovae. . . . . . . . . . . . . . . . . . . . 222224 7.3.2 Neutron Star Mergers . . . . . . . . . . . . . . . . . . 222246 7.3.3 r-Process Overview . . . . . . . . . . . . . . . . . . . . 222246 8 Nuclear Processes in Explosive Binary Stars 222391 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222391 8.2 Nova Explosions . . . . . . . . . . . . . . . . . . . . . . . . . 223302 8.3 X-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . 223334 8.4 Thermonuclear Runaway. . . . . . . . . . . . . . . . . . . . . 223346 8.5 The rp-Process. . . . . . . . . . . . . . . . . . . . . . . . . . . 223379 8.6 X-Ray Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . 223491 8.7 Accretion Processes on Neutron Stars and Black holes . . . . 223491 9 Formation of stars and galaxies 224413 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224413 9.2 Life cycle of Stars . . . . . . . . . . . . . . . . . . . . . . . . . 224424 10 Role of Computation in Nuclear Astrophysics 225535 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225535 10.2 Computational versus Analytic Methods . . . . . . . . . . . . 225579 10.3 Major Areas of Application of CNA . . . . . . . . . . . . . . 225579 10.3.1 Stellar structure and evolution . . . . . . . . . . . . . 225680 10.3.2 Radiation transfer and stellar atmospheres . . . . . . 225680 10.3.3 Astrophysical fluid dynamics . . . . . . . . . . . . . . 225680