Table Of ContentNuclear 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
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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
