Coupled Reaction Channels Calculations
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Original Proposal

 

Computer Program FRESCO

Nuclear Reactions for Astrophysics

Table of Contents

Preface page vii
Sources of quotations x
Acknowledgements xi
1 Nuclei in the Cosmos 1
1.1 Nuclei 1
1.2 Primordial nucleosynthesis 5
1.3 Reactions in light stars 9
1.4 Heavy stars 17
1.5 Explosive production mechanisms 20
1.6 Outlook 26
2 Reactions of nuclei 28
2.1 Kinds of states and reactions 28
2.2 Time and energy scales 31
2.3 Collisions 34
2.4 Cross sections 42
3 Scattering theory 48
3.1 Elastic scattering from spherical potentials 48
3.2 Multi-channel scattering 74
3.3 Integral forms 89
3.4 Identical particles 102
3.5 Electromagnetic channels 110
4 Reaction mechanisms 125
4.1 Optical potentials 125
4.2 Single-nucleon binding potentials 129
4.3 Coupling potentials 133
4.4 Inelastic couplings 137
4.5 Particle rearrangements 145
4.6 Isospin transitions 154
4.7 Photo-nuclear couplings 157
5 Connecting structure with reactions 168
5.1 Summary of structure models 168
5.2 Folded potentials 181
5.3 Overlap functions 185
5.4 General matrix elements 190
6 Solving the equations 194
6.1 Elastic scattering 194
6.2 Classifications 196
6.3 Multi-channel equations 198
6.4 Multi-channel bound states 208
6.5 R-matrix methods 211
6.6 Coupled asymptotic wave functions 219
7 Approximate solutions 222
7.1 Few-body adiabatic scattering 222
7.2 Eikonal methods 230
7.3 First-order semiclassical approximation 237
7.4 WKB approximation 240
8 Breakup 247
8.1 Three-body wave equations 247
8.2 Continuum Discretized Coupled Channel method 252
8.3 Other breakup measures and methods 263
9 Three-body nuclei 266
9.1 Definitions of halo and deeply bound states 266
9.2 Three-body models for bound states 268
9.3 Three-body continuum 276
9.4 Reactions with three-body projectiles 278
10 R-matrix phenomenology 288
10.1 R-matrix parameters 288
10.2 Single-channel R matrix 289
10.3 Coupled-channels R matrix 297
10.4 Combining direct and resonant contributions 303
11 Compound-nucleus averaging 306
11.1 Compound-nucleus phenomena 306
11.2 Approximations neglecting interference 309
11.3 Hauser-Feshbach models 311
11.4 Level densities 319
11.5 Average amplitudes and the optical model 321
12 Stellar reaction rates and networks 332
12.1 Thermal averaging 332
12.2 Reaction networks 342
12.3 Equilibria 345
12.4 Sensitivities to nuclear data 351
13 Connection to experiments 355
13.1 New accelerators and their methods 355
13.2 Detection 359
13.3 Direct measurements 364
14 Spectroscopy 370
14.1 Transfer spectroscopy 370
14.2 Knockout spectroscopy 381
14.3 Inelastic spectroscopy 385
14.4 Breakup spectroscopy 386
14.5 Charge-exchange spectroscopy 389
15 Fitting data 394
15.1 χ2 measures 394
15.2 Fitting cross-section harmonic multipoles 400
15.3 Fitting optical potentials 401
15.4 Multi-channel fitting 402
15.5 Searching 405
 

Appendices
Appendix A Symbols 410
Appendix B Getting started with FRESCO 423
Select bibliography 444
Index 446

Note that these are page numbers in the latex pages, not the printed version.