Selected works of Hans A. Bethe: with commentary

CONTENTS......Page 8
Preface......Page 6
 § 1. Introduction......Page 15
§ 2. Outline of the Solution......Page 18
§ 3. Holohedral and Hemihedral Symmetry......Page 20
§ 4. Cubic - HolohedraI Symmetry ( e.g., NaCl, Ca in CaF2)......Page 22
§ 5. Hexagonal, Tetragonal , and Rhombic (Holohedral) Symmetries......Page 25
§ 6. Orientation\'of a Half-Integral Angular Momentum in the Crystal. Double Valued Group Representations......Page 29
§ 7. The Tetragonal Double Group......Page 30
§ 8. Double - Valued Representations of the Hexagonal and Cubic Symmetry Groups......Page 33
§ 9. Eigenfunction of an Atom with Several Electrons......Page 35
§ 10. Zeroth - Order Eigenfunctions for an Uncoupled Electron in the Crystal......Page 37
§ 11. Elgenfunctions for Tetragonal and Hexagonal Symmetry......Page 39
§ 12. Eigenfunctions for Cubic (- Holohedral ) Symmetry......Page 42
§ 13. Connection between the Splitting-Up of Terms and the Interpretation of Spherical Harmonics as Potentials of Multipoles......Page 45
§ 14. The Angular Distribution of the Electron Density in a Strong CrystallineField......Page 47
§ 15. Interaction of Electrons of Different Shells as Oriented in the Crystal......Page 50
§ 16. Interaction of Oriented Electrons of the Same Shell......Page 54
§ 17 Interaction between Orbital Angular Momentum and Spin......Page 57
§ 18. General Formula for the Term of an Electron in an Ionic Crystal......Page 59
§ 19. Expansion of Squares and Products of Spherical Harmonics in Terms of Spherical Harmonics......Page 65
§ 20. The Derivatives of the Lattice Potential......Page 69
§ 21. The Splitting Pattern for Cubic Symmetry......Page 72
§ 22. The Splitting Pattern for Tetragonal Symmetry. Measure of the \"Tetragonality\"......Page 75
§ 23. Prospects for Applications of the Theory......Page 83
The Electron Affinity of Hydrogen......Page 84
1. Introduction......Page 91
2. Notation......Page 94
3. General Scattering Formula......Page 96
4. Energy Relationships......Page 99
5. Collisions and X- Ray Scattering......Page 103
6. Evaluation of the Matrix Elements......Page 105
7. Collisions at a Definite Angle......Page 111
8. Generalized f-Sum Rule......Page 115
9. Excitation of Certain Energy Levels......Page 117
10. Total Number of Collisions and Deceleration......Page 120
11. f-Sum Rules......Page 124
12. Deceleration......Page 129
13. Comparison of the Stopping Cross Section with EarIier Theories and with Observation......Page 133
14. Excitation of Optical Levels......Page 139
15. Excitation of X-Ray Levels......Page 141
16. Angular Distribution of Elastic Collisions......Page 145
17. Angular Distribution of Inelastic Scattering......Page 149
18. Primary Ionization......Page 151
19. Secondary Ionization......Page 156
20. Summary of the Results......Page 158
Literature Cited......Page 162
On the Theory of Metals, I. Eigenvalues and Eigenfunctions of a Linear Chain of Atoms......Page 166
On the Quantum Theory of the Temperature of Absolute Zero......Page 196
\"Correction\"......Page 197
On the Stopping of Fast Particles and on the Creation of Positive Electrons......Page 198
Introduction......Page 200
§ 1. The Cross-section for the Energy-loss by Radiation......Page 201
§ 2. Creation of Positive Electrons......Page 205
§ 3. Effect of Screening......Page 207
§ 4. Radiation Probability as Function of Impact Parameter......Page 211
§ 5. The Radiation Emitted by Fast Electrons......Page 213
§ 6. Energy Loss of Fast Electrons by Radiation......Page 215
§ 7. Comparison with Experiment. Limits of the Quantum Theory......Page 220
1. Energy Distribution......Page 223
3. Total Cross-section......Page 225
4. Absorption Coefficient for Light of Short Wave-length......Page 228
Summary......Page 229
The \"Neutrino\"......Page 230
Quantum Theory of the Diplon......Page 234
1-INTRODUCTION......Page 235
2-WAVE EQUATION FOR H2......Page 236
3-ABSORPTION OF ϒ-RAYS BY DIPLONS......Page 238
4-CAPTURE OF NEUTRONS BY PROTONS......Page 240
6-DISINTEGRATION OF DIPLONS UNDER ELECTRON BOMBARDMENT......Page 242
7-LIMITATIONS OF THE EMPLOYED MODEL......Page 244
SUMMARY......Page 245
The Scattering of Neutrons by Protons......Page 246
SUMMARY......Page 253
Statistical Theory of Superlattices......Page 256
1-INTRODUCTION. ANALOGY TO FERROMAGNETISM......Page 258
2-ORDER AT LARGE AND SMALL DISTANCES. INFLUENCE OF THE NUMBER OF DIMENSIONS......Page 259
3-DEFINITION OF THE TWO DEGREES OF ORDER......Page 261
4-QUALITATIVE DISCUSSION OF THE TRANSITION POINT......Page 262
5-APPROXIMATION FOR VANISHING LONG-DISTANCE ORDER......Page 264
6-FIRST APPROXIMATION INCLUDING LONG-DISTANCE ORDER......Page 268
8-SECOND APPROXIMATION......Page 273
9-RESULTS......Page 277
SUMMARY......Page 280
Theory of Bremsstrahlung and Pair Production. I. Differential Cross Section......Page 282
I. INTRODUCTION AND GENERAL DESCRIPTION OF METHOD......Page 283
II. WAVE FUNCTION......Page 285
III. COMPARISON OF THE WAVE FUNCTION WITH THE SOLUTION IN RADIAL WAVES......Page 286
IV. THE MATRIX ELEMENT IN BREMSSTRAHLUNG......Page 288
VI. EVALUATION OF THE PAIR MATRIX ELEMENT AND CROSS SECTION......Page 290
VII. SMALL-ANGLE APPROXIMATION......Page 293
VIII. THE CROSS SECTION FOR BREMSSTRAHLUNG......Page 294
(a) General......Page 296
(b) The Order of Magnitude of I1 and I2......Page 297
(d) Other Contributions......Page 298
X. ESTIMATE OF ERROR......Page 299
Masses of Light Atoms from Transmutation Data......Page 300
The Maximum Energy Obtainable from the Cyclotron......Page 304
Deviations from Thermal Equilibrium in Shock Waves......Page 306
Contents......Page 309
SUMMARY......Page 311
NOTATION......Page 315
SUBSCRIPTS......Page 316
Par. 1. The Energy Content of Gases......Page 317
Tables......Page 325
Specific Heat......Page 327
A. Translation and Rotation......Page 330
Theory......Page 332
Influence of foreign gases, experimental difficulties......Page 337
Excitation and De-excitation......Page 339
Evaluation of Experiments......Page 341
Experimental Results......Page 342
Several Degrees of Freedom......Page 344
C. Dissociation......Page 346
Vibrations......Page 348
Dissociation......Page 355
The Formation of Deuterons by Proton Combination......Page 358
§1. INTRODUCTION......Page 359
§2. THE PROBABILITY OF POSITRON EMISSION......Page 360
§3. THE COLLISION CROSS SECTION......Page 361
§5. RESULT......Page 364
Energy Production in Stars......Page 366
§1. INTRODUCTION......Page 367
§2. FORMULA FOR ENERGY PRODUCTION......Page 368
H4 and Li4......Page 370
Be7......Page 371
§4. REACTION RATES AT 2 .107 DEGREES......Page 372
§5. THE REACTIONS FOLLOWING PROTON COMBINATION......Page 374
Assumption A: Li4 stable......Page 375
Assumption B: Li4 unstable,He2 more stable than H3......Page 376
§6. TRIPLE COLLISIONS OF ALPHA-PARTICLES......Page 377
Reactions of B9......Page 378
§7. THE CARBON-NITROGEN GROUP......Page 379
§8. REACTIONS WITH HEAVIER NUCLEI......Page 381
§9. AGREEMENT WITH OBSERVATIONS......Page 382
§10. THE MASS-LUMINOSITY RELATION......Page 384
Assumption A : Li4 stable......Page 387
§12. STELLAR  EVOLUTION......Page 388
Energy Production in Stars......Page 390
HISTORY......Page 391
PROPERTY OF STARS......Page 392
THERMONUCLEAR REACTIONS......Page 395
NUCLEAR REACTIONS IN MAIN SEQUENCE STARS......Page 396
EXPERIMENTAL RESULTS......Page 397
THE COMPLETION OF THE PROTON-PROTON CHAIN......Page 400
EVOLUTION OF A STAR......Page 401
BUILDUP AND DISPERSAL OF ELEMENTS......Page 405
REFERENCES......Page 406
The Electromagnetic Shift of Energy Levels......Page 408
Theory of the Effective Range in Nuclear Scattering......Page 412
I. INTRODUCTION......Page 413
II. NEUTRON-PROTON SCATTERING, EFFECTIVE RANGE......Page 414
III. DETERMINATION OF RANGE FROM PARA-HYDROGEN SCATTERING......Page 415
IV. ENERGY DEPENDENCE OF EFFECTIVE RANGE......Page 417
V. PROTON-PROTON SCATTERING : THEORY......Page 418
VI. ANALYSIS OF PROTON-PROTON SCATTERING EXPERIMENTS......Page 421
VII. COMPARISON OF PROTON-PROTON AND NEUTRON-PROTON SCATTERING......Page 422
VIII. ACKNOWLEDGMENTS......Page 425
Nuclear Many-Body Problem......Page 426
I. INTRODUCTION......Page 427
II. DEFINITION OF SELF-CONSISTENT FIELD......Page 430
III. REACTION MATRIX......Page 432
IV. CONCERNING THE PROOF OF THE METHOD......Page 434
V. DISCUSSION AND COMPARISON WITH THE HARTREE-FOCK METHOD......Page 437
VI. ACTUAL AND MODEL WAVE FUNCTIONS......Page 438
VII. DEFINITION OF THE MATRICES Ḡ AND I......Page 440
VIII. SPIN CONSIDERATIONS......Page 441
IX. INFINITE NUCLEUS......Page 443
X. EXCLUSION PRINCIPLE......Page 446
XI. INTERACTION IN S STATES ONLY......Page 449
XII. CLUSTER TERMS......Page 452
XIII. THE DEPENDENCE ON THE MASS NUMBER A......Page 456
XIV. TERMS OF ORDER 1/A......Page 457
XV. TERMS NOT CONSERVING MOMENTUM......Page 458
XVI. PROBLEMS FOR A FINITE NUCLEUS......Page 459
APPENDIX. SPIN CONSIDERATIONS FOR THREE-PARTICLE CLUSTER TERMS......Page 463
Effect of a Repulsive Core in the Theory of Complex Nuclei......Page 466
1. INTRODUCTION......Page 467
2. DERIVATION OF THE SCHRÖDINOER EQUATION......Page 468
3. EQUATION FOR S STATES......Page 472
4. REPULSIVE CORE ONLY......Page 473
5. ATTRACTIVE POTENTIAL......Page 477
6. EFFECTIVE MASS......Page 479
REFERENCES......Page 483
Neutron Star Matter......Page 484
1. Introduction......Page 485
2. Equilibrium conditions......Page 489
3. Nuclear matter energy......Page 493
4. Nuclear surface energy......Page 500
Neutron Star Models with Realistic High-Density Equations of State......Page 502
I. ASTROPHYSICAL CONSIDERATIONS......Page 503
II. EQUATION OF STATE......Page 504
III. CALCULATIONS......Page 506
IV. RESULTS AND DISCUSSION......Page 507
REFERENCES......Page 509
Equation of State in the Gravitational Collapse of Stars......Page 512
1. Introduction......Page 513
2. Electron fraction, energy and entropy......Page 516
3. Electron capture rate......Page 522
4. Neutrino trapping......Page 529
5. Entropy of nuclei and of nuclear matter......Page 531
6. Equation of state during collapse......Page 533
7. Densities above nuclear density......Page 539
NUCLEAR SYMMETRY ENERGIES......Page 543
SHELL-MODEL DESCRIPTION OF ELECTRON CAPTURE......Page 545
DIFFUSION OF NEUTRINOS......Page 549
TRAPPING CRITERION......Page 551
DISSOCIATION OF NEUTRON-RICH NUCLEI......Page 553
ELECTRON NUMBERS, ENTROPIES AND TEMPERATURES, AS FUNCTIONS OF DENSITY ρ......Page 555
References......Page 558
Equation of State of a Very Hot Gas of Electrons and Neutrinos......Page 560
APPENDIX......Page 561
REFERENCES......Page 565
SN 1987A: An Empirical and Analytic Approach......Page 566
2. THE NEUTRINO OBSERVATIONS......Page 567
3. CONVECTION AND ACCRETION......Page 568
4. THE GAIN RADIUS......Page 569
5. TEMPERATURE DISTRIBUTION......Page 570
7. DETERMINATION OF THE GAIN RADIUS......Page 571
8. ENERGY SUPPLY......Page 572
10. COLLISIONS BETWEEN NEUTRINOS AND ELECTRONS......Page 573
12. START OF THE SHOCK......Page 574
13. THE SHOCK......Page 575
14. OPEN QUESTIONS......Page 576
REFERENCES......Page 577
The Supernova Shock......Page 578
1. INTRODUCTION......Page 579
3. SHAPE OF THE SHOCK......Page 580
4. DENSITY......Page 581
5. NEUTRINO HEATING......Page 582
6. VIRIAL THEOREM......Page 583
7. THE RUNNING SHOCK......Page 584
9. NUCLEOSYNTHESIS......Page 585
12. DISSOCIATION ENERGY......Page 586
16. Yℯ IN THE NUCLEOSYNTHESIS REGION......Page 587
17. CONCLUSIONS......Page 588
CALCULATION OF η......Page 589
ENTROPY AT THE H-He INTERFACE......Page 590
REFERENCES......Page 591
Breakout of the Supernova Shock......Page 592
2. SAHA......Page 593
4. ENERGY......Page 594
REFERENCES......Page 595
List of Publications......Page 596