Selected Works of Hans A. Bethe: With Commentary (World Scientific Series in 20th Century Physics)

Hans Bethe received the Nobel Prize for Physics in 1967 for his work on the production of energy in stars. He helped to shape classical physics into quantum physics and increase the understanding of the atomic processes responsible for the properties of matter and of the forces governing the structures of atomic nuclei. This collection of papers by Hans Bethe dates from 1928, when he received his PhD, to the present. 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 Hans A Bethe received the Nobel Prize for Physics in 1967 for his work on the production of energy in stars. A living legend among the physics community, he helped to shape classical physics into quantum physics and increased the understanding of the atomic processes responsible for the properties of matter and of the forces governing the structures of atomic nuclei.This collection of papers by Prof Bethe dates from 1928, when he received his PhD, to now. It covers several areas and reflects the many contributions in research and discovery made by one of the most important and eminent physicists of all time. Special commentaries have been written by Prof Bethe to complement the selected papers.