The Physics of the Manhattan Project (eBook)

The Physics of the Manhattan Project 3
Preface 7
References 10
Contents 11
Chapter 1: Energy Release in Nuclear Reactions, Neutrons, Fission, and Characteristics of Fission 15
1.1 Notational Conventions for Mass Excess and Q-Values 16
1.2 Rutherford and the Energy Release in Radium Decay 17
1.3 Rutherford´s First Artificial Nuclear Transmutation 19
1.4 Discovery of the Neutron 20
1.5 Artificially-Induced Radioactivity and the Path to Fission 28
1.6 Energy Release in Fission 33
1.7 The Bohr-Wheeler Theory of Fission: The $$ {{{{/bf Z^2}}} {/bf /left/ {A} /right.}} $$ Limit Against Spontaneous Fission 34
1.8 Energy Spectrum of Fission Neutrons 39
1.9 Leaping the Fission Barrier 41
1.10 A Semi-Empirical Look at the Fission Barrier 46
References 50
Chapter 2: Critical Mass and Efficiency 52
2.1 Neutron Mean Free Path 53
2.2 Critical Mass: Diffusion Theory 58
2.3 Effect of Tamper 64
2.4 Estimating Bomb Efficiency: Analytic 71
2.5 Estimating Bomb Efficiency: Numerical 79
2.5.1 A Simulation of the Hiroshima Little Boy Bomb 82
2.6 Another Look at Untamped Criticality: Just One Number 85
References 87
Chapter 3: Producing Fissile Material 88
3.1 Reactor Criticality 88
3.2 Neutron Thermalization 91
3.3 Plutonium Production 94
3.4 Electromagnetic Separation of Isotopes 97
3.5 Gaseous (Barrier) Diffusion 103
References 108
Chapter 4: Complicating Factors 110
4.1 Boron Contamination in Graphite 111
4.2 Spontaneous Fission of 240Pu, Predetonation, and Implosion 113
4.2.1 Little Boy Predetonation Probability 118
4.2.2 Fat Man Predetonation Probability 118
4.3 Tolerable Limits for Light-Element Impurities 121
References 125
Chapter 5: Miscellaneous Calculations 127
5.1 How Warm is It? 127
5.2 Brightness of the Trinity Explosion 128
5.3 Model for Trace Isotope Production in a Reactor 132
References 137
Chapter 6: Appendices 138
6.1 Appendix A: Selected Delta-Values and Fission Barriers 138
6.2 Appendix B: Densities, Cross-Sections and Secondary Neutron Numbers 139
6.2.1 Thermal Neutrons (0.0253eV) 139
6.2.2 Fast Neutrons (2MeV) 139
6.2.2.1 References 140
6.3 Appendix C: Energy and Momentum Conservation in a Two-Body Collision 140
6.4 Appendix D: Energy and Momentum Conservation in a Two-Body Collision that Produces a Gamma-Ray 143
6.5 Appendix E: Formal Derivation of the Bohr-Wheeler Spontaneous Fission Limit 145
6.5.1 E1: Introduction 145
6.5.2 E2: Nuclear Surface Profile and Volume 146
6.5.3 E3: The Area Integral 149
6.5.4 E4: The Coulomb Integral and the SF Limit 150
6.5.5 References 155
6.6 Appendix F: Average Neutron Escape Probability from Within a Sphere 155
6.7 Appendix G: The Neutron Diffusion Equation 157
6.7.1 References 165
6.8 Appendix H: Questions 165
6.9 Answers 172
6.10 Appendix I: Further Reading 173
6.10.1 General Works 174
6.10.2 Biographical and Autobiographical Works 175
6.10.3 Technical Works 177
6.10.4 Websites 178
6.11 Appendix J: Useful Constants and Conversion Factors 179
6.11.1 Rest Masses 179
Index 180