Contents
1 Energy Release in Nuclear Reactions, Neutrons, Fission,
and Characteristics of Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1 Notational Conventions for Mass Excess and Q-Values . . . . . . .
1
1.2 Rutherford and the Energy Release in Radium Decay . . . . . . . . .
3
1.3 Rutherford’s First Artificial Nuclear Transmutation . . . . . . . . . . .
5
1.4 Discovery of the Neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.5 Artificially-Induced Radioactivity and the Path to Fission . . . . . . 14
1.6 Energy Release in Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.7 The Bohr-Wheeler Theory of Fission: The Z
2 /A Limit
Against Spontaneous Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.8 Energy Spectrum of Fission Neutrons . . . . . . . . . . . . . . . . . . . . 26
1.9 Leaping the Fission Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.10 A Semi-empirical Look at the Fission Barrier . . . . . . . . . . . . . . . 35
1.11 A Numerical Model of the Fission Process . . . . . . . . . . . . . . . . . 39
1.12 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2 Critical Mass, Efficiency, and Yield . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1 Cross-Sections, Mean Free Path, and the Diffusion Equation . . . . 52
2.2 Critical Mass: Bare Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.3 Critical Mass: Tamped Core . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.4 Critical Mass: Tamped Composite Core . . . . . . . . . . . . . . . . . . . 76
2.5 Estimating Yield—Analytic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.6 Estimating Yield—Numerical . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.6.1 A Simulation of the Hiroshima Little Boy Bomb . . . . . . 95
2.7 History Lesson: Criticality Considered in 1939 . . . . . . . . . . . . . . 98
2.8 Criticality and Yield: Approximate Methods . . . . . . . . . . . . . . . . 102
2.8.1 Bare Critical Mass: Simplified Boundary Condition . . . . 102
2.8.2 Bare Critical Mass: An Even Simpler Approach . . . . . . . 102
xix
1 Energy Release in Nuclear Reactions, Neutrons, Fission,
and Characteristics of Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1 Notational Conventions for Mass Excess and Q-Values . . . . . . .
1
1.2 Rutherford and the Energy Release in Radium Decay . . . . . . . . .
3
1.3 Rutherford’s First Artificial Nuclear Transmutation . . . . . . . . . . .
5
1.4 Discovery of the Neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.5 Artificially-Induced Radioactivity and the Path to Fission . . . . . . 14
1.6 Energy Release in Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.7 The Bohr-Wheeler Theory of Fission: The Z
2 /A Limit
Against Spontaneous Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.8 Energy Spectrum of Fission Neutrons . . . . . . . . . . . . . . . . . . . . 26
1.9 Leaping the Fission Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.10 A Semi-empirical Look at the Fission Barrier . . . . . . . . . . . . . . . 35
1.11 A Numerical Model of the Fission Process . . . . . . . . . . . . . . . . . 39
1.12 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2 Critical Mass, Efficiency, and Yield . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1 Cross-Sections, Mean Free Path, and the Diffusion Equation . . . . 52
2.2 Critical Mass: Bare Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.3 Critical Mass: Tamped Core . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.4 Critical Mass: Tamped Composite Core . . . . . . . . . . . . . . . . . . . 76
2.5 Estimating Yield—Analytic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.6 Estimating Yield—Numerical . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.6.1 A Simulation of the Hiroshima Little Boy Bomb . . . . . . 95
2.7 History Lesson: Criticality Considered in 1939 . . . . . . . . . . . . . . 98
2.8 Criticality and Yield: Approximate Methods . . . . . . . . . . . . . . . . 102
2.8.1 Bare Critical Mass: Simplified Boundary Condition . . . . 102
2.8.2 Bare Critical Mass: An Even Simpler Approach . . . . . . . 102
xix