Theoretical Nuclear Physics

I. General Properties of the Nucleus.- 1. Introduction.- 2. Quantum States, Binding Energy, Binding Fraction.- 3. Stable and Unstable Nuclei, Fission, Alpha-Decay, Beta-Decay.- A. "Dynamical" Instability.- B. Beta-Radioactivity.- 4. Size of the Nuclei.- A. Scattering of High-Energy Neutrons by Nuclei.- B. The Yield of Nuclear Reactions Initiated by Protons or Alpha-Particles.- C. Alpha-Decay Lifetimes.- D. Maximum Energy of Some Beta-Rays.- 5. The Coulomb Barrier.- 6. Angular Momentum, Spin.- 7. Electric and Magnetic Moments.- A. Electric Moments.- B. Magnetic Moments.- 8. Statistics.- Symbols.- II. TWO-BODY PROBLEMS AT LOW ENERGIES.- 1. Introduction.- 2. The Ground State of the Deuteron; Simplified Discussion (Central Forces Assumed).- 3. Neutron-Proton Scattering.- A. Simple Theory.- B. Comparison with Experiment: The Spin Dependence of Nuclear Forces.- C. The Effect of Chemical Binding.- D. Coherent Scattering of Neutrons by Protons.- 4. Proton-Proton Scattering.- 5. The Tensor Force.- A. Experimental Discovery of the Existence of Non-central Forces.- B. General Form of the Non-central Force.- C. Properties of the Tensor Force.- D. The Ground State of the Deuteron: Dynamics.- E. The Ground State of the Deuteron: Quadrupole Moment.- F. The Ground State of the Deuteron: Magnetic Moment.- G. Neutron-Proton Scattering below 10 Mev.- Symbols.- III. Nuclear Forces.- 1. Introduction.- 2. Stability of a nucleus against Collapse. The Impossibility of Attractive Forces between All Pairs.- 3. Exchange Forces.- A. Qualitative Considerations.- B. Formal Definition of Exchange Forces.- 4. The Saturation Conditions.- A. The Comparison Theorem.- B. Saturation Conditions for Mixed Wigner and Majorana Forces.- C. The Complete Saturation Conditions for Central Forces.- D. Saturation Conditions for Tensor Forces.- 5. The Isotopic Spin Formalism.- Symbols.- IV. Two-Body Problems at High Energies.- 1. Introduction.- 2. Neutron-Proton Scattering at Energies between 10 and 30 Mev.- 3. Neutron-Proton Scattering at Energies Larger than 30 Mev.- 4. Proton-Proton Scattering.- Symbols.- V. Three- and Four-Body Problems.- 1. Introduction.- 2. The Ground State of the Triton; Central Forces.- 3. The Ground State of the Alpha-Particle; Central Forces.- 4. H3 and He3: The Equality of Neutron-Neutron and Proton-Proton Forces.- 5. The Ground State of the Triton; Tensor Forces.- Symbols.- VI. Nuclear Spectroscopy: I. General Theory.- 1. The Systematics of Stable Nucle.- A. Stability Conditions.- B. Discussion of Stable Nuclei.- 2. The Semi-Empirical Mass Formula of Weizsacker.- 3. Detailed Study of the Symmetry Effect.- 4. The Symmetry Energy and the Systematics of Stable Nuclei.- 5. Nuclear Magnetic Moments in Light Elements.- 6. The Spectroscopic Classification of Nuclear Energy Levels.- Symbols.- VII. Nuclear Spectroscopy: II. Special Models.- 1. Introduction.- 2. The Uniform Model of Wigner.- A. Theory.- B. Comparison with Experiment.- 3. The Independent-Particle Model.- A. Introduction.- B. The P Shell Configurations.- C. The Energy of the Ground State.- D. Nuclear Magnetic Moments on the Independent-Particle Model.- E. Criticism of the Independent-Particle Model.- 4. The Alpha-Particle Model of the Nucleus.- A. Outline of the Theory.- B. Criticism of the Alpha-Particle Model.- 5. The Liquid Drop Model.- Symbols.- VIII. Nuclear Reactions: General Theory.- 1. Introduction.- A. Description of a Nuclear Reaction.- B. Channels.- C. Energy Relations.- 2. Cross Sections.- A. Geometrical Limitations on Reaction and Scattering Cross Sections.- B. The Determination of Cross Sections from the Conditions at the Nuclear Surface, for Neutrons with l=0.- C. The Determination of Cross Sections from the Conditions at the Nuclear Surface. General Case.- D. The Angular Distribution of Elastically Scattered Particles.- E. The Reciprocity Theorem for Nuclear Reactions.- 3. The Compound Nucleus, Continuum Theory.- A. The Bohr Assumption.- B. Nuclear Reactions, Cross Sections, and Emission Rates.- 4. Determination of Cross Sections, Continuum Theory.- 5. Transmission of Potential Barriers.- 6. The Decay of the Compound Nucleus.- A. Competition; Evaporation Model.- B. Secondary Nuclear Reactions.- 7. Resonance Theory; Qualitative Treatment.- A. The Occurrence of Resonances.- B. The Compound Nucleus, Level Widths, Qualitative Description.- C. Interpretation of D and ?.- D. Cross Sections for Nuclear Reactions.- E. Behavior of Nuclear Cross Sections near Threshold.- 8. Resonance Theory; Determination of Cross Sections.- A. Pure Resonance Scattering.- B. Resonance Scattering and Resonance Reactions.- 9. Resonance Theory; Decaying States of the Compound Nucleus.- A. The Potential Well Model.- B. The Actual Nucleus.- 10. Spin And Orbital Angular Momentum.- A. l=0 Neutrons.- B. Particles with arbitrary l.- Symbols.- IX. Nuclear Reactions; Application of the Theory to Experiments.- 1. Introduction.- 2. Neutron-Induced Reactions.- A. Low and Intermediate Energy, Intermediate Nuclei.- B. Low Energy, Heavy Nuclei.- C. Intermediate Energy, Heavy Nuclei.- D. High Energy, Intermediate and Heavy Nuclei.- E. Very High Energy, Intermediate and Heavy Nuclei.- 3. Proton- and Alpha-Particle-Induced Reactions.- A. High Energy, Below Neutron Reaction Threshold.- B. High Energy, Above Neutron Reaction Threshold.- C. Very High Energy.- 4. Neutron-, Proton-, and Alpha-Particle-Induced Reactions at Ultrahigh Energies.- 5. Reactions with Light Nuclei.- A. B10(n,?)Li7.- B. Proton Reactions with Li7.- C. Reactions Leading to the Compound Nucleus N15.- 6. Deuteron-Induced Reactions.- Symbols.- X. Formal Theory of Nuclear Reactions.- 1. The Scattering Matr.- A. The General Form of the Wave Functions.- B. Definition of the Scattering Matrix.- C. Cross Sections Expressed in Terms of the Scattering Matrix.- 2. Conservation and Reciprocity Theorems for Nuclear Reactions.- A. Ingoing and Outgoing Waves.- B. The Conservation Theorems.- C. Time Reversal.- D. The Reciprocity Theorem.- E. Reciprocity and Detailed Balance.- 3. The Angular Distribution of Reaction Products.- A. The Reaction Amplitude.- B. The Conservation of Parity.- C. Limitations Imposed by the Complexity of the Incident Beam.- D. Limitations Imposed by the Complexity of the Compound Nucleus.- 4. The Wigner Many-Level Formula.- A. The Compound Nucleus as a "Black Box".- B. The Derivative Matrix.- C. The Relation between The Derivative Matrix and the Scattering Matrix.- D. The Resonance Levels of the Compound Nucleus.- E. Derivation of the Many-Level Dispersion Formula.- F. Discussion of the Many-Level Dispersion Formula.- G. The Single-Level Breit-Wigner Formula.- Symbols.- XI. Spontaneous Decay Of Nuclei.- 1. Energetic Considerations.- 2. General Theory of Alpha-Decay.- 3. Discussion of Experimental Data.- Symbols.- XII. Interaction of Nuclei with Electromagnetic Radiation.- 1. Introduction.- 2. Multipole Radiation and Selection Rules.- A. Multipole Radiation.- B. Selection Rules.- 3. The Probability of Multiple Emission and Absorption.- A. The Source of the Field.- B. The Energy Emitted per Second, and Its Angular Distribution.- C. Transition to Quantum Mechanics: (1) Emission and Absorption.- D. Transition to Quantum Mechanics: (2) The Matrix Elements.- 4. Radiative Transitions in the Two-Body Problem.- A. Transitions Into and Out of the Continuum; Cross Sections.- B. Radiative Neutron-Proton Capture; Selection Rules.- C. Radiative Neutron-Proton Capture; Computation of the Cross Section and Comparison with Experiment.- D. Photodisintegration of the Deuteron; Magnetic Dipole Effect.- E. Photodisintegration of the Deuteron; Electric Dipole Effect.- F. Photodisintegration of the Deuteron; Energies above 10 Mev.- 5. Internal Conversion.- A. Conversion Coefficients.- B. 0?0 Transitions.- C. Internal Pair Formation.- 6. Transitions Between Low-Lying States Of Nucle.- A. Theoretical Estimates.- B. Experimental Material; Nuclear Isomers.- C. Directional Correlations between Successively Emitted Gamma-Rays.- 7. Transitions Involving Highly Excited States.- A. General Considerations.- B. Sum Rules.- C. Estimates of Matrix Elements Involving Highly Excited Nuclear States.- D. Radiative Capture of Neutrons.- E. Nuclear Photoeffect 651 SYMBOLS.- XIII. Beta-Decay.- 1. Introduction.- 2. The Neutrino Hypothesis and the Shape of the Beta-Spectrum Selection Rules for "Allowed" Transitions.- 3. Orbital Electron Capture.- 4. The Half-Lives of Beta-Emitters and Evidence Concerning the Selection Rules in Allowed Transitions.- 5. Detailed Theory Of Beta-Decay; Transitions Of Order.- A. The Matrix Element.- B. Non-relativistic Treatment.- C. Relativistic Treatment.- 6. Determination of Matrix Elements; Favored and Unfavored Transitions.- 7. Beta-Transitions of Higher Order.- A. Non-relativistic Theory: Selection Rules, Matrix Elements.- B. Non-relativistic Theory: Angular Correlation, Spectrum Shape, Lifetime.- C. Relativistic Theory: Selection Rules, Matrix Elements.- D. Relativistic Theory: Angular Correlation, Spectrum Shape, Lifetime.- Symbols.- XIV. Nuclear Shell Structure.- 1. Evidence for the Existence Of "Magic Numbers".- 2. The Nuclear Shell Model.- 3. General Considerations.- Symbols.- Appendix A. Angular Momentum Operators and Eigenfunctions.- 1. Rotations and Angular Momenta.- 2. Spherical Harmonics.- 3. Expansion of a Plane Wave into Spherical Waves.- 4. Intrinsic Spin.- 5. Vector Addition of Angular Momenta.- Symbols.- Appendix B. Multipole radiation.- 1. Vector Spherical Harmonics.- 2. Electric and Magnetic Multipole Expansion in Free Space.- 3. Energy and Angular Momentum of the Multipole Radiation.- 4. The Sources of Multipole Radiation; Multipole Moments.- 5. Expansion of a Plane Wave into Multipole Fields.- 6. The Absorption Probability of a Light Quantum.- Symbols.- References.