Advances in Nuclear Physics: Volume 7

ISBN-13: 9781461590460 / Angielski / Miękka / 2013 / 329 str.

Michel Baranger; Erich Vogt

Opis

As much by chance as by design, the present volume comes closer to having a single theme than any of our earlier volumes. That theme is the properties of nuclear strength functions or, alternatively, the problem of line spreading. The line spreading or strength function concepts are essential for the nucleus because of its many degrees of freedom. The description of the nucleus is approached by using model wave functions-for example, the shell model or the collective model-in which one has truncated the number of degrees of freedom. The question then is how closely do the model wave functions correspond to the actual nuclear wave functions which enjoy all the degrees of freedom of the nuclear Hamiltonian? More precisely, one views the model wave functions as vectors in a Hilbert space and one views the actual wave functions as vectors spanning another, larger Hilbert space. Then the question is: how is a single-model wave function (or vector) spread among the vectors corresponding to the actual wave functions? As an example we consider a model state which is a shell-model wave function with a single nucleon added to a closed shell. Such a model state is called a single-particle wave function. At the energy of the single-particle waVe function one of the actual nuclear wave functions may resemble the single-particle wave function closely.

Spis treści

1 Nucleon—Nucleus Collisions and Intermediate Structure.- 1. Introduction.- 2. A Simple Model of a Resonance Process.- 2.1. The Model and Its Stationary State Solutions.- 2.2. Time-Dependent Picture.- 2.3. Applications of the Simple Model.- 2.4. Mixing Times in Nuclear Excitations.- 3. Nucleon—Nucleus Scattering and Intermediate Structure.- 3.1. Review of the Models of Nuclear Resonance Reactions.- 3.2. Physical Picture of Nucleon—Nucleus Scattering.- 3.3. The Optical-Model Strength Function as a Function of Mass Number.- 3.4. Shell-Model Investigations of Doorway States.- 3.5. Vibrations as Doorway States.- 3.6. Doorway States and Isobaric Analog Resonances.- 3.7. Electromagnetic Interactions and Intermediate Structure.- 3.8. Intermediate Structure in Fission.- 3.9. Doorway States and Partial Width Correlations.- 3.10. Intermediate Structure and the High-Energy Neutron Tail in Neutron Evaporation Spectra.- 3.11. Intermediate Structure and Statistical Fluctuations.- 3.12. Experimental Observations of Intermediate Structure in Total Neutron Cross Sections.- 4. Theoretical Framework for Intermediate Resonances.- 4.1. Shell-Model Theory of Nuclear Reactions.- 4.2. Theory of Average Cross Sections.- 5. Summary.- References.- 2 Coulomb Mixing Effects in Nuclei: A Survey Based on Sum Rules.- Abstract.- 1. Introduction.- 2. Sum-Rule Approach to Coulomb Mixing.- 3. Evaluation of Sum-Rule Quantities for Separate Isospins...- 3.1. Oscillator Shell Model.- 3.2. Shell Model with Correlations.- 3.3. Specification of ?(T?).- 3.4. Specification of N(T?).- 4. Total Isospin Impurities of States.- 4.1. Parent States.- 4.2. Analog States.- 5. Superallowed Fermi Transitions.- 6. Isobaric Mass Formula.- 6.1. First-Order Energy.- 6.2. Second-Order Energy.- 6.3. Correlated Model.- 6.4. Configuration States.- 6.5. Observed Values.- 7. Analog States: General Remarks and Lowest-Order Effects.- 7.1. ?Ec in Terms of Relative Coulomb Potential and Exact Parent State.- 7.2. ?Ec in Terms of Coulomb Energy and Unperturbed Parent State.- 7.3. First-Order Shift ?1and Pseudo-First-Order Shift ?1?.- 8. Analog States: Second-Order Shifts and Width.- 8.1. Estimate of ?Ec - ?1? = [?(-+) + ?(+-)].- 8.2. Estimate of (?2a - ?2p).- 8.3. Comparison of ?1 and ?1?.- 8.4. Implications for the Nolen—Schiffer Anomaly.- 8.5. Spreading Width.- 9. Second-Order Effects in Model Calculations.- 9.1. Coulomb Shift of Single-Particle States.- 9.2. Model Analog.- 9.3. Analysis of Shift Calculated from the Model.- 9.4. Analysis of Spreading Width Calculated from the Model.- 10. Conclusions.- Acknowledgment.- Appendix 1 Corrections from More Accurate Treatment of the Coulomb Potential.- Appendix 2 Explicit Treatment of Effect of Correlations on Second-Order Coulomb Mixing.- Appendix 3 Shell-Model Sum Rules for the One- and Two-Body Coulomb Forces.- Appendix 4 Coulomb Mixing Properties of Oscillator Orbitals.- References.- 3 The Beta Strength Function.- 1. Introduction.- 2. Beta-Transition Rates between Individual Nuclear Levels.- 2.1. The Fermi Transitions.- 2.2. The Gamow-Teller Transitions.- 2.3. Forbidden Transitions.- 3. Expected Properties of the Beta Strength Function.- 3.1. The Shell Model and Effects of Pairing.- 3.2. The Correlations.- 3.3. Fluctuations.- 4. Experimental Results on Beta Strength.- 4.1. Nuclear Level Schemes.- 4.2. Total Absorption Spectrometry.- 4.3. The Systematics of Beta Halflives.- 4.4. Beta-Delayed Particle Emission.- 4.5. Muon-Capture and Electromagnetic Transitions.- 5. Concluding Remarks.- Acknowledgments.- References.- 4 Gamma-Ray Strength Functions.- 1. Introduction.- 2. Theoretical Background.- 2.1. Nomenclature.- 2.2. Strength Functions.- 2.3. Spectral Distributions.- 3. Experimental Methods.- 3.1. Photoexcitation Method.- 3.2. Spectrum Fitting Method.- 3.3. Sequential Extraction Method.- 3.4. High-Resolution Gamma-Ray Method.- 3.5. Comparison of Methods.- 4. Properties of Gamma-Ray Strength Functions.- 4.1. General Properties.- 4.2. Detailed Properties.- 5. Discussion.- 5.1. General.- 5.2. Compatibility of Strength Functions.- 5.3. E1 Strength Function.- 5.4. M1 Strength Function.- 6. Conclusion.- Acknowledgments.- References.