Book contents
- Frontmatter
- Contents
- Preface to the second edition
- Preface to the first edition
- Constants of nature, conversion factors and notation
- Glossary of some important symbols
- 1 Prologue
- 2 Leptons and the electromagnetic and weak interactions
- 3 Nucleons and the strong interaction
- 4 Nuclear sizes and nuclear masses
- 5 Ground-state properties of nuclei: the shell model
- 6 Alpha decay and spontaneous fission
- 7 Excited states of nuclei
- 8 Nuclear reactions
- 9 Power from nuclear fission
- 10 Nuclear fusion
- 11 Nucleosynthesis in stars
- 12 Beta decay and gamma decay
- 13 Neutrinos
- 14 The passage of energetic particles through matter
- 15 Radiation and life
- Appendix A Cross-sections
- Appendix B Density of states
- Appendix C Angular momentum
- Appendix D Unstable states and resonances
- Further reading
- Answers to problems
- Index
5 - Ground-state properties of nuclei: the shell model
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to the second edition
- Preface to the first edition
- Constants of nature, conversion factors and notation
- Glossary of some important symbols
- 1 Prologue
- 2 Leptons and the electromagnetic and weak interactions
- 3 Nucleons and the strong interaction
- 4 Nuclear sizes and nuclear masses
- 5 Ground-state properties of nuclei: the shell model
- 6 Alpha decay and spontaneous fission
- 7 Excited states of nuclei
- 8 Nuclear reactions
- 9 Power from nuclear fission
- 10 Nuclear fusion
- 11 Nucleosynthesis in stars
- 12 Beta decay and gamma decay
- 13 Neutrinos
- 14 The passage of energetic particles through matter
- 15 Radiation and life
- Appendix A Cross-sections
- Appendix B Density of states
- Appendix C Angular momentum
- Appendix D Unstable states and resonances
- Further reading
- Answers to problems
- Index
Summary
Nuclear potential wells
In the last chapter, we set out a semi-empirical theory for the binding energy of an atomic nucleus, and quantum-mechanical considerations came in only rather indirectly. Experimental atomic masses show deviations from the smooth curve given by the semi-empirical mass formula, deviations which we said were of quantum-mechanical origin. Since a nucleus in its ground state is a quantum system of finite size, it has angular momentum J, with quantum number j which is some integral multiple of ½. If j ≠ 0 the nucleus will have a magnetic dipole moment, and it may have an electric quadrupole moment as well.
The nuclear angular momentum and magnetic moment manifest themselves most immediately in atomic spectroscopy, where the interaction between the nuclear magnetic moment and the electron magnetic moments gives rise to the hyperfine structures of the electronic energy levels. In favourable cases both j and the magnetic moment may be deduced from this hyperfine splitting.
The observed values of nuclear angular momenta give strong support to the validity of a simple quantum-mechanical model of the nucleus: the nuclear shell model. In this model, each neutron moves independently in a common potential well that is the spherical average of the nuclear potential produced by all the other nucleons, and each proton moves independently in a common potential well that is the spherical average of the nuclear potential of all the other nucleons, together with the Coulomb potential of the other protons.
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- Chapter
- Information
- An Introduction to Nuclear Physics , pp. 56 - 73Publisher: Cambridge University PressPrint publication year: 2001