Chapter 7 Further Reading: Beyond the Single Particle

Textbooks

Primary References

• Casten, R. F. Nuclear Structure from a Simple Perspective, 2nd ed. (Oxford University Press, 2000). Chapters 5-7 provide an exceptionally clear treatment of pairing, the seniority scheme, two-particle configurations, and collective models. Casten's physical intuition and emphasis on systematics make this an ideal companion to the present chapter.

• Bohr, A. and Mottelson, B. R. Nuclear Structure, Volume I: Single-Particle Motion (Benjamin, 1969) and Volume II: Nuclear Deformations (Benjamin, 1975). The definitive treatment by the founders of the unified model. Volume I, Chapter 3 covers the Nilsson model and particle-vibration coupling. Volume II develops the collective framework in full. Advanced, but every nuclear structure physicist should own these volumes.

• Heyde, K. L. G. Basic Ideas and Concepts in Nuclear Physics, 3rd ed. (Institute of Physics Publishing, 2004). An excellent intermediate textbook covering the shell model, pairing, and deformation at the advanced undergraduate / beginning graduate level.

Advanced Treatments

• Talmi, I. Simple Models of Complex Nuclei: The Shell Model and Interacting Boson Model (Harwood Academic, 1993). The authoritative treatment of the seniority scheme and fractional parentage coefficients by one of the originators of the formalism. Technical but essential for anyone pursuing shell-model calculations.

• Lawson, R. D. Theory of the Nuclear Shell Model (Oxford University Press, 1980). A rigorous mathematical treatment of the shell model including two-body matrix elements, configuration mixing, and effective interactions.

• Ring, P. and Schuck, P. The Nuclear Many-Body Problem (Springer, 1980; reprinted 2004). The standard graduate text on many-body theory applied to nuclei, including BCS pairing, Hartree-Fock-Bogoliubov, the random phase approximation, and the generator coordinate method.

• Nilsson, S. G. and Ragnarsson, I. Shapes and Shells in Nuclear Structure (Cambridge University Press, 1995). Written by Nilsson himself (with Ragnarsson), this is the definitive treatment of the Nilsson model, deformation, and the connection between single-particle and collective motion.

Review Articles

• Caurier, E., Martinez-Pinedo, G., Nowacki, F., Poves, A., and Zuker, A. P. "The Shell Model as a Unified View of Nuclear Structure," Reviews of Modern Physics 77, 427 (2005). A comprehensive review of the interacting shell model, covering effective interactions, computational methods, and applications across the nuclear chart. Essential reading for understanding the state of the art.

• Dean, D. J. and Hjorth-Jensen, M. "Pairing in Nuclear Systems: From Neutron Stars to Finite Nuclei," Reviews of Modern Physics 75, 607 (2003). A thorough review of nuclear pairing, from the BCS model to modern treatments, with connections to neutron star physics.

• Walker, P. and Dracoulis, G. "Energy Traps in Atomic Nuclei," Nature 399, 35 (1999). An accessible review of nuclear isomers, covering the three types (spin, shape, K-isomers) and their applications. An excellent entry point to the isomer literature.

• Walker, P. M. and Dracoulis, G. D. "Exotic Isomers in Deformed Atomic Nuclei," Hyperfine Interactions 135, 83 (2001). A more detailed treatment of $K$-isomers and their nuclear structure implications.

• Kondev, F. G., Dracoulis, G. D., and Kibédi, T. "Configurations and Hindered Decays of $K$-Isomers in Deformed Nuclei," Atomic Data and Nuclear Data Tables 103-104, 50 (2015). A comprehensive compilation of $K$-isomers with nuclear structure analysis.

Landmark Papers

• Nilsson, S. G. "Binding States of Individual Nucleons in Strongly Deformed Nuclei," Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddelelser 29, No. 16 (1955). The original Nilsson model paper. Still worth reading for its clarity and physical insight.

• Bohr, A., Mottelson, B. R., and Pines, D. "Possible Analogy between the Excitation Spectra of Nuclei and Those of the Superconducting Metallic State," Physical Review 110, 936 (1958). The paper that imported BCS theory into nuclear physics, recognizing the pairing analogy between nuclei and superconductors.

• Brown, B. A. and Wildenthal, B. H. "Status of the Nuclear Shell Model," Annual Review of Nuclear and Particle Science 38, 29 (1988). The paper establishing the USD effective interaction for the $sd$-shell, a milestone in the interacting shell model.

• Brown, B. A. and Richter, W. A. "New 'USD' Hamiltonians for the $sd$ Shell," Physical Review C 74, 034315 (2006). The updated USDB and USDA interactions.

Data Resources

• NNDC (Brookhaven National Nuclear Data Center): https://www.nndc.bnl.gov/. The primary online source for nuclear structure data, including level schemes, transition rates, moments, and half-lives. The NuDat and ENSDF databases are indispensable.

• Atomic Mass Evaluation (AME2020): Published in Chinese Physics C 45, 030002-030003 (2021) by Wang, Huang, Kondev, Audi, and Naimi. The definitive compilation of measured atomic masses, essential for computing binding energies, separation energies, and pairing gaps.

• RIPL-3 (Reference Input Parameter Library): https://www-nds.iaea.org/RIPL-3/. Includes Nilsson model parameters, single-particle levels, and deformation parameters for nuclei across the chart.

Computational Resources

• NuShellX: A widely used shell-model code for small to medium model spaces, freely available for educational use. Implements the Lanczos algorithm for eigenvalue extraction.

• KSHELL: A modern, high-performance shell-model code by N. Shimizu (University of Tokyo). Handles dimensions up to $\sim 10^{10}$. Source available at https://doi.org/10.5281/zenodo.6897160.

• BIGSTICK: A shell-model code developed by C. W. Johnson and colleagues, designed for shared-memory parallel architectures. Well-documented and suitable for learning shell-model computation.

For the Curious Student

• Audi, G., Kondev, F. G., Wang, M., Huang, W. J., and Naimi, S. "The NUBASE2020 Evaluation of Nuclear Physics Properties," Chinese Physics C 45, 030001 (2021). Includes a complete listing of nuclear isomers with half-lives, spins, and excitation energies.

• Jain, A. K., Maheshwari, B., Garg, S., Patial, M., and Singh, B. "Atlas of Nuclear Isomers," Nuclear Data Sheets 128, 1 (2015). A comprehensive atlas of all known isomers organized by mass region.

• The story of the hafnium bomb controversy is told accessibly in: Weinberger, S. The Imagineers of War: The Untold Story of DARPA (Knopf, 2017), Chapter 19. For the physics arguments, see the JASON report JSR-04-330 (2004).