Further Reading — Chapter 8: Collective Motion: Vibrations, Rotations, and Nuclear Deformation

Primary Textbook References

K. S. Krane, Introductory Nuclear Physics (Wiley, 1988), Chapter 5: "Nuclear Models." Sections 5.2 (collective structure) and 5.3 (collective models) provide an accessible introduction to vibrational and rotational models at the undergraduate level. Krane's treatment of rotational band systematics and the E(4+)/E(2+) ratio as a structural indicator is particularly clear.
S. S. M. Wong, Introductory Nuclear Physics, 2nd ed. (Wiley-VCH, 2004), Chapter 6. Good undergraduate treatment with worked examples for rotational spectra and the phonon model.

R. F. Casten, Nuclear Structure from a Simple Perspective, 2nd ed. (Oxford University Press, 2000). An outstanding and highly readable intermediate text that develops the collective models with exceptional physical intuition. Chapters 4 (vibrations), 5 (rotations), and 6 (the IBA) are directly relevant. Casten's treatment of the symmetry triangle and structural evolution across the nuclear chart is the definitive pedagogical reference. This is the single most recommended supplementary text for this chapter.
W. Greiner and J. A. Maruhn, Nuclear Models (Springer, 1996). A thorough development of both geometric (Bohr-Mottelson) and algebraic (IBA) collective models. Includes detailed derivations of the rotational energy formula, the cranking model, and the Bohr Hamiltonian.

A. Bohr and B. R. Mottelson, Nuclear Structure, Vol. II: Nuclear Deformations (Benjamin, 1975; reprinted by World Scientific, 1998). The definitive treatise on collective nuclear motion by two of its creators. Volume II covers rotational and vibrational motion in encyclopedic detail, including the original development of the unified model. Essential for any serious student of nuclear structure, though demanding.
P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer, 1980). Advanced graduate text with rigorous treatments of the cranking model, Hartree-Fock-Bogoliubov theory in rotating frames, and the microscopic foundations of collective motion.
D. J. Rowe and J. L. Wood, Fundamentals of Nuclear Models: Foundational Models (World Scientific, 2010). A modern graduate text that develops collective models from group-theoretic foundations. Particularly strong on the algebraic structure of the IBA and its relationship to geometric models.

F. Iachello and A. Arima, The Interacting Boson Model (Cambridge University Press, 1987). The monograph by the model's creators. Develops the IBA from its algebraic foundations through all three dynamical symmetry limits, with applications to specific nuclei. Indispensable for anyone working with the IBA.
R. F. Casten and D. D. Warner, "The Interacting Boson Approximation," Reviews of Modern Physics 60, 389 (1988). Comprehensive review of the IBA's successes and limitations, with extensive comparison to experimental data across the nuclear chart.
F. Iachello, "Dynamic Symmetries at the Critical Point," Physical Review Letters 85, 3580 (2000). The original paper introducing the E(5) critical-point symmetry. Accessible and remarkably concise.
F. Iachello, "Analytic Description of Critical Point Nuclei in a Spherical-Axially Deformed Shape Phase Transition," Physical Review Letters 87, 052502 (2001). The X(5) critical-point symmetry paper, describing the first-order phase transition between spherical and deformed shapes.

P. J. Twin et al., "Observation of a Discrete-Line Superdeformed Band up to 60$\hbar$ in $^{152}$Dy," Physical Review Letters 57, 811 (1986). The discovery paper. A landmark in nuclear structure physics.
R. V. F. Janssens and T. L. Khoo, "Superdeformed Bands in Nuclei," Annual Review of Nuclear and Particle Science 41, 321 (1991). A thorough early review of superdeformation, covering the theory of shell structure at extreme deformation and the experimental systematics.
B. Singh, R. Zywina, and R. B. Firestone, "Table of Superdeformed Nuclear Bands and Fission Isomers," Nuclear Data Sheets 97, 241 (2002). Comprehensive compilation of all known superdeformed bands. An essential data reference.

A. Johnson, H. Ryde, and J. Sztarkier, "Evidence for a 'Singularity' in the Nuclear Rotational Band Structure," Physics Letters B 34, 605 (1971). The discovery of backbending in $^{160}$Dy.
R. Bengtsson and S. Frauendorf, "Quasiparticle Spectra Near the Yrast Line," Nuclear Physics A 327, 139 (1979). Development of the cranked shell model for understanding high-spin phenomena, including a systematic treatment of band crossings.
I. Ragnarsson, S. G. Nilsson, and R. K. Sheline, "Shell Structure in Nuclei," Physics Reports 45, 1 (1978). Foundational paper on Nilsson model calculations at all deformations, including predictions for superdeformed and hyperdeformed shapes.

R. F. Casten, "Quantum Phase Transitions and Structural Evolution in Nuclei," Progress in Particle and Nuclear Physics 62, 183 (2009). A modern review by the pioneer of the symmetry triangle, covering the experimental evidence for quantum phase transitions and critical-point symmetries.
P. Cejnar, J. Jolie, and R. F. Casten, "Quantum Phase Transitions in the Shapes of Atomic Nuclei," Reviews of Modern Physics 82, 2155 (2010). Comprehensive review of shape phase transitions in nuclei, including both mean-field and algebraic (IBA) perspectives.

National Nuclear Data Center (NNDC): https://www.nndc.bnl.gov/ The Evaluated Nuclear Structure Data File (ENSDF) and the Nuclear Data Sheets are the primary sources for experimental level energies, transition rates, and moments used throughout this chapter.
Brookhaven ENSDF database: Interactive access to adopted level schemes for all known nuclei. Essential for the exercises and the progressive project.
RIPL-3 (Reference Input Parameter Library): https://www-nds.iaea.org/RIPL-3/ Includes deformation parameters, level densities, and optical model parameters for nuclear structure and reaction calculations.

A. Bohr, "Rotational States of Atomic Nuclei," Ph.D. thesis, Copenhagen (1954); reprinted in A. Bohr, Collected Works, ed. O. Hansen (World Scientific, 2008). Bohr's doctoral thesis, which laid the foundations for the collective model. A remarkable document that introduced the $(\beta, \gamma)$ parameterization and the theory of rotational spectra.
Nobel Prize lectures by A. Bohr, B. R. Mottelson, and L. J. Rainwater (1975): Available at https://www.nobelprize.org/. These lectures provide accessible overviews of the development of the collective model and its experimental verification.