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Shape phase transitions and critical-point phenomena in atomic nuclei

Nature Physics volume 2, pages 811–820 (2006)Cite this article

Abstract

Atomic nuclei exhibit phase transitions as a function of the number of their constituent protons and neutrons. These phase transitions are not of the usual thermodynamic type, but rather they are quantum phase transitions in the equilibrium shape and structure of the ground and low-lying states. This realization has sparked a new area of research, focusing on the concept of 'critical-point symmetries', which describe the structure of nuclei at phase-transitional points. Both macroscopic (geometric or algebraic) and microscopic (shell-model) aspects of these phase transitions and of changes in structure with proton and neutron number in nuclei are discussed, along with an interpretation in terms of simple Landau theory. Finally, some alternative scenarios and schematic models for different classes of nuclei based on other simple potentials are briefly summarized.

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Figure 1: Symmetry triangle for nuclear structure.
Figure 2: Evolution of the characteristic collective observable, R4/2, and its derivative with respect to either ζ (a,b) or χ (c), for the three legs of the symmetry triangle showing phase-transitional behaviour24,25.
Figure 3: Energy surfaces illustrating the evolution of structure in regions of a, second-order and b, first-order phase transitions.
Figure 4: Characteristic predictions of X(5) and comparisons to relevant data.
Figure 5: Portion of the N–Z chart showing the stable nuclei (grey boxes) and the locus of P ∼ 5 (blue contours) where candidates for X(5) should appear83.
Figure 6

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Acknowledgements

I thank my principal collaborators in much of the work summarized here, in particular, F. Iachello, N. V. Zamfir, M. A. Caprio, E. A. McCutchan, R. Krücken, Jan Jolie, P. von Brentano, V. Werner, N. Pietralla, D. D. Warner, M. Fetea, K. Heyde, D. S. Brenner, and R. B. Cakirli. I am grateful to them, as well as to the following, for numerous discussions of the physics underlying this review: I. Talmi, S. Pittel, A. Frank, R. Bijker, W. Nazarewicz, P. Van Isacker, T. Otsuka, A. Dewald, J. N. Ginocchio, S. Heinze, A. Vitturi and A. Leviatan. I especially thank E. A. McCutchan and P. Farnsworth for extensive and valuable help in preparing this work. Finally, I am grateful to Jan Jolie and the Institut für Kernphysik in Köln, Germany where much of this manuscript was written during a stay in the Spring of 2006. Work supported by US DOE Grant No. DE-FG02-91ER-40609.

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Casten, R. Shape phase transitions and critical-point phenomena in atomic nuclei. Nature Phys 2, 811–820 (2006). https://doi.org/10.1038/nphys451

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