Shape coexistence in nuclei

Shape coexistence is a very peculiar nuclear phenomenon consisting in the presence in the same nuclei, at low excitation energy, and within a very narrow energy range, of two or more states (or bands of states) which: (a) have well defined and distinct properties, and, (b) which can be interpreted in terms of different intrinsic shapes. Indeed, the very concept of shape requires to work in an intrinsic reference frame, which is not always easy to define. In a sense, the main problem when dealing with shape coexistence in nuclei is the shape itself, as the articles in this focus issue will document in detail. The realm of nuclear shapes is dominated by those of quadrupole type, characterized by two shape parameters β and γ, and we speak of prolate and oblate shapes, axial or triaxial. Permanent octupole and hexadecapole deformed nuclei are scarce, (or just non existing) and not very well documented experimentally, and will not be treated here, because, in any case, no hint of shape coexistence has been unveiled yet.

To establish experimentally the shape of a nucleus and hence the presence of shape coexistence demands the use of the full panoply of available experimental tools. In particular, conversion electron spectroscopy to measure E0 transitions, coulex and in-beam techniques to extract E2 transition probabilities and spectroscopic quadrupole moments, the measure of magnetic and quadrupole moments via the hyperfine splitting of the atomic spectra, etc. These are the topics discussed in the experimental articles which follow. Although pervasive to all the nuclear chart, in recent years much effort has been devoted to the manifestations of shape coexistence far from stability, both in the neutron rich and neutron deficient regimes. The latter is represented in this volume for the regions around ¹⁸⁶Pb, a famous case of triple shape coexistence (spherical, oblate and prolate), and in the heavy N = Z nuclei at and beyond ⁷²Kr. The former includes nuclei in the islands of inversion at N = 20–28 and N = 40. The relationship of shape coexistence and α clustering in light nuclei and its experimental signatures, is addressed as well.

The description of shape coexistence is an important challenge for the nuclear theory as well. The concept of a nuclear shape is natural in semiclassical models liquid drop like, and in mean field, Hartree–Fock based ones, which explicitly break rotational invariance. The problem with these is that to go from the intrinsic to the laboratory frame where the experimental data live, it is compulsory to restore the symmetries, a procedure which can (and indeed must) blur somehow the interpretation of the parameters defining the intrinsic shapes. Approaches which take care of the nuclear deformation directly in the laboratory frame such as the configuration interaction shell model (CI-SM) produce results that can be compared directly with the experiment, but need auxiliary tools to be read in terms of nuclear shapes. This generates a fruitful exchange between different descriptions, where a primordial role is played by the group theoretical models, be it fermionic, like these based in Elliott's SU3, its variants and extensions, or bosonic as in the case of the IBM. The present issue covers a variety of choices, from the purely quantum geometrical one to the relativistic mean field. Special emphasis is made in the most microscopical views, those which are in the context of the the CI-SM. To set a dictionary that makes it possible to translate the laboratory frame language to to the intrinsic frame is not easy at all, and some of the contributions to this focus issue propose interesting ways to solve this problem.

One can imagine that the only relevant physical case is that of coexistence. This postulate will be only valid in the macroscopic limit. Instead, in the nuclear physics world, mixing is never absent. Therefore there may be other interesting manifestations of the nuclear dynamics. Shape coexistence implies the existence of neatly distinct shapes; however, there can be situations in which configurations with different (but not so different) shapes mix. The catch here is what are the shapes which can do it. A mixture of spherical and well deformed shapes is difficult to describe with our standard vocabulary. The same happens with the quantal mixing of prolate and oblate shapes. The many body dynamics can produce even more exotic hybrids, which I dub shape entangled states. All in all, the topic of this focus issue anticipates a lot of intellectual excitement for a large community of nuclear physics researchers.