Shape coexistence in atomic nuclei

Shape coexistence in nuclei appears to be unique in the realm of finite many-body quantum systems. It differs from the various geometrical arrangements that sometimes occur in a molecule in that in a molecule the various arrangements are of the widely separated atomic nuclei. In nuclei the various "arrangements'' of nucleons involve (sets of) energy eigenstates with different electric quadrupole properties such as moments and transition rates, and different distributions of proton pairs and neutron pairs with respect to their Fermi energies. Sometimes two such structures will "invert'' as a function of the nucleon number, resulting in a sudden and dramatic change in ground-state properties in neighboring isotopes and isotones. In the first part of this review the theoretical status of coexistence in nuclei is summarized. Two approaches, namely, microscopic shell-model descriptions and mean-field descriptions, are emphasized. The second part of this review presents systematic data, for both even- and odd-mass nuclei, selected to illustrate the various ways in which coexistence is observed in nuclei. The last part of this review looks to future developments and the issue of the universality of coexistence in nuclei. Surprises continue to be discovered. With the major advances in reaching to extremes of proton-neutron number, and the anticipated new "rare isotope beam'' facilities, guidelines for search and discovery are discussed