Physics reports-review section of physics letters vol:215 issue:3-4 pages:101-201
Shape coexistence in doubly even nuclei is reviewed. Two main theoretical approaches are presented. The first is essentially the shell model with the excitation of pairs of protons and/or neutrons across closed shells or subshells together with a residual proton-neutron interaction. The second is the deformed mean-field approach. The first is broadly defined so that it includes various truncation schemes to the shell model including generalized seniority and the interacting boson model. The presentation of the theory has two main aims: to provide a framework into which the majority of theoretical studies of shape coexistence can be placed and to provide a framework within which a unified view can be discussed. Selected experimental data are shown from O-16 to U-238. Our criteria for selection emphasize detailed spectroscopic evidence ("fingerprints") for coexisting shapes.