  Shape coexistence in even-even nuclei is observed when the ground state band
of a nucleus is accompanied by another K=0 band at similar energy but with
radically different structure. We attempt to predict regions of shape
coexistence throughout the nuclear chart using the parameter-free proxy-SU(3)
symmetry and standard covariant density functional theory. Within the
proxy-SU(3) symmetry the interplay of shell model magic numbers, formed by the
spin-orbit interaction, and the 3-dimensional isotropic harmonic oscillator
magic numbers, leads to the prediction of specific horizontal and vertical
stripes on the nuclear chart in which shape coexistence should be possible.
Within covariant density functional theory, specific islands on the nuclear
chart are found, in which particle-hole excitations leading to shape
coexistence are observed. The role played by particle-hole excitations across
magic numbers as well as the collapse of magic numbers as deformation sets in
is clarified.
