  Systematics of B(E2) transition rates connecting the first excited 0+ state
to the first excited 2+ state of the ground state band in even-even nuclei
indicates that shape coexistence of the ground state band and the first excited
K=0 band should be expected in nuclei lying within the stripes of nucleon
numbers 7-8, 17-20, 34-40, 59-70, 96-112 predicted by the dual shell mechanism
of the proxy-SU(3) model, avoiding their junctions, within which high
deformation is expected. Systematics of the excitation energies of the first
excited 0+ states in even-even nuclei show that shape coexistence due to
proton-induced neutron particle-hole excitations is related to a first-order
shape/phase transition from spherical to deformed shapes, while shape
coexistence due to neutron-induced proton particle-hole excitations is observed
along major proton shell closures.
