Signatures for shape coexistence and shape/phase transitions in even-even nuclei

Systematics of B(E2) transition rates connecting the first excited $0_2^+$ state to the first excited $2_1^+$ 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 $0_2^+$ 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.