Multifaceted character of shape coexistence phenomena in atomic nuclei

This article is devoted to a review of decay properties of excited 0${}^{+}$ states in regions of the nuclear chart well known for shape coexistence phenomena. Even–even isotopes around the Z=20 (Ca), 28 (Ni), 50 (Sn), 82 (Pb) proton shell closures and along the Z=36 (Kr), Z=38 (Sr) and Z=40 (Zr) isotopic chains are mainly discussed. The aim is to identify examples of extreme shape coexistence, namely highly deformed structures, well localized in the Potential Energy Surface in the deformation space, which could lead to $\gamma$ decays substantially hindered. This is in analogy to the 0${}^{+}$ fission shape isomers in the actinides region and to the superdeformed (SD) states at the decay-out spin in medium/heavy mass systems. In this survey, the Hindrance Factor (HF) of the E2 transitions de-exciting 0${}^{+}$ states or SD decay-out states is a primary quantity which is used to differentiate between types of shape coexistence. The 0${}^{+}$ states, examined with the help of the hindrance factor, reveal a multifaceted scenario of shape coexistence. A limited number of 0${}^{+}$ excitations (in the Ni, Sr, Zr and Cd regions) exhibit large HF values ($>$10), some of which are associated with the clear separation of coexisting wave functions, while in most cases the decay is not hindered, due to the mixing between different configurations. Comparisons with theory predictions based on various models are also presented, some of which shed light on the microscopic structure of the considered states and the origin of the observed hindrances. The impact of shape ensembles at finite temperature on the decay properties of highly-excited states (Giant Dipole Resonances) is also discussed. This research area offers a complementary approach for identifying regions where extreme shape coexistence phenomena may appear.