Impact of Shape Coexistence on Nuclear Stability

Nuclear decay properties are conventionally predicted assuming nuclei decay from their ground-state configurations. However, this often neglects a fundamental structural complexity which is the phenomenon of shape coexistence, where nuclei possess multiple competing configurations at nearly degenerate energies. When both parent and daughter nuclei can exist in different energy minima, multiple decay pathways become possible. We systematically investigate how shape coexistence influences nuclear decay for approximately 1500 even-even nuclei ($8 \leq Z \leq 118$, $8 \leq N \leq 184$) using the Nilsson-Strutinsky method and relativistic mean-field calculations with NL3$^*$, DD-ME2, and DD-PC1 functionals. We identify around 400 nuclei exhibiting competing energy minima separated by less than 1 MeV. For these shape-coexisting nuclei, we calculate $\alpha$, $\beta^+$ and $\beta^-$ decay half-lives considering all possible transition pathways between the competing minima. Our results demonstrate that shape coexistence substantially impacts decay predictions, with half-lives showing variations up to nearly one logarithmic unit depending on which configurations participate in the transition. Comparison with experimental data from NUBASE2020 shows that pathways involving the second minimum sometimes reproduce measured lifetimes more closely than conventional ground-state to ground-state assumptions. Branching ratios exhibit even stronger sensitivity, with certain nuclei displaying complete inversions of the dominant decay mode depending on configuration choice. These pathway-dependent variations are not due to model uncertainties but reflect inherent structural effects. The correlation between the shape dynamics and nuclear stability establishes the shape coexistence as an essential component in predictive nuclear structure and astrophysics studies.