Impact of nuclear deformation of parent and daughter nuclei on one proton radioactivity lifetimes.

The influence of nuclear deformation on proton-decay half-lives has been systematically studied in microscopic theoretical frameworks for a wide range of nuclei with Z<82. Correlation between 1p-decay half-lives and the deformed nuclear shapes of both the parent and daughter nuclei is investigated. Since the deformations of proton emitters and their residual nuclei impact the potential barrier and disintegration energy which are crucial for the accurate determination of half-lives, we incorporate these nuclear deformations of both the emitters and residues in a phenomenological manner and propose a new semi-empirical formula to estimate the 1p-decay half-lives. The robustness of this formula is demonstrated by the accurate predictions of the measured values while making it reliable for forecasting the properties of other potential proton emitters. The phenomenon of shape coexistence as observed in several proton emitters and their respective daughter nuclei, is particularly significant in this context due to secondary minima in the potential energy surfaces of both the nuclei. Accounting for these factors significantly affects the estimation of half-lives and branching ratios by introducing additional decay pathways and altering transition probabilities between different nuclear shapes.