Impact of microscopic structural transitions on particle stability and lifetimes of hot nuclei

The impact of temperature-induced deformations and shape fluctuations on the particle stability and decay processes has been investigated across the isotopes of hot nuclear systems with $Z = 28$ to $50$, with focus on astrophysically crucial pathways at excitation energies relevant to stellar environments. We perform global finite-temperature analysis using the statistical theory of hot nuclei combined with the triaxially deformed Nilsson Hamiltonian and Strutinsky's prescription, and explore the interplay between deformation, shell quenching, separation energies, and $β$-decay characteristics at finite temperatures. Our results show that around critical temperatures $T_c \approx 1$--$2$ MeV, where the shell quenching effects become predominant, the nuclear deformation reduces and the shape undergoes a transition to the spherical configuration. Our computed neutron and proton separation energies, which usually decrease with increasing temperature, implying the reduced binding in hot nuclei, occasionally show an enhancement in some nuclei at reduced deformation around $T_c$ that shifts the last unbound nucleon to the bound, stabilizing the nucleus by shifting the drip-line boundaries. A few nuclei are found to show one- and two-neutron drip line expansion with temperature. Moreover, the temperature-induced changes in deformation strongly correlate with the marked variations in our calculated $Q_β$ values and lifetimes, underscoring their impact on weak interaction rates. These findings provide insight into the sensitivity of particle stability and weak-interaction observables to thermal effects and may serve as complementary inputs for modeling nuclear processes in hot astrophysical environments.