Properties of hot finite nuclei and associated correlations with infinite nuclear matter

This work aim to study the various thermal characteristics of nuclei in view of the saturation and critical behavior of infinite nuclear matter. The free energy of a nucleus is parametrized using the density and temperature-dependent liquid-drop model and interaction among nucleons is worked out within the effective relativistic mean-field theory (E-RMF). The effective mass (m,$^*$) and critical temperature of infinite symmetric nuclear matter ($T_c$) of a given E-RMF parameter force play a seminal role in the estimation of thermal properties. A larger (m$^*$) and $T_c$ of the E-RMF set estimate larger excitation energy, level density, and limiting temperature $(T_l)$ for a given nucleus. The limiting temperature of a nucleus also depends on the behavior of the nuclear gas surrounding the nucleus, making the equation of state (EoS) at subsaturation densities an important input. A stiff EoS in the subsaturation region estimates a higher pressure of the nuclear gas making it less stable. Since the $T_c$ plays an important part in these calculations, we perform a Pearson correlation statistical study of fifteen E-RMF parameter sets, satisfying the relevant constraint on EoS. Effective mass seems to govern the thermal characteristics of infinite as well as finite nuclear matter in the framework of E-RMF theory.