Temperature-dependent symmetry energy of neutron-rich thermally fissile nuclei

Background: The density-dependent symmetry energy coefficient plays a crucial role in understanding a variety of issues in nuclear physics as well as nuclear astrophysics. It is quite interesting and crucial to determine the symmetry energy coefficient and its related observables for neutron-rich thermally fissile nuclei at finite temperature. Purpose: We evaluate the symmetry energy coefficient, neutron pressure, and symmetry energy curvature of a finite nucleus from the corresponding quantities of infinite nuclear matter. Moreover, we correlate an effective symmetry energy coefficient and its related observables with the neutron skin thickness of neutron-rich thermally fissile nuclei at a finite temperature. Methods: The temperature-dependent relativistic mean field model (TRMF) is used to obtain the ground and excited state bulk properties of finite nuclei and the energy density, pressure, and the symmetry energy for infinite nuclear matter. The TRMF model with FSUGarnet, IOPB-I, and NL3 parameter sets is used for the present analysis. The effective nuclear matter properties are used to estimate the corresponding quantities of finite nuclei by using the local density approximation. Results: Nuclear bulk properties such as binding energy, quadrupole deformation, root-mean-square charge radius of the nuclei, and the equation of state and symmetry energy for infinite symmetric nuclear matter are estimated within the TRMF model. The nuclear matter observables at the local density of the nuclei serve as an input to obtain the effective symmetry energy coefficient, neutron pressure, and the symmetry energy curvature of U-234,U-236,U-250 and Pu-240 nuclei. The influence of temperature and density on these properties for neutron-rich thermally fissile nuclei is observed. A correlation is established between the neutron skin thickness and the neutron pressure of the nuclei. Conclusions: The studied properties of nuclei such as effective symmetry energy coefficient, neutron pressure and symmetry energy curvature can be used in the synthesis of neutron-rich thermally fissile nuclei. The method presented here (fully microscopic) can be used further to study the properties of exotic and superheavy nuclei from the corresponding quantities of nuclear matter and vice versa.