Bulk and neutron–proton asymmetry coefficients of the semi-empirical mass formula tuned to ground state mass excess of AME2020 and/or FRDM(2012)

Abstract

Davidson et al. has extended Seeger’s mass formula to non-zero excitation energies by introducing temperature-dependent coefficients in the liquid drop energy part of the semi-empirical mass formula, but did not consider the nuclear shape and shell effects. The semi-empirical mass formula of Davidson et al. is applicable for nuclear temperatures less than or equal to 4 MeV. The mass excess calculated using this mass formula with/without nuclear shape and shell effects does not reproduce the ground state mass excesses of the new atomic mass evaluation data AME2020 and/or FRDM(2012) with its coefficients at zero temperature. So, the coefficients of the semi-empirical mass formula with nuclear shape and shell effects are required to be tuned to reproduce the ground state mass excess of all the nuclei available in the recent atomic mass evaluation data AME2020 and/or FRDM(2012). The bulk and neutron–proton asymmetry coefficients of the semi-empirical mass formula of Davidson et al., including the nuclear shape and shell effects, have been tuned to reproduce the mass excess data for all known 9420 nuclei which include all the nuclei of AME2020 (Z $=$ 1-118 and A $=$ 1-295) and of FRDM(2012) (Z $=$ 8-136 and A $=$ 16-339, except 3456 nuclei which are also available in the AME2020 data) at zero temperature. The tuned bulk and neutron–proton asymmetry coefficients reproduce the ground state mass excess of the new atomic mass evaluation data AME2020 and/or FRDM(2012) within a difference of less than 1 MeV and can be used for the applications/investigations in the areas of physics where high energies are experienced or nuclei involved are in excited states, e.g., fusion–evaporation and fusion–fission processes in heavy-ion reactions. The mass excess calculated for the excited states of nuclei is compared with the excited state mass excess of the NUBASE2020 evaluation data and is in good agreement with it.