Investigation of empirical heat capacity in hot-rotating A ∼ 200 nuclei

The empirical heat capacities of some hot-rotating A similar to 200 nuclei (Re-184, Tl-200, Po-211, and At-212) have been investigated by combining the angular-momentum dependent back-shifted Fermi gas (BSFG) model of nuclear level density (NLD) with the experimental NLD data extracted from the neutron-evaporation spectra at the average total angular momentum ⟨J⟩ = 12 PLANCK CONSTANT OVER TWO PI. The parameters of the BSFG are obtained by fitting its NLD to the corresponding measured data using an advanced package of program modeling (CPM) provided by Python feature of IBM decision optimization CPLEX. The results obtained show that the shell correction plays an important role in the formation of empirical S-shaped heat capacity, which serves as a fingerprint for the pairing phase transition in finite nuclear systems. The Re-184 nucleus, which is deformed and has small shell correction, exhibits a weaker S-shaped heat capacity than the remaining three spherical Tl-200, Po-211, and At-212 nuclei that have large shell effects. This result contrasts with that recently predicted by the microscopic exact pairing plus independent-particle model at finite temperature (EP + IPM), in which the S-shaped heat capacity was predicted in Re-184 only. This discrepancy between the heat capacities obtained within the BSFG and EP + IPM models suggests that an NLD model capable of well describing the experimental data while also having intrinsic and as complete as possible physical interpretations is still required in order to provide the exact description of nuclear thermodynamic quantities. In addition, more experimental NLD data in other mass and higher energy regions are also demanded.