Systematic investigation on semi-empirical thermodynamic quantities of excited nuclei using canonical ensemble

Abstract

Semi-empirical thermodynamic quantities (TQs) of 78 nuclei ranging from $^{43}$Sc to $^{243}$Pu have been systematically investigated in the temperature region below 1 MeV using the thermodynamic canonical ensemble. The latter is carried out by taking into account the experimental nuclear level density (NLD) data measured using the Oslo method for the low-excitation region below the neutron binding energy $B_n$ combining with the back-shifted Fermi gas NLD model for the excitation energy from $B_n$ to about 250 MeV. In particular, the uncertainty of the TQs propagating from the fluctuation of the experimental NLD data has been, for the first time, calculated. The results obtained indicate that the uncertainty of TQs due to the experimental NLD is incomparable with the changes caused by the nuclear structure effects. The free energy of even-even nuclei behave differently from that of odd-$A$ ones. The total energy in the \rev{low-temperature region below $T_E \simeq 0.4-0.6$ MeV for medium-mass nuclei and $T_E \simeq 0.2-0.4$ MeV for heavy-mass ones slowly varies. When temperature is from $T_E$ to 1 MeV, the total energy} increases extremely faster than the increase of temperature, exhibiting the constant-temperature behavior. The entropy exhibits an abrupt change in their slope at \rev{$T_S \simeq 0.2-0.4$ MeV} in medium-mass nuclei and \rev{$T_S \simeq 0.5-0.6$ MeV} in heavy-mass ones. \rev{The existence of $T_E$ and $T_S$ has been interpreted due to the breaking of the first Cooper pair.} Finally, the heat capacity shows strongly pronounced $S$-shape in nuclei belong to rare-earth region. \rev{The temperatures defined at the center of the $S-$shaped heat capacities, which are known to closely relate to the critical temperature of the pairing phase transition $T_C$, are quite close to those theoretically predicted, namely $T_C \approx 0.5\Delta-0.6\Delta$ with $\Delta = 12A^{-1/2}$ being the empirical pairing gap at zero temperature.} The semi-empirical TQs obtained in the present work can be, therefore, a reliable data source to test and/or validate many nuclear thermodynamical models and to examine some nuclear structure properties such as pairing and deformation.