Proton entropy excess and possible signature of pairing reentrance in hot nuclei

The entropy excess caused by one proton (proton entropy excess) has been extracted for several pairs of medium and heavy mass nuclei such as ($^{237}$U and $^{238}$Np), ($^{231}$Th and $^{232}$Pa), ($^{211}$Po and $^{212}$At), ($^{196}$Pt and $^{197}$Au), and ($^{90}$Y and $^{91}$Zr) using the available nuclear level density data. The nature of entropy excess as a function of excitation energy E⁎ is found in a reasonable agreement with the microscopic calculations based on the exact pairing plus independent-particle model at finite temperature (EP+IPM). It is observed that the proton entropy excess is ∼0.1−0.5kB for the spherical systems and ∼1.0−1.2kB for the deformed ones, which is notably smaller than that of neutron entropy excess (∼1.3−2.0kB). This is due to the effect of Coulomb interaction as well as the single-particle level density of protons, which is less than that of neutrons. Moreover, a peak-like structure in the entropy excess observed at low E⁎<1 MeV is possibly associated with the pairing reentrance phenomenon caused by the weakening of blocking effect in odd nuclei at low temperature within the EP+IPM. However, this peak-like structure, which is more pronounced in the spherical nuclei than in the deformed isotopes, is not well supported by experimental observation due to strong fluctuations of the measured data. Hence, further experimental and theoretical studies are called in order to understand this effect.