Role of Fluctuations on the Pairing Properties of Nuclei in the Random Spacing Model

The influence of thermal fluctuations on fermion pairing is investigated using a semiclassical treatment of fluctuations. When the average pairing gaps along with those differing by one standard deviation are used, the characteristic discontinuity of the specific heat at the critical temperature Tc in the BCS formalism with its most probable gap becomes smooth. This indicates the suppression of a second order phase transition as experimentally observed in nanoparticles and several nuclei. Illustrative calculations using the constant spacing model and the recently introduced random spacing model are presented.