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 $T_c$ 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 nano-particles and several nuclei. Illustrative calculations using the constant spacing model and the recently introduced random spacing model are presented.