# Role of fluctuations on the pairing properties of nuclei in the random spacing model

## TL;DR

This paper investigates how thermal fluctuations affect fermion pairing in nuclei, showing that fluctuations smooth out the specific heat discontinuity at the critical temperature, aligning theory with experimental observations.

## Contribution

It introduces a semiclassical fluctuation treatment within the random spacing model to better understand pairing properties in nuclei.

## Key findings

- Fluctuations smooth the specific heat discontinuity at T_c.
- Suppression of second order phase transition observed.
- Results align with experimental data on nano-particles and nuclei.

## Abstract

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.