Pairing properties from random distributions of single-particle energy levels

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© 2018 American Physical Society. Exploiting the similarity between the bunched single-particle energy levels of nuclei and of random distributions around the Fermi surface, pairing properties of the latter are calculated to establish statistically based bounds on the basic characteristics of the pairing phenomenon. When the most probable values for the pairing gaps germane to the BCS formalism are used to calculate thermodynamic quantities, we find that while the ratio of the critical temperature Tc to the zero-temperature pairing gap is close to its BCS Fermi gas value, the ratio of the superfluid to the normal phase specific heats at Tc differs significantly from its Fermi gas counterpart. The largest deviations occur when a few levels lie closely on either side of the Fermi energy but other levels are far away from it. The influence of thermal fluctuations, expected to be large for systems of finite number of particles, were also 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 Tc in the BCS formalism was transformed to a shoulderlike structure indicating the suppression of a second-order phase transition as experimentally observed in nanoparticles and several nuclei. Contrasting semiclassical and quantum treatments of fluctuations for the random spacing model is currently underway.