Elsevier

Annals of Physics

Volume 199, Issue 2, 1 May 1990, Pages 227-267
Annals of Physics

Phase transition induced by particle number in a model finite system

https://doi.org/10.1016/0003-4916(90)90379-3Get rights and content

Abstract

Large exact spectra of a nuclear shell model with a simplified pairing force are analyzed by statistical methods. The canonical heat capacity shows a two-fluid structure with a clear signature of the pairing transition as a function of particle number. A phenomenological expression for the heat capacity is found. The entropy of pairs is used as a microscopic gap function to define a quasiparticle spectrum, which is shown to contain an uncoupled particle in a mean field at low temperatures. A thermodynamical gap function is defined and it is shown that a gap can exist for T > 0 while vanishing for T = 0.

The canonical temperature is compared to several definitions based on local properties of spectra. The noncanonical heat capacity is obtained for them through a study of entropy fluctuations. It is found that the fluctuations in the microscopic entropies of pairs and of uncoupled particles map regularly onto a two-dimensional coordinate net in the macroscopic entropy-temperature plane.

At all stages of the calculation both the symmetries of a finite system and the Pauli principle are treated exactly.

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    Present adress: Max-Planck Institut für Kernphysik, D-6900 Heidelberg, Federal Republic of Germany.

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