Pairing and thermodynamics properties of finite-systems with fixed number of particles

D Gambacurta,D Lacroix,S Ershov,A Zubov,T Shneydman,A Vdovin

doi:10.1051/epjconf/20123804004

Abstract

A canonical description of the thermodynamical pairing properties of small systems is achieved by using the Variation After Projection approach at finite temperature. The minimization of the free energy is made by a direct evaluation of the energy and full diagonalization of the entropy. We use the Richardson - pairing model whose exact solution allows to study the reliability of different approaches. We show that the Projection After Variation approach, that is usually performed at zero temperature with rather good success, provides a quite poor description at finite temperature. On the contrary, the Variation After Projection applied at finite temperature provides a perfect reproduction of the exact canonical properties of odd or even systems from very low to high temperature.

Highlights

The study of hot nuclei properties and the search for possible phase transitions, as for example the shape, pairing and liquid-gas one, have been extensively investigated in recent decades to understand the temperature dependence of nuclei and nuclear matter properties
A canonical description of the thermodynamical pairing properties of small systems is achieved by using the Variation After Projection approach at finite temperature
We show that the Projection After Variation approach, that is usually performed at zero temperature with rather good success, provides a quite poor description at finite temperature

Summary

Introduction

The study of hot nuclei properties and the search for possible phase transitions, as for example the shape, pairing and liquid-gas one, have been extensively investigated in recent decades to understand the temperature dependence of nuclei and nuclear matter properties. A natural extension of these approaches able to provide a canonical description of finite system at thermal equilibrium has been proposed already some times ago [1] by considering a many-body projected statistical density operator D N, preserving the good particle number. Other extensions have been proposed by adding quantum fluctuation associated to RPA modes described on top of a BCS plus Lipkin-Nogami projection approach [5] or in the static path approximation [6]. [1] were very promising, this method has never been applied due to its complexity We apply it for the first time (see [11]) to the Richardson hamiltonian at thermal equilibrium and show that this approach provides a proper description of both thermal and quantal fluctuations from very low to high temperature

Description of the method and applications to the Richardson Model

Conclusions and outlook