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Journal of Anhui University

Comparison for the treatment of paring correlations in SLAP and BCS methods

Cao Xiang-yan

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

The shell-model-like approach(SLAP)and BCS methods were used to treat the pairing correlations for an ideal model.The total energy,pairing energy,particle energy and particle occupation together with their evolutions with the pairing strength were obtained.The research indicated that the phase transition from the super fluid to the normal reflected by BCS was clearer,but SLAP might be more reasonable method for describing physics parameters which had obvious relations with the particle number.

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The shell-model-like approach(SLAP)and BCS methods were used to treat the pairing correlations for an ideal model.The total energy,pairing energy,particle energy and particle occupation together with their evolutions with the pairing strength were obtained.The research indicated that the phase transition from the super fluid to the normal reflected by BCS was clearer,but SLAP might be more reasonable method for describing physics parameters which had obvious relations with the particle number.
The BCS and/or Hartree-Fock-Bogoliubov theories are extended by treating the effect of four quasiparticle states perturbatively. The approach is tested on the pairing Hamiltonian, showing that it combines the advantage of standard perturbation theory, valid at low pairing strength, and of nonperturbative approaches breaking the particle number, valid at higher pairing strength. Including the restoration of particle number further improves the description of pairing correlation. In the presented test, the agreement between the exact solution and the combined perturbative plus projection is almost perfect. The proposed method scales friendly when the number of particles increases and provides a simple alternative to other more complicated approaches.
In this work, a new functional is introduced to treat pairing correlations in finite many-body systems. Guided by the projected BCS framework, the energy is written as a functional of occupation numbers. It is shown to generalize the BCS approach and to provide an alternative to Variation After Projection framework. Illustrations of the new approach are given for the pairing Hamiltonian for various particle numbers and coupling strengths. In all case, a very good agreement with the exact solution is found.
Particle-number projection is applied to the modified BCS (MBCS) theory. The resulting particle-number-projected MBCS theory, taking into account the effects due to fluctuations of particle and quasiparticle numbers at finite temperature, is tested within the exactly solvable multilevel model for pairing as well as the realistic 120Sn^{120}\mathrm{Sn}120Sn nucleus. The signature of the pseudogap in the crossover region above the critical temperature of superfluid-normal phase transition is discussed in terms of the pairing spectral function.
In a Fermi gas with a Fashbach resonance, one can tune the strengthof the paring interaction by adjusting the threshold energy of Feshbachresonance. The super-fluid density s is always equal to the total carrierdensity  at T  0 which it vanishes at the super-fluid phase transition c T .These properties are satisfied in both Fermi and Bose super-fluid. There is acrucial difference between s in a Fermi superfluid and that in a Bose superfluid.In a mean field BCS theory originates from the thermal dissociationof cooper pairs.There it was observed that that if one increases the strength of thepairing interaction BCS type normal fluid density dominated by quasi-particleexcitation change into BES type normal fluid density dominated byBogoliubov collective excitations. As super-fluid density s plays animportant role in two fluid hydrodynamics these evaluated results would beuseful in the study of dynamical properties in the BCS-BEC crossover regionat finite temperature.