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Nuclear Physics A

Comparison between exact and approximate treatments of the pairing interaction for finite Fermi systems

J. Dukelsky, G.G. Dussel, Jorge G. Hirsch, Peter Schuck

Published Jan 30, 2003• 35 citations
Publisher
DOI
10.1016/s0375-9474(02)01361-1

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We consider a very asymmetric system of fermions with an interaction characterized by a positive scattering length only. The minority atoms pair and form a Bose-Einstein condensate of dimers, while the surplus fermions interact only indirectly through the exchange of Bogoliubov sound modes. This interaction has a finite range, the retardation effects are significant, and the surplus fermions will form a PPP-wave superfluid. We compute the PPP-wave pairing gap in the BCS and Eliashberg approximations with only energy-dependence approximations, and demonstrate their inadequacy in comparison with a full treatment of the momentum and energy dependence of the induced interaction. The pairing gap computed with a full momentum and energy dependence is significantly larger in magnitude, and that makes it more likely that this new exotic paired phase could be put in evidence in atomic trap experiments.
A systematic comparison is conducted for pairing properties of finite systems at nonzero temperature as predicted by the exact solutions of the pairing problem embedded in three principal statistical ensembles, as well as the unprojected (FTBCS1+++SCQRPA) and Lipkin+++Nogami projected (FTLN1+++SCQRPA) theories that include the quasiparticle number fluctuation and coupling to pair vibrations within the self-consistent quasiparticle random-phase approximation. The numerical calculations are performed for the pairing gap, total energy, heat capacity, entropy, and microcanonical temperature within the doubly folded equidistant multilevel pairing model. The FTLN1+++SCQRPA predictions agree best with the exact grand-canonical results. In general, all approaches clearly show that the superfluid-normal phase transition is smoothed out in finite systems. A novel formula is suggested for extracting the empirical pairing gap in reasonable agreement with the exact canonical results.