Accuracy of BCS-based approximations for pairing in small Fermi systems

Details Accuracy of BCS-based approximations for pairing in small Fermi systems Accuracy of BCS-based approximations for pairing in small Fermi systems

2008-08-21

arxiv.org/abs/0808.3009v1

Phys.Rev.C78:064318,2008

Physics

Nuclear Physics

Nuclear Theory

10 pages; 14 figures

Scientific paper

10.1103/PhysRevC.78.064318

We analyze the accuracy of BCS-based approximations for calculating correlation energies and odd-even energy differences in 2-component fermionic systems with a small number of pairs. The analysis is focused on comparing BCS and projected BCS treatments with the exact solution of the pairing Hamiltonian, considering parameter ranges appropriate for nuclear pairing energies. We find that the projected BCS is quite accurate over the entire range of coupling strengths in spaces of up to about 20 doubly degenerate orbitals. It is also quite accurate for two cases we considered with a more realistic Hamiltonian, representing the nuclei around 117Sn and 207Pb. However, the projected BCS significantly underestimates the energies for much larger spaces when the pairing is weak.

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