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

Journal Article · Mon Dec 15 04:00:00 EST 2008 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PHYSREVC.78.064318· OSTI ID:21199429

Sandulescu, N ^[1]; Bertsch, G F ^[2]

---

1. Institute of Physics and Nuclear Engineering, R-76900 Bucharest (Romania)
2. Institute of Nuclear Theory and Department of Physics, University of Washington, Seattle, Washington 98105-6694 (United States)

We analyze the accuracy of BCS-based approximations for calculating correlation energies and odd-even energy differences in two-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 {approx}20 doubly degenerate orbitals. It is also quite accurate for two cases we considered with a more realistic Hamiltonian, representing the nuclei around {sup 117}Sn and {sup 207}Pb. However, the projected BCS significantly underestimates the energies for much larger spaces when the pairing is weak.

• OSTI ID: 21199429
• Journal Information: Physical Review. C, Nuclear Physics, Journal Name: Physical Review. C, Nuclear Physics Journal Issue: 6 Vol. 78; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
APPROXIMATIONS
BCS THEORY
COUPLING
ELECTRON CORRELATION
EXACT SOLUTIONS
FERMIONS
HAMILTONIANS
LEAD 207
PAIRING ENERGY
SIMULATION
TIN 117