# Correlation energy of the pairing Hamiltonian

@article{Hagino2000CorrelationEO, title={Correlation energy of the pairing Hamiltonian}, author={Kouichi Hagino and George F. Bertsch}, journal={Nuclear Physics}, year={2000}, volume={679}, pages={163-174} }

Abstract We study the correlation energy associated with the pair fluctuations in BCS theory. We use a schematic two-level pairing model and discuss the behavior of the correlation energy across shell closures, including the even-odd differences. It is shown that the random phase approximation (RPA) to the ground state energy reproduces the exact solutions quite well both in the normal fluid and in the superfluid phases. In marked contrast, other methods to improve the BCS energies, such as…

## 22 Citations

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## References

SHOWING 1-10 OF 53 REFERENCES

Pairing correlations studied in the two-level model.

- Physics, MedicinePhysical review. C, Nuclear physics
- 1992

It is found that conclusions regarding the quality of the BCS approximation as well as various approximate projection methods are not valid in the more general N=\ensuremath{\Omega} case when the pairing interaction is weak.

Lipkin-Nogami pairing scheme in self-consistent nuclear structure calculations.

- Physics, MedicinePhysical review. C, Nuclear physics
- 1996

The Lipkin-Nogami scheme is investigated in connection with nuclear Hartree-Fock models, andounced effects on deformation energy surfaces were found, leading to sizable differences in the deformation energies.

Pairing in the limit of a large number of particles

- Physics
- 1977

Expressions for the ground and excited state energies of a system of nucleons interacting through pairing forces are given as a power series in inverse powers of the number of particles. The…

Selfconsistent and renormalized particle particle RPA in a schematic model

- Physics
- 1998

The dynamical effects of ground state correlations for excitation energies and transition strengths near the superfluid phase transition are studied in the soluble two level pairing model, in the…

Comparative study on the validity of the renormalized random-phase approximation

- Physics
- 1998

The consistency of the renormalized random-phase approximation ~RRPA!, to treat correlations nearby a phase transition, is analyzed. The results of the RRPA and its quasiparticle version ~RQRPA! for…

Pairing fluctuations in rapidly rotating nuclei

- Physics
- 1989

Empirical evidence for the existence of pair fluctuations in rapidly rotating nuclei in connection with the pair gap is reviewed. The quantities considered are single-particle energies (routhians)…

Exact pairing calculations in a large Nilsson-model basis: comparison with BCS and Lipkin-Nogami methods

- Physics
- 1996

Abstract Full many-body calculations of the spectra of heavy deformed nuclei become prohibitively large and one is forced to employ approximate mean-field methods. The deformation is accounted for by…

Random-phase approximation approach to rotational symmetry restoration in a three-level Lipkin model

- Physics
- 2000

We study an extended Lipkin-Meshkov-Glick model that permits a transition to a deformed phase with a broken continuous symmetry. Unlike simpler models, one sees a persistent zero-frequency Goldstone…

Nuclear pairing models

- Physics
- 1992

Abstract We calculate nuclear pairing gaps for nuclei throughout the periodic system in both the BCS and Lipkin-Nogami pairing models. The energy levels required for the calculations are obtained…

A study of some approximations of the pairing force

- Physics
- 1961

Abstract The quasi-particle and the boson approximation are used in the study of the first 0+ excited state of the pairing force: a special case is chosen for its simplicity, which allows us to study…