2018 Impact factor 2.481
Hadrons and Nuclei
Eur. Phys. J. A 16, 181-191 (2003)
DOI: 10.1140/epja/i2002-10089-5

Energies of the ground state and first excited $\mth{0^{+}}$ state in an exactly solvable pairing model

N. Dinh Dang

RI-beam factory project office, RIKEN, 2-1 Hirosawa, Wako, 351-0198 Saitama, Japan and Institute for Nuclear Science and Technique, VAEC, Hanoi, Vietnam

dang@postman.riken.go.jp

(Received: 24 July 2002 / Published online: 28 January 2003)

Abstract
Several approximations are tested by calculating the ground-state energy and the energy of the first excited 0+ state using an exactly solvable model with two symmetric levels interacting via a pairing force. They are the BCS approximation (BCS), Lipkin-Nogami (LN) method, random-phase approximation (RPA), quasiparticle RPA (QRPA), the renormalized RPA (RRPA), and renormalized QRPA (RQRPA). It is shown that, in the strong-coupling regime, the QRPA which neglects the scattering term of the model Hamiltonian offers the best fit to the exact solutions. A recipe is proposed using the RRPA and RQRPA in combination with the pairing gap given by the LN method. Applying this recipe, it is shown that the superfluid-normal phase transition is avoided, and a reasonably good description for both of the ground-state energy and the energy of the first excited 0+ state is achieved.

PACS
21.60.Jz - Hartree-Fock and random-phase approximations.
21.60.-n - Nuclear-structure models and methods.

© Società Italiana di Fisica, Springer-Verlag 2003