DOI: 10.1140/epja/i2002-10089-5
Energies of the ground state and first excited
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.
21.60.Jz - Hartree-Fock and random-phase approximations.
21.60.-n - Nuclear-structure models and methods.
© Società Italiana di Fisica, Springer-Verlag 2003
