Abstract
An extended Lipkin-Meshkov-Glick model for testing the proton-neutron random-phase approximation method is developed, taking into account explicitly proton and neutron degrees of freedom. Besides the proton and neutron single-particle terms two types of residual proton-neutron interactions, one simulating a particle-particle and the other a particle-hole interaction, are included in the model Hamiltonian so that the model is exactly solvable in an isospin basis. The behavior of the first excited (collective) state obtained by (i) exact diagonalization of the Hamiltonian matrix and (ii) with the is studied as a function of the model parameters and the two results are compared with each other. Furthermore, charge-changing operators simulating nuclear beta decay and their action on eigenfunctions of the model Hamiltonian are defined and transition amplitudes of them are calculated using exact, the Tamm-Dancoff, and eigenfunctions.
- Received 13 October 1999
DOI:https://doi.org/10.1103/PhysRevC.64.017303
©2001 American Physical Society