Investigation of Ground-State Correlations for a Model Hamiltonian of the Nucleus

The importance of ground-state correlations in the spectroscopy of a finite many-particle system, such as the nucleus, is investigated for the model Hamiltonian of Lipkin, Meshkov, and Glick. In particular, we have investigated their effect on the solution of the equations of motion for excitation energies, transition matrix elements, and the correlation energy of the ground state. Methods are studied for calculating the correlations needed to make the necessary corrections to the equations of motion. Also studied is the behavior, with increase of interaction strength, of the phase transition from the spherical to the strongly deformed intrinsic states, in the projected Hartree-Fock scheme.