The phonon vacuum state in a Lipkin model

Abstract

The action of the long-range residual force on the expectation value of observables in the nuclear ground states is evaluated by finding optimal values for the coefficients of the canonical transformation which connects the phonon vacuum state with the independent-particle ground-state using the two-level Lipkin-Meshkov-Glick (LMG) model. After estimating the improvements over the predictions of the independent-particle approximation we compare the ground and first excited states wave functions, obtained using the presented approach, with those, obtained using the conventional random phase approximation (RPA) and its extended version. The problem with overbinding of the nuclear ground state calculated using the RPA is shown to be removed if one sticks to the prescriptions of the present approach. The reason being that the latter conforms to the original variational formulation.