Microscopic and non-adiabatic Schr\"odinger equation derived from the Generator Coordinate Method based on 0 and 2 quasiparticle HFB states

A new approach called the Schr\"odinger Collective Intrinsic Model (SCIM) has been developed to achieve a microscopic description of the coupling between collective and intrinsic excitations. The derivation of the SCIM proceeds in two steps. The first step is based on a generalization of the symmetric moment expansion of the equations derived in the framework of the Generator Coordinate Method (GCM), when both Hartree-Fock-Bogoliubov (HFB) states and two-quasi-particle excitations are taken into account as basis states. The second step consists in reducing the generalized Hill and Wheeler equation to a simpler form to extract a Schr\"odinger-like equation. The validity of the approach is discussed by means of results obtained for the overlap kernel between HFB states and two-quasi-particle excitations at different deformations.