Microscopic and nonadiabatic Schrödinger equation derived from the generator coordinate method based on zero- and two-quasiparticle 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+BCS (HF+BCS) 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 HF+BCS states and two-quasiparticle excitations at different deformations.