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A new approach called the Schr\"odinger Collective Intrinsic Model (SCIM) hasbeen developed to achieve a microscopic description of the coupling betweencollective and intrinsic excitations. The derivation of the SCIM proceeds intwo steps. The first step is based on a generalization of the symmetric momentexpansion of the equations derived in the framework of the Generator CoordinateMethod (GCM), when both Hartree-Fock-Bogoliubov (HFB) states andtwo-quasi-particle excitations are taken into account as basis states. Thesecond step consists in reducing the generalized Hill and Wheeler equation to asimpler form to extract a Schr\"odinger-like equation. The validity of theapproach is discussed by means of results obtained for the overlap kernelbetween HFB states and two-quasi-particle excitations at differentdeformations.

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