Microscopic particle-vibrator model: A new fermion-boson expansion

The elements for a microscopic foundation of the particle-vibrator model are derived in the form of a new fermion-boson expansion in which valence particles or holes added to a closed shell are treated essentially as fermion degrees of freedom, while particle-hole excitations of the closed shell itself are treated as bosons. The Pauli principle is completely fulfilled without redundancy. The generalizations of both the non-unitary Dyson and the unitary Holstein-Primak off representations are given, as well as an equivalent intermediate unitary representation.