Dyson representation of the interacting boson model with pairing plus quadrupole pairing plus quadrupole-quadrupole forces

With a usual choice of the effective nucleon-nucleon interactions consisting of a pairing force, a quadrupole pairing force, and a quadrupole-quadrupole force, the microscopic approach, as described in our previous work, based on the Dyson boson expansion and based on the so-called modified Jancovici-Schiff substitution is followed to obtain a set of eigenequations for determining the IBM bosons and to find the microscopic expressions of the coefficients appearing in the interaction terms of the IBM Hamiltonian. The results given in the present paper can be used directly in calculating the collective spectra of nuclei with identical valence nucleons outside closed shells