Microscopic analysis of nuclear collective motions in terms of the boson expansion theory. Pt. 1

A normal-ordered linked-cluster boson expansion theory, previously worked out by one of the authors (T.K.) and Tamura, has been developed further by reformulating it in a 'physical' quasiparticle subspace which contains no spurious particle-number excitation modes. The expansion coefficients of the collective hamiltonian for low-lying quadrupole motions are determined starting from a microscopic fermion hamiltonian including self-consistent higher-order (many-body) interactions derived in our previous work. The contributions from the non-collective states with all possible non-collective one-boson excitations having Iπ = 0+-4+, which can directly couple to the collective states with one or two phonons, are taken into account in a systematic and compact way. (orig.)