Two- and four-quasiparticle states in spherical vibrational nuclei

Expressions are derived in the modified Tamm-Dancoff (TD) approximation which take into account the mixing of zero-, two-, and four-quasiparticle states for the description of the collective vibrational states of spherical nuclei. The proposed method is free from two very important defects inherent in the higher random-phase approximation (HRPA), namely, nonorthonormality and redunancy of the four-quasiparticle basic states. The relative merits of the present method over the existing one (HRPA) are discussed.