Semiclassical treatment of the interaction between individual and quadrupole collective degrees of freedom

Two types of interactions between a system of paired spherical shell-model nucleons and a phenomenological quadrupole vibrational core are treated semiclassically: one induces a specific dependence of the gap parameter on the core's angular momentum while the other one renormalizes the single-particle energies by a β2 term. The former case enables one to make the same interpretation for a sequence of states of the same angular momentum J-horizontal band - as RPA multiphonon states describing vibrations of small amplitudes around the ground state Jsub(g)+. A vertical band J, J+2, ... is built by an approximative projection of angular momentum from a variational trial function. Application to 188Pt shows a good agreement with experiment. The second type of interaction renormalizes the energy of the quadrupole mode and shifts the zero-point energy. Using the phase-space coordinates one defines three distinct boson representations for the quasispin operators, which are useful for improving the RPA approach. One concludes that the particle-core interaction affects essentially not only the states lying beyond the crossing point of yrast collective and 2 q.p. bands but also the low-lying collective states. (orig.)