Proton-neutron correlations and shell model for collective motions

A new truncation method for shell-model spaces is proposed, based on the proton-neutron correlations. The dominance of the quadrupole force in the $p-n$ interactions is established by the investigation of empirical matrix elements in the $\mathrm{pf}$ shell. A truncation scheme based on the quadrupole component of the $p-n$ interactions is applied to the $N=30\mathrm{}$ nuclei and compared with exact shell-model calculations. Satisfactory agreement between the two results suggests the wide validity of the present truncation method when applied to collective phenomena in nuclei. A relation between the shell model and the particle-vibration model is discussed.