Sharing of collective multipole strength in the nuclear particle-hole model.

Abstract

A procedure is given for defining explicitly the noncollective states of the degenerate schematic model for nuclear particle-hole configurations. The method is based on the view that the degenerate model is an approximation to the nondegenerate particle-hole model. In the collective-noncollective basis with a single force type, the separable particle-hole Tamm-Dancoff Hamiltonian matrix is transformed into one which is diagonal except for the row and column of the one collective state. The multipole strength of any noncollective state of the nondegenerate problem is given in perturbation theory in terms of the collective-noncollective matrix elements, which are expressed in terms of the parameters of the assumed separable multipole interaction. Application of the sharing formulas is made to Landau damping of the collective state due to mixing with the noncollective states. The relative contribution to the width due to the nondegeneracy and the nonseparable nature of the interaction are examined. Another application examines the random-phase-approximation energy distribution of isospin shared by the isoscalar and isovector collective states with the noncollective states over the giant quadrupole resonance region in $^{118}\mathrm{Sn}$.