Evidence for state dependence of the imaginary part of the empirical optical potential

From the observed neutron scattering from /sup 89/Y and /sup 208/Pb at energies from 5 to 10 MeV, there is empirical evidence that the shape of the surface imaginary part of the neutron optical model potential depends upon energy; the radius increases and the diffuseness decreases with decreasing energy. It is shown that the empirical energy dependence for the radius of the surface imaginary potential is approximately the same as that for the positions of the surface nodes for those partial waves which have the same orbital angular momentum l and total neutron angular momentum j = l +- (12 as for the unoccupied bound single-particle states. The fact that those nodes are clustered near the center of the imaginary potential has the effect of reducing absorption for those partial waves. Therefore, the empirical variation in radius can be reinterpreted by a model for which the radius of the imaginary potential is constant but its strength depends upon the neutron orbital. This dependence can be adequately described by dividing the partial waves into two groups, one with the same quantum numbers l and j as for the bound unfilled orbitals and the other for the unbound states. In the case of n+/sup 208/Pb, for an assumed constant imaginary radius, the quality of the optical model descriptions to the data is improved and the dispersion-relation constraint is more nearly satisfied if the partial waves associated with the quasibound single-particle states are also included with those associated with the unoccupied bound single-particle states.