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

From the observed neutron scattering from ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ 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±(1/2 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${+}^{208}$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. However, since the surface nodes for wave functions associated with the quasibound states are not clustered with those associated with the bound states, this optical model potential is not equivalent to the more conventional model which does not have a state dependence but does have an energy-dependent radius for the surface imaginary potential. Furthermore, this model cannot be replaced by one with only a parity dependence in the imaginary potential depth because the parity of the quasibound states is opposite to the parity of the dominant bound states.