The effect of collective excitations on the optical model.

A simple model is proposed for the description of the scattering of neutrons by a vibrational even-even nucleus employing a complex spheroidal well surface interaction. This model is particularly convenient since it allows an exact analytic solution, which can be written in the form of correction terms to the spherical optical model. The application of this model to the s wave strength function results in a splitting of the single peak at A= 55. The inclusion of the effect of octupole excitation introduces desirable but minor modifications. Determination of the total neutron cross sections with this model substantiates the view that the flattening of giant resonances away from closed shell regions can be attributed to the effect of quadrupole excitation. There is also some evidence from this model that the effect of collective excitations could account for the characteristic shift of the maxima associated with these resonances. The scattering and reaction cross sections as well as the differential shape elastic scattering are also calculated