Analytical calculation of fusion barrier distributions

The eigenchannel approximation is applied to the calculation of fusion cross section for the case when the intrinsic nuclear excitations are treated as simple-harmonic vibrations. The resulting expression has been expressed as an average over a smooth distribution of fusion barriers. The mean-barrier parameters are obtained from the optical model, and the nuclear oscillation parameters from the liquid-drop model or expressed in terms of electromagnetic transition strengths, so that the obtained barrier distribution does not, in principle, involve any free parameter. The target excitation energies are subsequently taken into account by replacing the incident energy in the expression for the transmission coefficient by the mean value of the initial and final kinetic energies in each channel. As a result, the barrier distribution becomes more extended towards larger barriers and shows strong oscillatory behavior. These oscillations are strongly reduced when the barrier distributions are represented as the derivative of the fusion cross section. Corrections for angular momentum transfer are discussed in terms of the concept of tangential friction. The calculated distributions df fusion barriers are in reasonable agreement with the empirical distributions corresponding to the interaction of O-16 with vibrational target nuclei, but fail in the case of rotational nuclei where the present formalism is hardly justified. The distributions are shown to be useful in resolving the parameter ambiguity of the optical potential. {[}S0556-2813(98)01509-X].