Qualitative properties of the discrete random walk evolution of projectile-like (N, Z) values on the dinuclear liquid-drop surface

A discrete random walk calculation of the evolution of the (N, Z) distribution of projectile-like fragments from a nuclear heavy ion collision is presented. It incorporates energy conservation explicitly for each nucleon transfer, utilizing the liquid drop energies of osculating dinuclei to estimate the (N, Z) dependence of the ground state energy of the system. The results show that energy conservation and the liquid-drop energy surface suffice to prescribe the characteristic shapes in (N, Z) of the distributions when the transfer probabilities are defined by the total nuclear level densities; the rate at which the distribution spreads, on the other hand, is dominated by the fraction of the kinetic energy which is assumed to be dissipated by mechanisms other than nucleon transfer. Possible alternative prescriptions for the transfer probabilities are considered and shown to be qualitatively in disagreement with the observations at higher total kinetic energy loss (TKEL). Also it is shown that the overall width, sigma2sub(A), is less sensitive to such variations of the transfer probabilities than sigma2sub(Z), and how this feature is a natural consequence of the dinuclear energy surface. Finally, a residual discrepancy between calculation and observation at low TKEL values is identified as the most prominent remnant weakness of the description. (orig.)