Influence of the impact parameter on element distributions in dissipative heavy-ion collisions

The ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$+ ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$ reaction at laboratory bombarding energies of 940, 1130, and 1422 MeV is interpreted on the basis of a phenomenological classical model and a diffusion model for damped collisions. Initial angular momenta, interaction times, and charge diffusion coefficients are deduced with the above models from experimental data reported previously. The bombarding energy dependence of the model parameters and the effect of deformation on the dinuclear system in the exit channel are discussed. An analytical relation is suggested between the variance ${{\sigma }_Z}^2$ of the element distribution and the ratio $\frac{E}{l_g}$, where $E$ is the measured final total kinetic energy and $l_g$ is the grazing orbital angular momentum. This semiempirical formula is applied to sixteen heavy-ion systems at bombarding energies well above the Coulomb barrier. In a plot of $\ln {{\sigma }_Z}^2$ versus $\frac{E}{l_g}$ all the experimental data fall on parallel lines with displacements that are reasonably well correlated with $\frac{E_0}{l_g}$, where $E_0$ is the bombarding energy in the c.m. system. In a model-dependent explanation of this empirical relation, evidence is found that the variance of the element distributions ${{\sigma }_Z}^2$ is determined by the initial relative angular momentum $\frac{l}{l_g}$.