A quantum-mechanical model of coupled proton and neutron asymmetries and the fast charge equilibration process in deep-inelastic collisions

A quantum-mechanical model of coupled harmonic oscillators in collective coordinates of proton and neutron asymmetries is solved analytically, in a non-perturbative formalism, for the charge and neutron distributions in deep-inelastic reactions. The time evolution of the mean values (centroids) and the variances (widths) is studied for the initial distribution taken to be a two-dimensional Gaussian function. Model calculations are presented that show the detailed dependence of the relevant quantities on the variables of our model. Fits to the experimental data are made for the reactions ¹²⁹Xe on ¹¹⁶Sn and ¹²⁴Sn.