Microscopic calculation of the form factors for deeply inelastic heavy-ion collisions within the statistical model

Agassi, Ko, and Weidenmüller have recently developed a transport theory of deeply inelastic heavy-ion collisions based on a random-matrix model. In this work it was assumed that the reduced form factors, which couple the relative motion with the intrinsic excitation of either fragment, represent a Gaussian stochastic process with zero mean and a second moment characterized by a few parameters. In the present paper, we give a justification of the statistical assumptions of Agassi, Ko, and Weidenmüller and of the form of the second moment assumed in their work, and calculate the input parameters of their model for two cases: ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ on ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ on ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$. We find values for the strength, correlation length, and angular momentum dependence of the second moment, which are consistent with those estimated by Agassi, Ko, and Weidenmüller. We consider only inelastic excitations (no nucleon transfer) caused by the penetration of the single-particle potential well of the light ion into the mass distribution of the heavy one. This is combined with a random-matrix model for the high-lying excited states of the heavy ion. As a result we find formulas which relate simply to those of Agassi, Ko, and Weidenmüller, and which can be evaluated numerically, yielding the results mentioned above. Our results also indicate for which distances of closest approach the Agassi-Ko-Weidenmüller theory breaks down.

[NUCLEAR REACTIONS Random-matrix model and shell model used to calculate distribution of form factors.]