Two-Dimensional Random Walk Process in Heavy Ion Collisions

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Abstract
Two-dimensional random walk model is applied to describe the interrelation between the energy loss and the mass transfer in heavy ion collisions. To take account of the energy loss associated with the mass transfer, we introduce the diagonal steps to the ordinary two-dimensional random walk process. The average of the total kinetic energy loss Eloss, as a function of the mass fragmentation, has a minimum at the initial mass fragmentation for the interaction time not very much exceeding the relaxation time. The results obtained from the present model are compared with some experimental data. They are in fairly good agreement with the experimental ones. The optimum values of the fractional energy or the distances of the neighboring sites ΔE, are ∼10 MeV for the 16O(88 MeV)+21Al reaction and ∼24 MeV for the 40Ar(388 MeV)+232Th reaction. These values of ΔE are not contradictory to the assumptions inherent in the present model. We see that the smaller the magnitude of the step is, the less prominent the minima of the Eloss as functions of the mass of the reaction products are. In the limit of the infinitesimal steps, i.e., the Fokker-Planck version, the minima disappear. So, in the context of the present model, the finite magnitude of the steps of the walker is suggested, together with the existence of diagonal steps.

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