Two-dimensional random walk on the ground state energy surface: The N-Z distributions from nuclear heavy-ion collisions

The nucleon transfer process in deep inelastic collision is formulated as a two-dimensional random walk process on the N-Z plane. The probability of each step is assumed to be proportional to the available final state density which is determined by the ground state energy surface of the colliding dinuclear system. Here a model problem is considered, where the long and narrow valley in the energy surface is replaced by a slot with a flat bottom. Even in this crude model, good agreement is obtained between the calculated widths of the N-Z distribution and the experimental values, indicating that the ground state energy surface plays an important role in the mass and charge transfer phenomena in deep inelastic processes.