Transport equation for deep inelastic heavy ion reactions and fast fission: Exploiting locally harmonic approximations in a multidimensional phase space

The description of deep inelastic reactions and fast fission as stochastic processes requires the numerical resolution of classical transport equations of the Fokker-Planck type for at least five collective variables i.e. in a ten-dimensional phase space. In order to make the collision problem workable when the phase space involved has more than two degrees of freedom, we propose a numerical approximation sticking to the local harmonic approximation (LHA). We solve the set of equations for the second moments of the distribution with the LHA, including small time intervals of frozen spreading of the statistical distribution in cases where the moment expansion breaks down. More elaborate techniques exist, but they are not yet easily practicable in a phase space with more than two degrees of freedom and have never been tested in such cases. The above approximation leads to accurate results in a two-dimensional phase-space problem so that we think that it can be validly applied in a physical problem requiring more collective degrees of freedom. © 1986.SCOPUS: ar.j