2-BODY COLLISIONS AND TIME-DEPENDENT HARTREE-FOCK THEORY

The time-dependent Hartree-Fock (TDHF) theory is generalized in order to include the effect of two-body collisions (i.e. the residual interaction). This is achieved by adding a collision integral into the TDHF equations, similar to the one ordinarily used in the Boltzmann equation. It is shown, that two-body collisions arise from the imaginary part of the effective interaction between two nucleons whereas the Hartree-Fock field is associated to the real part of the same interaction. There is thus no double counting when the collisions are added to a single particle field. Various approximations for the collision integral are discussed and their accuracy evaluated. Special effort is made in order to obtain conserving approximations. It is shown that for discrete fields, energy as well as momentum conservation is achieved by off-shell scattering processes. In the light of a previous paper, it is argued that two-body collisions should dominate the irreversible processes above some critical energy (roughly 200 MeV per nucleon). Below this energy the irreversible effects due to the single particle field and the collisions are expected to be of the same order of magnitude. © 1979 Springer-Verlag.