  Three variants of mean field methods for atomic and nuclear reactions are
compared with respect to both conception and applicability: The time--dependent
Hartree--Fock method solves the equation of motion for a Hermitian density
operator as initial value problem, with the colliding fragments in a continuum
state of relative motion. With no specification of the final state, the method
is restricted to inclusive reactions. The time--dependent mean field method, as
developed by Kerman, Levit and Negele as well as by Reinhardt, calculates the
density for specific transitions and thus applies to exclusive reactions. It
uses the Hubbard--Stratonovich transformation to express the full
time--development operator with two--body interactions as functional integral
over one--body densities. In stationary phase approximation and with Slater
determinants as initial and final states, it defines non--Hermitian,
time--dependent mean field equations to be solved self--consistently as
boundary value problem in time. The time--independent mean field method of
Giraud and Nagarajan is based on a Schwinger--type variational principle for
the resolvent. It leads to a set of inhomogeneous, non--Hermitian equations of
Hartree--Fock type to be solved for given total energy. All information about
initial and final channels is contained in the inhomogeneities, hence the
method is designed for exclusive reactions. A direct link is established
between the time--dependent and time--independent versions. Their relation is
non--trivial due to the non--linear nature of mean field methods.
