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Three variants of mean field methods for atomic and nuclear reactions arecompared with respect to both conception and applicability: The time--dependentHartree--Fock method solves the equation of motion for a Hermitian densityoperator as initial value problem, with the colliding fragments in a continuumstate of relative motion. With no specification of the final state, the methodis restricted to inclusive reactions. The time--dependent mean field method, asdeveloped by Kerman, Levit and Negele as well as by Reinhardt, calculates thedensity for specific transitions and thus applies to exclusive reactions. Ituses the Hubbard--Stratonovich transformation to express the fulltime--development operator with two--body interactions as functional integralover one--body densities. In stationary phase approximation and with Slaterdeterminants as initial and final states, it defines non--Hermitian,time--dependent mean field equations to be solved self--consistently asboundary value problem in time. The time--independent mean field method ofGiraud and Nagarajan is based on a Schwinger--type variational principle forthe resolvent. It leads to a set of inhomogeneous, non--Hermitian equations ofHartree--Fock type to be solved for given total energy. All information aboutinitial and final channels is contained in the inhomogeneities, hence themethod is designed for exclusive reactions. A direct link is establishedbetween the time--dependent and time--independent versions. Their relation isnon--trivial due to the non--linear nature of mean field methods.Comment: 21 pages, to be published in European Physical Journal

Mean field methods for atomic and nuclear reactions: The link between time–dependent and time–independent approaches