Mean field methods for atomic and nuclear reactions: The link between time-dependent and time-independent approaches
J. Uhlig - J.C. Lemm - A. Weiguny
Institut für Theoretische Physik I, Universität Münster, D-48149 Münster, Germany
Received: 7 January 1998 / Revised version: 20 April 1998 Communicated by F. Lenz
Abstract
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.
PACS
03.65.Nk Nonrelativistic scattering theory -
24.10.-i Nuclear-reaction models and methods -
34.10.+x General theories and models of atomic and molecular collisions and interactions
(including statistical theories, transition state, stochastic and trajectory models, etc.)
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