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Journal of Physics Condensed Matter

Correlation effects in dynamical charge-transfer processes

E. C. Goldberg, Mario C. G. Passeggi

Published Aug 16, 1993• 4 citations
Publisher

Abstract

The Keldysh-Green function approximate solutions of the correlation effects on the charge-exchange probabilities for a scattered atom from a three-atom linear chain within the Anderson model are compared with exact results for different velocities of the moving atom.
DOI
10.1088/0953-8984/5/33a/087

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The Green function formalism introduced by Keldysh for irreversible processes is applied to the calculation of the time-dependent charge exchange probabilities in scattering problems. Considering the initial state of two non-interacting subsystems described by an independent particle model, their interaction is taken in a first stage, as evolving in time according to a time-dependent Hartree - Fock (TDHF) scheme. The equations of motion for the two-times Green functions are subsequently obtained in Dyson-like form by including the residual electronic correlations expanded perturbatively up to second order. It is shown that, by solving these equations of motion, this in turn allows one to calculate the two-particle correlation functions at equal times, as required to describe the fractions of charge in each subsystem. This procedure contrasts with that of considering expectation values of the correlation functions taken between the corrected TDHF state up to an equivalent order in the perturbation. In order to test the advantages of this method we have applied this scheme to the scattering of an atom from a three-substrate atom chain described by an Anderson Hamiltonian, where comparisons with exact solutions can be easily established. We found that, in this case, the fractions of charges carried by the scattered particle obtained with our proposal compare fairly well with exact results, within an ample range of parameter selection.
This work is mainly devoted to the description of processes that involve the interaction between an atom and a surface, in which a strong Coulomb repulsion on the atomic site (U)(U)(U) limits the charge exchange to one electron (infinite-UUU limit). In this limit, the Anderson Hamiltonian for a many-fold (N)(N)(N) of states localized on the atomic site can be represented in terms of auxiliary bosons and physical operators in the mixed boson-electron space can be defined. In this work the Hamiltonian is solved by defining appropriate Green's functions for physical operators. Then we solved the equations of motion of these Green's functions, up to a second order in the atom-surface coupling, either for the stationary case or for a real time-dependent problem. We show that our approach reproduces the known exact results in the nondegenerate (N=1)(N=1)(N=1) case, and for $N\ensuremath{\succ}1$ gives excellent agreement with exact calculations and approximations valid for large NNN (the 1∕N1∕N1∕N expansion). Finally, the accurate description of dynamical processes is shown by the comparison with the exact results available for a small four-level system. In this case we also compare with results obtained by using the noncrossing approximation and with the usual spinless model calculation.
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