Time- dependent exchange perturbation theory

Permutation Symmetry in Coherent Electrons Scattering by Disordered Media

“…Here, n is the set of quantum numbers of atoms in the initial state, and p is the momentum of the incident electron. Regarding the exchange perturbation theory method [27,28], the final state of the whole system can be described by the non-symmetric wave function m, p − Q) = |m • p − Q , which is a simple product of the atomic function |m , antisymmetrized with internal electron permutations, and a free electron function p − Q , where Q is the total momentum transferred to the medium. It should be underlined that the operator (2) describing electron interaction with atoms has a non-symmetric form regarding the interatomic electron permutations (the exchange of numbered atomic electrons with the free electron of incident):…”

“…where  is the antisymmetrization operator [27,28]. Acting on a non-symmetric wave function, operator  performs antisymmetrization:…”

“…At the same time, the complete Hamiltonian of the system Ĥ = Ĥ0 + V retains its invariance: Â Ĥ = 0. This discrepancy means a serious problem related to the fact that the zero-order wave function, antisymmetrized with respect to center-to-center electron permutations, is not an eigenfunction of the non-invariant Hamiltonian Ĥ0 [27], and the corrections are obtained by applying an asymmetric operator of interactions containing non-physical contributions. In [27,28], a special symmetric form of the perturbation operator and zeroth Hamiltonian were developed.…”

“…This discrepancy means a serious problem related to the fact that the zero-order wave function, antisymmetrized with respect to center-to-center electron permutations, is not an eigenfunction of the non-invariant Hamiltonian Ĥ0 [27], and the corrections are obtained by applying an asymmetric operator of interactions containing non-physical contributions. In [27,28], a special symmetric form of the perturbation operator and zeroth Hamiltonian were developed. It allows corrections of the wave functions, properly antisymmetrised, and the energy corrections to be obtained by using the correct antisymmetric basis of the wavefunctions:…”

“…We will take into account the identity of the incident electrons and electrons belonging to multielectron scatterer atoms. An invariant exchange perturbation theory method [27,28] is applied for the development of the cross-section for the weak localization scattering process while taking into account exchange effects. It is shown that, in spite of isotropic scattering by each individual scatterer, the number of electrons and their spin state in the open shell of the atom radically affect the resulting angular dependence of the scattering cross-section of incident electrons.…”