Green's function method in quantum chemistry: New numerical algorithm for the Dirac equation with complex energy and Fermi-model nuclear potential

Autor: D. E. Sukharev, Alexander V. Glushkov, L. Lovett, O. Yu. Khetselius, A. V. Loboda, S. V. Malinovskaya
Rok vydání: 2009
Předmět:
Zdroj: International Journal of Quantum Chemistry. 109:1717-1727
ISSN: 1097-461X
0020-7608
DOI: 10.1002/qua.22200
Popis: We present a new effective approach to construction of the electron Green function for the Dirac equation with a nonsingular central nuclear Fermi-model potential and complex energy. We represent the radial Green function as a combination of two fundamental solutions of the Dirac equation. The approach proposed includes a procedure of generating the relativistic electron functions Ψ with performance of the gauge invariance principle. To reach the gauge invariance principle performance, we use earlier developed QED perturbation theory approach. In the fourth order of the QED perturbation theory (PT) there are diagrams, whose contribution into imaginary part of radiation width ImdE for the multielectron system accounts for many-body correlation effects. A minimization of the functional ImdE leads to integral-differential Kohn-Sham-like density functional equations. Further check for the gauge principle performance is realized by means of the Ward identities. In the numerical procedure we use the effective algorithm, within which a definition of the Dirac equation fundamental solutions is reduced to solving the single system of the differential equations. This system includes also the differential equations for the Fermi-model nuclear potential and equations for calculating the integrals of the ∫ ∫ dr1dr2 type in the Mohr formula for definition of the self-energy shift to atomic levels energies. Such an approach allows to compensate a main source of the errors, connected with numerical integration ∫dξ and summation on χ in the Mohr expressions during calculating the self-energy radiative correction to the atomic levels energies. Some numerical illustrations of applying the approach within QED PT to calculate the intermediate and high-Z Li-like ions transitions energies are presented. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
Databáze: OpenAIRE
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