Green's Function of the Dirac Equation with Complex Energy and Non-singular Central Nuclear Potential

• Published in: Reconsideration of Foundations-5 2009-06, Vol.1232, p.259-266
• Main Authors: Svinarenko, A A, Glushkov, A V, Loboda, A V, Sukharev, D E, Dubrovskaya, Yu V, Mudraya, N V, Serga, I N
• Format: Article
• Language: English
• Subjects: Charge distribution; Construction; Differential equations; Dirac equation; Energy (nuclear); Energy of formation; Estimates; Formalism; Green's functions; Mathematical models; Nuclear potential; Numerical analysis; Perturbation theory
• ISSN: 0094-243X

We report the further development of an effective approach to construction of the electron Green's function (GF) for the Dirac equation with a complex energy and non-singular central nuclear potential. The nuclear charge distribution and the corresponding nuclear potential are received within the relativistic mean field (RMF) model. The Green's function is usually represented as a combination of two fundamental solutions of the Dirac equation. In the numerical procedure we use the Ivanov-Ivanova effective numerical algorithm and reduce a definition of the Dirac equation fundamental solutions to solving the system of differential equations, which includes the differential equations for the RMF nuclear potential too. As an application, we estimate the self-energy shift correction to atomic levels energies within the Mohr covariant procedure and presented GF approach and calculate the transitions energies for some heavy Li-like multi-charged ions within the QED many-body perturbation theory formalism.