Український математичний конгрес - 2009

Андрей Лобода (Одесский государственный экологический университет, Одесса, Украина)

QED energy formalism to modelling processes in a plasma of multicharged ions: Debye shielding approximation

In the theory of the non-relativistic atom a convenient field procedure is known for calculating the energy shifts E of degenerate states [1]. This procedure is connected with the secular matrix M diagonalization. In constructing M, the Gell-Mann and Low adiabatic formula for dE is used. A similar approach, using the Gell-Mann and Low formula with the QED scattering matrix, is applicable in the relativistic atom theory [2]. The method is a consistently electrodynamics one, allowing for the uniform consideration of a variety of induced and spontaneous processes different by their physical nature and with any number of photons. In contrast to the non-relativistic case, the secular matrix elements are already complex in the second order of the perturbation theory (PT) (first order of the inter-electron interaction). Their imaginary parts are connected with the radiation decay (radiation) possibility. The total energy shift of the state is usually presented in the form: dE = RedE + i ImdE, Im E = -/2 , where  is interpreted as the level width, and the decay possibility P = . The whole calculation of the energies and decay probabilities of a non-degenerate excited state is reduced to calculation and diagonalization of the complex matrix M. We firstly develop the uniform quantum energy approach to numerical modeling spectra of the multicharged ions plasma and its fundamental characteristics. The method proposed is based on the ab initio QED perturbation theory formalism with using the relativistic Dirac Hamiltonian for electron-nuclear and electron-electron potentials, gauge-invariant scheme of generation of the optimal one-electron representation and the Debye shielding approximation.

References :
1. A.V. Glushkov, Relativistic Quantum Theory, Odessa, Astroprint, ed.1, 2008.-900P.
2. A.V. Glushkov, A.V. Loboda et al, Int. J. Quant. Chem. -2005.-Vol.109.-P.561-572; J.Phys.CS.-2005.-Vol.11.-P.188-198.
3. Glushkov A.V., Khetselius O.Yu., Loboda A.V., Svinarenko A.A., Frontiers in Quantum Systems in Chemistry and Physics (Berlin, Springer).-2008.-Vol.18.-P. 201-220.