Український математичний конгрес - 2009
Наталья Мудрая (Одесский государственный экологический университет, Одесса, Украина)
QED-DFT formalism to autoionization resonances in quantum systems in an external field: New scheme
It is known that a consistent theory of the autoionization resonances is to take into account correctly a definite number of the correlation (polarization, relaxation) effects, including the energy dependence of the vacancy mass operator, the continuum pressure, spreading of the initial state over a set of configurations etc. [1-5]. It should be reminded that hitherto these effects are not described adequately in the modern theoretical schemes. As example, let us remind such wide-spread methods as the : Dirac-Fock, relativistic Hartree-Fock methods, random phase approximation (RPA) and RPA with exchange, different model and pseudo potential schemes, density-functional formalism and its relativistic generalization etc. (see e.g. ). We present a new relativistic density functional theory scheme to description of the autoionization resonances in atomic spectra in an external fields within the S-matrix Gell-Mann and Low formalism and the relativistic perturbation theory. New scheme has to be applied to studying the autoionization phenomena characteristics in the atomic and molecular (obviously heavy) systems, and quasi-molecules and solids. The novel elements consist in an implementation of the relativistic Dirac-Kohn-Sham density functional theoretical scheme to the S-matrix Gell-Mann and Low formalism and using the optimized electron wave functions basis’s of the QED perturbation theory  in order to describe the fundamental characteristic of quantum systems in an external field .