A Theoretical Study of Transition Probabilities for Rare Gas Atoms in an Alternating Electric Field

Abstract

In this work, the in∞uence of an external electric fleld on the behavior of transition probabilities between energy levels was investigated, and dependences of these characteristics on frequency and strength of the electric fleld were obtained. It was found that the transition probabilities and lifetimes of the energy levels in the electric fleld have a polynomial dependence on the electric fleld strength, and the higher the electric fleld frequency is, the bigger the polynomial degree is. The dependences of the transition probabilities and lifetimes on the electric fleld strength and frequency were investigated for the He, Ne, Ar and Kr atoms. In this paper, the in∞uence of an external electric fleld on the behavior of transition probabilities between energy levels was investigated, and dependences of these characteristics on frequency and strength of the electric fleld were obtained. Rare gas atoms under the efiect of the circular polar- ized electric fleld (electric flelds of such polarization are generated in a high-frequency discharge in electrodeless lamps (1) and under laser excitation (2)) were chosen as subjects for study. Rare gases are widely used in plasma physics, therefore, this problem is topical both from a theoretical point of view and for practical applications of the calculation results. In particular, the calculated prob- abilities are necessary at a solution of the population density balance equations and at calculation of the spectral line intensities and lifetimes of the energy levels in the electric fleld (3). In the circular polarized electric fleld, the non-stationary Schrodinger equation, the energies and wave functions of atoms in the electric fleld are determined from, can be reduced to the stationary one. In traditional works, the stationary Schrodinger equation is solved in the framework of perturbation theory (4). However, it is much more convenient to solve this equation by the method of the energy matrix diagonalization (5). This method, free from limitations inherent in perturbation theory, is suitable for a wide range of frequency and strength of the electric fleld. The wave functions and energies of atoms in the electric fleld obtained from the energy matrix diagonalization are used for calculating the transition probabilities between the Stark levels. And then the lifetimes of the Stark levels are calculated using the obtained transition probabilities. This theoretical method was realized in a special software package written in FORTRAN. By virtue of calculation complexity, a systematic study of dependences of the Stark efiect, tran- sition probabilities and lifetimes on frequency and strength of the electric fleld was not performed to the present day. This work makes up this deflciency. 2. CALCULATION METHOD In a circular polarized electric fleld, the non-stationary Schrodinger equation is written as i @ˆn(~) @t = ‡ _