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Quadratic Stark corrections to the wave functions, matrix elements, and probabilities of transitions between the singlet states 1 S 0 and 1 P 1 of helium atoms are calculated. The coefficients of the polynomials that depend on the effective principal quantum number of the upper level v f and that approximate the numerical values of the polarizabilities, the quadratic corrections to the wave functions, and the probabilities of transitions to highly excited Rydberg states with large v f are determined. The results of calculations testify that the probabilities of all σ transitions n i 1 S 0 → n f 1 P 1 and π transitions to the states with n f > n i /2 are decreased with increasing electric field strength, except for the transition 21 S 0 → 21 P 1, whose probability increases both for σ and for π transitions. [ABSTRACT FROM AUTHOR]

Perturbation theory for the wave function of a hydrogen-like atom in a homogeneous electric field of strength F makes it possible to obtain the Rayleigh-Schrödinger series with the coefficients of F[sup N] (N = 0, 1, 2, …) being linear combinations of the Sturm function, which represents the unperturbed state, with 8N² functions of the corresponding complete set with indices adjacent to the parabolic quantum number of the initial level. A method for recursive analytic calculation of the coefficients of the linear combination for any order N is developed. General expressions for corrections to the matrix elements and intensities of the radiation transitions between Stark sublevels are obtained. Analytic formulas and numerical values of the corrections up to the fourth order for the Lyman and Balmer series are presented. A comparison with the available data for transitions between the Stark components of Rydberg states is given. [ABSTRACT FROM AUTHOR]