Higher orders of perturbation theory for the Stark effect on an atomic multiplet

Abstract

The contribution of higher order corrections to the Stark energy is calculated in the anticrossing region of atomic multiplet sublevels. Perturbation theory for close-lying levels is presented that is based on the Schro dinger integral equation with a completely reduced Green’s function. Analytic formulas are obtained for the splitting of two interacting fine-structure sublevels as a function of the field strength. These formulas take into account fourth-order resonance and nonresonance corrections to both the diagonal and the off-diagonal matrix elements of the dipole moment operator. By the method of the Fues model potential, a numerical analysis of radial matrix elements of the second, third, and fourth orders is carried out that determine a variation in the transition energy between n 3 P 0 and n 3 P 2 sublevels of a helium atom for n=2, 3, 4, 5 in a uniform electric field. It is shown that the contribution of the fourth-order corrections in the vicinity of anticrossing of levels for n=2, 3, 4, 5 amounts to 0.1, 5, 10, and 15% of the total variation of energy, respectively. A comparative anal-ysis is carried out with the results of calculations obtained by the method of diagonalization of the energy matrix, which, together with resonance terms, takes into account other states of the discrete spectrum with n≤6.