Higher-order Stark effect on an excited helium atom

Degenerate perturbation theory is used to study dipole susceptibilities of an excited helium atom in an external electric field. The dependence of the perturbed energy of levels in atoms on fine-structure effects and on the higher-order Stark effect is investigated. Numerical results have been obtained for the $\mathrm{}\left(1s3p\right)\mathrm{}{}^3{P}_0$ and $\mathrm{}\left(1s3p\right)\mathrm{}{}^3{P}_2$ states of helium. The magnitude of the electric field and the energy separation at the $0^{-}\times 0^{-}$ anticrossing are calculated. Calculations of polarizabilities and hyperpolarizabilities are carried out using sums of oscillator strengths and, alternatively, with the excited electron Green function. An estimate is given based on the model potential method for the contribution of an infinite series over the bound states, including the integral over the continuum, for second- and higher-order matrix elements. The relativistic approach for evaluating reduced dipole matrix elements based on the relativistic no-pair Hamiltonian and including both the Coulomb and Breit interactions (configuration-interaction method) is analyzed.