Dynamic hyperpolarizabilities of excited states of hydrogen

On the basis of the generalized Sturm expansion of the radial part of the Coulomb Green function, a computational method is proposed and numerical results are presented for the dynamic hyperpolarizability γ and the corrections E(4) (quadratic in the light intensity) to the quasi-energy of the ground and excited states of hydrogen with principal quantum numbers n≤5 in a monochromatic light field. In this approach, the problem is reduced to the summation of well-convergent double series of the hypergeometric kind, which ensures reliable numerical results both for states with a large n, and in a wide range of field frequencies ω, including the above-threshold frequency range of ℏω≪|En| (|En| is the ionization potential of the state |nlm〉 under investigation). We consider the frequency dependence of γ and E(4), their differences for the cases of linear and circular polarizations of the field, and the relation between their real and imaginary parts, which determine the laser field-induced corrections to the position and width of energy levels. For n=5, the significant role of mixing the |nlm〉 states with different values of l by a laser field in the region of resonances on intermediate bound states is demonstrated. The linear (in intensity) corrections to the photoionization cross section for excited states are analyzed and the threshold intensity corresponding to the onset of atomic level stabilization is estimated for a number of states with n=3 and n=5.