Hydrogen Atom Confined in Gaussian Potential: Polarizabilities, Hyperpolarizabilities, and Stark Shifts in an External Electric Field

The dipole polarizability and hyperpolarizability of the hydrogen atom confined in spherical Gaussian potential under the influence of an external electric field are calculated within the sum-over-states framework, where all system eigenenergies and wave functions are obtained using the generalized pseudospectral method. It is interestingly found that the Gaussian potential produces a stronger suppression effect on the hyperpolarizability than on the polarizability, especially at moderate values of confinement radius. By analyzing the second- and fourth-order energy corrections for the ground state of the hydrogen atom under an external electric field, we define the maximal electric field strength where the perturbation approximation of the field–atom interaction is applicable. Based on the accurate ground state energies, polarizabilities, and hyperpolarizabilities, as well as the corresponding $Z$-scaling laws, the Stark shifts of hydrogenic ions confined in Gaussian potentials are estimated over a wide range of confinement radius and potential depth.