Polarizability and hyperpolarizability of the helium atom

Abstract

The zeroth, first and second order perturbed Schrödinger equations for the helium atom in an external electric field have been solved to high accuracy through the variation principle. A ground-state energy, differing by only about 1 part in 10⁹ from Pekeris's extrapolated figure, was obtained with a wave function ϕ₀ containing 181 adjustable parameters (compared to Pekeris's 1078). The first-order wave function ϕ₁, and hence the second-order energy and polarizability of the atom, was obtained with up to 84 adjustable parameters in ϕ₁. The polarizability α is 1.38319 a.u. = 0.204956 × 10^–24 cm³= 0.228044 × 10^–40 C²m² J^–1. The dipole shielding factor differs from its exact value of unity by a few parts in 10⁵. The second-order wave function ϕ₂, and hence the fourth-order energy and hyperpolarizability γ, were obtained for various wave functions ϕ₀ and ϕ₁, and with up to 106 adjustable parameters in ϕ₂. Smooth convergence was obtained, yielding γ= 43.10 a.u. = 2.171 × 10^–38 e.s.u. = 2.688 × 10^–63 C⁴m⁴J^–3. However, an extension to ϕ₁ may be needed before an accurate value of γ can be computed. Accurate values have also been obtained for the δ-values of the unperturbed atom and for the quadrupole and octopole polarizabilities.