Polarizability and hyperpolarizability of the helium atom

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.