Hydrogen-Atom Polarizability as a Hartree–Fock Perturbation Expansion: A Geometric Approximation to Atomic Polarizabilities

The hydrogen-atom dipole polarizability α is obtained by a double perturbation expansion based on a Hartree–Fock H0. The expansion α = α0 + λα1 + λ2α2 + ···, where λ is the continuous parameter for the Hartree–Fock perturbing potential, is found to be extremely close to a geometric series with αi+1 / αi = 0.433 ± 0.002. Computation of α as α0[1 − (α1 / α0)]−1 gives 4.499a03 in excellent agreement with the exact value 92a03. The origin of this geometric character is examined and its applicability to some many-electron polarizabilities is demonstrated empirically.