Variational Calculations of Dipole Polarizabilities of Helium-Like Ions

The dipole polarizabilities of a number of helium-like ions are calculated by a variational procedure, using the analytic ground state wave functions calculated for these ions by Green, Mulder, Lewis, and Woll. Our values agree well with those obtained by Sternheimer by a numerical solution of the first-order Schr\"odinger equation in the presence of an electric field. The basis for the convergence of our variational procedure is discussed along with its advantages and disadvantages relative to Sternheimer's procedure.Comparison is also made with experimental values of the polarizabilities. For helium, our value (0.218 A³) is within 7% of the experimental value (0.204 A³). For the ions Li⁺, Be⁺⁺, B⁺⁺⁺, the agreement is only fair. The diamagnetic susceptibilities are also calculated in order to test the accuracy of the ground state wave functions. The agreement of our values here with the experimental ones is very good.