Electrical polarizability of the ground state of hydrogenic donors in magnetic fields

A relatively simple and accurate calculation is presented for the electrical polarizability of the ground state of a hydrogenic atom in magnetic fields for which 0<γ<5, where γ is the conventional dimensionless magnetic field. The exact polarizability to order γ² is calculated analytically in the limit of small γ. At higher values of γ numerical calculations are facilitated by the introduction of a new three-parameter trial function for the hydrogen-atom problem which gives remarkably accurate energies for γ~<1. Previous calculations are found to underestimate seriously the polarizability when the electric field is perpendicular to the magnetic field, especially when γ is not very small.