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 $0<\mathrm{}\gamma <5\mathrm{}$, where $\gamma$ is the conventional dimensionless magnetic field. The exact polarizability to order ${\gamma }^2$ is calculated analytically in the limit of small $\gamma$. At higher values of $\gamma$ 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 $\gamma \stackrel{\sim }{<}1$. Previous calculations are found to underestimate seriously the polarizability when the electric field is perpendicular to the magnetic field, especially when $\gamma$ is not very small.