Stark Effect and Series Limits

Energy of conditionally periodic and aperiodic orbits in hydrogen-like atoms under the influence of an external electric field.—It is shown that the energy of a conditionally periodic orbit in a hydrogen-like atom under the influence of a homogeneous external field $F$ must be less than $-\left(\frac{3}{2}\right){\left[\frac{\mathrm{eF}{p}_{\phi }}{m^{\frac{1}{2}}}\right]}^{\frac{2}{3}}$. Aperiodic orbits of less, as well as of greater, energy than this value can exist, and in one class of these the electron may approach the nucleus within distances comparable with the dimensions of periodic orbits. The lower limit of the energy of these orbits is approximately $-2e{\mathrm{}\left(\mathrm{eF}\right)\mathrm{}}^{\frac{1}{2}}$.