In the study of complex atomic spectra by the methods of Slater and Condon, it is desirable that one have a complete set of orthogonal wave functions more nearly correct than the hydrogenic ones. A set of variable-scale wave functions is described in this paper and applied to some simple cases. They are hydrogenic functions of a function of the radius, such that close to the nucleus they behave like the wave functions about a charge $\mathrm{Ze}$ and far from the nucleus they behave like the wave function about a charge $e$. The scale function is chosen so that the integrals arising in calculation can be handled analytically. These functions are not so accurate as the analytic representations of the Hartree functions, but they from a complete orthogonal set, and thus can be used for perturbation problems.

• Received 5 January 1933

DOI:https://doi.org/10.1103/PhysRev.43.337