Eigenenergies and oscillator strengths for the Hulthén potential

A detailed study of the bound-state properties of the Hulth\'en potential is presented. Accurate eigenenergies are obtained for the Hulth\'en potential by numerical integration of the Schr\"odinger equation. One-parameter variational calculations are carried out. The variational results are practically identical to the exact energies, except in the high-screening region. The critical screening parameter is calculated for various values of l for n\ensuremath{\le}10 by a numerical solution of the wave equation. The energy eigenvalues obtained by a variety of methods are compared and discussed. The variational wave functions are employed to calculate absorption oscillator strengths for 1s\ensuremath{\rightarrow}2p, 1s\ensuremath{\rightarrow}3p, and 2p\ensuremath{\rightarrow}3d transitions.