Relative accuracy of length and velocity forms in oscillator-strength calculations

A procedure is given for comparing the accuracy of the length and velocity oscillator strengths for electric dipole transitions between bound states. Based upon qualitative use of upper- and lower-bound formulas, the procedure applies to electronic systems of any size, and emphasizes the importance of such factors as the transition energy, the magnitude of the transition moments, spatial diffuseness, momentum distributions, and quality of the wave functions. The method is illustrated with a set of 36 trial transitions for the two-electron atoms He and ${\mathrm{Li}}^{+}$, where a variety of simple functions of varying quality are available to describe states of different nuclear charge and multiplicity, and where accurate $f$ values are available for comparison. The procedure proves to have high predictive power for cases where one $f$ value is clearly to be preferred, and it accurately identifies other cases where the $f$ values are of comparable quality. In addition, the method gives some qualitative assessment of the degree of preference for each formula.