Dependence of extrema in the generalized oscillator strengths on momentum transfer and effective nuclear charge for atomic transitions

Generalized oscillator strengths f(K) for one‐electron atomic transitions involving atoms in the first through third rows of the Periodic Table are studied within the first Born approximation. A one‐electron model employing hydrogenlike orbitals is used with appropriate effective nuclear charges. For single electron excitations, the Born matrix element ${\text{f(K) = 2Δ E|∫ φ}}_b^{*}{\mathrm{e\hspace{0.17em}}}^{\mathrm{iK}\mathrm{·\; r}}{\phi }_a{\mathrm{dV|}}^2{\mathrm{/K}}^2$ can be scaled to yield a reduced generalized oscillator strength $\mathcal{f}\mathrm{\hspace{0.17em}(\kappa )}$ which depends on the ratio of effective nuclear charges ζ(final)/ζ(initial), and a reduced momentum transfer κ = K /ζ(initial). Transitions to a Rydberg series exhibit extrema in f(K) which are nearly the same for all members of the series, whereas excitations to different series exhibit a different number and positioning of the extrema. This behavior suggests that trends in generalized oscillator strengths can be used as an experimental tool to probe various types of transitions and to unravel Rydberg series. Comparison of theoretical calculations with available experimental results yields good agreement and new experimental goals are suggested.