Power Series Representation of Generalized Oscillator Strengths

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Abstract
Expansion of generalized oscillator strengths in powers of the momentum change K (of the colliding electron) generally leads to series with finite radii of convergence. From a study of singularities of the function for complex values of K it is possible to transform the series into one which converges for all physically attainable values of K. The transformation depends on the ionization potential and the excitation energy, both of which can be determined experimentally. The transformed series should be useful in fitting experimental data and in the extrapolation of oscillator strengths. It is especially useful, however, when applied to transitions for which a few terms of the series in inverse powers of K can be obtained. As an example the 11S→21S transition in helium is treated. The mere determination of the degree of the first nonvanishing term in the inverse power series is enough to severely restrict the form of series and, in fact, to sum the first six terms. These terms, which involve only one adjustable constant, fit the experimental data to within 3.5% and the deviation is mainly due to experimental error.