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Rigorous upper and lower bounds are prescribed in the form of approximate quadratures for a variety of oscillator-strength sums. The required integration points and weights are determined from continued-fraction approximants and linear programming techniques, employing oscillator-strength moments as inputs to the method. Illustrative bounds are provided in the cases of atomic hydrogen, helium, and neon, for odd-integer sums and for the mean energies associated with stopping, straggling, excitation, and the Lamb shift.
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Yates et al. (1970) studied this question.
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