Analytic curve fits to helium transition integrals

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Abstract
It is pointed out that a helium transition integral, and hence its associated generalized oscillator strength, has eight poles in the q plane, where q is the momentum transfer. They constitute four conjugate pairs lying on the imaginary axis. This analytic behaviour is exhibited in the formulae derived by Crothers and McEachran in 1970, whereas the expression assumed by Lassettre in 1965 contains only one pair of poles. The further six poles are directly attributable to the indistinguishability of the bound electrons. The accurate numerical 11S to 21S generalized oscillator strengths calculated by Bell et al. in 1969 are curve-fitted by interpolating six of the values with an analytic expression exhibiting the required eight poles, whose orders are partially determined by the requirements of orthogonality and the correct asymptotic fall-off with respect to q. The accurate numerical 11S to 21S first Born proton impact cross sections obtained by Bell et al. in 1968 are reproduced with less than 0.1% error over the entire range (5 to 5000 keV) of proton impact energies.

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