Extrapolation to high principal quantum numbers of radial integrals in the Coulomb approximation

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Abstract
Recent developments in the study of high Rydberg states require the calculation of radial integrals for dipole transitions between states of large effective principal quantum numbers nu , nu ' and non-zero quantum defect. The method of Bates and Damgaard (1949) breaks down in such cases, while that of Edmonds and Kelly (1978) makes it possible to reach nu =40, which is often inadequate. The authors present a technique of extrapolation based on data given by the latter method, which, by judicious choice of the variable of expansion, makes it possible to obtain radial dipole integrals for arbitrarily large nu , nu ' in terms of four functions of the difference nu - nu ' with convenient symmetry properties. These functions have been tabulated and representative curves are shown here.

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