High-precision variational eigenvalues are obtained for the 10D, 10F, 10G and 10H states of helium by the application of multiple basis set methods. The accuracy is sufficient to provide the first definitive test of asymptotic expansion methods extensively developed by Drachman for Rydberg states of high angular momentum. The results are also compared with recent high-precision measurements for the 10G-1OH and IOF-1OG transition frequencies, and interpreted in terms of predicted long-range

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... dation corrections. Bethe logarithms are calculated and Lamb shift corrections included. Small residual discrepancies persist which could be explained by uncalculated radiative shifts.