High precision eigenvalues for the Rydberg sates of helium up to n = 16.

In previous work, high precision eigenvalues for all states of helium up to n = 10 and L = 7 have been obtained by the use of double basis sets in Hylleraas coordinates [1].. In the present work, we show that triple basis sets using three sets of individually optimized nonlinear parameters for different distance scales yield an order of magnitude improvement in accuracy for basis sets of the same size for the Rydberg P-states states of helium.  They also allow an extension of high precision calculations for the nonelativistic energies and wave functions up to at least n = 16 with little loss of accuracy. A summary of the methods used and a comparison with asymptotic expansions [2] will be presented.

[1] G.W.F. Drake and Z.-C. Yan, Phys. Rev. A. 46, 2378 (1992).

[2] R. Drachman, Phys. Rev. A 47, 694 (1993)..

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