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High Precision Calculations for Helium

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Springer Handbook of Atomic, Molecular, and Optical Physics

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Abstract

Exact analytic solutions to the Schrödinger equation are known only for hydrogen and other equivalent two-body systems (Chap. 9). However, very high precision approximations are now available for helium and other three-body systems that are essentially exact for all practical purposes. This chapter summarizes the computational methods and tabulates numerical results for the ground state and several excited states up to n = 10 and L = 7. General formulas are presented for the evaluation of matrix elements in Hylleraas coordinates. Relativistic and quantum electrodynamic effects are included, along with quantum defect extrapolations to states of higher n and asymptotic expansions to states of higher angular momentum L. Radiative transitions are discussed and oscillator strengths tabulated for a wide variety of transitions.

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Acknowledgements

The author is grateful to R.N. Hill and J.D. Morgan III for suggesting some of the material inSect. 12.1. This work was supported by the Natural Sciences and Engineering Research Council of Canada.

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  1. Dept. of Physics, University of Windsor, N9B 3P4, Windsor, ON, Canada

    Gordon W. F. Drake

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  1. Gordon W. F. Drake
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Correspondence to Gordon W. F. Drake .

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  1. Dept. of Physics, University of Windsor, N9B 3P4, Windsor, ON, Canada

    Gordon W. F. Drake

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Drake, G.W.F. (2023). High Precision Calculations for Helium. In: Drake, G.W.F. (eds) Springer Handbook of Atomic, Molecular, and Optical Physics. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-73893-8_12

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