High Precision Calculations for Helium

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.