Abstract
Publisher Summary This chapter reviews the computational methods that are available for the low-lying and Rydberg states of helium and gives summary of the most important results. It describes the theoretical contributions to the energy, including the nonrelativistic Schrodinger equation and relativistic, relativistic recoil, anomalous magnetic moment, and quantum electrodynamic (QED) corrections. The chapter also summarizes the asymptotic method, using a formalism somewhat different from that employed by Drachman. The advantage is that the formalism is better adapted to the calculation of quantities other than the energy. The chapter gives a parallel summary of high precision variational methods for Rydberg states and then compares the results with the asymptotic expansions. The comparison establishes the range of the validity of asymptotic expansions and provides a strong confirmation of both approaches. The chapter discusses the methods of analyzing high precision data, including modifications to the quantum defect method, and then reviews the QED shifts that have been obtained from recent experiments. The chapter also provides measurements for transitions among the n = 10 states of helium, with the aim of observing the Casimar–Polder effect.
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