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arXiv · 1703.01555

Atomic Two-Body $(Z\alpha )^6$ Predictions

John H. Connell
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Abstract

For muonic hydrogen, positronium, and ordinary hydrogen, we show that the existence of a relativistic two-body wave equation whose energy levels are physically accurate to order $(Z\alpha )^4$ (where $Z\alpha$ is the binding coupling constant) implies a previously unknown two-body Sommerfeld energy formula which can be used to predict energy terms to order $(Z\alpha )^6$ using simple algebra. Two such terms are verified to be physically correct by earlier $(Z\alpha )^6$ calculations for positronium. For muonic hydrogen and ordinary hydrogen, these terms are predictions.

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John H. Connell. 2017-03-05. Atomic Two-Body $(Z\alpha )^6$ Predictions. https://arxiv.org/abs/1703.01555

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