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arXiv · 0706.3017

Relativistic Three-Fermion Wave Equations in Reformulated QED and Relativistic Effects in Muonium Minus

Mark Barham·Jurij W. Darewych
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Abstract

The variational method, within the Hamiltonian formalism of reformulated QED is used to determine relativistic wave equations for a system of three fermions of arbitrary mass interacting electromagnetically. The interaction kernels of the equations are, in essence, the invariant $\mathcal{M}$ matrices in lowest order. The equations are used to obtain relativistic $O(α^2)$ corrections to the non-relativistic ground state energy levels of the Muonium negative ion ($μ^+ e^- e^-$) as well as of $\mathrm{Ps}^-$ and $\mathrm{H}^-$, using approximate variational three-body wave functions. The results are compared with other calculations, where available. The relativistic correction for Mu$^-$ is found to be $-1.0773 \times 10^{-4}$ eV.

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Mark Barham, Jurij W. Darewych. 2007-06-20. Relativistic Three-Fermion Wave Equations in Reformulated QED and Relativistic Effects in Muonium Minus. https://arxiv.org/abs/0706.3017

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