Abstract
The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several 2S → 2P transition frequencies in the muonic helium-3 ion, μ3He+. This ion is the bound state of a single negative muon μ- and a bare helium-3 nucleus (helion), 3He++.A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting. These values are essential for the determination of the helion rms charge radius and the nuclear structure effects to the hyperfine splitting in μ3He+. With this review we continue our series of theory summaries in light muonic atoms [see A. Antognini et al., Ann. Phys. 331, 127 (2013); J.J. Krauth et al., Ann. Phys. 366, 168 (2016); and M. Diepold et al. arXiv:1606.05231 (2016)].Graphical abstract
Highlights
A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting
Several ideas exist to solve the puzzle [15], some within the standard model [16,17] and others proposing muon specific forces beyond the standard model [18,19,20,21]. These ideas lead to predictions which can be tested with precise charge radius determinations in muonic helium ions
Following long-established conventions we assign the measured 2S1/2 → 2P1/2 energy difference a positive sign, i.e. E(2P) – E(2S) > 0. This is in accord with almost all publications we review here and we will mention explicitly when we have inverted the sign with respect to the original publications where the authors calculated level shifts
Summary
Following long-established conventions we assign the measured 2S1/2 → 2P1/2 energy difference a positive sign, i.e. E(2P) – E(2S) > 0 This is in accord with almost all publications we review here and we will mention explicitly when we have inverted the sign with respect to the original publications where the authors calculated level shifts. The group of Ivanov, Karshenboim, Korzinin, and Shelyuto is referred to “Karshenboim group” for simplicity Their calculations are found in Korzinin et al [52] and in Karshenboim et al [53] for Lamb shift and fine structure contributions. The group of Bacca, Barnea, Hernandez, Ji, and Nevo Dinur, situated at TRIUMF and Hebrew University, has performed ab initio calculations on two-photon exchange contributions of the Lamb shift. “Perturbation theory” is abbreviated as “PT”, and SOPT and TOPT denote 2nd and 3rd order perturbation theory, respectively
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