Topical Review

Theory of the n = 2 levels in muonic helium-3 ions

¹ Max–Planck–Institut für Quantenoptik, 85748 Garching, Germany
² TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada
³ Johannes Gutenberg-Universität Mainz, QUANTUM, Institut für Physik & Exzellenzcluster PRISMA, 55099 Mainz, Germany
⁴ Institute for Particle Physics and Astrophysics, ETH Zurich, 8093 Zurich, Switzerland
⁵ Paul Scherrer Institute, 5232 Villigen, Switzerland

^a e-mail: bfranke@triumf.ca
^b e-mail: jkrauth@uni-mainz.de
^c e-mail: pohl@uni-mainz.de

Received: 30 April 2017
Received in final form: 13 July 2017
Published online: 21 December 2017

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A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting.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)].