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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 $mathrm{2Srightarrow2P}$ transition frequencies in the muonic helium-3 ion, $mathrm{mu^3He^+}$. This ion is the bound state of a single negative muon $mu^-$ and a bare helium-3 nucleus (helion), $mathrm{^3He^{++}}$. A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting.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 $mathrm{mu^3He^+}$. With this review we continue our series of theory summaries in light muonic atoms; see Antognini et al., Ann. Phys. 331, 127 (2013), Krauth et al., Ann.Phys. 366, 168 (2016), and Diepold et al., ArXiv 1606.05231 (2016).
The present knowledge of Lamb shift, fine- and hyperfine structure of the $mathrm{2S}$ and $mathrm{2P}$ states in muonic deuterium is reviewed in anticipation of the results of a first measurement of several $mathrm{2S-2P}$ transition frequencies in
We provide an up to date summary of the theory contributions to the 2S-2P Lamb shift and the fine structure of the 2P state in the muonic helium ion $(mathrm{mu^4He})^+$. This summary serves as the basis for the extraction of the alpha particle charg
We present the detection of the highly forbidden $2^{3!}S_1 rightarrow 3^{3!}S_1$ atomic transition in helium, the weakest transition observed in any neutral atom. Our measurements of the transition frequency, upper state lifetime, and transition str
We present a precise calculation of the Lamb shift $(2P_{1/2}-2S_{1/2})$ in muonic ions $(mu ^6_3Li)^{2+},~(mu ^7_3Li)^{2+}$, $(mu ^9_4Be)^{3+},~(mu ^{10}_4Be)^{3+}$, $(mu ^{10}_5B)^{4+},~(mu ^{11}_5B)^{4+}$. The contributions of orders $alpha^3dival
Isotope shifts of the 2$p_{3/2}$-2$p_{1/2}$ transition in B-like ions are evaluated for a wide range of the nuclear charge number: Z=8-92. The calculations of the relativistic nuclear recoil and nuclear size effects are performed using a large scale