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

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 $2S\to 2P$ transition frequencies in the muonic helium-3 ion, ${\mu }^3\mathrm{H}{\mathrm{e}}^{+}$. This ion is the bound state of a single negative muon ${\mu }^{-}$ and a bare helium-3 nucleus (helion), ${}^3\mathrm{H}{\mathrm{e}}^{++}$. A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting.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 ${\mu }^3\mathrm{H}{\mathrm{e}}^{+}$. 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).

arXiv comment27 pages, continues series of theory summaries from muonic hydrogen up to muonic helium-4, revised manuscript, updated numbers

References in corpus (48)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Chiral effective field theory and nuclear forces
• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• Muonic hydrogen and the proton radius puzzle
• The Proton Radius Puzzle
• Extreme ultraviolet frequency comb metrology
• Theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen
• Muonic hydrogen and MeV forces
• Frequency metrology in quantum degenerate helium: Direct measurement of the 2 3S1 - 2 1S0 transition
• New Parity-Violating Muonic Forces
• Higher order proton structure corrections to the Lamb shift in muonic hydrogen
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• Lamb Shift in Light Muonic Atoms - Revisited
• Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius
• Lamb Shift in Muonic Hydrogen. I. Verification and Update of Theoretical Predictions
• Zemach Moments for Hydrogen and Deuterium
• Theory of the n=2 levels in muonic deuterium
• Constraints on muon-specific dark forces
• Nuclear structure corrections in muonic deuterium
• Nuclear structure contribution to the Lamb shift in muonic deuterium
• Proton Polarizability Contribution: Muonic Hydrogen Lamb Shift and Elastic Scattering
• New Measurement of Compton Scattering from the Deuteron and an Improved Extraction of the Neutron Electromagnetic Polarizabilities
• Higher-order recoil corrections for triplet states of the helium atom
• Nuclear Polarization Corrections to mu-d Atoms in Zero-Range Approximation
• Relativistic Reduced-Mass and Recoil Corrections to Vacuum Polarization in Muonic Hydrogen, Muonic Deuterium and Muonic Helium Ions
• Zemach moments of 3He and 4He
• Nuclear recoil effect in the Lamb shift of light hydrogen-like atoms
• Relativistic recoil corrections to the electron-vacuum-polarization contribution in light muonic atoms
• Higher-order recoil corrections for singlet states of the helium atom
• Review of experimental and theoretical status of the proton radius puzzle
• Higher-Order Nuclear-Size Corrections in Atomic Hydrogen
• Lamb shift in muonic deuterium atom
• Nuclear Corrections to Hyperfine Structure in Light Hydrogenic Atoms
• Two-photon exchange correction to $2S$-$2P$ splitting in muonic helium-3 ions
• Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H
• The ${\alpha }^2(Z\alpha {)}^{4}m$ contributions to the Lamb shift and the fine structure in light muonic atoms
• Radiative Correction to the Nuclear-Size Effect and Hydrogen-Deuterium Isotopic Shift
• Radiative nonrecoil nuclear finite size corrections of order $\alpha (Z\alpha {)}^5$ to the hyperfine splitting of S-states in muonic hydrogen
• Hyperfine Structure of S-States in Muonic Helium Ion
• Proton Radius, Darwin-Foldy Term and Radiative Corrections
• Experiments towards resolving the proton charge radius puzzle
• Weak Interaction Contributions in Light Muonic Atoms
• Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil
• The recoil correction to the proton-finite-size contribution to the Lamb shift in muonic hydrogen
• Muonic bound systems, virtual particles and proton radius
• Fine and hyperfine structure of the muonic ^3He ion
• Extending theories on muon-specific interactions
• Update on nuclear structure effects in light muonic atoms

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• Comprehensive theory of the Lamb shift in light muonic atoms
• Ab initio calculation of nuclear structure corrections in muonic atoms
• Theory of the Lamb shift and Fine Structure in muonic ${}^4\mathrm{He}$ ions and the muonic ${}^3\mathrm{He}{-}^4\mathrm{He}$ Isotope Shift
• The next generation of laser spectroscopy experiments using light muonic atoms
• High-Precision Ramsey-Comb Spectroscopy Based on High-Harmonic Generation
• Zemach moments and radii of 2,3H and 3,4He
• Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory
• QED theory of the nuclear recoil with finite size
• Corrections of two-photon interactions in the fine and hyperfine structure of the P-energy levels of muonic hydrogen
• Hyperfine structure of S-states in muonic ions of lithium, beryllium and boron
• Revisiting the helium isotope-shift puzzle with improved uncertainties from nuclear structure corrections
• Relativistic and Recoil Corrections to Vacuum polarization in muonic systems: Three--photon exchange, gauge invariance and numerical values
• A theory vade mecum for PSI experiments
• Demonstration of Ramsey-Comb Precision Spectroscopy in Xenon at Vacuum Ultraviolet Wavelengths Produced with High-Harmonic Generation