Theory of the hyperfine structure of the S states of muonic tritium
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, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Theory of the Hyperfine Structure of the S States of Muonic Tritium A. P. Martynenkoa,*, F. A. Martynenkoa, and R. N. Faustovb a
b
Samara State University, Samara, 443001 Russia Institute of Educational Informatics, Federal State Enterprise “Federal Research Center of Informatics and Control,” Russian Academy of Sciences, Moscow, 119333 Russia *e-mail: [email protected] Received February 6, 2017
Abstract—The hyperfine structure of the energy spectrum of the S levels of muonic tritium has been calculated using the quasi-potential method in quantum electrodynamics (QED). The α5- and α6-order effects on the polarization of vacuum, the structure and recoil of the nucleus, and relativistic corrections have been taken into account. The obtained numerical values of hyperfine splittings of 239.819 meV (1S state) and 29.965 meV (2S state) can be treated as reliable estimates for comparing with future experimental data of the CREMA collaboration, and hyperfine structure interval Δ12 = 8Δ E hfs (2S) – Δ E hfs (1S) = –0.100 meV can be used for verifying the QED predictions. The resultant precision values of hyperfine splitting are also important for calculating the rates of formation of (μ dt) mesomolecules in muonic catalysis reactions. DOI: 10.1134/S1063776117060140
1. INTRODUCTION Negatively charged muons, like electrons, can form hydrogen-like atoms with nuclei. Muonic tritium (μt) consists of a negative muon and a triton. The triton is the β– radioactive nucleus with a half-life of about 12 years. The lifetime of muonic tritium is determined by the decay time of muon, τμ = 2.19703(4) × 10–6 s. Although the muon is an unstable particle, its lifetime is sufficient for precision investigation of the energy levels of (μt). Since the triton spin is the same as the proton spin (1/2), the structure of its energy levels has the same form as for muonic hydrogen. The difference in the positions of energy levels is primarily due to the difference in the masses of the nuclei and their structures. As for conventional muonic hydrogen, there are a number of effects for the polarization of vacuum, the structure and polarizability of the nucleus, and recoil, which substantially affect the hyperfine structure of the spectrum [1–13] (see the literature cited in [4, 13]). The magnitudes of these effects are characterized by the power of fine structure constant α. Our previous studies [14–16] have shown that the high-precision calculation of the hyperfine structure (HFS) of energy levels must include these corrections in the fifth and sixth orders in α in the first and second orders of perturbation theory. These corrections may increase due to the emergence of logarithmic factors lnα and ln(m1/m2) (logarithm of the ratio of the particle masses). This study is aimed at analysis of possible
interactions between a muon and a triton, which lead to corrections on the order of α5–α6 in the hyperfine splitting of the S energy levels and their subsequent analytic and numerical calculation.
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