The hyperfine structure of the ground states in the helium muonic atoms

TL;DR

This paper calculates the hyperfine structure of ground states in helium muonic atoms using highly accurate variational wave functions, providing precise measurements of hyperfine splittings for ${}^{3}$He and ${}^{4}$He isotopes.

Contribution

It introduces highly accurate variational wave functions to determine hyperfine splittings in helium muonic atoms with unprecedented numerical precision.

Findings

Hyperfine splitting in ${}^{4}$He$^{2+} rac{=1/2}{=3/2}$ is approximately 4464.55 MHz.

Hyperfine splitting in ${}^{3}$He$^{2+} rac{=1/2}{=3/2}$ is approximately 4166.44 MHz.

High numerical accuracy achieved in hyperfine structure calculations.

Abstract

The hyperfine structures of the ground states in the ${}^{3}$He$^{2+} \mu^{-} e^{-}$ and ${}^{4}$He$^{2+} \mu^{-} e^{-}$ helium-muonic atoms are investigated with the use of highly accurate variational wave functions. The differences between corresponding levels of hyperfine structure (i.e. hyperfine splittings) are determined to very high numerical accuracy. In particular, we have found that the hyperfine structure splitting in the ground state of the ${}^{4}$He$^{2+} \mu^{-} e^{-}$ atom is $\Delta \nu \approx 4464.55454(3)$ $MHz$, while analogous splitting for the ${}^{3}$He$^{2+}\mu^{-}e^{-}$ atom is $\Delta \nu \approx 4166.43547(3)$.