Finite-size and relativistic effects onto hyperfine interaction of muonic hydrogen

<jats:title>Abstract</jats:title> <jats:p>Muonic hydrogen is an exotic atom where a muon instead of an electron is bound to a proton. The comparably high mass of the muon (≈ 207 · <jats:italic>m<jats:sub>e</jats:sub> </jats:italic>) has two important effects, (i) the reduced mass of the system becomes more important, and (ii) the muon is localized much closer to the nucleus. Thus, muonic hydrogen is not only excellently suitable for evaluating highly precise quantum electrodynamic (QED) calculations, but may also be used for assessing new approaches including finite nuclear size (FNS) effects to evaluate the proton structure and improve calculation schemes for the hyperfine splittings of many-particle systems, as e.g. to be implemented in density functional theory (DFT) software packages. Here, starting from Dirac’s equation we calculate the relativistic hyperfine splitting of the ground state and several excited states of muonic hydrogen analytically for different charge and magnetization models. The FNS related hyperfine shifts are compared with the differences between QED calculations and experimental measurements. This comparison also allows to unravel the role of the reduced mass, which is on one hand crucial in case of muonic atoms, but on the other hand is by no means well defined in relativistic quantum mechanics.</jats:p>