Determining the antiproton magnetic moment from measurements of the hyperfine structure of antiprotonic helium

Recent progress in the spectroscopy of antiprotonic helium has allowed for measuring the separation between components of the hyperfine structure (hfs) of the (37,35) metastable states with an accuracy of $300\mathrm{kHz}$, equivalent to a relative accuracy of $3\times {10}^{-5}$. The analysis of the uncertainties of the available theoretical results on the antiprotonic helium hfs shows that the accuracy of the value of the dipole magnetic moment of the antiproton (currently known to only 0.3%) may be improved by up to two orders of magnitude by measuring the splitting of appropriately selected components of the hfs of any of the known metastable states. The feasibility of the proposed measurement by means of an analog of the triple resonance method is also discussed.

Figure 1

Hyperfine structure of a pair of parent and daughter states of $\overline{p}{}^4\mathrm{He}$ and of the dipole transition $\left(nL\right)\to \left(n^{\prime }{L}^{\prime }\right)$ between them. The transitions between states of the $F_{-}$ and $F_{+}$ doublets are denoted by $m_{-}$, $m_{+}$, and $m_0$ depending on $\Delta J$; the transitions within the $F_{\pm }$ doublets are labeled as $s_{\pm }$. The transitions between homologous doublets of the parent and daughter states are denoted by $d_{\pm }$, and between the homologous components of the doublets by $d_{\pm }^{1,2}$.

Figure 2

Asymmetric depopulation of the hyperfine states $J_{-}$ and $J_0$ of the $F_{-}$ doublet.