Lamb shifts and fine-structure splittings for the muonic ionsμ−-Li,μ−-Be, andμ−-B: A proposed experiment

Detailed calculations are presented for the energy splittings of the states 2$s_{1/2}$-2$p_{1/2}$ and 2$s_{1/2}$-2$p_{3/2}$ for the muonic ions ${\mu }^{\mathrm{-}}$-Li, ${\mu }^{\mathrm{-}}$-Be, and ${\mu }^{\mathrm{-}}$-B obtained by numerical integration of the Dirac equation. It is shown that there is severe cancellation between the vacuum polarization and finite nuclear size contributions to the energy differences, leading to transition frequencies which lie in the visible region of the spectrum. As a consequence of the cancellation, a measurement of the transition frequency would provide a sensitive probe of nuclear size and structure. The system ${\mu }^{\mathrm{-}}$ ${\mathrm{-}}^7$Li appears to offer particularly good possibilities for performing such an experiment.