Hyperfine Effects in Muonic Bi and Pb

We have investigated the $K$ and $L$ transitions in the muonic spectra of ${\mathrm{Bi}}^{209}$ and of the separated isotopes ${\mathrm{Pb}}^{206}$, ${\mathrm{Pb}}^{207}$, and ${\mathrm{Pb}}^{208}$, using a Ge(Li) spectrometer. Our isotope shifts in Pb, in excellent agreement with the optical data, are half those predicted by the $A^{\frac{1}{3}}$ law. The agreement between our shifts and the optical shifts strongly suggests the absence of nuclear polarization by the muon. We have studied the $M1\mathrm{}$ and $E2\mathrm{}$ hyperfine (hf) interactions in ${\mathrm{Bi}}^{209}$. The $M1\mathrm{}$ results, although not sensitive enough to distinguish models of nuclear magnetization distributions, rule out a point magnetic dipole. The $E2\mathrm{}$ constants, when used in conjunction with the measured isotone shift between ${\mathrm{Bi}}^{209}$ and ${\mathrm{Pb}}^{208}$, suggest a quadrupole distribution produced by an $h_{\frac{9}{2}}$ proton and a slightly (∼1%) deformed ${\mathrm{Pb}}^{208}$ core. We have examined the effects of $E3\mathrm{}$ mixing of ${\mathrm{Bi}}^{209}$ nuclear levels on the $K$ and $L$ intensity ratios and on the interpretation of the hf constants.