Precise Measurement of the Muonic X Rays in the Lead Isotopes

Abstract

The size and shape of the nuclear charge distribution was determined for the Pb isotopes from precise measurements of their $\ensuremath{\mu}$-atomic transition energies. Use of the $2p\ensuremath{-}1s$ transitions was avoided in determining the nuclear parameters because of the perturbation caused by the presence of the muon in the $1s$ orbit. A simple two-parameter Fermi distribution was used in the analysis, but the rms radius determined thereby should be fairly model-independent. We find ${〈{r}^{2}〉}^{\frac{1}{2}}=5.4839\ifmmode\pm\else\textpm\fi{}0.0028$ fm for ${\mathrm{Pb}}^{206}$. This quantity increases by 0.0139\ifmmode\pm\else\textpm\fi{}0.0011 fm in going to ${\mathrm{Pb}}^{208}$. The calculated energy of the $1s$ level is found to be too high by 6.8\ifmmode\pm\else\textpm\fi{}2.3 keV, an effect which we have interpreted as being due to nuclear polarization, although the inadequacies in our treatment of the radiative corrections and of the effect of nuclear motion may account for a part of this difference. The measurement of the $4f\ensuremath{-}3d$ and $5g\ensuremath{-}4f$ transition energies provides a check of the vacuum-polarization correction, which is just at the limit of the higher-order contributions. The intensity ratios $\frac{I(2{p}_{\frac{3}{2}}\ensuremath{-}1{s}_{\frac{1}{2}})}{I(2{p}_{\frac{1}{2}}\ensuremath{-}1{s}_{\frac{1}{2}})}$ are found to be anomalously low for all three Pb isotopes and by as much as (12\ifmmode\pm\else\textpm\fi{}3)% in the case of ${\mathrm{Pb}}^{208}$. In general, the intensities are reasonably well described by a cascade calculation, but the indication is that radiationless transitions do occur which can raise the Pb nucleus to an excited state. We detect prompt nuclear $\ensuremath{\gamma}$ rays corresponding to this process. Some 15 $\ensuremath{\mu}$-capture $\ensuremath{\gamma}$ rays with yields \ensuremath{\ge}0.01 per $\ensuremath{\mu}$ capture are reported for ${\mathrm{Pb}}^{206}$. One with a yield of 0.18 per $\ensuremath{\mu}$ capture is attributed to the ${\frac{3}{2}}^{+}\ensuremath{\rightarrow}{\frac{1}{2}}^{+}$ g.s. transition in ${\mathrm{Tl}}^{205}$, following the emission of one neutron.