Muonic x rays in lead isotopes

Abstract

Results of an experiment to measure muonic transition energies in separated lead isotopes are presented. The main results are as follows: 1. Muonic spectra of the four lead isotopes ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ were studied with high resolution. No anomalous splitting or broadening of the lines was detected. The effect of the natural linewidth could, however, be observed. 2. An anomaly was found in the $3d$ fine structure splitting whose measured value turned out to be larger than the calculated value by nearly 300 eV (or 10 standard deviations) in all four isotopes. 3. Except for this anomaly, the lower levels of muonic lead can be described adequately with the help of a two-parameter Fermi distribution of the nuclear charge. There is no evidence in the x-ray data for a central depression in the nuclear density. 4. We determine the nuclear polarization in the ground state of all four isotopes of lead and find values ranging from -7.3 ± 2.2 to -10.1 ± 1.1 keV, which are somewhat higher than, but not inconsistent with, the best theoretical predictions of -6.8 ± 2.0 keV. This analysis is made possible by our ability to measure the weak transitions involving the $2s$ level. 5. We find a slight and regular increase in nuclear density, going from ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}$ to ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The skin-thickness parameter $t$ appears, however, to be practically the same in all four isotopes measured.