Nuclear Polarization and Charge Parameters Using the Muonic2sState

Abstract

Muonic x-ray transition energies have been measured in $^{120}\mathrm{Sn}$, $^{138}\mathrm{Ba}$, $^{140}\mathrm{Ce}$, $^{142}\mathrm{Ce}$, and $^{206}\mathrm{Pb}$ using a high-efficiency Ge(Li) detector. Precise measurements and relative-intensity measurements have made it possible to identify transitions to and from the $2s$ state in each of these targets. There is good agreement between theoretical and experimental relative intensities for these transitions, except for the $^{206}\mathrm{Pb}$ nucleus. These transition energies, together with those from the $2p\ensuremath{-}1s$, $3d\ensuremath{-}2p$, and $4d\ensuremath{-}2p$ transitions are used to deduce sets of nuclear charge parameters. It has been found that for each target except $^{120}\mathrm{Sn}$, the best agreement between theory and experiment is obtained by applying the theoretical nuclear polarization corrections to all levels with $n>1$, and varying the nuclear polarization induced by the muon in the $1s$ state. The nuclear polarization values determined were 5.8 \ifmmode\pm\else\textpm\fi{} 1.5 keV for $^{120}\mathrm{Sn}$, 6.7 \ifmmode\pm\else\textpm\fi{} 1.4 keV for $^{138}\mathrm{Ba}$, 6.5 \ifmmode\pm\else\textpm\fi{} 1.3 keV for $^{140}\mathrm{Ce}$, 7.0 \ifmmode\pm\else\textpm\fi{} 1.4 keV for $^{142}\mathrm{Ce}$, and 5.5 \ifmmode\pm\else\textpm\fi{} 1.7 keV for $^{206}\mathrm{Pb}$. These results are in fair agreement with the most recent theoretical predictions.