Determination of the isotopic change in nuclear charge radius from extreme-ultraviolet spectroscopy of highly charged ions of Xe

Abstract

The electron-beam ion trap (EBIT) at the National Institute of Standards and Technology (NIST) was employed for the measurement and detailed analysis of the $\ensuremath{\delta}\ensuremath{\lambda}(^{124}\mathrm{Xe},^{136}\mathrm{Xe})$ isotopic shifts of the Al-like $3{s}^{2}3p\phantom{\rule{4pt}{0ex}}^{2}P_{1/2}\ensuremath{-}3{s}^{2}3p\phantom{\rule{4pt}{0ex}}^{2}P_{3/2}$, Al-like $3{s}^{2}3p\phantom{\rule{4pt}{0ex}}^{2}P_{1/2}\ensuremath{-}3{s}^{2}3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$, Mg-like $3{s}^{2}\phantom{\rule{4pt}{0ex}}^{1}S_{0}\ensuremath{-}3s3p\phantom{\rule{4pt}{0ex}}^{1}P_{1}$, Mg-like $3{s}^{2}\phantom{\rule{4pt}{0ex}}^{1}S_{0}\ensuremath{-}3s3p\phantom{\rule{4pt}{0ex}}^{3}P_{1}$, Na-like $3s\phantom{\rule{4pt}{0ex}}^{2}S_{1/2}\ensuremath{-}3p\phantom{\rule{4pt}{0ex}}^{2}P_{1/2}$ (${D}_{1}$), and Na-like $3s\phantom{\rule{4pt}{0ex}}^{2}S_{1/2}\ensuremath{-}3p\phantom{\rule{4pt}{0ex}}^{2}P_{3/2}$ (${D}_{2}$) transitions. Systematic analysis revealed possible line blends and contributing experimental uncertainties. Highly accurate atomic-structure calculations were conducted and used to determine the $\ensuremath{\delta}{\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}}^{136,124}$ difference in the mean-square nuclear charge radii of the two xenon isotopes. In the present work, $\ensuremath{\delta}{\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}}^{136,124}$ of 0.276 $\ifmmode\pm\else\textpm\fi{}$ 0.030 ${\mathrm{fm}}^{2}$ was obtained from the weighted average of the Na-like ${D}_{1}$, Mg-like $3{s}^{2}\ensuremath{-}3s3p$ and Al-like $3{s}^{2}3p\ensuremath{-}3{s}^{2}3p$ and $3{s}^{2}3p\ensuremath{-}3{s}^{2}3d$ transitions. This result confirms the value previously determined from the Na-like ${D}_{1}$ transition of 0.269 $\ifmmode\pm\else\textpm\fi{}$ 0.042 ${\mathrm{fm}}^{2}$. The uncertainty of our result is half of that of previous results for the same isotopes obtained from x-ray spectroscopy of muonic atoms, laser spectroscopy of neutral xenon atoms, and a global evaluation of charge radii. Our result is slightly outside the uncertainty of the value obtained from a King plot analysis of comparable precision. The present work illustrates that extreme-ultraviolet spectroscopy of highly charged ions is a viable approach for measurements of charge nuclear radii differences and can be used to benchmark conventional methods.