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 $\delta \lambda ({}^{124}\mathrm{Xe},{}^{136}\mathrm{Xe})$ isotopic shifts of the Al-like $3s^{2}3p{}^{2}P_{1/2}-3s^{2}3p{}^{2}P_{3/2}$, Al-like $3s^{2}3p{}^{2}P_{1/2}-3s^{2}3d{}^{2}D_{3/2}$, Mg-like $3s^2{}^{1}S_0-3s3p{}^{1}P_1$, Mg-like $3s^2{}^{1}S_0-3s3p{}^{3}P_1$, Na-like $3s{}^{2}S_{1/2}-3p{}^{2}P_{1/2}$ ($D_1$), and Na-like $3s{}^{2}S_{1/2}-3p{}^{2}P_{3/2}$ ($D_2$) transitions. Systematic analysis revealed possible line blends and contributing experimental uncertainties. Highly accurate atomic-structure calculations were conducted and used to determine the $\delta {〈r^2〉}^{136,124}$ difference in the mean-square nuclear charge radii of the two xenon isotopes. In the present work, $\delta {〈r^2〉}^{136,124}$ of 0.276 $\pm$ 0.030 ${\mathrm{fm}}^2$ was obtained from the weighted average of the Na-like $D_1$, Mg-like $3s^2-3s3p$ and Al-like $3s^{2}3p-3s^{2}3p$ and $3s^{2}3p-3s^{2}3d$ transitions. This result confirms the value previously determined from the Na-like $D_1$ transition of 0.269 $\pm$ 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.

• Received 11 March 2020
• Accepted 22 May 2020

DOI:https://doi.org/10.1103/PhysRevA.101.062512