Hydrogenic Lamb shift inGe31+and the fine-structure Lamb shift

Abstract

Using x-ray diffraction and beam-foil spectroscopy, we have determined precise wavelengths for Lyman ${\ensuremath{\alpha}}_{1}$ and Lyman ${\ensuremath{\alpha}}_{2}$ in hydrogenic germanium of $1.166\phantom{\rule{0.2em}{0ex}}993\phantom{\rule{0.2em}{0ex}}8\ifmmode\pm\else\textpm\fi{}33\ifmmode\pm\else\textpm\fi{}169$ and $1.172\phantom{\rule{0.2em}{0ex}}433\phantom{\rule{0.2em}{0ex}}6\ifmmode\pm\else\textpm\fi{}39\ifmmode\pm\else\textpm\fi{}170\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. Hydrogenic germanium ${\mathrm{Ge}}^{31+}$ $1s\text{\ensuremath{-}}2{p}_{3∕2}$ and $1s\text{\ensuremath{-}}2{p}_{1∕2}$ Lamb shifts are measured to be $66\phantom{\rule{0.2em}{0ex}}080\ifmmode\pm\else\textpm\fi{}237\ifmmode\pm\else\textpm\fi{}1121$ and $67\phantom{\rule{0.2em}{0ex}}169\ifmmode\pm\else\textpm\fi{}281\ifmmode\pm\else\textpm\fi{}1237\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, respectively. This $14\phantom{\rule{0.3em}{0ex}}\mathrm{ppm}$ measurement of the wavelengths thus provides a 1.8% measurement of the $2p\text{\ensuremath{-}}1s$ Lamb shift and is an improvement by a factor of 3 over previous work. Fitting the full two-dimensional dispersion relation, including Balmer and Lyman series, limits random and systematic correlation of parameters. Dominant systematics are due to diffraction parameters including crystal thickness and alignment, differential Doppler shifts due to the variable location of spectral emission downstream of the beam-foil target, and dielectronic, $2s\text{\ensuremath{-}}1s$, and $4f\text{\ensuremath{-}}2p$ satellites. Models developed are applicable to all relativistic plasma modeling in beam-foil spectroscopy at accelerators. The technique also reports the germanium $2{p}_{3∕2}\text{\ensuremath{-}}2{p}_{1∕2}$ fine structure as $397\phantom{\rule{0.2em}{0ex}}617\ifmmode\pm\else\textpm\fi{}251\ifmmode\pm\else\textpm\fi{}512\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, representing a 0.14% measurement of the fine structure and a 71% measurement of the QED contribution to the hydrogenic germanium fine structure, an improvement of a factor of 6 over previous work. We also report a precise measurement of heliumlike resonances and fine structure.