Strong Interaction Shift and Width of the 1<i>s</i>Level in Pionic Hydrogen

Abstract

The $3p\ensuremath{-}1s$ x-ray line of pionic hydrogen was measured with a reflecting bent crystal spectrometer. The strong interaction energy level shift and the total decay width of the $1s$ state, obtained from the transition energy and the linewidth, are ${\ensuremath{\varepsilon}}_{1s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}7.127\ifmmode\pm\else\textpm\fi{}0.028\left(\mathrm{stat}\right)\ifmmode\pm\else\textpm\fi{}0.036(\mathrm{syst})\phantom{\rule{0ex}{0ex}}\mathrm{eV}$ (attractive) and ${\ensuremath{\gamma}}_{1s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.97\ifmmode\pm\else\textpm\fi{}0.10\left(\mathrm{stat}\right)\ifmmode\pm\else\textpm\fi{}0.05\left(\mathrm{syst}\right)\phantom{\rule{0ex}{0ex}}\mathrm{eV}$. The corresponding hadronic $\ensuremath{\pi}N$ s-wave scattering lengths for elastic scattering and single charge exchange are ${a}_{{\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}p}^{h}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.0885\ifmmode\pm\else\textpm\fi{}{0.0009m}_{\ensuremath{\pi}}^{\ensuremath{-}1}$ and ${a}_{{\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n}^{h}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}0.136\ifmmode\pm\else\textpm\fi{}{0.010m}_{\ensuremath{\pi}}^{\ensuremath{-}1}$.