Strong Interaction Shift and Width of the 1s Level in Pionic Hydrogen

The $3p-1s$ 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 ${\varepsilon }_{1s}=-7.127\mathrm{}\pm 0.028\left(\mathrm{stat}\right)\pm 0.036\left(\mathrm{syst}\right)\mathrm{eV}$ (attractive) and ${\gamma }_{1s}=0.97\mathrm{}\pm 0.10\left(\mathrm{stat}\right)\pm 0.05\left(\mathrm{syst}\right)\mathrm{eV}$. The corresponding hadronic $\pi N$ s-wave scattering lengths for elastic scattering and single charge exchange are $a_{{\pi }^{-}p\to {\pi }^{-}p}^h=0.0885\mathrm{}\pm {0.0009m}_{\pi }^{-1\mathrm{}}$ and $a_{{\pi }^{-}p\to {\pi }^{0}n}^h=-0.136\mathrm{}\pm {0.010m}_{\pi }^{-1\mathrm{}}$.