Determination of the $\mathit{S}$-Wave Scattering Length in Pionic Deuterium with a High Resolution Crystal Spectrometer

The pionic deuterium $3P-1S$ x-ray transition was measured with a quartz crystal spectrometer in combination with a cyclotron trap and charge coupled device detectors. The strong interaction shift and total decay width of the $1S$ level are ${\epsilon }_{1S}\left(\mathrm{shift}\right)=2.48\mathrm{}\pm 0.10$ eV (repulsive), ${\gamma }_{1S}\left(\mathrm{width}\right)=1.02\mathrm{}\pm 0.21$ eV, where the statistical and systematic errors were added linearly. They yield the total pionic deuterium $S$-wave scattering length: $a_{{\pi }^{-}d}=-0.0264\mathrm{}(\pm 0.0011)+i0.0054\mathrm{}(\pm 0.0011)m_{\pi }^{-1\mathrm{}}$.