The strong-interaction shift πD 1s and broadening Γ πD 1s in pionic deuterium have been determined in a high statistics study of the πD(3p − 1s) X-ray transition using a high-resolution crystal spectrometer. The pionic deuterium shift will provide constraints for the pion-nucleon isospin scattering lengths extracted from measurements of shift and broadening in pionic hydrogen. The hadronic broadening is related to pion absorption and production at threshold. The results are πD 1s = (−2356 ± 31) meV (repulsive) and Γ πD 1s = (1171 + 23 − 49 ) meV yielding for the complex πD scattering length aπD = [−(24.99 ± 0.33) + i (6.22 + 0.12 −0.26 )] × 10 −3 m −1 π . From the imaginary part, the threshold parameter for pion production is obtained to be α = (251 + 5 −11 ) µb. This allows, in addition, and by using results from pion absorption in 3 He at threshold, the determination of the effective couplings g0 and g1 for s-wave pion absorption on isoscalar and isovector N N pairs.
The hadronic width of the ground state of pionic hydrogen has been redetermined by X-ray spectroscopy to be $$\varGamma ^{\pi \mathrm {H}}_{1s}=(856\,\pm \,16_\mathrm{stat}\,\pm \,22_\mathrm{sys})$$ Γ 1 s π H = ( 856 ± 16 stat ± 22 sys ) meV. The experiment was performed at the high-intensity low-energy pion beam of the Paul Scherrer Institute by using the cyclotron trap and a high-resolution Bragg spectrometer with spherically bent crystals. Coulomb de-excitation was studied in detail by comparing its influence on the line shape by measuring the three different transitions K$$\alpha $$ α , K$$\beta $$ β , and K$$\gamma $$ γ at various hydrogen densities. The pion-nucleon scattering lengths and other physical quantities extracted from pionic-atom data are in good agreement with the results obtained from pion-nucleon and nucleon-nucleon scattering experiments and confirm that a consistent picture is achieved for the low-energy pion-nucleon sector with respect to the expectations of chiral perturbation theory.
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