A new determination of the π−H and π−D 2P-1s strong interaction shifts using crystal diffraction

Abstract The 2P-1S X-ray transition energy in pionic hydrogen (π − H ) and pionic deuterium (π − D ) has been measured using a curved graphite crystal spectrometer. E 2 P −1 S (π − H ) = 2434.5 ± 0.4( stat ) ± 0.3 (syst) eV , E 2 P −1 S (π − D ) = 2592.1 ± 0.8 ( stat ) ± 0.5 (syst) eV . The deduced strong interaction shifts ΔE(π − H ) = −4.9 ± 0.4 ( stat ) ± 0.3 (syst) eV , ΔE(π − D ) = +5.5 ± 0.8 ( stat ) ± 0.5 (syst) eV , corresponding to the S-wave scattering lengths Re a π− p 0 = +0.084 ±0.009 fm , Re a π− d 0 = −0.083 ± 0.014 fm , are compared with recent calculations. The X-ray yield is found to be 0.04 ± 0.02 2P-1S X-rays per stopped π − in saturated hydrogen vapour of 3 atm pressure.