The strong interaction shift and width of the ground state of pionic hydrogen

The 3p-1s transition in pionic hydrogen was investigated with a high-resolution crystal spectrometer system. From the precisely measured transition energy, together with the (calculated) electromagnetic energy, the strong interaction shift of the 1s state was obtained as ɛ_1s = -7.127 ± 0.028(stat.)± 0.036(syst.) eV (attractive). From the natural line width, measured for the first time, we determine the decaywidth of the 1s state: Γ_1s^(decay) = 0.97 ± 0.10(stat.)± 0.05(syst.) eV. With the recently calculated electromagnetic corrections the s-wave scattering lengths of an isospin symmetric strong interaction are deduced. The scattering length for elastic scattering of a negative pion on a proton is a_{π^-p→ π^-p}^h = 0.0885±0.00003(stat.)±0.0006(syst.) m_π^-1. The scattering lengthe for single charge exchange is found to be a_{π^-p→ π⁰n}^h = -0.136 ± 0.007(stat.) ± 0.003(syst.) m_π^-1. The experiment was performed at the Paul Scherrer Institute (PSI) in Switzerland. A focussing crystal spectrometer with an array of bent crystals, the cyclotron trap (a magnetic system designed to increase the particle stop density) and a CCD (charge-coupled device) detector system were employed. The results from the pionic hydrogen experiment — together with those from the pionic deuterium experiment — were used to test the isospin symmetry of the strong interaction. The present data are still consistent with isospin sysmmetry.