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 epsilon 1s = -7.127 +/- 0.028(stat.) +/- 0.036(syst.) eV (attractive). From the natural line width, measured for the first time, we determine the decay width of the 1s state: Gamma(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(pi-p-->pi-p)(h) = 0.0885 +/- 0.0003(stat.) +/- 0.0006(syst.)m(pi)(-1). The scattering length for single charge exchange is found to be a(pi-p-->pi 0n)(h) = -0.136 +/- 0.007(stat.) +/- 0.003(syst.)m(pi)(-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 symmetry.