Cascade processes and the kinetic-energy distribution of pionic hydrogen atoms

The previously unmeasured neutron time-of-flight distributions for the reaction ${\mathrm{\pi }}^{\mathrm{-}}$p→${\mathrm{\pi }}^0$n in gaseous targets at pressures of 17 and 40 bar have been measured. The kinetic energy of the ${\mathrm{\pi }}^{\mathrm{-}}$p atoms at the instant of the nuclear reaction has been evaluated from the Doppler broadening of the neutron time-of-flight spectra. Evidence was found for ${\mathrm{\pi }}^{\mathrm{-}}$p atoms with kinetic energies of 75 eV. The present experimental data were interpreted within a cascade model that takes the evolution of the kinetic-energy distribution during the cascade into account. The parameters of the model were determined from experiments measuring neutron time of flight in liquid hydrogen and x-ray yields in gas. Coulomb deexcitation is responsible for the significant fraction of the high-energy component, whose intensities are compatible with the calculations of Bracci and Fiorentini [Nuovo Cimento 43A, 9 (1978)]. Stark mixing is found to be significantly stronger than in the commonly used straight-line approximation; the initial mean kinetic energy of 1–2 eV is consistent with the results of muonic hydrogen. The model therefore describes the cascade of pionic hydrogen over a range of pressures of three orders of magnitude. The implications for high-resolution x-ray measurements of the 1S-level nuclear width are discussed.