The proposed experiment depends on a good knowledge of the kinetic energy distribution at the instant of the X-ray transitions. Recent experiments [54,55,65] with liquid hydrogen using a neutron time-of-flight ( nToF) method found a large fraction of ``high energy'' atoms at the states where the pion capture occurs. Experiments in the gaseous state at support the result of the experiments with liquid hydrogen . The data obtained with the nToF method allow to calculate the kinetic energy distribution at the instant of nuclear reaction in a model independent way as shown in Appendix 2. Also measurements with muonic hydrogen at pressures in the 100 mbar region show a significant high kinetic energy component .
This high energy component is attributed to the Coulomb deexcitation
A significant improvement can further be achieved by performing a combined fit of the and data with the cascade model. The atomic cascade in the atom does not involve any nuclear reaction while all the deexcitation processes are very similar to the case. As a result, the cascade in the atom allows to study the Coulomb deexcitation directly by observing the Doppler broadening of the X-ray lines .
The measurement of the Coulomb deexcitation via the observation of the Doppler broadening of muonic hydrogen X-rays is therefore an essential part of the planned experiment.