Present knowledge of Coulomb deexcitation.

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Present knowledge of Coulomb deexcitation.

The proposed experiment depends on a good knowledge of the $(\pi ^{-}p)$ 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'' $(\gg 1eV)$ $\pi p$ atoms at the states where the pion capture occurs. Experiments in the gaseous state at $40bar$ support the result of the experiments with liquid hydrogen [66]. 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 [67].

This high energy component is attributed to the Coulomb deexcitation

$\begin{displaymath} (\pi ^{-}p)_{i}+p\rightarrow (\pi ^{-}p)_{f}+p\end{displaymath}$

in which the transition energy is transferred into the kinetic energy of the $\pi p$ atom and the proton. The rates of the Coulomb deexcitation have been calculated by several groups. The results differ by more than one order of magnitude [46,47,48,49,53] . This uncertainty can be greatly reduced by fitting the experimental data with the atomic cascade model, see [56,52] and references therein. The recent experimental observations of high energy components in the $\pi ^{-}p$ and $\mu ^{-}p$ kinetic energy distributions stimulated further theoretical studies of deceleration and acceleration mechanisms [57,58,59]. We plan to upgrade our cascade model by including the results of these new calculations and using a more accurate model of the Stark mixing with the strong interaction effects directly taken into account [60]. We also expect to benefit from the final results of the measurements of the $\pi ^{-}p$ kinetic energy distribution at the instant of nuclear reaction [61,66], which can be extracted in a model independent way ( see Appendix 2).

A significant improvement can further be achieved by performing a combined fit of the $\pi ^{-}p$ and $\mu ^{-}p$ data with the cascade model. The atomic cascade in the $\mu ^{-}p$ atom does not involve any nuclear reaction while all the deexcitation processes are very similar to the $\pi ^{-}p$ case. As a result, the cascade in the $\mu ^{-}p$ atom allows to study the Coulomb deexcitation directly by observing the Doppler broadening of the X-ray lines [62].

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.

Next: Yields of X-ray transitions Up: Atomic cascade. Previous: The different cascade processes. Contents

Pionic Hydrogen Collaboration
1998