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Combined analysis of \( \mu ^{-}p\) and \( \pi ^{-}p\) data.

The comparison of the calculated Doppler broadening of the \( \mu ^{-}p\) \( K\alpha \) and \( K\beta \) lines with the result of the proposed experiment will allow us to perform a fine tuning of the Coulomb and deceleration rates. The \( \pi ^{-}p\) data on the kinetic energy distribution obtained with the nToF method will also be used for this goal. By transferring this information into the \( \pi ^{-}p\) part of the cascade calculations we are confident that the current uncertainties in the calculated energy distributions of the \( \pi ^{-}p\) atom at the instant of the X-ray transitions will be reduced to the level allowing to predict the Doppler broadening correction to the X-ray lines profile with an error of better than 1% in the hadronic width.

Pionic Hydrogen Collaboration