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Independent fits.

The spectra were first fitted without using any theoretical input for the velocity distribution. The only fixed parameter was the value of the resolution function which will also be known during the real experiment. The velocity distribution was taken into account by a very crude assumption: the influence of the Doppler effect was included into the fit function by convoluting rectangular boxes corresponding to the possible Coulomb deexcitation processes. The width of the boxes was taken according to the transition energies of the allowed Coulomb deexcitations. The height of the boxes was fitted freely. This procedure resulted in the values shown in Table 12 for the relative precision in the determination of the strong interaction Lorentzian width:


Table 12: Fit results as a function of intensity. A \( 1\sigma \) error is given.
Transition Intensity relative error of \( \Gamma _{L} \)[%]
\( \pi H_{3\rightarrow 1} \) 5000 4.9
\( \pi H_{3\rightarrow 1} \) 10000 3.3
\( \pi H_{3\rightarrow 1} \) 20000 2.4
\( \pi H_{3\rightarrow 1} \) 40000 2.3
\( \pi H_{2\rightarrow 1} \) 10000 3.4
\( \pi H_{2\rightarrow 1} \) 20000 3.6


It can be stated that above a certain level the increase in intensity does not any longer significantly reduce the error of the result. This feature is more pronounced for the \( 2\rightarrow 1\) transition than for the \( 3\rightarrow 1\) transition. Such a saturation effect in the level of precision is explained by the influence of the unknown velocity distribution which contributes to the systematic error of the fit procedure.

next up previous contents
Next: Correlated fits. Up: Results of simulation tests. Previous: Results of simulation tests.   Contents
Pionic Hydrogen Collaboration
1998