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Rate estimates.

Rate estimates are based on extensive tracking simulations and data from a feasibility study at the \( \pi E5\) channel carried out with the new cyclotron trap (see Figure 6). The rates in Table 6 are given for a target gas pressure of \( 1bar \) and \( 15bar\) at room temperature on the basis of the following assumptions:

For the moment a possible improvement made by a better injection efficiency or any other kind of possible optimization is not taken into account. We take this attitude as we can not yet prove or demonstrate the exact numbers gained by improvements in future.

Table 6: The number of expected X-ray events/h is given for different transitions. The two pressures indicate the two typical pressure regions \( 1-3\) bar and \( 15-40\) bar. A stop rate reduction by a factor of ten is assumed for muons. The integrated reflectivity of the Si crystal used for Figure 6 was 73 \( \mu rad\). The error in the quoted number of events is estimated to be on the level of 20%.
Transition Int. reflectivity Events/h
  \( [\mu rad] \) \( 1bar \) \( 15bar\)
\( \mu H_{2\rightarrow 1} \) 14.7 4 75
\( \mu H_{3\rightarrow 1} \) 17.1 2 57
\( \pi H_{2\rightarrow 1} \) 34.8 13 106
\( \pi H_{3\rightarrow 1} \) 29.8 5 79
\( \pi N_{6\rightarrow 5} \) 34.8 40 -
\( \pi O_{6\rightarrow 5} \) 29.8 40 -

The pressure dependence of the rates urges to perform the experiment at higher pressures i.e. working with a cryogenic target. Therefore the experiment will start with an investigation of the \( 15-40\) bar region first and continue with lower pressures in a second step with a well tuned apparatus at the lowest feasible pressure. The rates of between 50 and 100 entries/h is sufficient to collect several \( 10^{4} \) X-ray events in total in a three weeks measuring time. It should be recalled that about \( 10^{4} \) events are sufficient to determine the shift with an accuracy of \( 4\cdot 10^{-4} \) and also open the possibility to determine the width on the \( 10^{-2} \) level. The values for nitrogen and oxygen are given for a set-up optimized to pion stops. The experiment with a combination of nitrogen and oxygen gas is highly valuable as it allows for a direct check of the two-crystal method.

The numbers are also representative for other measurements like pionic Ne or C. For these gases as well as for nitrogen and oxygen the maximum tolerable partial pressure is at about \( 1bar \). This limitation is given by the self absorption of the low energy X-rays in the target gas.

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Pionic Hydrogen Collaboration