Calibration of the spectrometer.

The understanding and tuning of the crystal spectrometer proceeds in different steps. These steps can be subdivided into tests without pion beam and calibrations during the experiment itself.

1. The quality of a crystal is given in terms of its intrinsic resolution and luminosity. These quantities have been measured at ESRF for the existing crystals still in flat form for different points of their surface. The reflection properties of a bent crystal spectrometer also depend on the bending process and on the chosen geometrical form which can be influenced by shielding the diameter crystal disks with special diaphragms. These measurements and optimizations require a high rate of X-rays and should therefore not be performed with pion beams. We plan measurements with an ECR source which will also be used to check the two crystal setup discussed in chapter 4.3.
2. The results of step 1 must be counterchecked with pionic X-rays of negligible width. These measurements can not be done simultaneously with the pionic hydrogen measurement except perhaps the simultaneous measurement of the with the and the with the , respectively. For a survey measurement with other pionic lines the spectrometer and the shielding has to be rebuilt for each measurement. Also these measurements will be partially devoted to check the two crystal set-up discussed in chapter 4.3.
3. The pionic hydrogen measurement itself will be surveyed by a simultaneous muonic hydrogen measurement with two crystals as discussed below. The validity of this method, i.e. the assumption that the relative response functions of the two crystals is sufficiently understood, must be investigated and established in step 1 and in special measurements in step 2.

• Testing and tuning of the bent crystals.
• Test experiments with pions.
• The two-crystal set-up.