Measurements and simulations on position dependencies in the response of single PWO crystals and a prototype for the $\overline{P}ANDA$ EMC

The PANDA experiment, which will be located at the future Facility for Antiproton and Ion Research, aims at the study of strong interaction within the charm sector via antiproton- proton collisions. An essential component of the PANDA detector to achieve the ambitious physics goals is the Electromagnetic Calorimeter (EMC). Reason for this is particularly its high detection efficiency for photons and electrons over a large dynamic range, since most of the expected physics channels are accompanied by secondary photons. The EMC is based on second generation lead tungstate scintillator crystals and thus features a very compact design and improved performance. To guarantee a homogeneous and precise energy and momentum response, an exact knowledge on the incident particle position is mandatory. In the scope of this work, non-uniformities in the light yield of single lead tungstate crystals with tapered geometry are investigated. This effect was studied with the SLitrani simulation package in comparison to a series of dedicated experimental setups. The so called precision setup allowed for a comparative measurement of the response to cosmic muons and low energetic photons. Furthermore, an analogous beam measurement was performed with 80 MeV protons. Both, simulation and experiments agree that, in case of the PANDA crystal geometry types, the obtained light yield increases quadratically with the distance of the location of the energy deposition inside the crystal to the photo sensor. A clear correlation of the observed amount of non-uniformity to the mean tapering angle of the individual crystal geometry type could be determined. Furthermore, no significant difference in non-uniformity was observed for the three different particle species. Therefore, the observed non-uniformities can be regarded as independent of the exact mechanism of the energy deposition. Hence, the main effect governing the obtained non-uniformities is the interplay of the focussing caused by the high amount of internally reflected scintillation light and the intrinsic absorption in the crystal. Various techniques to achieve a light yield uniformisation, including wrapping and crystal surface modifications, have been investigated. Among these, emery polishing of one crystal surface succeeded in a partial uniformisation of the response to photons with an acceptable light yield loss compared to an intrinsically uniform untapered crystal type. However, an evaluation of the influence on a matrix of 60 crystals based on GEANT4 simulations showed that, in spite being beneficial for energies above several hundred MeV energy, due to the inherent light yield loss entailing a resolution loss in the low energy regime, a uniformisation is not recommendable for the PANDA Barrel EMC. In case of the end caps, the straight geometry of the implemented crystals does not require uniformisation. The position response of the prototype PROTO60, representing a subsection of the PANDA Barrel EMC comprised of 6 times 10 lead tungstate crystals, was investigated during a 15 GeV/c positron beam test at CERN SPS. Due to the availability of a high resolution reference position provided by a tracking station based on two double-sided silicon strip detectors, linearity and resolution of the incident particle position reconstructed with PROTO60 could be investigated extensively. Both deployed reconstruction techniques, based on a centre of gravity algorithm with either logarithmic weighting or linear weighting with successive S-curve correction, yield comparable results. An overall position resolution of 1.1 mm could be achieved. However, for incident positions located at the crystal junctions, an improved resolution down to 0.5 mm is obtained. These results, which represent the high energy limit of the PANDA EMC, are superior to the stated specifications. In addition, a comparison of the achieved resolution to the upper limit deduced from the convolution of photon beam and detector resolution at energies up to 1.5 GeV leads to the conclusion that also in the low energy regime a resolution superior to the specifications is achievable. The achieved results specific for the PANDA EMC design are compared to recent experiences of the CMS electromagnetic calorimeter, showing many similarities.