This thesis discusses one of the probes of a Quark Gluon Plasma (QGP):\ud direct photon emission. The QGP is a state of matter that is\ud hypothesized to exist at high baryon densities and high temperature.\ud These circumstances are only available for experiments in heavy-ion\ud collisions, and even there the presence of the QGP cannot be measured\ud directly. Several indications of a QGP have already been detected in\ud experiments at the SPS collider at CERN, but the evidence is still\ud inconclusive whether the QGP has been seen.\ud \ud \ud \ud The direct photon signal consists of the photons emitted in the early\ud phases of a collision, partly in thermal processes. The spectrum of\ud these photons is highly dependent on the thermal evolution of the\ud medium, and a phase transition from the QGP to hadronic matter will have\ud a detectable effect on this thermal spectrum. Observation of the direct\ud signal is complicated by the presence of a high number of other photon\ud sources during the collision, mainly the decay of neutral mesons, in the\ud later phases of the collision. One way that this background can be\ud estimated is by an invariant-mass analysis, in which the invariant mass\ud is calculated of all pairs of detected photons.\ud \ud \ud \ud in this thesis, an alternative method is proposed to eliminate the decay\ud photons from the detected photon signal. The method depends on the\ud measurement of the photon spectrum for several centrality classes. By\ud subtracting a scaled peripheral photon spectrum from the central photon\ud spectrum, the decay photon spectrum can be eliminated, and the remaining\ud signal consists of direct photons only. Because this analysis uses the\ud ratio of measured spectra at different centralities, it is less\ud sensitive to a number of systematic effects, compared to the invariant\ud mass analysis.\ud \ud \ud \ud Our inclusive photon analysis has been performed on the photon data of\ud Pb+Pb collisions in the WA98 experiment at a beam energy of 158 GeV per\ud nucleon.. Using our method, it was possible to produce a direct photon\ud spectrum for transverse photon momenta between 0.5 GeV/c and 2.0 GeV/c.\ud For the lower part of this interval, this is the first time that a\ud direct photon signal has been extracted. At higher momenta, the results\ud show a good correspondence with earlier results of the WA98 invariant\ud mass analysis.\ud \ud \ud \ud The results are compared with the outcome of a simple hydrodynamical\ud model first proposed by Bjorken. This shows that the direct photon\ud signal that we found is compatible with an initial temperature of about\ud 300 MeV, and a transition temperature of 180 MeV. With these\ud parameters, the model shows that most of the thermal photons originate\ud in the QGP/hadron gas mix during the phase transition, or in the\ud following hadron gas phase
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