Using free electron laser excitation in the XUV range, CaWO₄ samples were exposed to ultra-short, intense photon pulses (photon energy 89.84 eV, 10 muJ average pulse energy, 25 fs pulse length), and their luminescence was studied with time-resolved spectroscopy. In the decay curves measured in the temperature range 8-300 K, a non-exponential emission decay with shortening of the life times over the first few mus is observed, which depends on the excitation density. Using a model for dipole-dipole interaction of excitons under non-uniform excitation densities, the structure of the decay curves can be reproduced in good agreement with the experimental data, and parameters for the initial exciton interaction can be calculated. Financial support by the Estonian Science Foundation (grants N 6538 and 0548J) and by the European Community Research Infrastructure Action in the FP6 Program of the EU (Contract RII3-CT-2004-506008 (IA-SFS)) is gratefully acknowledged. PACS: 41.60.Cr, 52.59.Rz, 61.80.Ba, 61.82.Ms, 71.35.Aa, 78.47.+p

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