Density distribution of cold exciton clouds generated into a strain-induced potential well by two-photon excitation in Cu$_2$O is studied at 2 K. We find that an anomalous spike, which can be interpreted as accumulation of the excitons into the ground state, emerges at the potential minimum. The accumulation can be due to stimulated scattering of cold excitons, mediated by acoustic phonon emission. Possibility of the formation of the thermodynamic Bose-Einstein condensate of paraexcitons has been discussed.
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