Structural defects in the surface region of magnesium aluminate spinel ($MgAl_2O_4$) crystals irradiated with 450 MeV Xe ions were analyzed by using $^4He$ backscattering in channeling geometry (RBS/C). Monte-Carlo simulations applied for the interpretation of channeling spectra permitted to determine the concentration of radiation-induced defects. They showed that the defect distributions are depth dependent, likely due to annihilation of defects at the surface of the crystals. The cross-section for the formation of defects by swift Xe ions, and consequently the diameter of an ion track, were estimated using single-impact-model calculations.