DBPAS has been used to characterize atomic level defect structures in materials. In this investigation the numerical analysis of the Doppler spectra was restricted to the determination of the shape parameter, S, defined as the ratio between the total amount of counts in a central portion of the spectrum and the total amount of counts. As samples were exposed by X-ray increasing from 3, 6, and 9 Gy with 6 MV, and 10 MV each and also by E-beam increasing the energies with 6 MeV, 9 MeV, 12 MeV, and 20 MeV. The S-parameter values were increased as increasing the exposed time and the energies. The S-parameters of the large and small size grains in $CaWO_4$ were measured. The S-parameter of the small size grains in $CaWO_4$ was resulted in larger values.