Well, Raman spectroscopy analyzes the vibrations of the materials and thus the force constants. If you damage a solid by irradiation, of course you will convert a well-defined environment into a range of ideal and defected/stressed environments, thus creating a range of perturbations on the spring constant. Therefore the band you measured will no longer be the signal of a single, ideal vibration, but actually a convolution of mildly shifted bands.
In our field (diamond analysis), the shifting and broadening Raman is a good tool to determine the stress caused by non-ideal growth, see e.g.
Article Defects and stress analysis of the Raman spectrum of diamond films
Raman experiments give information concerning the phonon spectrum of the material. Here, especially the crystallinity of the sample determines the line width. Ion irradiation reduces the periodicity of the crystal lattice. By anniling the periodicity could be restored.