The radiation must be causing the material to expand. Often radiolysis of polymers can result in the decomposition and the production of gases that might exert a force on the polymer causing it to expand. This would be seen in XRD as a shift to smaller theta values. The peaks might broaden slightly as well.
Gamma irradiation indeed introduces a lot of defects in the structure, making the polymer swell (and this effect may be used for producing thermo-shrinkable polymers, which is a somewhat conterintuitive effect but due to the temperature-induced healing of such defects). Therefore, not only the lattice parameter should increase, at least at the beginning, producing the shift of the peak, but at the end there will be no more peak at all, as all the crystalline phase will be converted into an amorphous one.