The ultraviolet (UV) absorption spectra of quartz KUVI glasses (type IV) irradiated with rhenium ions with an energy of 30 keV are studied. It was found that with increasing ion fluence (510^15 – 510^17 cm^ 2), a characteristic fan-shaped broadening of the optical absorption edge of glasses is observed. The results are interpreted within the framework of the generalized Urbach rule (approximation of quasidynamic disorder induced by ion irradiation). Based on the dose dependence of the characteristic Urbach energy, an estimate was made of the effective cross section for the process of radiative disordering of the glass matrix. It was found that this value varies within 1.0710^-17 cm^2 –1.210^-18 cm^2 with increasing fluence. The optical gap width of the implanted samples was determined by the Tauts method for direct allowed interband transitions. Based on the principle of equivalence of static and dynamic structural disorder, a ratio of the constants of second-order deformation potentials was found, which determines the relationship between the Urbach energy and the optical gap width of silica glass matrix SiO2. This work was supported by the Ministry of Education and Science of the Russian Federation (Government Task No. 3.1485.2017 / 4.6) and the Russian Government (Act 211, Contract No. 02.A03.21.0006).