Systematic low-temperature measurements of the thermal conductivity, specific heat, dielectric constant, and temperature-dependent ultrasound velocity were made on a single piece of vitreous silica. These measurements were repeated after fast neutron irradiation of the material. It was found that the irradiation produced changes of the same relative magnitude in the low-temperature excess specific heat C/sub ex/, the thermal conductivity kappa, and the anomalous temperature dependence of the ultrasound velocity ..delta..v/v. A corresponding change in the temperature dependent dielectric constant was not observed. It is therefore likely that kappa and ..delta..v/v are determined by the same localized excitations responsible for C/sub ex/, but the temperature dependence of the dielectric constant may have a different, though possibly related, origin. A consistent account for the measured C/sub ex/, kappa, and ..delta..v/v of unirradiated silica is given by the tunneling-state model with a single, energy-dependent density of states. Changes in these three properties due to irradiation can be explained by altering only the density of tunneling states incorporated in the model.