We report a study by electron paramagnetic resonance on the E'(alpha) point defect in amorphous silicon dioxide (a-SiO(2)). Our experiments were performed on gamma-ray irradiated oxygen-deficient materials and pointed out that the (29)Si hyperfine structure of the E'(alpha) consists of a pair of lines split by approximately 49 mT. On the basis of the experimental results, a microscopic model is proposed for the E'(alpha) center, consisting of a hole trapped in an oxygen vacancy with the unpaired electron sp(3) orbital pointing away from the vacancy in a back-projected configuration and interacting with an extra oxygen atom of the a-SiO(2) matrix.