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The radiation hardness of the AToM chips of the BaBar Silicon Vertex Tracker has been investigated by means of irradiation with photons from a 60Co source and 0.9 GeV electrons. The increase in noise and the decrease in gain of the amplifier have been measured as a function of the applied capacitive load and the absorbed dose. Different beam intensities have been used to study the effect of different dose rates to the AToM radiation damage. The chip digital functionalities have been tested up to a dose of 5.5 Mrads for the 60Co photons and 9 Mrads for the 0.9 GeV electrons. In addition a pedestal shift for the irradiated channels has been observed in the test with electrons but is not present in the irradiation with photons. This effect reproduces qualitatively the behavior observed since 2002 in the front-end electronics of the installed BaBar Silicon Vertex Tracker. After some investigation of the chip layout, this peculiar behavior could be associated to radiation damage in a well-identified component of the AToM. The results of the radiation tests are presented and used to extrapolate the lifetime of the installed detector and its performance in the next few years.