  The decay widths \phi \to \gamma f_0(980) and \phi \to \gamma a_0(980) are
calculated taking into account the finite widths of the scalar resonances
f_0(980) and a_0(980). The latter are shown to be essential in order to obtain
meaningful results. Simultaneously we also study the decays \phi\to \gamma
\pi^0\pi^0 and \gamma \pi^0\eta where a good reproduction of the recent
experimental data is obtained, pointing out the necessity of a \phi\gamma
K^0\bar{K}^0 contact vertex. The calculated decay rates to \gamma f_0(980) and
\gamma a_0(980) are in good agreement with the experimental ones without
invoking isospin breaking in the couplings of the f_0(980) and a_0(980)
resonances to the K^+ K^- and K^0 \bar{K}^0 channels, at odds with recent
proposals. The derived formula for calculating these \phi radiative decay
widths can be also applied in their own experimental analyses in order to
obtain more precise results.
