  It is argued that radiative decays of scalars a0/f0(980) can serve as a
decisive tool in establishing the nature of the latter. In particular,
predictions for the widths of the radiative decays S->gamma V (S=a0/f0(980),
V=omega/rho/gamma) are given in the framework of the molecule model of the
scalars. Finite-range corrections are discussed in detail for the two-gamma
decays of hadronic molecules, with a special attention payed to the interplay
of various scales involved in the problem and to the gauge invariance of the
amplitude. The results are applied to the two-photon decay of the f0(980), and
the existing experimental data on this decay are argued to support the molecule
assignment for the scalar f0(980).
