The internal structure of exotic charmonium (R) states is
still a subject of debate. Some of the popular pictures used to describe them
are tetraquark, meson molecule or mixtures of those with charmonium.
One way to shed light into the nature of these states is to study their
radiative decays. We expect that their decay widths into
two photons will vary from one configuration to another. The
direct experimental measurement of these widths in the reaction
$R \to \gamma \gamma$ is difficult. However, they manifest themselves
also indirectly in the production, through photon-photon fusion, of the
resonance $R$ in ultraperipheral nucleus-nucleus collisions (UPHIC), where the
production cross section is directly proportional to the decay width
$\Gamma (R \to \gamma \gamma)$. Once produced, the resonance $R$ will
decay mostly in hadronic channels but it may also decay into a photon pair.
In this case, the cross section will be proportional to the
squared $2 \gamma$ decay width, being even more sensitive to
the internal structure of the resonance. In this note we review the
predictions for exotic charmonium production in UPHIC and present,
for the first time, estimates
of the production cross section of exotic states which decay into two
photons.