  Using the fact that the c-quark inside a charmonium moves with a small
velocity v in the charmonium rest-frame, one can employ an expansion in v to
study decays of charmonia and results at the leading order for chi_{c0,2} -->
gamma gamma exist in the literature. We study corrections at the
next-to-leading order in the framework of nonrelativistic QCD(NRQCD)
factorization. The study presented here is different than previous approaches
where chi_{c0,2} is taken as a bound-state of a c cbar pair and a
nonrelativistic wave-function is used for the pair. We find that the
corrections are consist not only of relativistic corrections, but also of
corrections from Fock state components of chi_{c0,2} in which the c cbar pair
is in a color-octet state. For chi_{c2} there is also a contribution from a
Fock state component in which the pair is in a F-wave state. We determine the
factorization formula for decay widths in the form of NRQCD matrix elements
representing nonperturbative effects related to chi_{c0,2}, and calculate the
perturbative coefficients at tree-level. Because the NRQCD matrix elements are
unknown, a detailed prediction for the decay chi_{c0,2} --> gamma gamma can not
be made, but the effect of these corrections can be determined at certain
level. Estimations show that the effect is significant and can not be
neglected.
