  We present measurements of the differential cross section
$d\sigma/dp_{T}^{\gamma}$ for the associated production of a $c$-quark jet and
an isolated photon with rapidity $|y^{\gamma}|< 1.0$ and transverse momentum
$30 < p_{T}^{\gamma} < 300$ GeV. The $c$-quark jets are required to have
$|y^{jet}| < 1.5$ and $p_{T}^{jet} >15$ GeV. The ratio of differential cross
sections for photon+ c and photon+ b production as a function of
$p_{T}^{\gamma}$ is also presented. The results are based on data corresponding
to an integrated luminosity of 8.7 fb$^{-1}$ recorded with the D0 detector at
the Fermilab Tevatron $p\bar{p}$ Collider at $\sqrt{s}=$1.96 TeV. The obtained
results are compared to next-to-leading order perturbative QCD calculations
using various parton distribution functions, to predictions based on the
$k_{T}$-factorization approach, and to predictions from the Sherpa and Pythia
Monte Carlo event generators.
