  We calculate the cross-sections for the processes $\rho J/\psi\rightarrow
D^0\bar{D}^0$, $\rho J/\psi\rightarrow D^0\bar{D}^{0*}$ ($D^{0*}\bar{D}^{0}$)
and $\rho J/\psi\rightarrow D^{0*}\bar{D}^{0*}$ using a QCD-motivated many-body
overlap factor to modify the usual sum of two-body interaction model. The
realistic Cornell potential has been used for pairwise interaction in the four
quark Hamiltonian and noted to give lesser cross-sections as compared to the
quadratic potential. The Resonating group method is employed along with the
Born approximation which decouples its integral equations. It is pointed out
that the additional QCD effect (a gluonic field ovelap factor) result in a
significant suppression in the cross sections as compared to the more popular
sum of two-body interaction.
