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

$\rho J/\Psi$ Scattering in an Improved Many Body Potential