Elastic Electroproduction of $\rh0$ and $J/\Psi$ Mesons at large $Q^2$ at HERA

The total cross sections for the elastic electroproduction of $\rh0$ and $J/\Psi$ mesons for $Q^2$ $>$ 8 GeV$^2$ and $<W > \simeq 90$ GeV/c$^2$ are measured at HERA with the H1 detector. The measurements are for an integrated electron$-$proton luminosity of $\simeq$~3~pb$^{-1}$. The dependences of the total virtual photon$-$proton ($\gamma^* p$) cross sections on $Q^2$, $W$ and the momentum transfer squared to the proton ($t$), and, for the $\rho$, the dependence on the polar decay angle ($\cos \theta^*$), are presented. The $J/\Psi$ : $\rh0$ cross section ratio is determined. The results are discussed in the light of theoretical models and of the interplay of hard and soft physics processes.