  We present a leading-order pQCD calculation of the helicity-flip $\Delta\to
N\gamma^*$ matrix element $G_0$ (Coulomb quadrupole amplitude $C2$), taking
into account the transverse momenta of the quarks and the contribution from the
gluons. In the large $Q^2$ limit, its scaling behavior acquires a
double-logarithmic correction $\log^2{(Q^2/\Lambda^2)}$ compared with the
standard scaling analysis, due to the contribution from the orbital motion of
the small-$x$ partons. Based on this and on the latest JLab experimental
results of the $C2-M1$ ratio $R_{SM}$ at $Q^2$ = 3 $\sim$ 4 GeV$^2$, we make a
phenomenological prediction for the latter at higher values of $Q^2$.
