the difference between the $|Q{\bar Q}, R\rangle$ state used here, which is built by adding quark sources to the vacuum and the true ground state of the $Q{\bar Q}$ system as discussed in Sec. IIA. In other words the profile of the chromo-electric field distribution for such a state is not expected to agree with the profile of the flux-tube or action density. To illustrate this difference, in Fig. 2 we plot the energy density as a function of the magnitude of the distance transverse to the $Q\bar Q$ axis, $x_\perp = |\x_\perp|$, $\R\cdot \x = \R\cdot \x_\perp = 0$.

![\[fig1b\] $R^2 \langle \E^2(x) \rangle$ in units of $2b_C/\pi^3(\hbar c)^2 $ as a function of the distance $x$ transverse to the $Q{\bar Q}$ axis. The units and the setting are as in Fig. 1.](Fig1b.eps){width="3.in"}

Finally, in Fig. 3, we show the contour plot of the energy density as a function of the position in the $xz$ plane with quark and antiquark on the $z$ axis at $R/2$ and $-R/2$ respectively.

![\[fig2\] $R^2 \langle \E^2(x) \rangle$ as a function of position in the $xz$ plane. The units and the same setting as in Fig. 1. ](Fig2.eps){width="3.in"}

It is clear from Figs. 