wishes to have the confining potential grow linearly at large distances then it is necessary to set $\alpha = 1$, [*i.e.*]{} $d(p) \propto \mu/p$ for $p/\mu < 1$. In this case, assuming that the long-range behavior of the potential is of the form $V_C(r) = b_C r$, we obtain from [Eq. (\[vc\])]{}, $$b_C = C_F d^2(\mu)\mu^2/(8\pi). \label{bc}$$ We use the Coulomb string tension $b_C  = 0.6 \mbox{ GeV}^2$. For the $Q\bar Q$ system the long-range contribution to the electric fields is then given by, $$\begin{gathered}
\langle \E^2(\x,\R) \rangle = 
  {{2b_C}\over {\pi^3}}
\biggl[
  {{(\R/2 - \x)} \over {|\R/2 -
  \x|^2}}\left(1-j_0(\mu|\R/2-\x|)\right) \\
 + (\x \to -\x) \biggr]^2. \label{elnof}\end{gathered}$$

![\[fig1\] $R^2 \langle \E^2(x) \rangle$ in units of $2b_C/\pi^3(\hbar c)^2 $ as a function of the distance $x$ along the $Q{\bar Q}$ axis. We employ the $f(p) = 1$ approximation. The quark and the antiquark are located at $R/2=5\mbox{ fm}$ and $-R/2 = -5\mbox{ fm}$ respectively. The renormalization scale $\mu=1.1\mbox{ GeV}$ is calculated from [Eq. (\[bc\])]{} using $d(\mu) = 3.5$ from Ref. [@as1]. The dashed line is the contribution from the two self energies, the dash-dotted line represents mutual interactions and the solid line is the total.](Fig1a.eps){width="3.in"}

In Fig. 1 we show the Coulomb 