p^2 f(p) j_0(pr), \label{fl}$$ and $j_0, j_1$ are Bessel’s functions. We note that the expression in [Eq. (\[el\])]{} is not necessarily positive. In the limit $f(p)=1$, the matrix element of the square of the inverse of the FP operator is approximated by the square of matrix elements (cf. [Eq. (\[disp\])]{}) and $\langle \E^2\rangle$ becomes positive.

The expression for $\langle \E^2\rangle$ for the three quark system is derived by taking the expectation value of the Coulomb operator, ${\hat V}_C$ in a color-singlet state $\epsilon_{ijk}Q_i(\z_1) Q_j(\z_2)
 Q_k(\z_3) |\Psi[\A]\rangle$, which gives

$$\langle \E^2(\x,\R_i) \rangle = {{C_F}\over {(4\pi)^2}} 
  \sum_{ij=1}^3 \xi^{QQQ}_{ij} \int d\r f_L(r) {{ \z_i - \x - \r/2 } \over 
 { |\z_i - \x - \r/2| } }
\cdot
{{ \z_j - \x + \r/2 } \over 
 { |\z_j - \x + \r/2| }} d'_L(\z_i - \x - \r/2) 
 d'_L(\z_j - \x + \r/2)$$

where $\xi^{QQQ}_{ij} = 1$ if $i = j$ and $\xi^{QQQ}_{ij} = -1/2$ if $i \ne j$. We note that the energy density for the $QQQ$ system comes from two-body correlations between the $QQ$ pairs.

 Numerical results 
===================

We first consider the simple approximation to the expectation value of the Coulomb kernel of [Eq. (\[disp\])]{} in which $f(p)=1$. If one 