  We have recently proposed a density functional scheme for calculating the
ground-state pair density (PD) within the Jastrow wave function PDs of the
lowest-order (LO-Jastrow PDs) [M. Higuchi and K. Higuchi, Phys. Rev. A
\textbf{75}, 042510 (2007)]. However, there remained an arguable problem on the
$N$-representability of the LO-Jastrow PD. In this paper, the sufficient
conditions for the $N$-representability of the LO-Jastrow PD are derived. These
conditions are used as the constraints on the correlation function of the
Jastrow wave function. A concrete procedure to search the suitable correlation
function is also presented.
