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We have recently proposed a density functional scheme for calculating theground-state pair density (PD) within the Jastrow wave function PDs of thelowest-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 sufficientconditions for the $N$-representability of the LO-Jastrow PD are derived. Theseconditions are used as the constraints on the correlation function of theJastrow wave function. A concrete procedure to search the suitable correlationfunction is also presented.

$N$-representability of the Jastrow wave function pair density of the lowest-order