In the Jastrow theory applied to low cluster order it is necessary to restrict the variation of the two-body correlation factor $f\left(r\right)\mathrm{}$ to the domain of functions corresponding to acceptable convergence of the cluster expansion for the energy. We examine in detail two constraints which have received some attention: the "normalization condition" and the "orthogonality (or average Pauli) conditions." The former constraint is motivated by the requirement that the liquid structure factor $S\left(k\right)\mathrm{}$ vanish at zero wave number; the latter, by the Pauli principle in the Fermi medium. It is shown that two-body Jastrow theory cannot obey both constraints exactly for a state-independent correlation factor $f\not\equiv 1$, but that the requirement $S\left(0\right)=0\mathrm{}$ is automatically satisfied in (two-body) Brueckner reaction-matrix theory as a trivial consequence of the fulfillment, by definition of this theory, of the Pauli principle in the medium.

• Received 24 January 1972

DOI:https://doi.org/10.1103/PhysRevC.5.1553