Static Structure Factor of LiquidHe3in the Long-Wavelength Limit

The relation $S^{\mathrm{}\left(0\right)\mathrm{}}\mathrm{}\left(k\right)=\frac{\hslash k}{2m{c}_0}$ as $k\to 0$ is derived for Fermi liquids in the strong-coupling limit. $S^{\mathrm{}\left(0\right)\mathrm{}}\mathrm{}\left(k\right)\mathrm{}$ is the contribution to the static structure factor $S\left(k\right)\mathrm{}$ from the zero-sound excitation with velocity $c_0$. Together with simple sum-rule arguments, we present some upper and lower bounds on $S\left(k\right)\mathrm{}$.