In this article, we have used a newly presented direct correlation function (DCF) and predicted the small-k behavior of the structure factor, S(k), for liquid rubidium and cesium, and this behavior is in very good agreement with the experimental data. For these calculations, the effective pair potentials have obtained using the modified hyper-netted-chain (MHNC) theory. These effective pair potentials are also accurate for the range in which no pseudopotential, or Lennard-Jones (U) potential, is adequate to present the thermodynamic behavior of alkali metals. We have also compared our model with the Percus-Yevick theory and random phase approximation in regard to predicting S(k) at low k, and a better agreement has been obtained. Because the applied model for the DCF generates S(k) accurately at low k, we have used it to evaluate some reported effective pair potentials for alkali metals, including LJ (n-m) and also exp-6 types. The results show that these potentials are not very accurate, at least for the moderate densities, in regard to predicting S(k), although these potentials are able to generate the pressure-volume-temperature (p-v-7-) behavior of alkali metals precisely.