Analytical expressions for the local-field factor G(q) and the exchange-correlation kernel K_(xc)(r) of the homogeneous electron gas

We present an analytical expression for the local field factor G(q) of the homogeneous electron gas which reproduces recently published Quantum Monte--Carlo data by S. Moroni, D.M. Ceperley, and G. Senatore [Phys. Rev. Lett. 75, 689 (1995)], reflects the theoretically known asymptotic behaviours for both small and large q limits, and allows to express the exchange-correlation kernel K_{xc} analytically in both the direct and reciprocal spaces. The last property is particularly useful in numerical applications to real solids