EN
Modified effective range theory in analytical form is used to extrapolate elastic cross-sections down to thermal energies for positron scattering from five atomic and molecular targets including Ar, H_2, N_2, C_6H_6 (benzene) and C_6H_{12} (c-hexane). The derived scattering parameters are then used to estimate the annihilation rates for chosen elements using a simple formula by Gribakin. We show that a combination of two simple models has a potential for accurate parameterization of coefficients describing the interaction of thermal positrons with non-polar targets of low polarizability such as Ar and N_2.