  We analyze low-energy scattering of positrons on Ar atoms and N2 molecules
using Modified Effective-Range Theory (MERT) developped by O'Malley, Spruch and
Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. We use formulation of MERT
based on exact solutions of Schroedinger equation with polarization potential
rather than low-energy expansions of phase shifts into momentum series. We show
that MERT describes well experimental data, provided that effective-range
expansion is performed both for s- and p-wave scattering, which dominate in the
considered regime of positron energies (0.4 - 2 eV). We estimate the values of
the s-wave scattering lenght and the effective range for e+ - Ar and e+ - N2
collisions.
