  We analyze the low-energy e-N2 collisions within the framework of the
Modified-Effective Range Theory (MERT) for the long-range potentials, developed
by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. In
comparison to the traditional MERT we do not expand the total cross-section in
the series of the incident momentum \hbar k, but instead we apply the exact
analytical solutions of the Schroedinger equation for the long-range
polarization potential, as proposed in the original formulation of O'Malley et
al. This extends the applicability of MERT up to few eV regime, as we confirm
using some simplified model potential of the electron-molecule interaction. The
parameters of the effective-range expansion (i.e. the scattering length and the
effective range) are determined from experimental, integral elastic cross
sections in the 0.1 - 1.0 eV energy range by fitting procedure. Surprisingly,
our treatment predicts a shape resonance that appears slightly higher than
experimentally well known resonance in the total cross section. Agreement with
the experimentally observed shape-resonance can be improved by assuming the
position of the resonance in a given partial wave. Influence of the quadrupole
potential on resonances is also discussed: we show that it can be disregarded
for N2. In conclusion, the modified-effective range formalism treating the
long-range part of the potential in an exact way, reproduces well both the very
low-energy behavior of the integral cross section as well as the presence of
resonances in the few eV range.
