Modified effective-range theory (MERT) was developed in the 1960s to describe electron and positron scattering from atoms. The theory was frequently used to extrapolate measured total cross sections down to the zero-energy region, which is inaccessible experimentally. However, the applicability of the model was usually limited to the very low energy range where experimental data to be extrapolated are rare. We have proposed [Idziaszek and Karwasz, Phys. Rev. A 73, 064701 (2006)] a different way of employing MERT by exploiting the properties of an analytical solution of the Schrödinger scattering equation with the long-range polarization potential. This alternative approach allows the validity of MERT to be extended to higher energies. At present we are applying this procedure for electron and positron scattering on He, H${}_2$, Ar, and CH${}_4$. The scattering amplitude and the effective-range parameters for $s$ and $p$ partial waves are obtained through a fitting inversion procedure applied to integral cross sections spanning most or all of the elastic region. The derived parameters are then used to obtain differential and momentum transfer cross sections; the agreement with experiments is very good.

• Received 6 May 2013

DOI:https://doi.org/10.1103/PhysRevA.88.012704