Electron-CH4scattering in the Ramsauer-Townsend minimum region (0.10–1.0 eV)

We report ab initio calculations for the electron-${\mathrm{CH}}_4$ elastic scattering around the Ramsauer-Townsend (RT) minimum region (0.1–1.0 eV). A model potential approach, in the fixed-nuclei and one-center-expansion formalism, is employed in which the total optical potential is composed of three interaction terms: an accurate static potential of the Hartree-Fock level, an exchange interaction in the Hara free-electron-gas-exchange approximation (plus the orthogonalization), and a semiempirical polarization of the form &) ${}_{}{}^6{}_{}{}^{}$, where $r_c$ is an adjustable parameter. The final results on the total and momentum-transfer cross sections compare reasonably well with experimental data. In particular, a shallow RT structure rather than a pronounced dip in the total cross section is reproduced, which is in good agreement with recent measurements. We also determine the scattering length to be a=-3.4 a.u. by extrapolating our very-low-energy eigenphases (E≃0.001 eV) to the limit of zero energy: From a simple s-wave analysis, this value gives the RT minimum position around 0.4 eV, which is in close agreement with the correct value.