Comparative study of low-energy electron-helium scattering in different environments

Momentum-transfer cross sections at the Fermi momentum are calculated by the phase-shift method using the Kohn-Sham density-functional theory applied to the helium-extended electron-gas system. Results obtained for electron–neutral-atom scattering in vacuum below the first ionization threshold are compared. Approximations in both theoretical frameworks are tested. A remarkable similarity between the values of the best cross sections is found. The role of the Friedel sum rule for the phase shifts and the Levinson theorem in this problem are discussed.