Ab initio calculation of scattering length and cross sections at very low energies for electron-helium scattering

The multiconfiguration Hartree-Fock method for continuum wave functions has been used to calculate the scattering length and phase shifts over extremely low energies ranging from 0 to 1 eV very accurately for electron-helium scattering. The scattering length is calculated very accurately with wave functions computed exactly at zero energy, resulting in an upper bound of 1.1784. The electron correlation and polarization of the target by the scattering electron, which are very important in these calculations, have been taken into account in an accurate ab initio manner through the configuration-interaction procedure by optimizing both bound and continuum orbitals simultaneously at each kinetic energy of the scattered electron. Detailed results for scattering length, differential, total, and momentum-transfer cross sections obtained from the phase shifts are presented. The present scattering length is found to be in excellent agreement with the experimental result of Andrick and Bitsch [J. Phys. B 8, 402 (1975)] and the theoretical result of O'Malley, Burke, and Berrington [J. Phys. B 12, 953 (1979)]. There is excellent agreement between the present total cross sections and the corresponding experimental measurements of Buckman and Lohmann [J. Phys. B 19, 2547 (1986)]. The present momentum-transfer cross sections also show remarkable agreement with the experimental results of Crompton, Elford, and Robertson [Aust. J. Phys. 23, 667 (1970)]