Complex-correlation KohnT-matrix method of calculating total and elastic cross sections: Electron-hydrogen elastic scattering

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We report on a study of electron-hydrogen scattering using a method [Bhatia, Schneider, and Temkin, Phys. Rev. Lett. 70, 1936 (1993)] that allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex-``radial'' correlation functions, in a (Kohn) T-matrix formalism. The complex-correlation Kohn T-matrix method is reviewed in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz [Phys. Rev. 124, 1468 (1961)], but they are more accurate and outside his error bounds at a couple of energies.