Effect of Virtual Excitation of the2sState on the Elastic Scattering of Electrons by Atomic Hydrogen

The elastic scattering of electrons by hydrogen atoms, for electron energies below the first threshold of excitation of the atom (10.2 ev), is investigated numerically making full allowance for exchange and for the virtual excitation of the $2s$ state. Singlet and triplet phases for the $s$, $p$, and $d$ partial waves have been obtained. While the calculation is essentially preliminary to a more extensive eigenfunction expansion calculation for this problem, which would allow for nonspherical distortion of the atom, the results do show that significant changes from the first exchange approximation may be expected as one includes more states in the expansion. In particular, just below the $n=2\mathrm{}$ excitation threshold the singlet $s$ phase and the triplet $p$ phases begin to increase sharply, and what may be a Wigner cusp shows in the total cross section. Predicted angular distributions are compared with the recent measurements of Gilbody, Stebbings, and Fite. The phase shifts are compared with those of the exchange approximation, and also with those of Geltman, who performed a variational calculation allowing for the virtual excitation of the $2s$ and $3s$ states.