Variational Calculations on Electron-Helium Scattering

Calculations have been made on the elastic scattering of low-energy electrons by helium using a variational procedure which takes polarization and correlation effects into account by means of continuum Bethe-Goldstone equations. The convergence of the results is examined using two methods to obtain a complete set of basis functions. Results for the $s$, $p$, $d$, and $f$ waves are presented. The width of the ${}_{}{}^2{}_{}{}^{}S$ closed-channel resonance below the $n=2\mathrm{}$ threshold is found to be 0.015 eV, in comparison with the 0.015-0.020-eV estimates of Andrick and Ehrhardt from experiment and the 0.01-eV estimate of Simpson and Fano.