Precision calculation of the lowestS1resonance ine-H scattering

The lowest ${}_{}{}^1{}_{}{}^{}S$ resonance in electron-hydrogen scattering has been calculated using a Hylleraas correlation function with up to 95 terms in the optical potential formalism. The results including estimated errors are $E_r=9.55735\mathrm{}\pm 5\times {10}^{-5\mathrm{}}$ eV, ${\Gamma }^{\mathrm{BW}}=0.04717\mathrm{}\pm 2\times {10}^{-5\mathrm{}}$ eV. These results should be useful for experimental calibration purposes; they are compared to previous, calculated and experimental results. The conventional or Breit-Wigner width ${\Gamma }^{\mathrm{BW}}$ above is different from the width which comes naturally out of the Feshbach formalism. A simple formula relating the two is derived.