Extrapolation of Electron-Rare Gas Atom Cross Sections to Zero Energy

Modified effective-range formulas recently developed for electron-atom scattering are employed first to analyze the Ramsauer-Kollath (RK) electron-rare gas atom cross sections, and then to compare them with determinations of the same quantities made by different and newer methods. It is found that these cross sections can be extrapolated unambiguously down to zero energy. The extrapolated RK scattering lengths are found to be approximately 1.19, 0.24, -1.70, -3.7, and $-6.5\mathrm{}{a}_0$ for He, Ne, Ar, Kr, and Xe, respectively. Good agreement is found, in general, both in sign and magnitude with the pressure shift estimates of the scattering lengths. Momentum transfer cross sections are also extended down to zero energy and are compared with some drift velocity and microwave results. The best agreement is found with the Gilardini and Brown curve for Ne, and with those of Pack, Phelps, Frost, and Voshall for the other rare gases, although there are some differences with the latter. In particular, a "pressure effect" is discussed in connection with these results.