A collision cross section study of the 1 1S → 2 1P and 1 1S → 2 1S transitions in helium at kinetic energies from 200–700 eV. Failure of the Born approximation at large momentum changes

Abstract

Differential collision cross sections have been determined for the 1 ¹S → 2 ¹S and 1 ¹S → 2 ¹P transitions in helium at scattering angles within the range 7.5°−35° and kinetic energies of 200, 300, 400, 500, and 700 eV. Multiple scattering errors have been eliminated by determining the ration of inelastic to elastic cross section as a function of pressure (the dependence is linear) and extrapolating to zero pressure. The error in the absolute cross sections is less than 5% in most instances. Where large corrections for multiple scattering are necessary the error bound is 6%. Generalized oscillator strengths (f) have been calculated from the data for both transitions and compared with the Born approximation calculations (f_B) of Kim and Inokuti [Phys. Rev. 175, 176 (1968)]. At a scattering angle of 30° the ratio f_B/f (which would be unity if the Born approximation were accurate) decreases from the value 0.86 at 200 eV to 0.16 at 500 eV for the transition 1 ¹S → 2 ¹P. At smaller values of the squared momentum change (between 0.5 and 2.5 a.u.) deviations from the Born approximation are still significant (about twice our experimental error) and approach to the Born limit is very slow, imperceptible in fact from 300 to 700 eV. Despite the poor agreement between the differential cross sections measured by us and those calculated from the Born approximation, we have found excellent agreement between the integrated (over angle) cross sections calculated from our measurements and those obtained from the Born approximation (with a small correction for exchange). The reasons for the above observations are discussed, where feasible, and comparisons are made with the experimental the theoretical results of other investigators.