Differential and Integral Cross Sections for Excitation of the2P1State of Helium by Electron Impact

Abstract

Differential scattering cross sections for excitation of helium by electron impact from its ground state to its $2^{1}P$ excited state have been measured at four incident electron energies in the range 26-55.5 eV for scattering angles between 10\ifmmode^\circ\else\textdegree\fi{} and 70\ifmmode^\circ\else\textdegree\fi{}, and at 81.6 eV for scattering angles between 10\ifmmode^\circ\else\textdegree\fi{} and 80\ifmmode^\circ\else\textdegree\fi{}. These differential cross sections have been placed on an absolute scale by normalizing them to the experimental absolute integral cross sections of Jobe and St. John. These experimental differential and integral cross sections have been compared with the results predicted by the Born approximation, and by several other first-order approximations in which direct excitation is calculated in the Born approximation and exchange scattering by various Ochkurlike approximations. The calculations provide reliable tests of these scattering theories since they are made using the accurate generalized oscillator strengths of Kim and Inokuti. As expected, these first-order theories are poor near threshold and exchange is important at high scattering angles for all energies. Further, the absolute magnitude of the calculated integral and small-angle differential cross sections is too large and is within 50% of experiment only at energies greater than 80 eV. These first-order models are in qualitative agreement with the experimental angular dependence at 34-81.6 eV for scattering angles between 10\ifmmode^\circ\else\textdegree\fi{} and 40\ifmmode^\circ\else\textdegree\fi{}. At higher scattering angles (corresponding to momentum transfers greater than about 1.6 a.u.), the calculated differential cross sections fall well below the experimental ones. The phase between the direct and exchange scattering amplitudes was found to be important at all energies, and is apparently not predicted correctly by any of the first-order models examined here. Some approximations for the exchange (e.g., Ochkur approximation and the post interaction form of the Ochkur-Rudge approximation) were found to be better for integral cross sections and some (e.g., prior Ochkur-Rudge approximation) were better for differential cross sections. The use of good analytic self-consistent-field (SCF) wave functions for both the ground and excited states was tested by computing generalized oscillator strengths from them and comparing these results with the calculations using the accurate generalized oscillator strengths. The SCF functions yield differential cross sections in quantitative disagreement (20%) with the accurate results, although the energy and angle dependence of the cross sections is predicted qualitatively correctly.