Total Cross Sections for Inelastic Scattering of Charged Particles by Atoms and Molecules. III. Accurate Bethe Cross Section for Ionization of Helium

The Bethe cross section σᵢ for ionization of He by fast charged particles is accurately evaluated by a subtraction σᵢ=σₜₒₜ-σₑₓ, where σₜₒₜ is the total inelastic scattering cross section and σₑₓ is the sum of all discrete-excitation cross sections. Our earlier work has given a highly precise value of σₜₒₜ, and recent results on discrete excitations enables one to determine σₑₓ. The resulting "counting" ionization cross section for a particle of charge ze and velocity v=βc is ${{σ}}ᵢ={8{π}{{a}₀}²{z}²}{m{{v}²}{R}}\{0.489[ln({{{β}}²}{1{-}{{β}}²}){-}{{β}}²]+5.526\},$ where $m$ is the electron mass, ${a}₀$ is the Bohr radius, and $R$ is the Rydberg energy. Among numerous measurements, the electron-impact data by Smith are most consistent with our result and suggest a gradual attainment of the Bethe asymptotic behavior near 1-keV incident electron energy.