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 ${\sigma }_i$ for ionization of He by fast charged particles is accurately evaluated by a subtraction ${\sigma }_i={\sigma }_{\mathrm{tot}}-{\sigma }_{\mathrm{ex}}$, where ${\sigma }_{\mathrm{tot}}$ is the total inelastic scattering cross section and ${\sigma }_{\mathrm{ex}}$ is the sum of all discrete-excitation cross sections. Our earlier work has given a highly precise value of ${\sigma }_{\mathrm{tot}}$, and recent results on discrete excitations enables one to determine ${\sigma }_{\mathrm{ex}}$. The resulting "counting" ionization cross section for a particle of charge $\mathrm{ze}$ and velocity $v=\beta c$ is ${\sigma }_i=\frac{8\pi {a_0}^2{z}^2}{m\frac{v^2}{R}}\left\{0.489\left[\ln \left(\frac{{\beta }^2}{1-{\beta }^2}\right)-{\beta }^2\right]+5.526\mathrm{}\right\},$ 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.