Theoretical investigation of electronic relativistic effects onK-vacancy production by charged particles

Plane-wave Born-approximation calculations of $K$-shell ionization cross sections are made using one-electron Dirac and Dirac-Hartree-Fock wave functions to describe the $1s$ and continuum electronic orbitals. Calculations are reported for selected elements between Ca and $Z=170\mathrm{}$ and for values of the ratio of the ion velocity to the $K$-electron velocity $\frac{v_1}{v_K}\lesssim 0.2$. Simple relativistic correction factors are derived which, when multiplied by easily obtainable nonrelativistic cross sections, allow the accurate determination of relativistic $K$-shell ionization cross sections without having to perform further extensive calculations. The relativistic correction factors are compared with approximate correction factors discussed by Amundsen, Kocbach, and Hansteen.