Formulas for the total ionization cross section by electron impact based on the binary-encounter-dipole (BED) model and its simpler version, the binary-encounter-Bethe (BEB) model are extended to relativistic incident electron energies. Total ionization cross sections for the hydrogen and helium atoms from the new relativistic formulas are compared to experimental data. Relativistic effects double the total ionization cross section of H and He at incident electron energy $\approx 300\hspace{0.5em}\mathrm{keV}$ and dominate the cross section thereafter. A simple modification of the original BED-BEB formulas is proposed for applications to ion targets and inner-shell electrons of neutral atoms and molecules. The relativistic and nonrelativistic BEB cross sections are compared to the K-shell ionization cross sections by electron impact for the carbon, argon, nickel, niobium, and silver atoms. For carbon and argon, the relativistic effects are small, and both forms of the BEB cross sections agree well with available experimental data. For the nickel and heavier atoms, the relativistic increase of cross sections becomes noticeable from about 100 keV and higher in the incident electron energy. The empirical formula by Casnati et al. [J. Phys. B 15, 155 (1982)] after correcting for relativistic effects as shown by Quarles [Phys. Rev. A 13, 1278 (1976)] agrees well with the BEB cross sections for light atoms. However, the peak values of the Casnati cross sections become higher than the relativistic BEB peak cross sections as the atomic number increases. The BEB model is also applied to the total ionization cross section of the xenon atom, and the theory agrees well with experiments at low incident electron energies, but disagrees with experiment at relativistic incident energies.

Absolute energies of the $\mathrm{Ar}K$, $\mathrm{Kr}K$, and $\mathrm{Xe}{L}_1$, $L_2$, and $L_3$ levels have been determined from absorption edges measured with synchrotron radiation. The double-crystal x-ray monochromator was calibrated by a method that ties the energy scale directly to the crystal lattice constant and $\mathrm{hc}$. Theoretical model spectra were constructed from ≥ 4 Lorentzians representing the lowest-energy one-electron electric-dipole transitions to bound excited states, and an arc tangent representing transitions to higher bound states and to the continuum. The transition energies were found by minimizing ${\chi }^2$ for the fit of the theoretical spectrum shape to the data. Energy differences from optical spectral series were used to relate the excited-state energies to the vacuum level. Results are compared with earlier measurements and with theory.

In this paper, we used the multiconfiguration Dirac-Fock method to compute with high precision the 1${\mathit{s}}^2$2s2p ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_1$–1${\mathit{s}}^2$2s2p ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ separation energy in berylliumlike ions, including the relativistic contribution to electron-electron correlations and radiative corrections. The effect of the hyperfine interaction on both the energy and lifetimes of those levels has been evaluated. In the absence of nuclear magnetic moment the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ level can decay to the ground state only by an E1-M1 transition, with a very low probability. We show that the hyperfine interaction increases dramatically the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ transition probability.

The magnetic interaction has been shown to produce inversion of 1s2p ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$ and 1s2p ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ for Z≤3 and Z≥46. In this paper we have used the multiconfiguration Dirac-Fock method to compute with high precision the 2 ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$–2 ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ separation energy, including relativistic contributions to electron-electron correlations and radiative corrections. This energy happens to be very small around the crossing, so that the hyperfine interaction can mix both levels significantly. We have then computed the effect of this mixing on both the energy and lifetime of those levels. This calculation shows that a precise measurement of the $2^3$ ${\mathit{P}}_{0,\mathit{F}=\mathit{I}\mathrm{-}1}$–1${\mathit{S}}_0$F=I lifetime will enable us to measure the $2^3$ ${\mathrm{P}}_1$–2 ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ separation energy accurately even though the radiative width of the 2 ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ level is actually larger than the level separation.