Formulas for the total ionization cross section by electron impact based on the binary-encounter-dipole ͑BED͒ model and its simpler version, the binary-encounter-Bethe ͑BEB͒ 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 Ϸ300 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 ͑1982͔͒ after correcting for relativistic effects as shown by Quarles ͓Phys. Rev. A 13, 1278 ͑1976͔͒ 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.

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In this paper, we used the multiconfiguration Dirac-Fock method to compute with high precision the 1s 2s2p P& -1s 2s2p Po 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 Pz level can decay to the ground state only by an El-M1 transition, with a very low probability. We show that the hyperfine interaction increases dramatically the Po transition probability.PACS number(s): 31.30. Gs, 31.30.Jv, 32.70.Fw

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