Calculation of Electron Shake-Off Probabilities as the Result of X-Ray Photoionization of the Rare Gases

Abstract

The probability for either exciting or ionizing an electron from a given atomic orbital as the result of a sudden vacancy in one of the atomic shells, such as might occur with photoionization, has been calculated through the use of the sudden approximation. Calculations were made for each of the subshells of neon, argon, krypton, and xenon as a function of the location of the initial vacancy. The calculations were based on relativistic Hartree-Fock-Slater wave functions. The results were generalized in terms of the change in effective charge. For example, electron shake-off in the valence shell was found to be nearly independent of the location of the initial core vacancy, increasing slightly as one goes to the lower principal quantum numbers. The ionization potentials were also found to be nearly independent of the location of the core vacancy. The results of the electron-shake-off calculations were also used to obtain an evaluation of the relaxation energy arising from the promotion of a single vacancy, and compared with values obtained from binding-energy calculations. Results of the electron-shake-off calculations are applicable to any process that leads to a sudden creation of a vacancy in an atom. However, particular emphasis is given to photoelectron spectroscopy in discussing the results.