Comparison of different quantum mechanical methods for inner atomic shell photo-ionization followed by Auger decay

A numerical time-dependent quantum mechanical approach was developed previously for simulating the process of photoionization followed by Auger decay for cases where the photoelectron energy is not very large; the method accurately calculates the interaction between the two active electrons, but simplifies their interaction with the core electrons. More established theoretical methods, which take account of postcollision interaction effects, allow an accurate description of this process when the photoelectron energy is not too low. We demonstrate that using the time-dependent method (although with some simplifications that are needed for its numerical implementation) for low energy photoelectrons and more established methods for higher energy allows accurate calculations for nearly all possible combinations of electron energy. This is confirmed by performing calculations of the photoelectron energy and angular distributions for the 1 s photoionization of Ne, with a subsequent KLL Auger transition. By computing the energy and angular distributions for energies where the two groups of methods should agree and where they should disagree, we demonstrate their consistency and range of accuracy. For the regions where the methods disagree, we discuss the reasons for any discrepancies and the trends in the differences. In addition, some of our calculations are compared with existing experimental data for the same system. The agreement found in the comparison confirms the reliability of the theoretical approaches.