Nonsequential multiple ionization

Nonsequential double and multiple ionization are to a large part classical phenomena. Indeed, the S-matrix approach suggests a pertinent classical limit. We have summarized evidence that the latter reproduces the fully quantum-mechanical results very well in parameter regions where this can be expected. Finally, we have extended such classical avenues to a statistical description of nonsequential triple and quadruple ionization. For neon, such a classical statistical model yields a fair description of the available data. While a more microscopic description of these extremely involved phenomena lies in the future, we believe that the simple models summarized in this paper will remain valuable as benchmark results. 

Applicability of the modern TDDFT approaches for the treatment of multiple electron ionization processes is another problem related to the quality of time-dependent xc-energy functionals. Most of approximate xc functionals lack the important property of the exact functional, the discontinuity of its derivative with respect to the number of particles N, when N passes through integer values [78]. Several attempts to apply TDDFT with such approximate functionals for calculations of nonsequential double ionization were unsuccessful [79,80]. Recently it was shown [81] that the derivative discontinuity is crucial for correct description of double ionization. 

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