Ionization probability, multiple

Figure 1. Comparison at identical parameter values of experimental and quantum-mechanical values for the microwave field strength for 10% ionization probability as a function of microwave frequency. The field and frequency are classically scaled, u>o = and = q6, where no is the initially excited state. Ionization includes excitation to states with n above nc. The theoretical points are shown as solid triangles. The dashed curve is drawn through the entire experimental data set. Values of no, nc are 64, 114 (filled circles) 68, 114 (crosses) 76, 114 (filled squares) 80, 120 (open squares) 86, 130 (triangles) 94, 130 (pluses) and 98, 130 (diamonds). Multiple theoretical values at the same uq are for different compensating experimental choices of no and a. The dotted curve is the classical chaos border. The solid line is the quantum 10% threshold according to localization theory for the present experimental conditions.

The electronic many-body Hamiltonian in equation (1) is treated in the framework of the independent-electron frozen-core model. This means that there is only one active electron, whereas the other electrons are passive (no dynamic conelation is accounted for) and no relaxation occurs. In this model the electron-electron interaction is replaced by an initial-state Hartree-Fock-Slater potential [37]. This treatment is expected to be highly accurate for heavy collision systems at intermediate to high incident energies. The largest uncertainties of the independent-electron model will show up for low-Z few-electron systems, such as H -F H and H + He° or for high multiple-ionization probabilities. 

Figure 11. Normalized ratio of multiple ionization cross section of argon and absorption signal as a function of energy loss of fast electrons in the region of the L2 threshold. The measured points are from Ref. 102. The insert shows the calculated ionization probability in the Auger decay, following an L2-hole creation after t = 100 a.u. (From Ref. 106.)...

These results imply that the use of the representative single ion-pair distribution in the ionization produced by low-LET irradiation in liquid hydrocarbons can be approximately justified even though the track itself has considerable contribution from multiple-ion-pair spurs and short tracks. It also means that even in the case of an isolated ion-pair, the long-time limit of the existence probability is perturbed by the long-range coulombic field. 

As discussed above, heavy charged particles, particularly multiply charged heavy ions, have a relatively large probability for inducing multiple ionization involving outer, as... 

This results in a high probability of multiple ionization following the ejection of a K-shell electron. For instance, for Ne (Z = 10) the probability of subsequent ionization after the ejection of a K electron is as... 

Multiple-ionizations model is one of the most probable models because the huge energy deposited in the medium is considerably greater than the total energy needed to ionize the total number of water molecules along the ion track. This has been recently exploited in Monte Carlo simulations (see Fig. This model... 

We have seen, in the case of diatomic molecules, that two-dimensional covariance maps allow correlation of the ion pairs. The situation with regard to the multiple ionization of triatomic molecules is more complex. Similar two-dimensional maps serve to indicate correlations between pairs of ions but at high laser intensities it is probable that three ions will be produced. Although one might infer that three ions have been created simultaneously, the only sure way of confirming the creation and subsequent fragmentation of a triple ion is to use three-dimensional covariance mapping. 

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