Vacancy sharing probabilities

Figure 11. C> vacancy sharing probabilities W for various collision systems involving Ni, Br, and 1 projectiles as a function of the scaling parameters X from Eq. (35). The solid line follows from Eq. (32) with f = 2X. From Meyerhof. ...

Several subsequent studies have confirmed Meyerhof s analysis. In particular, precision measurements using the method of Auger spectroscopy have shown that Eq. (32) is able to predict X-vacancy sharing probabilities with accuracies of typically 10%. This is seen in Figure 12, where Auger data from different laboratories " are summarized. The experimental results are in excellent agreement with the Meyerhof-Demkov formula (32). Only the relatively light system B + C shows remarkable discrepancies from the theoretical curve. 

Figure 29. Vacancy sharing probabilities for the K and L shells in the systems B + Ar, C + Ar, N + Ar, and O + Ar as a function of the inverse projectile velocity. The data refer to the excitation of the lower-lying levels, i.e., the Ar i-shell orbitals for B -I- Ar and the K-shell orbitals of the lighter particle in the other systems. The dots refer to experimental results by Reed et al and the solid lines follow from three-state model calculations on the basis of the SHM matrix elements (18). The dashed line represents two-state calculations for O H- Ar by means of Nikitin s model." ...

In Cu(FexCr2-x)04 series gradual substitution of Fe " for Cr introduces Cu at O sites. When the amount of Cu " at O sites is lower, one can expect that most of the anionic vacancies formed during the reduction of Cu " to Cu is shared between Cu(I) and Cr (III) or Fe (III) ions. With increase in the amount of Cu " at O sites, reduction produces BMV shared between Cu(I) and Cu(I) in addition to BMV shared between Cu(I) and Cr(III) or Fe(III). In CF5 and CF6 which are having higher amount of CU at O sites than CF4, the probability for BMV shared between Cu(I) and Cu(I) is more. The similarity in activity of all the three catalysts shows that the BMV associated with Cu(I) and Cu(I) is less active than those vacancies shared between Cu(I) and Cr(III) or Fe(III). This indicates that the second cation is also involved in the structure of the catalytic site by sharing anionic vacancies with cuprous ions. 

Meyerhof was the first to apply the formula (32) to iC-vacancy sharing and to verify its scaling ability. The results are shown in Figure 11. The experimental sharing probabilities are deduced from W = < hI(o h + Cl), where cross sections for K excitation of the heavier and lighter collision partner, respectively. The experimental data compare well with the universal curve following from Eq. (32) by means of the scaling parameter... 

Screening effects from the inner shell have been examined also in the work devoted to double X-vacancy sharing. For the system S + Ar McDonald et alP have detected a 20% difference in the one-electron probability for transitions into the 2o- MO with one and two vacancies. However, for most heavier systems such effects have not been observed. The experimental results for double X-vacancy sharing have been shown to be in accordance with statistical rules for nonrelaxed orbitals such as those given in Eq. (28). Hence, as expected, the screening effects from inner shells diminish for heavier collision partners. 

Figure 14. Probability Wl for L-vacancy sharing as a function of the scaling parameter...

Finally, the coupled equations (9) for adiabatic states are integrated to determine probabilities for vacancy exchange. In the following sections, results are discussed for systems with three and four states. Prior to this study, the possibility is examined of applying the two-state models in the description of KL- and LX-vacancy sharing. 

In Figure 29, significant discrepancies between the SHM calculations and experiment are still observed. These discrepancies are partially understood. The transition probability in the LK systems is relatively small in the range of small incident velocities, so that, there, mechanisms other than vacancy sharing become important. Unilateral screening effects due to double vacancy production in the 4a- MO and/or two-electron transitions filling the double hole states are expected to be important. 

The model calculations of LK-vacancy sharing yield probabilities seperately for the excitation of 2s and 2p states. These data may be used to gain information about diabatic correlation rules. For LK systems two different rules have been proposed with respect to the diabatic state 3 da which corresponds to the 4or MO. Barat and Lichten proposed the correlation of the 3 da state with the 2p level, whereas Eichler et suggested the correlation with the 2s level. 

Figure 34. Cross sections for Ar L excitation in the collision systems Si -t- Ar and S + Ar as a function of the projectile energy. The experimental data are from Schneider el The curve labeled ROT refers to 6-2v-A

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