Double passage probability

Figure 8 also includes a Landau-Zener calculation assuming a simple two-state charge transfer system. In this case, the cross section is calculated from the simple double passage probability, P = 2p(l — p) ... 

For 6 > 0 1 a.u. the two sets of theoretical results differ primarily in the frequency of the oscillations. The difference is probably produced by the influence of translational factors. As mentioned above, the single-passage probability W is influenced by translational motion effects through the phase in Eq. (19). In addition, the double passage probability P is affected by the prefactor B(v). The influence of B(v) on the transition probability is not obvious. Here, it should only be noticed that with increasing velocity V the absolute value B(v) decreases so that H,2 is reduced. Then, it follows from Eq. (40) that the oscillation frequency of the double passage probability is reduced. 

Figure 16. Double passage probability PkW for 2

Figure 17. Double passage probability for 2cr-lo-vacancy transfer in the system + Ar. Experimental results are from Schuch et The solid line is drawn to guide the eye. The dashed curve represents calculations using the SHM matrix elements (18).

The coupled equations are integrated using the initial conditions c = S , which implies full occupation of the state m prior to the passage of the transition region. Let us denote the transition probability to state n for single and double passage of the transition region by W and F , respectively. These probabilities are obtained as a function of the impact parameter b from... 

Analogous relations are used for the single passage probability W . Total cross sections for single and double vacancy transfer are obtained from Eq. (4) where the probability P should be replaced by D and respectively. 

Following the analysis of Crothers, the transfer probability for the double passage of the transition region is obtained as... 

The same quantity but at smaller intemuclear distances is tested, when the double-passage process for vacancy transfer is examined. The transition probability exhibits oscillatory structures due to interferences between ingoing and outgoing parts of the collision. The related two-state formula shows that the oscillatory structure is superimposed on a smooth function already known from the single-passage process. Thus, the new information is implied in the oscillatory structure. The locations of the minima and maxima are determined by the difference of the related MO energies. Hence, the oscillatory structure allows for studying the formation of MO s at small... 

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