Excitation transfer cross sections

Figure 15 Calculated total and state-to-state excitation transfer cross sections in the de-excitation of He(2 P)-Ne. (From Ref. 151.) Both electron exchange and dipole-dipole interactions are included in the coupling matrix elements. The threshold energy into each exit channel is shown on the upper axis.

In principle, there is no way to directly measure the exchange process for 4He +4He scattering, as the particles are indistinguishable. But the cross section for metastability exchange can of course be calculated from the determined potentials assuming distinguishable particles.65 The expression for the total excitation transfer cross section is... 

Figure 22. Energy dependence of excitation transfer cross section for 3He- (23S) + 3He, calculated from poten-...

Note Differential elastic and excitation transfer cross sections have been measured for He(2 S) + Nc and for He(23S) + Ne for energies between 25 and 370 meV (1). Some of the data are shown in Fig. 52. It was possible to measure the differential excitation cross sections for the triplet system, too. A semiclassical two-state calculation was performed for the pumping transition of the red line of the HeNe-laser Hc(2 S)+ Nc— Hc + Ne(5S, lPt), which is the dominant transition for not too high energies (2). A satisfactory fit is obtained to the elastic and inelastic differential cross sections simultaneously, as well as to the known rate constant for excitation transfer. The Hc(215)+ Ne potential curve shows some mild structure, much less pronounced than those shown in Fig. 36. The excitation transfer for the triplet system goes almost certainly over two separate curve crossings. This explains easily the 80 meV threshold for this exothermic process as well as its small cross section, which is only 10% of that of the triplet system. 

To obtain a rough estimate of the excitation transfer cross section, consider first the adiabatic approximation, neglecting the Coriolis coupling (the so-called rotating-atom approximation ). The transfer is then associated with mere interference between gerade and ungerade states. As an example, the 2 time-dependent wave function can be written as... 

Integrating (86) over a rectilinear trajectory and using the Firsov cutoff parameter b in calculating the excitation transfer cross section we get... 

There are two kinds of pairs of terms with different Q. As discussed in Section II, if the terms do not cross, the transition probability will be exponentially small (as for case discussed above) with an extra small preexponential factor. If the terms do cross, there will be no exponential, and thus this case will give the main contribution to the excitation-transfer cross section. As seen from Figure 5.3 there are two crossing points Rs, each corresponding to pairs 1 , 0 and lu, 0 . Corresponding partial cross sections aif calculated using equation (14) are... 

Finally, the mean excitation transfer cross-section averaged over the initial polarizations is found to be ad) = 2.19, which is again in good agreement with the alue 2.26 obtained from the numerical calculations [27]. 

Velocity Dependence of the Cross Section. For S-P type interaction, the excitation transfer cross section was proportional to V1 for Case 1, and to tT2/5 for Case 3. For Case 2 the velocity dependence was not as simple. Here the ratio of the angular frequency of the resonant defect [a> = (Ei — Ef/tl) to the relative incident velocity (v)—i.e.> a = to/v is the most important parameter. If the ratio is small compared with the reciprocal of the interaction range a"1, the transfer will approach that of Case 1 (exact resonance). The cross ection will decrease monotonically with t at higher velocities. If a a"1, the cross section will be fairly small compared with that of exact resonance. Further, in the limit of t 0, the cross section would be zero, and would increase with v at low velocity region. Then, it will reach a maximum in between these regions for Case 2. This feature will hold for all inter-multipole types of interaction including the S-P type. However, the detailed and quantitative discussion on the velocity dependence for Case 2 is not this simple. On the other hand, the velocity dependence of the cross section for the resonance type excitation transfer (Cases 1 and 3) can be discussed more straightforwardly, not only for the S-P interaction case but also for other interaction cases (48, 69). 

If we can confine the problem to a two-level case—i.e., one initial and one final state—the velocity dependence of the excitation transfer cross section can easily be obtained. If the interaction has the form C R n, f) can be expressed as... 

Recently Schearer measured the cross section of the excitation transfer of 2 Po to 2 Pi and 2 Pj levels as a result of collisions with the ground-state helium atoms. For the 2 5 state, Colegrove et al. measured the excitation transfer cross section and compared with the calculation by Buckingham and Dalgarno. Fitzsimmons et al. and Pakhomov and Fugol discussed the transfer cross section obtained by the empirical potential from diffusion cross sections. 

Fig. 4. Excitation transfer cross section for He(F5) + He (2 / ) as a function of incident energy. C = 23.75 and C = 0 mean the cross sections with and without the van der Waals potential, respectively.

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