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Quantitative interpretation with both Landau-Zener and rotational coupling=A08-m5bii2

Chemi-ionization in collisions between Na and I can be explained via crossing of the potential energy surfaces of the collisions [The model is given in a mesoscopic Theoretical methods module (link type: 'depends on/is detailed in/wider range/project'; target: MESO-m3c-mod] . The Landau-Zener formula gives the transition probability between translationally coupled states. However, the Landau-Zener transition probability does not give an adequate quantitative explanation [This inadequacy is shown in another Interpretation module (link type: 'is detailed in/clarified in'; target: A08-m5bii1] of the experimentally determined differential cross sections of the chemi-ionization process. It is likely that rotationally induced transitions could explain the discrepancy of measured and calculated differential cross section.

The discrepancy that the rotational coupling could explain is where the calculated cross section is too small for collisions with large impact parameters [This discrepancy is shown in another Interpretation module (link type: 'is detailed in'; target: A08-m5bii1] . Fig. A08-m5bii2-F1 clearly shows for increasing kinetic energy an increasing deviation of the relative differential cross section at $\tau\approx 65$ eV degree without rotational coupling. Even the relative cross sections more separated from the minimum would lead for a fitting procedure to an unphysical energy dependence of the Landau-Zener coupling parameter H12.
[To the FULL figure] Figure A08-m5bii2-F1: Smoothed differential cross sections for five different collision energies. (a), (b), (c), (d), (e): Full curves show the measured relative differential cross section, averaged over the interference structures. Absolute differential cross sections, calculated semi-classically and also averaged over the interference structure, have been given by the dashed curves. Use has been made of H12=0.05 eV. (f): At Ei = 29.7 eV the curves show the calculated differential cross section for H12=0.04, 0.05 and 0.07 eV

We have calculated [particulars on the calculation method in the module Theoretical methods (link type: 'depends on/is detailed in'; target: A08-m3cii] the general shape of the differential cross sections of the chemi-ionization process again, now taking into account the rotational coupling [(link type: 'depends on/is detailed in/es-back'; target: Theoretical methods A08-m3ci2] .
[unfold the explanation and justification NOT AVAILABLE]

Fig. A08-m5bii2-F2 gives again the measured general shapes of the differential cross sections at kinetic colliding energies of 13.1, 20.7, 29.7, 38.7 and 55.0 eV. A comparison has been made with calculated cross sections taking into account some rotational coupling.
[To the FULL figure] Figure A08-m5bii2-F2: Smoothed differential cross section for five different collision energies.
(a), (b), (c), (d), (e): Full curves show the measured relative differential cross section, averaged over the interference structure. Dashed curves show calculated absolute cross sections using the coupling elements H12=0.0024 a.u. (0.065 eV): and H12>=0.04 a.u.
(f): Effect of rotational coupling on the minimum of the differential cross section due to collisions with large collision parameters. Abscissa and ordinate scales have been extended by a factor of two with respect to the corresponding figure (e). [Experimental part copied from the Treated results (link type: 'input from'; target A08-m4bi1)] [Theoretical part copied to the Treated results (link type: 'output to'; target A08-m4bii2)]

Indeed, the minimum in the differential cross section has been increased to a degree dependent on the kinetic energy.

Moreover, it is very obvious that now it is possible to find one set of coupling constants giving a good fit of measured and calculated cross sections for all energies. This set consists of the values H12=0.065 eV and Hrot=3 x 10-17 eV corresponding to the values of 0.0024 a.u. and 0.04 a.u., respectively.

A comparison of the corresponding cross section curves of Fig. A08-m5bii2-F1 and Fig. A08-m5bii2-F2 shows that rotational coupling at low kinetic energies increases the differential cross section only at the very minimum but for higher kinetic energies there is a rise over a larger -range. This feature makes it possible to use only one value of H12.

On the range $\tau=50\to 200$ eV degree Fig. 0.2f gives the dependence of the cross section on some values of rot at Ei = 55  eV. For increasing coupling constant, the maximum contribution of rotational coupling to chemi-ionization moves to collisions with smaller impact parameters.

It must be noted that for impact parameters $b\approx R_\c$ Eq. (E1)[This formula is given in the Theoretical methods (link type: 'INPUT FROM'; target: A08-m3ci2)]
P_{b,rot} (E1)
does not hold any more because a sufficient separation is supposed between the classical turning point and the crossing point Rc. (A similar remark to the Landau-Zener coupling has been made in A08-m5bii1 [Comparable restriction of the validity of the LZ approximation], point D.) For an incomplete passage of the transition region around Rc Eq. (E1) gives too large a value of Pb,rot. In the present case with the parameters used the resulting effect is the product Pb,rot(1-Pb,rot), too small for collisions with Ei = 55  eV and $b\approx R_\c$ and too large for the corresponding collisions at Ei = 13.1 eV. Indeed, a correction to this effect should improve the agreement of measured and calculated curves of Fig. F2a and Fig. 2c. It is suspected that the remaining apparent discrepancy of the relative intensities at $\tau\approx 65$ eV degree is due to convolution effects, measuring faults and the improper use of Eq. (E1) for $b\approx R_\c$.


Reliability
The estimated value H12=0.065 eV differs rather much from the value of 0.05 eV, estimated from total cross-section measurements [The value is input from a previous article (link type: 'input from/project'; target: A04-m4b)] on the collision energy range 2-20 eV. The effect of these two values on the absolute differential cross section can be observed from Fig. 0.1 (H12=0.05 eV) and Fig. 0.2 (H12=0.065 eV). At Ei = 55  eV the cross sections of Fig. F2 have hardly different values, while at Ei = 13.1  eV the cross sections differ by a factor of two. Of course, relative measurements on the differential cross section versus the kinetic energy should give a hint to the correct value of H12. However, at the present measurements it is impossible to distinguish in this way these values of H12. It is expected that the surface-ionization detector as well as the scattered-ion detector have large and unknown energy-dependent efficiencies.