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Qualitative interpretation=A05-m5ai

We have tried to interpret measured cross sections with a simple classical atom-atom model for ion-pair formation in molecular collisions [The interpretation depends on the theoretical method (link type: `DEPENDS ON/detailed in/wider range/project'; target:  MESO-m3c-mod)] . The transition to the ionic state takes place via crossing of the neutral and ionic ground states. The electron transition probability is calculated applying the Landau-Zener approximation; trajectories are calculated using the impact parameter approximation.

[To the FULL figure] Figure A08-m5ai-F1: K + Br2, chemi-ionization differential cross section (CM system), measured at colliding energies of 6.9 and 10.35 eV. For both energies equal units have been used on the ordinate. The $\tau $ scale changes beyond 300 eV.degree. [Also in A05-m4bi].

At least qualitatively the shape of the measured differential cross sections in M + X2 M+ + X- collisions can indeed be understood from the general shape of the deflection curve as sketched in figure A05-m5ai-F1 [Figure from a mesoscopic module (link type: `INPUT FROM/wider range/project'; target:  MESO-m3c-defl)] and the equation for the differential cross section [Equation  from a mesoscopic module(link type: `INPUT FROM/detailed in/wider range/project'; target:  theoretical methods, deflection function MESO-m3c-defl)  
$\displaystyle I(\theta)=\frac{1}{\sin \, \theta}\sum_{i=1,2,\ldots}\
P_{b_{i}}(1-P_{b_{i}})b_{i}\bigg\vert\frac{\dr b_{i}}{\dr {{\mit\Theta}.
}}\bigg\vert.$     (E1)

 
[To the FULL figure] Figure A05-m5ai-F2:The deflection function. [Figure from a mesoscopic module (link type: `INPUT FROM/wider range/project'; target:  MESO-m3c-defl)]

In order justify that statement, we compare as an example the measured K + Br2 cross-section curve (figure. A05-m5ai-F1 [The figure is obtained from the Treated results (link type: INPUT FROM; target:  A05-m4bi1]) with that to be expected classically, assuming that the value of Pb(1-Pb) does not change very much over the greater part of the b range; only in a very narrow region at $b\approx R_\mathrm{c}$ the ionization probability rapidly goes to zero.

For $\tau > 300$ eV degree the small differential cross section is due to the two small contributions of net repulsive scattering where $\dr b/\dr {{\mit\Theta} }$ is small.

With decreasing $\tau $ the classical rainbow angle where $\dr b/\dr {{\mit\Theta} }\to \infty$ gives rise to the rainbow structure at $\tau \lesssim 300$; the minimum at $\tau\approx 150$ is caused by the vanishing contribution for $b\approx R_\mathrm{c}$ because then $\dr b/\dr {{\mit\Theta} }$ as well as Pb tend to zero.

On account of the large value of $\dr b/\dr {{\mit\Theta} }$ around the inflection point on the ``covalent'' part of the deflection curve, a maximum is expected, seen indeed at $\tau\approx100$.

At last it can be seen from the $b-\tau$ curve that the small-angle cross section consists of four small contributions; the polar differential cross section in this region had to be at least two times the large-angle value for $\tau > 300$, in agreement with the measurements. However, the small maximum in this small-angle region, seen in all cross-section curves, cannot be explained by this classical model. (The small-angle errors mentioned above are not important enough to cause the maxima.) [Compare the classical with the quantum interpretation (link type: IS COMPARED WITH; target: A05-m5aii)]

Thus the general shape of the measured differential cross section can indeed be explained using a simple classical harpoon model, except for small angles.

Assumption

We assume that the value of Pb(1-Pb) does not change very much over the greater part of the b range; only in a very narrow region at $b\approx R_\mathrm{c}$ the ionization probability rapidly goes to zero. This assumption is justified for H12 = 4.5 x 10-2 eV, which is the estimated value for this system [The value is obtained in the Quantitative interpretation (link type: INPUT FROM; target:  interpretation A05-m5bi]