Qualitative interpretation=A05-m5ai






[Legenda]
[Contents of the thesis]
[Comments]






[Legenda]
[Contents of the thesis]
[Comments]

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 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.

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 and the equation for the differential cross section

$\displaystyle I(\theta)=\frac{1}{\sin \, \theta}\sum_{i=1,2,\ldots}\ P_{b_{i}}(1-P_{b_{i}})b_{i}\bigg\vert\frac{\dr b_{i}}{\dr {{\mit\Theta}. }}\bigg\vert.$ (E1)

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 ) with that to be expected classically, assuming that the value of P_b(1-P_b) 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 P_b 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.)

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 P_b(1-P_b) 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