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.

At least qualitatively
the shape of the measured differential cross sections in
M + X_{2} 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

(E1) |

Figure A05-m5ai-F2:The deflection function. |

In order justify that statement, we compare as an example the measured
K + Br_{2} 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
the ionization probability rapidly goes to zero.

For eV degree the small differential cross section is due to the two small contributions of net repulsive scattering where is small.

With decreasing
the classical rainbow angle where
gives rise to the rainbow structure at
;
the minimum at
is caused by the vanishing contribution for
because then
as well as P_{b} tend to zero.

On account of the large value of around the inflection point on the ``covalent'' part of the deflection curve, a maximum is expected, seen indeed at .

At last it can be seen from the 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 , 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.

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
the ionization probability rapidly goes to zero. This assumption is justified for
H_{12} = 4.5 x 10^{-2} eV,
which is the estimated value for this system