## Theoretical methods: LZ coupling=A08-m3ci1 |

According to the atom-atom model for ion-pair formation in molecular collisions, chemi-ionization in two-body collisions takes place *via* pseudo-crossing of the potential energy surfaces of the interacting atoms

Fig. A08-m3ci1-F1 shows the lowest ionic and covalent potential curves of sodium iodide. The general shape of the curves is explained in a mesoscopic module, and the precise shape is determined in another module
.
The species of the ionic electronic state, indicating the symmetry and multiplicity
properties, is given by . By building up the molecule from
the two separate neutral particles Na(^{2}S_{1/2})
and
I(^{2}P_{3/2}), the
*LS*-coupling gives rise to eight molecular states. One of them has the
same species as the ionic state, which can according to the Neumann-Wigner rule give rise to transitions.
We assume that we can ignore the exited covalent state, only taking into account the lowest states of the system, thus reducing the case to a two-state problem.

Then, for our collision process, one of the
eight collisions has the probability P_{b} for a diabatic transition at a single passage of the pseudo-crossing at R_{c}, given by the
Landau-Zener formula
.

Summarising, the following approximations have been used:

- 1.
- The Landau-Zener transition-probability formula.
- 2.
- The use of the Landau-Zener formula to collisions where the
distance of closest approach
*R*and the distance of pseudo-crossing R_{0}_{c}are not well separated - 3.
- The use of the diabatic potentials in the classical deflection function in spite of small deformation of the curves at the pseudo-crossing.
- 4.
- The use of a transition point in spite of a transition region around the pseudo-crossing predicted by the Landau-Zener theory.
- 5.
- The neglect of rotational coupling so far