where A is an electropositive particle (such as an alkali atom) and B an electronegative one (such as a halogen atom or molecule). In the diabatic representation , the states of the system are described as either purely ionic ( A

The typical shape of the A-B intermolecular potential is shown in Fig. MESO-m3c-mod-F1. The chemi-ionization process is seen to be endothermic with an energy

where I(A) represents the ionization potential of the electropositive particle and EA (B) the electron affinity of the electronegative particle. The ionic and covalent ground-state potential curves cross at the intermolecular distance

The crossing distance *R*_{c} is approximately given by

This approximation is quite good for large crossing distances (

The groundstates of the system are described by two curves.
There exist many analytical expressions to describe the ionic alkali-halide potential curve.
.
For the ionic-potential curve we have chosen a Rittner potential
of the form:

The covalent potential consists of a Van der Waals term and the repulsive term, for the ionic potential we add a coulombic term, a screened polarization term, dipole-dipole interaction and at last the endothermicity .

species and the multiplicity of the ionic and
covalent ground states are the same. At the crossing point the transitions between the covalent and the ionic configurations are induced by a strong coupling between the state
. The Landau-Zener theory provides a simple expression for this transition as a function of the radial velocity at the crossing point. At a collision, ionization of the
neutral particles takes place *via* such a non-adiabatic transition by electron transfer.

The potential curves of Fig. MESO-m3c-mod-F1 clearly show the two collision trajectories leading to chemi-ionization. Incoming on the covalent curve and outgoing on the ionic one, the particles follow either the *ionic* potential curve inside the crossing distance
with a covalent-ionic> transition at the first passing of *R*_{c} followed by a covalent-covalent crossing,
or the *covalent* potential curve inside the crossing distance *R*_{c}
(with a covalent-covalent transition followed by a covalent-ionic one).
The
former process will be indicated by ``ionic'' scattering, the latter one by ``covalent'' scattering. In terms of an electron jump between the two interactants, ionic scattering means that the electron has jumped from A to B when these first approached to the crossing distance *R*_{c} of each other and that it remains there during the transition that takes place the second time the particles are at *R*_{c}. In covalent scattering there is no charge transfer in a diabatic transition at the first passing of the crossing distance, but the electron jumps when the separating interactants are again at *R*_{c}.

In he two-dimensional case the transition probability between different configurations has been given firstly by Landau, Zener and Stueckelberg (commonly called the Landau-Zener theory and abbreviated here as L-Z theory). This theory has been criticized and extended by different authors . Transitions between multi-dimensional surfaces have been treated by Teller . Further work has been done during the last decade by Nikitin .

The probability *P _{b}*
for a covalent-ionic transition at a single passage of the crossing at

At thermal energies the probability of the electron jump will be close to unity, except for the largest *R*_{c} values. At higher energies, however, the probability for a transition from covalent to ionic at the crossing point decreases, while the
covalent-covalent transition probability increases: at centre of mass energies larger than
the probability that only one electron jump takes place is non-negligible, such that ion pair formation can occur due to an electron jump at the first crossing while passing the second time no change occurs or vice versa.
.

From the potential-energy curves and the transition probability, the total and differential cross sections for ion-pair formation via the different trajectories can be calculated via the deflection function.

In the simplified atom-atom model, it is assumed that the system has an isotropic, static two-body potential; vibrational and rotational degrees of freedom are neglected. The potential associated to harpoon reaction

Calculations on three-atomic systems are very difficult because they require a knowledge of the complete energy surfaces involved.
Moreover, the situation is complicated very much because multiple
passing of the crossing region is possible in contrast with the
two-atom case, where the crossing region is passed only twice during
the collision. An attempt has been made by Bjerre and Nikitin
to calculate cross sections for quenching of Na^{*} by N_{2}. This quenching
is also supposed to take place via crossings of potential surfaces.
They made trajectory calculations on three-dimensional crossing
surfaces, determining the transition probabilities at the crossings
by an extended L-Z theory. Such calculations are very computer-time
consuming and, because the knowledge of the potential energy surfaces
is very poor, one may not expect results with more than only
qualitative meaning.

It is known now that the quantitative validity of the L-Z theory is very limited. Moreover, this theory in its simple form is applicable neither to three-particle collisions nor to endothermic processes. Indeed it is found to be impossible to fit the energy dependence of the measured cross section with that predicted by the L-Z theory. However, one can try to use the results of the theory as a kind of ``adiabatic criterion'' to determine the position and also the order of magnitude of the maximum cross section of this type of inelastic processes.