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[Legenda]
[Contents of the thesis]
[Comments on this module]

Theoretical methods: Rotational coupling=A08-m3ci2

Chemi-ionization in collisions between Na and I can be explained via crossing of the two lowest $^1\Sigma^+$ diabatic potential energy surfaces of the NaI molecule . A transition between two states can take place when the states are coupled. The LZ model gives the probability of a diabatic transition between two states of the same species due to electronic coupling. In collisions between Na and I, only the lowest states play a role and are therefore taken into account .

A transition can also be caused by rotational coupling. Referring to the detailed description by Russek we only give the main features of rotational coupling as far as it is of interest for the present collision process.

Rotational coupling couples two states with different z components of angular momentum. The coupling takes place in the region of the crossing point of the potential curves. In case of LS coupling, the covalent ground state of NaI is split up into the $^1{\mit\Pi}$, $^3{\mit\Pi}$, $^1{\mit\Sigma}$ and $^3{\mit\Sigma}$ state while the ionic ground state of Na ⁺ + I^- only consists of the $^1{\mit\Sigma}$ state. Because rotational coupling acts only on the angular momentum and does not influence the spin, only the $^1{\mit\Pi}$ covalent state couples to the ionic $^1{\mit\Sigma}$ state. As with the Landau-Zener coupling, only one of the eight covalent entrance channels at the collision couples to the ionic state, pointing to a weight factor of 1/8. The probability for the $^1{\mit\Pi}\hbox{--}{}^1{\mit\Sigma}$ transition is given by:

(E1)

where H_rot is the coupling parameter, $\omega$ and v_r are the angular and radial relative velocities of the colliding particles at the level crossing  R_c.

The most striking contrast to the Landau-Zener transition probability P_b,LZ given by

(E2)

is the linear variation of the exponent with the relative velocity while the exponent of P_b,LZ varies inversely with the velocity. It is obvious that P_b,rot is large for high relative kinetic energies and for large impact parameters. Of course the probability to go from the covalent entrance channel to the ionic final state equals P_b,rot(1-P_b,rot), but also this product easily leads to larger probabilities in case of large values of E and b.