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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 [Particulars on the model in a mesoscopic Theoretical methods module (link type: 'is detailed in/elucidated in/wider range/project'; target: MESO-m3c-mod] . 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 [Arguments why we did this, involving an explanation why only those states play a role, are given in another Theoretical methods module (link type: 'is detailed in/explained in/argued in/sq-back'; target: A08-m3ci1] .

A transition can also [Compare with the LZ transition in another Theoretical methods module (link type: 'compare/sq-back'; target: A08-m3ci1] be caused by rotational coupling. Referring to the detailed description by Russek [link type: 'is detailed in/external'; target: R5] 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:
P_{b,rot} (E1)
where Hrot is the coupling parameter, $\omega$ and vr are the angular and radial relative velocities of the colliding particles at the level crossing  Rc.

The most striking contrast to the Landau-Zener transition probability Pb,LZ given by [The formula input from a mesoscopic Theoretical methods module (link type: 'input from/project/wider range'; target: MESO-m3c-mod#Pb]
P_{b,rot} (E2)
is the linear variation of the exponent with the relative velocity while the exponent of Pb,LZ varies inversely with the velocity. It is obvious that Pb,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 Pb,rot(1-Pb,rot), but also this product easily leads to larger probabilities in case of large values of E and b.