[Comments]

[Legenda]
[Show the characterisation of the module ]
[Show the Map of contents]
[Show the navigation menu of the module]
[Step back on the ESSAY-TYPE sequential path to 	the complex module Theoretical methods (link type: ESSAY-BACK/is part of/is aggregated in/generalised in/is summarised in/context in; target: A08-m3c)] [Next step on the ESSAY-TYPE sequential path to another Theoretical methods module (link type: ESSAY-NEXT/used for; target: A08-m3cii)]
[Step back on the complete sequential path to a complex Theoretical Methods module (link type: SEQ-BACK/is part of/is generalised in/ummarised in/context in; target: A08-m3ci)] [Next step on the COMPLETE sequential path to other Theoretical methods (link type: SEQ-NEXT/compared to; target: A08-m3ci2)]





























[Show the characterisation of the module ]
[Show the Map of contents]
[Show the navigation menu of the module]
[Step back on the ESSAY-TYPE sequential path to 	the complex module Theoretical methods (link type: ESSAY-BACK/is part of/is aggregated in/generalised in/is summarised in/context in; target: A08-m3c)] [Next step on the ESSAY-TYPE sequential path to another Theoretical methods module (link type: ESSAY-NEXT/used for; target: A08-m3cii)]
[Step back on the complete sequential path to a complex Theoretical Methods module (link type: SEQ-BACK/is part of/is generalised in/ummarised in/context in; target: A08-m3ci)] [Next step on the COMPLETE sequential path to other Theoretical methods (link type: SEQ-NEXT/compared to; target: A08-m3ci2)]

Theoretical methods: LZ coupling=A08-m3ci1

[Show the characterisation of the module ]

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 [More on the model in a mesoscopic module (link type: 'elaborated in/elucidated in/project/wider range'; target: MESO-m3c-mod]

Potential curves

[To the full figure]

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[MESO-m3c-mod (link type: 'explained in/To cause/is detailed in/project/wider range'; target: MESO-m3c-mod#crossing curves], and the precise shape is determined in another module [The exact figure is generated in the Interpretation (link type: 'input from'; target: Interpretation A08-m5bi]. The species of the ionic electronic state, indicating the symmetry and multiplicity properties, is given by $^1\MS^+$. By building up the molecule from the two separate neutral particles Na(2S1/2) and I(2P3/2), the LS-coupling gives rise to eight molecular states. One of them has the same species $^1\MS^+$ 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.

For the lowest states the important parameter H12 has been estimated experimentally by Moutinho et al. [The value is input fom a previous article (link type: 'input from/project'; target: A04-m4b]] from total cross section measurements for chemi-ionization of Na + I, giving a value H12=0.05 eV. Two different types of theoretical calculations by Herschbach and Grice [These values are input from other articles (link type: 'input from/external'; target: R10-m*] result in the values of 0.06 and 0.09 eV. These values of H12 all give, in our energy range from 10 up to 100 eV, a transition probability Pb of the order of 1/2 for the pseudo-crossing of the ionic and lowest covalent state. An estimation of the internuclear crossing distance of the ionic and excited covalent state leads to a value of the relevant H12 [This value is input from another article (link type: 'input from/external'; target: R11-m*] much smaller than for the former pseudo-crossing. Then the diabatic transition probability for the outer pseudo-crossing hardly differs from unity, so the excited covalent state is an unimportant outgoing channel. The first excited covalent state with species 1MS+ does have an avoided crossing with the ionic state at large internuclear distance, but this covalent state is not an incoming channel in the collisions considered, because all the thermal dissociated iodine atoms are in the 2P3/2 state. Therefore we shall ignore the excited covalent state in our considerations.
[Hide the details]

Then, for our collision process, one of the eight collisions has the probability Pb for a diabatic transition at a single passage of the pseudo-crossing at Rc, given by the Landau-Zener formula [The formula is given in a mesoscopic module (link type: 'input from/project/wider range'; target: MESO-m3c-mod#Pb)].

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 R0 and the distance of pseudo-crossing Rc are not well separated [Arguments against the applicability (link type: 'arguments/external'; target: R25)]
3.
The use of the diabatic potentials [These potentials are given in a mesoscopic module (link type: 'input from/project/wider range'; target: MESO-m3c-mod#U(R)] 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 [Compare this to the module about the rotation coupling (link type: 'compare/sq-next'; target: A08-m3ci2]