[Step back on the essay-path: Quantitative interpretation (link type: 'SEQ-BACK/essay_back/depens on'; target: A05-m5bi)] [Next step on the complete sequential path: Quantitative interpretation (link type: 'SEQ-NEXT'; target: A05-m6)]
[Step back on the essay-path: Quantitative interpretation (link type: 'ESSAY-BACK/sq-back/depends on'; target: A05-m5bi)] [Next step on the essay-path: Quantitative interpretation (link type: 'ESSAY-NEXT/out'; target: A05-m6a)]
[Show the characterisation of the module]
[Show the navigation menu of the module]
[Show the Map of contents]
[Legenda]


[Contents
of the thesis]
[Comments]
































































































[Step back on the essay-path: Quantitative interpretation (link type: 'SEQ-BACK/essay_back/depens on'; target: A05-m5bi)] [Next step on the complete sequential path: Quantitative interpretation (link type: 'SEQ-NEXT'; target: A05-m6)]
[Step back on the essay-path: Quantitative interpretation (link type: 'ESSAY-BACK/sq-back/depends on'; target: A05-m5bi)] [Next step on the essay-path: Quantitative interpretation (link type: 'ESSAY-NEXT/out'; target: A05-m6a)]
[Show the characterisation of the module]
[Show the navigation menu of the module]
[Show the Map of contents]
[Legenda]


[Contents
of the thesis]
[Comments]

Theoretical cross sections = A05-m5bii

Using a simple classical atom-atom model for ion-pair formation in molecular collisions [The interpretation depends on the theoretical methods (link type: 'DEPENDS ON/detailed in'; target:  A05-m3c)], we interpret the experimental differential cross section for chemi-ionization in alkali halide systems, by comparing the experimental cross sections to theoretical cross sections calculated with the model.

The differential cross sections for chemi-ionization of K + BR2 at colliding energies of 10.35 and 6.9 eV have been calculated [The calculation depends on mesoscopic theoretical methods (link type: DEPENDS ON/detailed in/wider range/project; target:  MESO-m3c-defl)], in a procedure in which the differential cross section is determined via the potential curves of the system and the classical deflection function [These are used as input in the calculation (link type: INPUT FROM; target:  A05-m5bi)], by fitting the calculated cross section with the experimental one [Input from the Treated results (link type: 'INPUT FROM'; target: A05-m4bi)].

The theoretical cross section is expressed by [This formula is given in the mesoscopic theoretical methods (link type: 'INPUT FROM/is detailed in/wider range/project'; target: MESO-m3c-defl)]
 
(E1)
in terms of the deflection function and the Landau-Zener transition probability given by [This formula is given in the mesoscopic theoretical methods (link type: 'INPUT FROM/is detailed in/wider range/project'; target: MESO-m3c-mod]
 
(E2)

where Ei represents the initial relative kinetic energy, the reduced mass of the colliding particles, and the slopes of the diabatic potential curves at the crossing point Rc and the resonance energy H12 is half the energy difference of the adiabatic potential curves at Rc.

The resulting classically calculated chemi-ionization differential cross section for K + BR2 are shown in Fig.A05-m5bii-F1.   
[to the FULL figure] Figure A05-m5bii-F1:K + BR2, classically calculated chemi-ionization differential cross section (CM system) at colliding energies of 6.9 and 10.35 eV and convoluted with the energy spread of the velocity selector. For both energies equal units have been used on the ordinate. The dotted lines indicate the dependence of the slope steepness for ``covalent'' scattering. At Ei= 10.35 eV and different values of the polarizability , and the ionic-well minimum the positions of the scattering angle for b=Rc scattering respectively the classical rainbow angle have been indicated along the abscissa. The values used in the calculations have been underlined.

The general shape of this calculated differential cross section agrees with the measured cross section, and therefore the simple classical atom-atom model [Details in the module Qualitative interpretation (link type: IS DETAILED IN; target: A05-m5a)] gives a qualitative interpretation of the measurements.

reliability interpretation

The qualitative agreement between the calculated curves with the measured curves [The measured curves for KBr2given in the experimental Treated results (link type: INPUT FROM; target: A05-m4bi2)] [The measured curves for LiBr2 and KI2 given in the experimental Treated results (link type: INPUT FROM; target: A05-m4bi2)] is good but there is only a poor quantitative agreement.

Of course, a bad agreement for the ``ionic'' part of the differential cross section is expected because of the very different results for the rainbow structure as calculated classically and quantum mechanically. Due to the choice of and H12, Fig. A05-m5bii-F1 shows the agreement of the inelasticity shifts and curve ratio; at the same time the sensitivities of the determination of the parameters and are shown.

For the the estimated value of H12, the value of Pb(1-Pb) does not change very much over the greater part of the b range; only in a very narrow region at the ionization probability rapidly goes to zero.

Now let us make a comparison between the differential cross section of K + BR2 and the measured one of Li + BR2. A few estimates can be made easily. For Li + BR2 the minimum in the cross-section curve for b =  Rc scattering occurs at as compared to 135 eV . degree for K + BR2. Because the inelasticity of the Li + BR2 collision will be larger. Indeed the endothermicity must be 1.1 eV larger due to the differences of ionization potential: I(Li) = 5.4 eV [This value is imported from elsewhere (link type: INPUT FROM/external; target: Rf(A05)9)] and I(K) = 4.3 eV. The classical rainbow at indicates a larger well depth of the ionic potential curve of Li-Br2.

The relative differential cross sections of K + BR2 and K + I2 are nearly completely identical so a good similarity of the molecular constants can be expected. Duchart et al. [(link type: 'AGREES WITH/external'; target: Rf(A05)11)] have measured the K +I2 differential cross section for elastic scattering at a kinetic collision energy of l00 eV. The distances between the maxima of their resolved rainbow are equal to the supernumerary spacing that we should predict for K + BR2 ionization scattering at 100 eV.

Thus the potential parameters we determined [This provides argumentation for the reliability in the other Quantitative interpretation module (link type: 'PROVIDES ARGUMENTATION FOR/is detailed in'; target: A05-m5bi] are rather reliable.