[Legenda]
[Contents of the thesis]
[Comments]
[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 , 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 , in a procedure in which the differential cross section is determined via the potential curves of the system and the classical deflection function , by fitting the calculated cross section with the experimental one .

The theoretical cross section is expressed by
 

(E1)

in terms of the deflection function and the Landau-Zener transition probability given by
 

(E2)

where E_i 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 R_c and the resonance energy H₁₂ is half the energy difference of the adiabatic potential curves at R_c.

The resulting classically calculated chemi-ionization differential cross section for K + BR₂ are shown in Fig.A05-m5bii-F1.   

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 gives a qualitative interpretation of the measurements.

reliability interpretation

The qualitative agreement between the calculated curves with the measured curves 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 P_b(1-P_b) 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 =  R_c 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 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. 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 are rather reliable.