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
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.
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 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 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.