[Legenda]
[Contents of the thesis]
[Comments on this module]
[Legenda]
[Contents of the thesis]
[Comments on this module]

Qualitative interpretation=A08-m5a

In the measured differential cross sections of the process Na + I Na⁺ + I^-, as shown in Fig. A08-m5a-F1,

Figure A08-m5a-F1: Relative polar differential cross section for chemi-ionization (CM system). The cross sections, measured at a colliding energy of 13.1 and 18.2 eV, have been set in scales with shifted zero points.

three parts can be distinguished: the cross sections at scattering angles between 0 and 65 eV degree, at angles between 65 and 250 eV degree, and at larger angles. Also, oscillation is visible in all three domains. Both the tripartition and the oscillations can be explained with the semi-classical atom-atom model for ion-pair formation in molecular collisions .  

Figure A08-m5a-F2: Polar differential cross section for chemi-ionization (CM system) at Ei = 13.1 eV, calculated in semi-classical approximation with the potential parameters of Table A08-m5bi-T1 and the coupling parameters H12=0.065 eV and Hrot=0 eV s. (a) Differential cross section with complete interference structure, calculated with the lowest-order stationary-phase approximation. The region of the classical rainbow angle $\theta_{\c{\rm l}.\rr\br}$ has been omitted. (b) Differential cross section calculated with the stationary-phase approximation and uniform rainbow approximation showing separated the long-wavelength interference structures due to a + c ($\tau=0\to65$, full curve), b + c ($\tau=65\to250$, full curve) and d + e ($\tau=0\to 2300$, dashed curve) interferences. (c) Full bars indicate the measured maxima of the interference structure on the differential cross section due to net-attractive scattering. Dashed bars indicate the maxima due to net-repulsive scattering.

We have calculated the theoretical differential cross sections via the deflection curve . The absolute value of the theoretical cross sections, which is shown in figure A08-m5bii1-F1 , is determined in the Quantitative interpretation, with the necessary potential parameters . Here we consider the qualitative features of the calculated curve.  

Figure A08-m5a-F3: Deflection curves for chemi-ionization scattering (CM system) at Ei = 13.1 eV

Fig.  A08-m5a-F2 demonstrates very clearly the tripartition of the theoretical cross section curve. The covalent scattering causes the narrow but high peak between 0 and 65 eV degree while the separated broader and lower part between 65 and 250 eV degree is due to ionic scattering. Both types of scattering supply small contributions to the very small differential cross section beyond the classical rainbow angle, due to net-repulsive scattering.

For covalent as well as ionic net-attractive scattering the contributions to the cross section go to zero at $\tau\approx 65$ because the deflection function $\dr b/\dr \MT\to0$ for b b_max. In addition there is a sharp decreasing value of the transition probability P_b for b b_max caused by the decreasing value of the radial velocity of the colliding particles at the pseudo-crossing R_c.

Eq. (E1)

$$I(\theta) \big\vert A\er^{\ir\alpha}+C\er^{\ir\gamma}+D\er^{\ir\delta}+ E\er^{\ir\varepsilon}\big\vert^2$$ =

$$A^2+C^2+D^2+E^2+2AC\cos(\alpha-\gamma)$$ =

$$+2AD\cos(\alpha-\delta)+2AE\cos(\alpha-\varepsilon)$$

$$+2CD\cos(\gamma-\delta)+2CE\cos(\gamma-\vare)$$

$$+2DE\cos(\delta-\vare).$$ (E1)

shows that the differential cross section contains six superposed or only one interference oscillation depending whether four or two scattering trajectories contribute to the cross section.

An estimation of the wavelengths of the different oscillations gives the result that only the interferences of a + c, b + c and the d + e branches have a wavelength of a few eV degrees or more on the -scale and only that kind of structure could be detected in our measurements .

Because in our case a + c and b + c interferences never occur together, the differential cross section contains only one or two superposed interesting oscillations. In the case of two oscillations one occurs from net-attractive scattering, the other one from net-repulsive scattering. Then, for our purpose, Eq. (E1) can be changed into:

$$I(\MT<0)=A^2+C^2+2AC\cos(\alpha-\gamma){\rm }$$ (E2a)

or  

$$I(\MT<0)=B^2+C^2+2BC\cos(\beta-\gamma){\rm }$$ (E2b)

and  

$$I(\MT\gt)=D^2+E^2+2DE\cos(\delta-\vare).$$ (E2c)

Actually Eqs. (2a) and (2c) for the theoretical differential cross section describe the Stueckelberg oscillations, that is the interference due to trajectories from different potentials. Those oscillations are shown in Fig. A08-m5a-F2b on the covalent scattering cross section peak and on the net-repulsive scattering differential cross section.

Eq. (2b) describes the interference of two contributions of ionic scattering, normally called rainbow scattering. The differential cross section shows the rainbow structure between $\tau\approx 65$ and $\tau\approx 250$ eV degree.

For the experimental differential cross sections, Fig. A08-m5a-F1 shows over a wide angular range all main features of the cross section of interest. The longwavelength Stueckelberg and rainbow oscillations due to net-attractive scattering interference have been resolved completely while the repulsive (Stueckelberg) interference can be seen clearly beyond 250 eV degrees. In the -range between 25 and 55 eV degrees there is some evidence of a double structure. Particularly on the 13.1 eV curve heavy and small maxima succeed each other and indicate a repulsive oscillation on that range with half the frequency of the attractive oscillation.

Thus the experimental and the theoretical differential cross sections of chemi-ionization in collisions between Na and I agree qualitatively.