[Step back on the complete sequential path: Interpretation (link type: 'SEQ-BACK/IS PART OF/IS GENERALISED IN; target: A08-m5)] [Next step on the complete sequential path: Quantitative interpretation (link type: 'SEQ-NEXT'; target: A08-m5b)]
[Step back on the essay-path: Theoretical methods (link type: 'ESSAY-BACK/DEPENDS ON'; target: A08-m3cii)] [Next step on the essay-path: Quantitative interpretation (link type: 'ESSAY-NEXT'; target: A08-m5bi)]
[Show the characterisation of the module]
[Show the navigation menu of the module]
[Show the Map of contents]
[Legenda]


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



















































































[Step back on the complete sequential path: Interpretation (link type: 'SEQ-BACK/IS PART OF/IS GENERALISED IN; target: A08-m5)] [Next step on the complete sequential path: Quantitative interpretation (link type: 'SEQ-NEXT'; target: A08-m5b)]
[Step back on the essay-path: Theoretical methods (link type: 'ESSAY-BACK/DEPENDS ON'; target: A08-m3cii)] [Next step on the essay-path: Quantitative interpretation (link type: 'ESSAY-NEXT'; target: A08-m5bi)]
[Show the characterisation of the module]
[Show the navigation menu of the module]
[Show the Map of contents]
[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. [To the FULL figure; copied from Treated results module (link type: 'INPUT FROM'; target: A08-m4bi1)] [To the FULL figure]
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 [Model given in Theoretical methods (link type: 'DEPENDS ON'; target: A08-m3c)] .  
[To the FULL figure] 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 [Calculation methods given in the module Theoretical methods (link type 'DEPENDS ON/is detailed in'; to: A08-m3ci1)] [Calculation methods given in the module Theoretical methods (link type 'depends on/is detailed in'; to: A08-m3cii)] the theoretical differential cross sections via the deflection curve [The general shape of the deflection curve is given in the mesoscopic module Theoretical methods (link type 'INPUT FROM/is detailed in/wider range/project'; to: MESO-m3c-defl#fig)] . The absolute value of the theoretical cross sections, which is shown in figure A08-m5bii1-F1 [figure of the theoretical cross sections copied from the Quantitative interpretation (link type: 'INPUT FROM'; target: A08-m5bii1)] , is determined in the Quantitative interpretation, with the necessary potential parameters [parameters copied from  the Quantitative interpretation (link type: 'input from'; to: A08-m5bi#table)]. Here we consider the qualitative features of the calculated curve.  
[To the FULL figure] 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 bmax. In addition there is a sharp decreasing value of the transition probability Pb for b bmax caused by the decreasing value of the radial velocity of the colliding particles at the pseudo-crossing Rc.

Eq. (E1) [Equation given in Theoretical methods (link type 'INPUT FROM'; to: A08-m3cii)]
$\displaystyle I(\theta)$ = $\displaystyle \big\vert A\er^{\ir\alpha}+C\er^{\ir\gamma}+D\er^{\ir\delta}+
E\er^{\ir\varepsilon}\big\vert^2$  
  = $\displaystyle A^2+C^2+D^2+E^2+2AC\cos(\alpha-\gamma)$  
    $\displaystyle +2AD\cos(\alpha-\delta)+2AE\cos(\alpha-\varepsilon)$  
    $\displaystyle +2CD\cos(\gamma-\delta)+2CE\cos(\gamma-\vare)$  
    $\displaystyle +2DE\cos(\delta-\vare).$ (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 [methods for the measurements given in Experimental methods (link type: 'DEPENDS ON'; to: A08-m3a)] .
[unfold details: estimation of the wavelength NOT AVAILABLE]

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:
 \begin{displaymath}
I(\MT<0)=A^2+C^2+2AC\cos(\alpha-\gamma){\rm
}
\end{displaymath} (E2a)
or  
\begin{displaymath}
I(\MT<0)=B^2+C^2+2BC\cos(\beta-\gamma){\rm
}
\end{displaymath} (E2b)
and  
\begin{displaymath}
I(\MT\gt)=D^2+E^2+2DE\cos(\delta-\vare).

\end{displaymath} (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.