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

Quantitative interpretation with both Landau-Zener and rotational coupling=A08-m5bii2

Chemi-ionization in collisions between Na and I can be explained via crossing of the potential energy surfaces of the collisions . The Landau-Zener formula gives the transition probability between translationally coupled states. However, the Landau-Zener transition probability does not give an adequate quantitative explanation of the experimentally determined differential cross sections of the chemi-ionization process. It is likely that rotationally induced transitions could explain the discrepancy of measured and calculated differential cross section.

The discrepancy that the rotational coupling could explain is where the calculated cross section is too small for collisions with large impact parameters . Fig. A08-m5bii2-F1 clearly shows for increasing kinetic energy an increasing deviation of the relative differential cross section at $\tau\approx 65$ eV degree without rotational coupling. Even the relative cross sections more separated from the minimum would lead for a fitting procedure to an unphysical energy dependence of the Landau-Zener coupling parameter H₁₂.

Figure A08-m5bii2-F1: Smoothed differential cross sections for five different collision energies. (a), (b), (c), (d), (e): Full curves show the measured relative differential cross section, averaged over the interference structures. Absolute differential cross sections, calculated semi-classically and also averaged over the interference structure, have been given by the dashed curves. Use has been made of H12=0.05 eV. (f): At Ei = 29.7 eV the curves show the calculated differential cross section for H12=0.04, 0.05 and 0.07 eV

We have calculated the general shape of the differential cross sections of the chemi-ionization process again, now taking into account the rotational coupling .

Fig. A08-m5bii2-F2 gives again the measured general shapes of the differential cross sections at kinetic colliding energies of 13.1, 20.7, 29.7, 38.7 and 55.0 eV. A comparison has been made with calculated cross sections taking into account some rotational coupling.

Figure A08-m5bii2-F2: Smoothed differential cross section for five different collision energies. (a), (b), (c), (d), (e): Full curves show the measured relative differential cross section, averaged over the interference structure. Dashed curves show calculated absolute cross sections using the coupling elements H12=0.0024 a.u. (0.065 eV): and H12>=0.04 a.u. (f): Effect of rotational coupling on the minimum of the differential cross section due to collisions with large collision parameters. Abscissa and ordinate scales have been extended by a factor of two with respect to the corresponding figure (e).

Indeed, the minimum in the differential cross section has been increased to a degree dependent on the kinetic energy.

Moreover, it is very obvious that now it is possible to find one set of coupling constants giving a good fit of measured and calculated cross sections for all energies. This set consists of the values H₁₂=0.065 eV and H_rot=3 x 10^-17 eV corresponding to the values of 0.0024 a.u. and 0.04 a.u., respectively.

A comparison of the corresponding cross section curves of Fig. A08-m5bii2-F1 and Fig. A08-m5bii2-F2 shows that rotational coupling at low kinetic energies increases the differential cross section only at the very minimum but for higher kinetic energies there is a rise over a larger -range. This feature makes it possible to use only one value of H₁₂.

On the range $\tau=50\to 200$ eV degree Fig. 0.2f gives the dependence of the cross section on some values of _rot at E_i = 55  eV. For increasing coupling constant, the maximum contribution of rotational coupling to chemi-ionization moves to collisions with smaller impact parameters.

It must be noted that for impact parameters $b\approx R_\c$ Eq. (E1)

(E1)

does not hold any more because a sufficient separation is supposed between the classical turning point and the crossing point Rc. (A similar remark to the Landau-Zener coupling has been made in A08-m5bii1 , point D.) For an incomplete passage of the transition region around R_c Eq. (E1) gives too large a value of P_b,rot. In the present case with the parameters used the resulting effect is the product P_b,rot(1-P_b,rot), too small for collisions with E_i = 55  eV and $b\approx R_\c$ and too large for the corresponding collisions at E_i = 13.1 eV. Indeed, a correction to this effect should improve the agreement of measured and calculated curves of Fig. F2a and Fig. 2c. It is suspected that the remaining apparent discrepancy of the relative intensities at $\tau\approx 65$ eV degree is due to convolution effects, measuring faults and the improper use of Eq. (E1) for $b\approx R_\c$.

Reliability
The estimated value H₁₂=0.065 eV differs rather much from the value of 0.05 eV, estimated from total cross-section measurements on the collision energy range 2-20 eV. The effect of these two values on the absolute differential cross section can be observed from Fig. 0.1 (H₁₂=0.05 eV) and Fig. 0.2 (H₁₂=0.065 eV). At E_i = 55  eV the cross sections of Fig. F2 have hardly different values, while at E_i = 13.1  eV the cross sections differ by a factor of two. Of course, relative measurements on the differential cross section versus the kinetic energy should give a hint to the correct value of H₁₂. However, at the present measurements it is impossible to distinguish in this way these values of H₁₂. It is expected that the surface-ionization detector as well as the scattered-ion detector have large and unknown energy-dependent efficiencies.