[Legenda] 

[Contents of the thesis] 

[Comments on this module] 



[Legenda] 

[Contents of the thesis] 

[Comments on this module] 
Based on the potential curves, the deflection function of the system can be calculated Starting with the deflection function, the classical differential cross section for chemiionization is given by :
(E1) 
The same impact parameters are important in the semiclassical treatment extended with the stationary phase approximation . Then the scattering amplitude is built up again either by four or by two contributions:
(E2) 
(E3) 
In the lowestorder stationaryphase approximation
the possible contributions
to
are then given by
=  
(E4a)  
=  
(E4b)  
=  
(E4c)  
=  
(E4d)  
=  
(E4e) 
For a certain scattering angle where four contributions form the cross section (for instance the contributions from the branches a, c, d and e), the differential cross section is given by:
=  
=  
(E5) 
(E6) 
However, the first problem in applying this approximation is that in the present case there does not exist a deflection curve for collision parameters from infinity down to the largest value of b that gives rise to chemiionization . Fortunately, the equation for shows that for the calculation of the differential cross section we only need the phaseshift differences of the relevant contributions. In our calculations therefore we have taken arbitrarily .
A second point is that due to the coulombic nature of the outgoing channel, the argument of the sine of the wave function contains a term with ln(2kR) , and therefore the validity of the semiclassical approximation is questionable. However, as in the asymptotic wave functions the phase shifts contain for all deflection branches this ln(2kR) term; this term cancels out for phaseshift differences and the problem is circumvented. Thus, the JWKB approximation can be applied in the present case.
The approximation that can be applied to the area of the rainbow angle is the uniform approximation of rainbow scattering , in which the actual shape of the deflection function is used. In our case it turns out that the uniform approximation is only necessary to describe the primary rainbow because the supernumerary rainbows calculated in this way completely coincide with the ones calculated by the stationaryphase method. .
In the uniform approximation of rainbow scattering the resulting
formula to calculate the rainbow structure for
,
being the interference of the b and c branches, reads:
(E7) 
(E8) 
The semiclassical differential cross section can be calculated using the stationary phase approximation, the uniform approximation of rainbow scattering and JWKB phase shifts.
The application of the semiclassical approximation on twostate collisional processes and the LandauZener theory have been discussed recently in a series of papers by Delos and Thorson . As far as the applicability of the semiclassical approximation is concerned, they conclude with four statements about kinetic energy and potential states of the collision partners . The collisional process discussed now does not fulfill completely those statements.