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This is a strong justification for the utilization of the “diffusion model” in describing
the stochastic dynamics exothermic AI process (Devdariani et al. 1988 ). Below
we discuss the question about the stochastization of the molecular Rydberg states
spectrum in more detail.
In the “diffusion model,” it is believed that for the endothermic process under
the passage of the image point of each pseudo-crossing of the dissociative ˇ state
potential curve U ˇ .R/ and intermediate Rydberg U
.R/ states of the XY quasi-
molecule (mixed by the nonadiabatic coupling of electronic and nuclear motions),
a change in the electron energy ı" is small compared to the energy change for
the entire act of collision, E ˇ . As a result, the act of the collisions leading to
ionization is regarded as the diffusion of the initial excitation energy " of the
intermediate complex states. As a result of its semiclassical motion nature, the
Rydberg electron collision process can be described in terms of the probability
density population states W.";t/with the energy " at time t , which is known to
be associated with R .
The quantity of the density W.";t/satisfies the following equation (Devdariani
et al. 1988 ):
@W .";t/
@j ."; t/
where j.";t/ D D.";t/.@W.";t/=@"/ is the excitation flow in the point " at the
time t ,andD.";t/is the diffusion coefficient in the energy space, equal to
Z p "" 0 ;t " 0 " 2 d" 0 Š
ı" 2
2ıt :
D.";t/ D
Here p."" 0 ;t/ is t he t ransition probability per unit time between the states with
energies " and " 0 , ı" 2 is the characteristic energy change in ıt time transition.
Equation 1.41 is solved together with the initial condition
W.";t !1 / ! ı." " o /
and the boundary condition W " D U ˇ .R/;t D 0 corresponding to the single
ionization probability. Analysis of the Eq. 1.41 solution shows that the initial delta
distribution at the time of convergence to the distances at which the ionization
exists broadens. For example, for thermal collisions of alkali atoms and n 10
such a broadening is equal to " 3:6 7:3 10 3 (Devdariani et al. 1988 ).
The ionization probability as a function of the parameter " o increases to a maximum
value when this parameter is of the order of " in the vicinity of " o U ˇ .R c /.The
ionization rate constant decay with further rise of n is associated with the decrease
of the ionization probability at small ", that in this model takes into account the
appropriate modification of the boundary conditions at " D U ˇ .R/.Itistrueifthis
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