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Theory of AI reaction
Near-Threshold AI Reactions of Atoms
We demonstrate the foregoing theory by the example of the behavior of the
endothermic AI reaction of atoms near its threshold. In presenting the general
theory, we have omitted a consideration of the subtle effects associated with the
manifestation of the resonance structure of the valence (non-Rydberg) and the ionic
configurations, which are particularly important when they are situated near the
threshold of the spectrum. Although the described formal scattering theory allows us
to analyze these special cases, we focus here on the simpler situation where during a
motion along the dissociative term U ˇƒ .R/ only the nearest closed vibronic channel
(main series) in the Rydberg states is populated, leaving aside the peculiarities of the
nonadiabatic rotational coupling. A semiclassical theory of the endothermic reaction
near the threshold E D E ˇ for AI was considered by Cohen ( 1976 ), Devdariani
( 1979 ), and Smirnov ( 1981 ). The total cross section can be represented as follows:
.2j C 1/ ˇ ˇ ˇ
ˇ; v .E/ ˇ ˇ ˇ
M c
g ˇ
E C E ˇ
T .j/
AI .E/ D
v ;j
where g ˇ is the statistical weight of the dissociative state, M c is the reduced mass of
the colliding atoms, X and Y, j is their angular momentum, and E ˇ is the threshold
energy of AI for the reaction in the center of mass system for ˇ channel (summation
over v is carried out over all open channels). For the case of the quasi-classical
motion neglecting the j and l momentum coupling, the situation j ¤ 0 differs from
j D 0 by the shift of the electronic terms through the value j 2 =2M c R 2 .Iffor
j ¤ 0 the distortion of their form in the R range, responsible for transitions, can
be neglected, then the probability hj T .j/
i does not depend on the momentum
j (this averaging corresponds to the conditions realized in the experiment). The
corresponding criterion may be formulated as
ˇ; v .E/ j
" v j R c .ˇ/ R e j R 1
where R c .ˇ/ is the crossing point of ionic and valence terms in the vicinity of which
the Frank-Condon transitions occurs, and R e is the equilibrium internuclear distance
in the XY C ion. When summing over j one must take into account also that the
transition to the XY C . v / state is possible only if " v >Bj 2 ,whereB D 1=2M c R 2
is the rotational constant of the XY C ion.
Under these conditions the averaged Rydberg resonances of the square modulus
of the amplitudes are equal to (Golubkov and Ivanov 1988 ):
V ˇ v 0 ;
v 0 < v 1;
ˇ ˇ ˇ
ˇ; v .E/ ˇ ˇ ˇ
V ˇ v 1 1 C
; v 0 D v 1:
T .j/
i . v / V ˇ v
. v / V ˇ v 1
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