Geoscience Reference
In-Depth Information
2
4
!.1
ı
v
0
;
v
1
/
C
ı
v
0
;
v
1
X
v
v
2
2
C
"
v
3
3
1
i
.
v
0
C
1/
.
v
0
C
1/
1
5
v
0
C1
D
.2!/
1=2
N
D
min
f
g
;
(.x/is the step function), which indicates that along with breaks for the threshold
values
E
D
E
v
should be observed a “small” step (at the energies E
D
E
v
1
ı
2
3
)
associated with the individual contribution of the individual Rydberg resonances. In
particular, the discrete structure cross section should be clearly observed for weakly
exothermic processes that do not require an initial kinetic energy to overcome the
reaction threshold. In this case, the calculation should be carried out by the general
formulas of the quantum scattering theory, without resorting to the pre-averaged
probability of the process (Eq.
1.31
). If ı
1/
v
3
, the step is naturally smoothed out,
and for ı
1
ı
3
it completely disappears. In this case, formula (
1.35
) transforms
in Eq.
1.32
.
According to Eq.
1.35
, the general formula for the rate constant k
AI
.T/ of the
endothermic reaction AI at temperatures
T
! can be written as
k
AI
.T/
D
AS.T/T
1=2
exp
E
ˇ
=T
;
(1.36)
where
A
D
8
2
R
e
2
1=2
E
ˇ
D
min
˚
E
ˇ
;
;
M
c
˛
ˇ
0
0
C
˛
ˇ
0
1
!
:
S.T/
D
X
ˇ
0
X
i
T
exp .
"
=T/
3
g
ˇ
0
V
ˇ
0
>N
Here "
is the position of the Rydberg resonance, measured from the threshold of
the reaction (the sum is taken over the configurations ˇ
0
in S.T/ having a common
threshold E
ˇ
of reaction). At low temperatures T
1
ı
N
3
(where
N
.2!/
1
=
2
),
Rydberg resonances can greatly affect the temperature dependence of the quantities
S.T/ in Eq.
1.36
.IfT
E
ˇ
, it occurs in the region with the exponentially small
k
AI
.T/. The exception is the reaction with a low energy threshold
E
ˇ
!
.At
higher temperatures (T
1
ı
N
3
), the value S.T/ becomes a constant (i.e., S
˛
ˇ0
C
˛
ˇ1
i
= ) and the presence of the Rydberg resonances only affects its value.
At T
!, for the evaluation of AI rate constant it is convenient to make use of the
linear approximation of the cross section (Eq.
1.33
), inserting
D
AI
.!/=!.In
this case the AI rate constant can be represented as follows:
k
AI
.T/
D
A
1
C
!
T
1=2
exp
E
ˇ
=T
;
2T
E
ˇ
(1.37)
