Chemistry Reference
In-Depth Information
As a result, one obtains the characteristic relaxation rate
MN
k
πD
2
12
k
2
ω
k
ω
0
D
2
24
π
(1)
(
ω
0
)
δ
(
ω
k
−
ω
0
)
=
θ
(
ω
0
)
≡
(176)
2
t
where
0
,ω
0
1
,ω>
0
≤
θ
(
ω
)
=
(177)
that enters the relaxation terms of the DME. In terms of
(1)
(
ω
0
) and
1
e
ω/
(
k
B
T
)
n
ω
≡
(178)
−
1
one obtains
R
(1)
αβ,α
β
=−
αα
,γγ
(1)
(
ω
γα
)
n
ω
γα
+
(1)
(
ω
α
γ
)
n
ω
α
γ
+
1
δ
β
β
Q
(1)
γ
β
β,γγ
(1)
(
ω
γβ
)
n
ω
γβ
+
(1)
(
ω
β
γ
)
n
ω
β
γ
+
1
δ
αα
γ
Q
(1)
−
(1)
(
ω
α
α
)
n
ω
α
α
+
β
)
(179)
1
+
Q
(1)
αβ,α
β
(1)
(
ω
αα
)
n
ω
αα
+
+
(
α
→
Remember that here all
(1)
(
ω
) with
ω<
0 are zero and
Q
(1)
is defined by
αβ,α
β
Eqs. (173) and (155).
Within the secular approximation, all relaxation terms in the DME are defined
by
αα
=
R
αα,α
α
α
=
α
[see Eqs. (58), (61)], and (63)], whereas for the direct
processes considered here one has
¯
(1)
αβ
0. For
(1)
αα
=
from Eq. (179), one obtains
2
(1)
αα
(1)
(
ω
α
α
)
n
ω
α
α
+
1
+
(1)
(1)
(
ω
αα
)
n
ω
αα
αα
=
2
(180)
D
2
where we used
α
α
2
(1)
(1)
(1)
(1)
∗
αα
(1)
αα
αα
·
=
αα
·
=
(181)
