Geoscience Reference
In-Depth Information
dx
e
x
r
x
ˇU.r/
.x
ˇU.a//
a
2
Z
2
p
G
a
.r;R/
D
r
2
:
ˇU.a/
Using the identities F.R/
D
G
a
.R;R/ and G
o
.R;R/
D
e
ˇU.R/
yields again
1
C
e
ˇU.R/
F.R/
e
ˇU.R/
e
ˇU.r/
C
G
a
.r;R/
:
n.R/
n.r/
D
3.6.3
Flux and Charging Efficiency
The expression for the flux follows from Eq.
3.29
:
Z
4
2
m
3
C.R/
e
ˇ.ECjU.R/j/
L
a
dE:
J.a;R;n
R
/
D
(3.168)
jU.R/j
Hence,
mˇ
2
3=2
Z
8
2
m
3
1
1
C
e
ˇjU.R/j
F.R/
e
ˇ.ECˇjU.R/j/
L
a
dE
˛
fm
.a;R/
D
ˇjU.R/j
2˛
o
1
C
e
ˇjU.R/j
F.R/
:
D
(3.169)
Dependence on the matching distance
R
is clearly seen. It enters via the multiplier
1=.1
C
F.R// and in the lower limit of the integral. The latter fact means that the
bound states of ions in the potential U.r/are taken into account. The value ˛
o
differs
from ˛
fm
by the lower limit of integration over
E
(
j
U.R/
j
instead of 0).
In the case of nonsingular repulsion, the result looks as follows:
mˇ
2
3=2
Z
8
2
m
3
1
1
C
e
ˇU.R/
F
rep
.R/
e
ˇ
.
EU.R/
/
L
a
dE
˛
fm
.a;R/
D
ˇU.R/
2e
ˇU.a/
˛
fm
.a/
1
C
e
ˇU.R/
F
rep
.R/
:
D
