Geoscience Reference
In-Depth Information
3.6.3.3
Short-Range Potentials
The consideration remains simple for the weak potentials such that ˇU.R/
1.In
this case the function F.r/at large r
a behaves as in the case of free condensation
with the particle radius replaced by a, where the modifier depends on the details
of the potential and
r
1
2
a
2
R
2
:
F.R/
D
(3.178)
Let us introduce
z
.a/, the free molecule enhancement factor
˛
fm
.a/
a
2
v
T
z
.a/
D
:
(3.179)
We obtain,
z
.a/
v
T
a
2
2DR
2
2
a
2
2R
3
q
1
D
(3.180)
2
a
2
R
2
On solving Eq.
3.180
gives
s
2D
2
z
.a/
v
T
2
R
D
C
2
a
2
:
(3.181)
and
2a
2
v
T
z
.a/
˛.a/
D
r
1
C
(3.182)
a
v
T
z
.a/
2D
2
2
1
C
It is possible to find .a/. To this end we simplify F.R/by ignoring U.R/ and
replacing the lower limit of integration by 0. After these simplifications we find
dx
e
x
r
x
.x
C
ˇ
j
U.r
/
j
/
r
2
Z
2
p
R
2
F.R/
D
0
dx
e
x
p
x
1
1
C
Z
r
2
R
2
2
p
1
2
ˇ
j
U.r
/
j
x
0
