Environmental Engineering Reference
In-Depth Information
D
p
8
T
/
where
m
is the atomic mass,
v
π
m
is the average thermal velocity of
T
atoms, and
n
is the number of cluster atoms.
2.1.4
Cross Section of Capture
We now turn our attention to the other limiting case of atomic scattering, where the
collision energy is small compared with the well depth
D
.Thedependenceofthe
collision impact parameter on the distance of closest approach, calculated on the
basis of relation (2.6), is given in Figure 2.6. This curve is divided into two regions,
whose boundary is separated by the arrow. Region 2 is not related to collisions of
particles, and hence will not be considered. Effectively, the region of impact pa-
rameters is divided into two parts, and their boundary corresponds to the impact
parameter
c
, the values of the impact parameter and the correspond-
ing distance of closest approach are comparable. If the collision impact parameter
is smaller than
c
.At
>
c
, the distance of closest approach
r
0
is close to
r
min
,definedby
U
(
r
min
)
0. Then collision capture occurs, and the bound system reduces its size
until finally a short-range repulsion halts the contraction.
Since the capture is governed by the long-range part of the interaction potential,
we can approximate the interaction potential by the dependence
U
(
R
)
D
C
/
R
n
.
D
The impact parameter for capture
c
is determined as the minimum of the depen-
(
r
0
) and, according to relation (2.6), the capture cross section is [1]
dence
C
(
n
2/
n
D
π
n
2)
2
c
σ
D
π
.
(2.20)
c
n
2
2
ε
The dependence of the cross section on parameters is similar to (2.8). In particular,
in the case of polarization interaction of an ion and atom,
U
(
R
)
α
is the atomic polarizability), the polarization cross section for capture of an atom
D
α
e
2
/(2
R
4
)(
Figure 2.6
The dependence of the impact parameter on the distance of closest approach for an
attractive interaction potential according to (2.6).
