Environmental Engineering Reference
In-Depth Information
and the critical radius for the Coulomb interaction of an electron and an ion is
b
e
2
/
T
. As a result, we have for the rate constant for process (2.70) [113]
D
N
e
D
e
10
m
1/
e
T
9/2
K
C
.
(2.71)
e
In this expression,
is the recombination coefficient, defined as the rate constant
for the decay of charged particles in the pairwise process, and
C
α
1isanumerical
coefficient. Formula (2.71) is valid if criterion (2.69) holds true; this now has the
form
N
e
e
6
/
T
3
1 and coincides with the condition of plasma ideality (1.3).
The rate constant for three body electron-ion recombination (2.70) may be ob-
tained in a simpler way on the basis of dimensional analysis. Indeed, the rate con-
stant for process (2.70) must depend only on the interaction parameter
e
2
, the elec-
tron mass
m
e
, and the thermal energy
T
e
(the electron temperature). There is only
one combination of these parameters that has the dimensions centimeters to the
sixth power per second for the rate constant for the three body process, and it can
be seen that this combination coincides with that given in (2.71). The value of the
numerical coefficient
C
in (2.71) is of interest. According to the nature of the pro-
cess, this value does not depend on the type of atom, because the nature of the
process is such that this coefficient is determined by properties of highly excited
states where the Coulomb interaction takes place between the atomic core and the
electron. Additional analysis gives
C
10
˙
0.3
for this value.
D
2
2.2.4
Autoionizing and Autodetaching States in Collision Processes
Autoionizing and autodetaching states are of importance as intermediate states in
collision processes. An autoionizing state is a bound state of an atom or positive
ion whose energy is above the boundary of the continuous spectrum, and hence an
electron can be released in the decay of such a state. For example, the autoionizing
state He(2s
2
,
1
S
) is the state of the helium atomwhere both electrons are located in
the excited 2s state, and as a result of such a decay one electron makes a transition
to the ground state, and the other electron ionizes. The scheme of this process is
He(2s
2
,
1
S
)
He
C
(1s,
2
S
)
!
C
e
C
57.9 eV .
(2.72)
An autodetaching state is identical to an autoionizing state, but occurs in a negative
ion. The decay of such a state proceeds with the formation of a free electron and an
atom or a molecule. An example of an autodetaching transition is
H
(2s
2
,
1
S
)
H(1s,
2
S
)
!
C
e
C
9.56 eV .
(2.73)
Formation of autoionizing and autodetaching states determines the character
of some collision processes involving electrons. These states give resonances in
cross sections as a function of the electron energy in both elastic and inelastic scat-
tering of electrons by atoms and molecules. They can be present as intermediate
