Geoscience Reference
In-Depth Information
U
(
R
)
X
+
ΔΣ
X
*
+
X
R
c
0
R
Fig. 1.4
Illustration of the quasi-crossing of covalent and ionic potential curves under the frame
of the “diffusion” model
1.3.2
General Equations of the Scattering Theory
In presenting the formal scattering theory of atoms X
C
Y
*
with a transition to
the final e
C
XY
C
state of the system, it is convenient to use a method of the
multichannel quantum defect (MQD) (Golubkov and Ivanov
2001
), which gives the
most complete and consistent description of the resonant scattering and the reactions
leading to the redistribution of particles. For simplicity, we exclude the valent X
*
Y
*
and ionic X
C
Y
configurations and represent the full Hamiltonian of the system
under consideration in the form .
„D
m
e
D
e
D
1/
1
2
r
1
r
C
H
q
;
H
D
H
0
C
V
;
H
0
D
(1.10)
1
2
r
is the operator of the kinetic energy of a weakly bonding electron,
r
is its coordinate read from the XY
C
ion center of mass, and
H
q
is the molecular
ion Hamiltonian dependent on the coordinate set
f
X
g
of the internal electrons (here,
q
Df
v
,
N
g
is the set of vibrational
v
and rotational
N
quantum numbers of the XY
C
ion). Note that the bound and autoionizing Rydberg states of the system belong to
the configuration XY
**
and differ only in sign (and magnitude) of the total energy
E
of the system, which can be conveniently measured from the ground state of the
molecular ion.
where
