Geoscience Reference
In-Depth Information
1
2
n
N
ƒ
.R/
2
:
U
nƒ
.R/
D
U
i
.R/
At n
!1
they are close to the ion U
i
.R/ term. Zero values of the second square
brackets define a set of the dissociative U
ˇƒ
.R/ terms, which intersect the ion
term at the pole E
D
U
i
.R/, in the points R
c
.ˇƒ/ determined by the condition
U
ˇƒ
.R
c
/
D
U
i
.R
c
/. Accounting for the interaction between them leads to a
characteristic pattern of the adiabatic terms where the transition of each pseudo-
crossing point is accompanied by the increase of adiabatic quantum defect
ƒ
.R/
by 1. To determine its explicit form is sufficient to replace in the second square
brackets in Eq.
1.29
the total energy in the adiabatic Rydberg U
nƒ
.R/ potential
using Eq.
1.18
and the expression of .R/
D
n
ƒ
.R/. Then, far from the
intersection point it is easy to obtain the
ƒ
.R/
'N
ƒ
.R/
C
ƒ
.R/ expression,
where
arctan
"
V
2
ƒ;ˇƒ
.R/
!#
:
1
ƒ
.R/
'
U
ˇƒ
.R/
When the value E>U
i
.R/, the magnitude of tan.R/
!
i and the solution
of Eq.
1.29
becomes
i
2
ˇƒ
.R/;
E
U
ˇƒ
.R/
N
ˇƒ
.R/
D
where the energy shift and the autoionization width are equal:
2
sin
2
N
ƒ
.R/
;
1
N
ˇƒ
.R/
D
ˇƒ
.R/
D
2V
2
ƒ;ˇƒ
.R/cos
2
N
ƒ
.R/:
Note: the autoionization width
ˇƒ
.R/ arises here by the jump at the transition
R
c
.ˇƒ/ point, which is typical for the Coulomb problem (Golubkov and Ivanov
2001
).
We considered the approximate approach, which can be described as “quasi-
adiabatic,” if the potential curves appear. Nevertheless, it is very useful, because
it allows without much difficulty demonstrating its effectiveness in addressing a
number of nonstationary problems of quantum mechanics (Demkov and Golubkov
2003
). The disadvantage of the approach is that the ionization channel is open only
when the R<R
c
region. In fact, as is shown next, the ionization process strictly
arises in the case of E
U
i
.R/
C
!=2.
The next principal drawback is that the heterogeneity of the ionization continuum
associated with the existence of closed channels of motion, which is the result
of the strong nonadiabatic coupling of the electronic and nuclear motions in the
intermediate Rydberg XY
**
complex, has disappeared in this approach.
