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to Eq.
1.11
without a free
t
term. Therefore, the total wave function (Eq.
1.43
)has
the form:
ˇ
ˇ
‰
q
˛
D
X
i
j
i
i
G
.c/
.E
E
i
/
h
i
j
j
q
i
Z
X
ˇ
1
j
ˇ
ih
ˇ
j j
q
i
E
E
ˇ
C
i
dE
ˇ
:
C
(1.44)
Hence, it is the superposition of a complete set of noninteracting basis states in a
coordinate wide range of the selected electrons. In the case of diatomic molecule
wave functions,
j
q
i
and
j
i
i
are given by Eq.
1.16
, which are valid for arbitrary
quantum numbers
l
and
N
.
A transition to the “chaotic” description of the orbitally degenerated and split
by nonadiabatic rotation coupling of highly excited levels of diatomic Rydberg
molecules was carried out by Lombardi and Seligman (
1993
). This approach does
not account for coupling with vibrational and dissociative channels. The authors of
this paper suggested that for the large quantum numbers
l
and
N
of Rydberg states
the angular momenta
J
,
l
,and
N
are fixed, so they retained only one term in the
expansion (Eq.
1.44
) with fixed
l
and
N
. They applied MQD theory (Golubkov and
Ivanov
2001
) for determining the positions of the molecular energy levels. Essen-
tially, this approximation eliminates the kinematic relationship between the weakly
bound electron motion and molecule rotations for given total angular momentum
J
.
Use of such “truncated” Rydberg molecular wave functions for determining the
respective dipole matrix elements (or time-dependent autocorrelation functions of
dipole moments) on the basis of a correctly calculated energy spectrum can indeed
reveal a random behavior.
This approximation is justified, once only one matrix element
h
i
j j
q
i
is large,
with other ones being ignored. For large principal quantum numbers n such
situations are rare. In most cases (especially in the case of strong nonadiabatic
coupling), these matrix elements are generally comparable (Balashov et al.
1984
). In
this case, the repulsion of two closely spaced Rydberg levels belonging to different
rotational series is determined substantially by the nonadiabatic interaction, which
may be comparable to the distance between these levels. As in the case “d” by
Gund, the energy difference between the ionization thresholds of these series under
the condition N
!=2B is of the order of the oscillation frequency ! (B is the
rotational constant of the molecular ion), where there is no reason to exclude the
vibrational degrees of freedom from general consideration. Moreover, most highly
excited Rydberg molecular states considered by Lombardi and Seligman (
1993
)are
the autoionization states (see Fig.
1.6
). The dynamics of electron behavior for these
states is described in terms of the scattering theory, where the energy eigenvalues
and corresponding wave functions are complex (Golubkov and Ivanov
2001
).
The problem becomes even more confused if the valent (non-Rydberg), ionic,
and dissociative configurations being essential components of the electronic struc-
ture of the excited molecules and having a significant effect on the resulting
