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where M c is the reduced mass of the quasi-molecule XY ** ,
D Œ.J ƒ/.J ˙ ƒ C 1/ 1 = 2 ; L ˙ D L ˙ iL :
The quantity Q v ;ˇƒ is defined as the radial part of the nuclear matrix element and
equal to
D v ˇ ˇ ˇ ˇ
ˇ ˇ ˇ ˇ
ˇƒ E :
R 2
Q v ;ˇƒ D
The projections L ˙ of the electron angular momentum operator L are defined
in the molecular frame system and affect the wave functions of the dissociative
channels ˇƒ at construction by the common quantum chemical rules. From
Eq. 1.26 it implies that unlike Eq. 1.25 the selection rule for Coriolis communication
is defined as
ƒ 1:
For homoatomic quasi-molecules X 2 the selection rules ( 1.25 )and( 1.27 )are
provided by the condition: g $ g; u
u . Note also that the part of the Coriolis
coupling proportional to ˝ L 2 ˛ ƒ ı ƒƒ 0 is included in the definition of the first term in
Eq. 1.24 because the selection rules for this interaction are the same as in Eq. 1.25 .
Thus, the formal construction of solutions of the AI problem is completed.
Nevertheless, to visualize the physical picture of phenomena is appropriate to turn
to the energy spectrum of the intermediate Rydberg quasi-molecule states and, for
clarity, to analyze the structure of its adiabatic terms.
Rydberg States of the XY ** Quasi-Molecule
From the integral equation ( 1.15 ) in the operator form, it follows that the eigenvalue
spectrum of the Rydberg energy of the intermediate complex XY ** is determined
by the poles of the collision T matrix, which satisfy the matrix equation
l; v ;N j Jl v N ih Jl v N j cot "
i X
p 2.E v E N E/
j ih j
D 1 ;
where E v and E N are the energies of vibrational and rotational motions. Matrix rank
for the given value of J equals the total number of channels taken into account
in e C XY C
and X *
C Y configurations. Solutions of the transcendental equation
( 1.28 ) represent a complicated set of complex spectral energy values, the imaginary
parts of which depend on the sign and the magnitude of the total energy E of the
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