In order to describe the rotational spectra of this class, Hund's coupling case
(b) was chosen as the starting point. The rotational levels are
characterized by the rotational angular momentum quantum number, N, and
the resultant angular momentum quantum number, J, which includes the
total electron spin angular momentum. If the molecule has nuclei with non-zero
nuclear spin, I, these are coupled to J to form the total angular
momentum quantum number F, whereby coupling case
(bJ) is assumed here.
For pure case (b
J)
the electric dipole transitions occur with the selection rules:
N = ± 1,
F = 0, ± 1,
and
J = 0, ± 1,
in the absence of external fields. Since an intermediate coupling case is
actually observed, transitions are allowed for
N = ± 3. The magnetic dipole transitions
occur with the selection rules:
N = 0, ± 2 and
J = 0, ± 1.
![]() |
(eq10) |
where , the vibrational state
dependence of the molecular parameters is given by:
![]() |
(eq11) |
where the Dunham coefficients, Ylj , are defined in section 2 and
![]() |
(eq12) |
![]() |
(eq13) |
The centrifugal distortion terms are defined as:
![]() |
(eq14) |
![]() |
(eq15) |
and | |
![]() |
(eq16) |
With these definitions, the rotational energy levels are given in the form [9]:
![]() |
(eq17) |
![]() |
(eq18) |
The sextic terms, H, of the rotational energy are neglected
because they cannot be determined from the data presently available for the
spectral observations on 3
electronic ground state molecules. The energy equations are utilized with the
selection rules stated above to allow the determination of the molecular
constants
B
,
,
, D
,
,
and
,
. Combining
the data available for various vibrational states allows the derivation of
potential coefficients, ai, and the expansion parameters of
and
Magnetic hyperfine structure has been described by Frosch and Foley
[10] in terms of the determinable parameters,
b and c. The nuclear electric quadrupole hyperfine structure is
described by Amano, et al. [11] and results in
determination of the constant, eQq, as defined in the discussion of
1
ground electronic state
molecules.
Symbols | (See section 2b for additional definitions.) | ||||||
ai | Dunham potential coefficients. | ||||||
![]() ![]() |
Spin-spin coupling parameter in the ![]() | ||||||
![]() ![]() |
Spin-spin vibrational constant (MHz). | ||||||
![]() ![]() |
Spin-rotation coupling parameter in the
![]() | ||||||
![]() ![]() |
Coefficient in the power series expansion of ![]() ![]() | ||||||
![]() ![]() |
Centrifugal distortion correction to ![]() ![]() | ||||||
![]() ![]() |
Centrifugal distortion correction to ![]() ![]() | ||||||
![]() ![]() ![]() |
Expansion coefficients of ![]() ![]() | ||||||
![]() ![]() |
Expansion coefficients of ![]() ![]() | ||||||
b, c | Magnetic hyperfine coupling constants:
|
|