LS
|
|
Spin orbit coupling, with the Ω
dependence from the Wigner-Eckart theorem; see for example Lefebvre-Brion and
Field, 2nd Edition Equation 3.4.36:

The perturbation parameter is the reduced matrix element arranged so that Λ' > Λ and Λ' > 0
(or S' > S if Λ' = Λ). It is perhaps more normal to quote the value including the 3j
symbol, but this is ambiguous when the spin-orbit operator connects
more than one component of a pair of states. Some common non-zero
values of the 3j symbol are tabulated below.
S.
|
Σ'
|
S
|
Σ
|
|
½
|
-½
|
½
|
½
|
|
½
|
½
|
½
|
½
|
|
1
|
0
|
0
|
0
|
|
1
|
1
|
0
|
0
|
|
1
|
1
|
1
|
1
|
|
1
|
1
|
1
|
0
|
|
|
Luncouple
|
J+nL-n+J-nL+n
|
L uncoupling; Using the default n = 1 this can be used to model the term omitted from the rotational operator.
The perturbation parameter is the value of the matrix element:

for Λ > 0 with the matrix element of L- derived by symmetry.
|
Suncouple
|
J+nS-n+J-nS+n |
S uncoupling. (Note that this term with
n = 1 is present in the normal
Hamiltonian within a single vibronic state; it only makes sense to add it as a
perturbation between states.) It checks for ΔΛ = 0 and |ΔΣ| = n, but does not check for ΔS = 0. S
is taken from the Ket.
|
Homog
|
|
Simple homogeneous perturbation with ΔΩ = 0; Use only if one of the other types is not appropriate.
|
aL
|
aI.L
|
Nuclear Spin Orbit perturbation
|
e
|
|
Nuclear magnetic dipole perturbation
|
eQq1 |
|
Nuclear electric quadrupole perturbation |