The perturbation operator is
H
0
¼
X
i\j
e
2
=r ij
The energies for all of the terms associated to the electronic configuration can be
calculated and expressed by the Condon–Shortley parameters F 0 F 2 and F 4 . These
parameters are abbreviations for the various repulsion integrals in the perturbation
determinant and allow the values can be determined by detecting the experimental
atomic transitions. The energy expressions as a function of these parameters are
independent of the atom, but the parameter values are there. The entire atomic
spectrum is fitted by the same F parameter values.
For the V(III) ion d
2
E
3 P À
3 F
ð
Þ¼15B
E
1 D À
3 F
ð
Þ¼5B þ 2C
B ¼ 866 cm
À1 and C=B ¼ 3:6:
Racah redefined the Condon–Shortley parameters to simplify the energy separation between the states
Scheme 3.1 Energy levels
obtained for a d
2
configuration
42
3 Perturbation Theory
H
0
¼
X
i\j
e
2
=r ij
The energies for all of the terms associated to the electronic configuration can be
calculated and expressed by the Condon–Shortley parameters F 0 F 2 and F 4 . These
parameters are abbreviations for the various repulsion integrals in the perturbation
determinant and allow the values can be determined by detecting the experimental
atomic transitions. The energy expressions as a function of these parameters are
independent of the atom, but the parameter values are there. The entire atomic
spectrum is fitted by the same F parameter values.
For the V(III) ion d
2
E
3 P À
3 F
ð
Þ¼15B
E
1 D À
3 F
ð
Þ¼5B þ 2C
B ¼ 866 cm
À1 and C=B ¼ 3:6:
Racah redefined the Condon–Shortley parameters to simplify the energy separation between the states
Scheme 3.1 Energy levels
obtained for a d
2
configuration
42
3 Perturbation Theory