Oscillator parity forbidden

More generally, it has been noted [116] that the oscillator strengths for fully allowed ED MD EQ transitions are in the approximate ratio of 1 10 5 10 6, respectively. However, ED transitions are parity forbidden in the case of f-f intraconfigurational transitions, so that the mechanism which enables such transitions for rare earth ions is via crystal-field mixing of fN wave functions with opposite parity wave functions such as fN-1d due to the odd terms HCP = B, C, (i) with f= 1,3,5,7 (which are usually ignored when... 

Kotzian (1991) and Kotzian et al. (1995) reported INDO/S-CI results for transition energies and relative oscillator strengths of the 4f—>4f excitations in the [R(H20) ] (R=Pr, Nd, Tm, n=8,9) complexes. These excitations are parity-forbidden for the free ion (Laporte selection rule), but may gain intensity due to admixture of opposite-parity character in a non-centrosymmetric environment The field of the water ligands leads only to a small perturbation of the free ion energy levels (Pr 4f, Nd 4f, Tm 4f ). Due... 

The induced absorption band at 3 eV does not have any corresponding spectral feature in a(co), indicating that it is most probably due to an even parity state. Such a state would not show up in a(co) since the optical transition IAK - mAg is dipole forbidden. We relate the induced absorption bands to transfer of oscillator strength from the allowed 1AS-+1 (absorption band 1) to the forbidden 1 Ak - mAg transition, caused by the symmetry-breaking external electric field. A similar, smaller band is seen in EA at 3.5 eV, which is attributed to the kAg state. The kAg state has a weaker polarizability than the mAg, related to a weaker coupling to the lower 1 Bu state. 

However, although f f transitions are, in principle, forbidden by the Laporte parity rule, most of the transitions in (RE) + ions occur at the electric dipole (ED) order. As we have already mentioned, this is an ED allowance due to the admixture of the 4f" states with opposite parity excited states 4f" 5d, as a result of the lack of inversion symmetry (ED forced transitions). The oscillator strength, /, for a / f absorption band can be estimated using expression (5.19). We now rewrite this expression as follows ... 

The Laporte rule states that transitions between states of the same parity, u or g, are forbidden i.e. u - g and g - u but g +-> g and u +-> u. This rule follows from the symmetry of the environment and the invoking of the Bom-Oppenheimer approximation, But since, due to vibrations, the environment will not always be strictly symmetrical, these forbidden transitions will in fact occur, though rather weakly (oscillator strengths of the order of 10 4). All the states of a transition-metal ion in an octahedral environment are g states, so that it will be these weak symmetry forbidden transitions (called d-d transitions) that will be of most interest to us when we study the spectra of octahedral complexes. 

Optical transitions between 4f" levels used for optical pumping and stimulated emission are predominantly of electric-dipole nature. Although f-f transitions are forbidden by Laporte s rule, if the rare earth is located in a non-centrosym-metric site, odd-order terms in the expansion of the static (or dynamic) crystal-field admix states of higher, opposite-parity configurations, such as 4f" 5d, into 4f" and transitions become allowed. The oscillator strengths of transitions between J states are small, 10 . - While ab initio calculations of the probabilities for electric-dipole transitions are not possible, spectral intensities can be treated using the Judd-Ofelt approach discussed below. 

---