Electric-dipole transition strength

They are called, respectively, electric-dipole transition strength (Z>ns), magnetic-dipole transition strength (M ), and rotational strength (R ). Then, the total transition strength is given as + Afjjj 2Rj ). This indicates that the effects for left- and right-circularly... 

The quantityis dimensionless and is the ratio of the strength of the transition to that of an electric dipole transition between two states of an electron oscillating in three dimensions in a simple harmonic way, and its maximum value is usually 1. 

Since the optical transitions near the HOMO-LUMO gap are symmetry-forbidden for electric dipole transitions, and their absorption strengths are consequently very low, study of the absorption edge in Ceo is difficult from both an experimental and theoretical standpoint. To add to this difficulty, Ceo is strongly photosensitive, so that unless measurements arc made under low light intensities, photo-induced chemical reactions take place, in some cases giving rise to irreversible structural changes and polymerization of the... 

The intensity of an electric dipole transition in absorption or emission depends, on one hand, on factors particular to the experiment measuring the intensity, e.g., the number density of molecules in the initial state of the transition and, for absorption experiments, the absorption path length and the intensity of the incident light. On the other hand, the intensity involves a factor independent of the experimental parameters. This factor, the line strength 5(f <— i), determines the probability that a molecule in the initial state i of the transition f <— i will end up in the final state f within unit time. 

If we assume that the initial state i and the final state f are both non-degenerate, then the line strength of the electric dipole transition between them [3] is given by... 

The absorption oscillator strength for an electric dipole transition between an initial state /) and a final state j) is given by... 

Another important quantity in the context of El transitions is the electric dipole line strength, defined as [7]... 

Vibrational circular dichroism arises from the interference of the electric dipole transition moment (p joi and the magnetic dipole transition moment (m )io and is proportional to the rotational strength, / ,o, where... 

The crystal field model may also provide a calciflation scheme for the transition probabilities between levels perturbed by the crystal field. It is so called weak crystal field approximation. In this case the crystal field has little effect on the total Hamiltonian and it is regarded as a perturbation of the energy levels of the free ion. Judd and Ofelt, who showed that the odd terms in the crystal field expansion might connect the 4/ configuration with the 5d and 5g configurations, made such calculations. The result of the calculation for the oscillator strength, due to a forced electric dipole transition between the two states makes it possible to calculate the intensities of the lines due to forced electric dipole transitions. 

The characteristic absorption and emission spectra of lanthanide compounds in the visible, near ultra-violet and infra-red is attributed to transitions between 4/ levels due to the fact that they present a sharp line with oscillators strengths typically of the order of 10 . These transitions are electric dipole forbidden but became allowed as forced electric dipole transitions. 

To estimate the oscillator strengths or transition probabilities for electric-dipole transitions is a very difficult problem. For such a transition, the operator is of the form... 

X being a 4/ wave function. From this expression, one estimates that the oscillator strengths should be about the same as for an ion situated in a noncentrosymmetric field (P 10 6). A rigorous formal treatment for the vibronically induced electric-dipole transitions has been developed by Satten (32-34),... 

The oscillator strength of an electric dipole transition from the / th orbital to the y th orbital is... 

Since the many-electron wave functions are obtained explicitly as linear combinations of the Slater determinants, the oscillator strengths of an electric dipole transition from the ith state to the /th state for linearly polarized light can be calculated by... 

Hence a quantum-mechanical system radiates energy spontaneously at the same rate as a classical oscillating static electric-dipole transition moment of strength ... 

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