Transition Probabilities—Oscillator Strengths

Spectral lines are often characterized by their wavelength and intensity. The line intensity is a source-dependent quantity, but it is related to an atomic constant, the transition probability or oscillator strength. Transition probabilities are known much less accurately than wavelengths. This imbalance is mainly due to the complexity of both theoretical and experimental approaches to determine transition probability data. Detailed descriptions of the spectra of the halogens have been made by Radziemski and Kaufman [5] for Cl I, by Tech [3] for BrIwA by Minnhagen [6] for II. However, the existing data on /-values for those atomic systems are extremely sparse. 

Oscillator strength, transition probability, lifetime and line intensity... 

MBPT significantly improves the electron transition wavelengths, line and oscillator strengths, transition probabilities as well as the lifetimes of excited levels. Therefore, it seems promising to generalize such an approach to cover the cases of more complex electronic configurations having several open shells, even with n > 2. 

Certain sum rules are known for oscillator strengths and transition probabilities as well. So, we can define the oscillator strength and probability of the transition between terms, respectively ... 

The sensitivity of the AAS determination is defined by the slope of the calibration curve in its initial straight part. A convenient characteristic of the sensitivity is the characteristic concentration - the analyte concentration that produces 1% absorption (or 0.0044 absorbance) signal. The characteristic concentrations of the elements for flame atomizers are between 0.01 and 10mgl , for electrothermal atomizers - 2-3 orders of magnitude lower. Factors affecting the sensitivity are the oscillator strength (the probability) of the corresponding electron transition, the type of the atomizer - flame or electrothermal - and the efficiency of atomization. 

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. 

Thus, in the saddle-poinl approximation, the absorption coefficient is the product of the averaged density of states (which is essentially the probability to find the necessary disorder fluctuation) and the oscillator strength of the optical transition between the two inlragap levels ... 

A term frequently used in place of the molar absorptivity e to describe the probability of a transition is the oscillator strength f, which can be related to e in the following way ... 

The dipole oscillator strength is the dominant factor in dipole-allowed transitions, as in photoabsorption. Bethe (1930) showed that for charged-particle impact, the transition probability is proportional to the matrix elements of the operator exp(ik r), where ftk is the momentum transfer. Thus, in collision with fast charged particles where k r is small, the process is again controlled by dipole oscillator strength (see Sects. 2.3.4 and 4.5). 

The literature on transition probabilities (or oscillator strengths) is vast, rapidly growing and difficult to summarize. A small selection for atoms and molecules is given in Allen, AQ and larger selections in... 

Probability of transitions. The Beer-Lambert Law. Oscillator strength... 

The corresponding quantum mechanical expression of s op in Equation (4.19) is similar except for the quantity Nj, which is replaced by Nfj. However, the physical meaning of some terms are quite different coj represents the frequency corresponding to a transition between two electronic states of the atom separated by an energy Ticoj, and fj is a dimensionless quantity (called the oscillator strength and formally defined in the next chapter, in Section 5.3) related to the quantum probability for this transition, satisfying Jfj fj = l- At this point, it is important to mention that the multiple resonant frequencies coj could be related to multiple valence band to conduction band singularities (transitions), or to transitions due to optical centers. This model does not differentiate between these possible processes it only relates the multiple resonances to different resonance frequencies. 

Relativistic Quantum Defect Orbital (RQDO) calculations, with and without explicit account for core-valence correlation, have been performed on several electronic transitions in halogen atoms, for which transition probability data are particularly scarce. For the atomic species iodine, we supply the only available oscillator strengths at the moment. In our calculations of /-values we have followed either the LS or I coupling schemes. 

The relativistic quantum defect orbitals lead to closed-form analytical expressions for the transition integrals. This allows us to calculate transition probabilities and oscillator strengths by simple algebra and with little computational effort. 

In Tables -A, we report oscillator strengths for some fine structure transitions in neutral fluorine, chlorine, bromine and iodine, respectively. Two sets of RQDO/-values are shown, those computed with the standard dipole length operator g(r) = r, and those where core-valence correlation has been explicitly introduced, Eq. (10). As comparative data, we have included in the tables /-values taken from critical compilations [15,18], results of length and velocity /-values by Ojha and Hibbert [17], who used large configuration expansions in the atomic structure code CIVS, and absolute transition probabilities measured through a gas-driven shock tube by Bengtson et al. converted... 

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. 

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