Transitions line intensities

The spatial localization of H atoms in H2 and HD crystals found from analysis of the hyperfine structure of the EPR spectrum, is caused by the interaction of the uncoupled electron with the matrix protons [Miyazaki 1991 Miyazaki et al. 1991]. The mean distance between an H atom and protons of the nearest molecules was inferred from the ratio of line intensities for the allowed (without change in the nuclear spin projections. Am = 0) and forbidden (Am = 1) transitions. It equals 3.6-4.0 A and 2.3 A for the H2 and HD crystals respectively. It follows from comparison of these distances with the parameters of the hep lattice of H2 that the H atoms in the H2 crystal replace the molecules in the lattice nodes, while in the HD crystal they occupy the octahedral positions. 

Fig. 11. Intensity of the single mode of Ar+ 514.5 nm as mode is swept through gain curve. The single mode will match the iodine transition line and will be absorbed ( 1).

In [49, 76], the line intensities for electric quadrupole and Zeeman (magnetic dipole) splitting and including the anisotropy of the /-factor are also given for / = 2 <-> 7g = 0 transitions (even-even isotopes, e.g., in the rare earth region or in W, Os). 

Electron correlations show up in two ways in the measured cross sections. If the initial target state is well described by the independent particle Hartree-Fock approximation, the experimental orbital (6) is the Hartree-Fock orbital. Correlations in the ion can then lead to many transitions for ionisation from this orbital, rather than the expected single transition, the intensities of the lines being proportional to the spectroscopic factors S K... 

H. N. Russell analyzes solar spectrum with theoretical transition probabilities and eye estimates of line intensities. Notes predominance of hydrogen (also deduced independently by Bengt Stromgren from stellar structure considerations) and otherwise similarity to meteorites rather than Earth s crust. M. Minnaert et al. introduce quantitative measurements of equivalent width, interpreted by the curve of growth developed by M. Minnaert, D. H. Menzel and A. Unsold. 

Another type of DOUBLE ENDOR, called special TRIPLE , has been introduced by Dinse et al.90 to study proton hf interactions of free radicals in solution. In a special TRIPLE experiment two rf fields with frequencies vp + Av and vp — Av are swept simultaneously. For systems with Tln < T,i this leads to a considerable signal-to-noise improvement and to TRIPLE line intensities which are directly proportional to the number of nuclei with the same hf coupling constant. It should be remembered, however, that in transition metal complexes in the solid state the resonance frequencies are not, in general, symmetrically placed about the free proton frequency vp and that the condition Tln < Tj,i is not always fulfilled. 

Fig. 29. Group-theoretical predictions of the polarizations of the vibronic transitions, allowed to second order, from the individual zero-field levels of the lowest triplet state of 2,3-dichIoro-quinoxaline to vibrational levels of the ground electronic state. Solid line transitions gain intensity by spin-orbit mixing between states which differ in the electronic type of one electron e.g., S n and T . The dashed line transitions require the mixing to occur between states of the same electronic type (e.g., S and T n ) and is expected to be weaker. The dash-dotted transition could involve the favorable mixing between states that differ in the electronic type of one electron, but a spin-vibronic perturbation is needed. (From Tinti and El-Sayed, Ref. ))...

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. 

Here I stands for the intensity of the spectral hnes N is the atom number density in cm Z is the partition function E and y are the energies and degeneracy s of the upper levels, respectively and A and A are the Einstein coefficient and wavelength, respectively, for the observed transitions. When changing the concentration Nt relative to that Nm the line intensities ft and 7m will likewise change, and according to (6.1) one should obtain a cahbration curve with constant slope (Davies et al. 1995 Ciucci et al. 1999 Hou and Jones 2000). 

Spectroscopists have always known certain phenomena that are caused by collisions. A well-known example of such a process is the pressure broadening of allowed spectral lines. Pressure broadened lines are, however, not normally considered to be collision-induced, certainly not to that extent to which a specific line intensity may be understood in terms of an individual atomic or molecular dipole transition moment. The definition of collisional induction as we use it here implies a dipole component that arises from the interaction of two or more atoms or molecules, leading at high enough gas density to discernible spectral line intensities in excess of the sum of the absorption of the atoms/molecules of the complex. In other... 

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

Line and multiplet strengths are useful theoretical characteristics of electronic transitions, because they are symmetric, additive and do not depend on the energy parameters. However, they are far from the experimentally measured quantities. In this respect it is much more convenient to utilize the concepts of oscillator strengths and transition probabilities, already directly connected with the quantities measured experimentally (e.g. line intensities). Oscillator strength fk of electric or magnetic electronic transition aJ — a J of multipolarity k is defined as follows ... 

Unlike line or oscillator strengths and transition probabilities, line intensities are directly measured quantities. 

Table 30.2. Wavelengths A (A), oscillator strengths / and ratios of line intensities I(lP — lD)/I(lP — S) in various approximations (a) for lsz2s2p5 lP — ls22s22p4 lD transition (b) for ls22s2p5 lP — ls22s22p4 lS transition...

For spectra corresponding to transitions from excited levels, line intensities depend on the mode of production of the spectra, therefore, in such cases the general expressions for moments cannot be found. These moments become purely atomic quantities if the excited states of the electronic configuration considered are equally populated (level populations are proportional to their statistical weights). This is close to physical conditions in high temperature plasmas, in arcs and sparks, also when levels are populated by the cascade of elementary processes or even by one process obeying non-strict selection rules. The distribution of oscillator strengths is also excitation-independent. In all these cases spectral moments become purely atomic quantities. If, for local thermodynamic equilibrium, the Boltzmann factor can be expanded in a series of powers (AE/kT)n (this means the condition AE < kT), then the spectral moments are also expanded in a series of purely atomic moments. 

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