Spectral lines oscillator strength

Figure 12. Electronic spectra and the results of open-shell PPP-like semiempirical calculations for radical ions. The vertical lines represent the allowed transitions, the wavy lines with arrows the forbidden ones. The right side scales denote the calculated spectral intensities, where f stands for the oscillator strength. Top left the absorption curve (146) redrawn to the log e vs. 0 (cm ) form calculations are taken from (59). Top right taken from (11). Bottom left taken from (143). Bottom right taken from (136), the absorption curve redrawn to the log e vs, 0 (cm" ) form.

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 or transition probability is the individual characteristic of a separate atom or ion. However, in reality we usually have to deal with a large number of them, where, depending on the specific physical situation, various elementary processes of excitation, ionization, recombination, etc. may take place. Real spectral lines are characterized by the intensity of radiation, defined in the conditions of natural isotropic excitation as... 

Taking advantage of advances in computational atomic and plasma physics and of the availability of powerful supercomputers, a collaborative effort - the international Opacity Project - has been made to compute accurate atomic data required for opacity calculations. The work includes computation of energy levels, oscillator strengths, photoionization cross-sections and parameters for pressure broadening of spectral lines. Several... 

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. 

The oscillator strength, P, of a spectral line for an electric dipole transition from the component A) of the ground state to the component B) of the excited state may be written... 

The sharp spectral lines of bound exciton complexes can be very intense (large oscillator strength). The line intensities will, in general, depend on the concentrations of impurities and/or defects present in the sample. 

The measured peak absorption coefficient, Kmax, for a discrete impurity transition depends on the oscillator strength of the transition and on the impurity concentration. The measured profile of a recorded line is the convolution product of its true profile by the instrumental function of the spectroscopic device used. It depends significantly on the ratio of the true FWHM of the line to the spectral resolution (the spectral band width) of the spectroscopic device. When this ratio is of the order of 3 or above, the measured FWHM can be considered as the true FWHM and the observed profile is close to the true profile. For lower values of this ratio, the measured FWHM increases steadily while the measured value of Kmax decreases, and it is assumed that when the ratio becomes l/3 or smaller, the measured FWHM is the spectral resolution and the measured profile the instrumental function. This effect is known as instrumental broadening. For isolated lines, the absorption coefficient can be integrated over the entire line to give an integrated absorption I A ... 

Penkin, N. P. and Komaravskii, V. A., "Oscillator strengths of spectral lines and lifetimes of excited levels of atoms of rare earth elements with unfilled 4f shells,"... 

Intensity variations reveal a variety of effects, both in the bound spectrum and above threshold. In order to study them, one needs to introduce the concept of oscillator strength, as a preliminary to discussing various factors which influence the intensities of spectral lines. 

In terms of the quantum-mechanical dipole matrix element Vjk 2 which determines the strength of an allowed spectral line from the wave-functions of states j > and k >, the oscillator strength is defined as... 

All these quantities are equivalent since they all depend on the same transition matrix element, although their units are not the same. The / value has the advantage of being a dimensionless quantity. With broad band illumination, the appropriate quantities are those which are integrated over the spectral feature, such as the / value or the Einstein coefficient. With narrow band illumination (i.e. a monochromatic source narrower than the spectral feature), it is appropriate to use a quantity which is defined point by point within the line profile, such as the absorption coefficient, the cross section, or the differential oscillator strength df/dE. 

Fig. 3. Quantum chemical calculations of optical absorption spectra of Ag4+. (a) The most stable rhombic structure, (b) The second lowest-energy isomer of the T-shape, of which total energy is higher than that of (a) by 0.02 eV. The bars indicate oscillator strengths solid lines show spectral prohies. Bond lengths in the A unit are indicated in the insets. The spectrum obtained for the most stable structure (a) best reproduces the experimental spectrum in Fig. 2. (Adapted from Ref. 7.)...

Fig. 5. The optical absorption spectrum and the electronic structure of Vs" ", (a) Experimental data, where a photodissociation action spectrum of a rare-gas complex, Vs+Ar, was measured by observing a photofragment, Vs+. (b) Density-functional calculation of the spectrum for the most stable isomer illustrated in the inset. The bars show oscillator strengths the solid line a spectral profile, (c) Density-of-states profiles of the majority or and the minority-spin electrons obtained by the density-functional calculation. The shadows indicate occupied electronic levels. The vanadium pentamer ion. Vs" ", was shown to be in the spin triplet state with a trigonal bipyramid structure, where the average bond length was 2.4...

It is well known that the accurate radiative decay widths and probabilities and oscillator strengths of atomic transitions are needed in astrophysics and laboratory, thermonuclear plasma diagnostics, fusion research and laser physics, etc. [1-27]. Spectral lines are usually characterized by their wavelength and oscillator strength. Typically, transition probabilities are known less accurately than wavelengths. Moreover, for many spectral lines of heavy atoms and especially multicharged... 

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