Oscillator strength, theoretical expression

C. Intensity Calculations.—The theoretical expression for the oscillator strength of a transition is given by4 ... 

Oscillator Strength (the/ number).—A theoretically derived quantity obtained from the transition moment and often used to express the... 

For weak coupling cases, Hush showed that the intensity of an intervalence transition was related to the extent of coupling between donor and acceptor. The derivation (11) begins by considering the theoretical expression for oscillator strength,... 

In order to obtain a theoretical expression for the oscillator strength, perturbation theory may be used to treat the interaction between electromagnetic radiation and the molecule. Since an oscillating field is a perturbation that varies in time, time-dependent perturbation theory has to be used. Thus, the Hamiltonian of the perturbed system is = 0) +... 

Hush applied Mulliken s theories of the transition dipole moment of charge transfer bands to the specific question of IT bands in mixed-valence complexes. By equating theoretical and experimental expressions for /, where / is the oscillator strength of the intervalence band, it is possible to derive an expression for metal-metal coupling (//ad). 

Table I. Theoretical expressions for the "oscillator strengths" of the LA, LO, TA, and TO phonon-assisted transitions in indirect materials. The subscript I refers to the phonon branch being considered. The spin orbit split band, is considered.

Table II. Theoretical expressions for the oscillator strength of the r-L LA and TO phonons. For the LA phonon, scattering from 12 5 is included. 

The theoretical expression for the absorption coefficient in this energy region is given by Eqs. (1), (2) and (4), and hence Bto = A f g. The constant Ag can be evaluated from known materials parameters. Thus we can obtain a value for fq-g (=Bq g/Ag ). Using this value, the expression for the oscillator strength listed in Table I and the experimentally determined ratio K o = 1.0 we compute U g and V-pg individually. From these values, the expressions for yTg and Vq-g from Eqs. (23), optical matrix elements (obtained from k " calculations), energy denominators obtained from the optical transitions and known phonon frequencies we find ... 

The quantitative treatment of the intensities of 3+ lanthanide absorption bands relates an experimentally determined quantity, a normalized band envelope, to a theoretical model based on the mechanisms by which radiation can be absorbed. The integrated absorption bands observed in a solution of known concentration can be used to calculate the number of classical oscillators in one ion, which is more commonly referred to as the probability for absorption of radiant energy P (oscillator strength) by the expression (Hoogschagen, 1946) ... 

Judd (1962) and Ofelt (1962) independently derived expressions for the oscillator strength of induced electric dipole transitions within the f configuration. This was a signal accomplishment. Much of the highly significant theoretical interpretation of the fluorescence process and the prediction of the properties of solid state lanthanide lasers, ch. 35, was made possible by this work. Since their results are similar, and were published simultaneously, the basic theory has become known as the Judd-Ofelt theory. However, Judd s expression, eq. (24.6), was cast in a form that could be directly related to oscillator strengths derived from lanthanide solution spectra, and he was the first to show that the model satisfactorily reproduced the experimental results for Nd (aquo) and... 

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