Oscillator strength model, optical

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. 

Dipole oscillator strengths form important input into all stopping models based on Bethe or Bohr theory. Emphasis has frequently been on total /-values which show only little sensitivity to the specific input. More important are differential oscillator-strength spectra, in particular at projectile speeds where inner-shell excitation channels are closed. Spectra bundled into principal or subshells [60] are sufficient for many purposes, but the best available tabulations are based on analysis of optical data rather than on theory, and such data are unavailable for numerous elements and compounds [61]. 

The relative success of the binary encounter and Bethe theories, and the relatively well established systematic trends observed in the measured differential cross sections for ionization by fast protons, has stimulated the development of models that can extend the range of data for use in various applications. It is clear that the low-energy portion of the secondary electron spectra are related to the optical oscillator strength and that the ejection of fast electrons can be predicted reasonable well by the binary encounter theory. The question is how to merge these two concepts to predict the full spectrum. 

The importance of the vibron model lies in the fact that it is the doorway state of the optical absorption. (The two-particle states have no oscillator strength, since we cannot create vibrations in the ground state.) Indeed, the creation of vibrations is subsequent to an electronic excitation of a molecule, in the approximation where the absorbing dipole is the sum of molecular dipoles (with the appropriate phase), which is the approximation of weak intermolecular forces. 

Besides these qualitative differences, there also exist quantitative discrepancies between the Hiickel model for polyenes and the experimental observations. The Hiickel theory predicts an order of magnitude larger oscillator strength in the absorption to the lowest dipole allowed state [4]. The bond length alternation required to fit the optical gap in polyenes within a Hiickel model is twice the experimentally observed bond alternation. Thus, the Hiickel model is mainly of pedagogical interest and one needs to go beyond it for dealing accurately with realistic conjugated systems. 

The theoretical treatments for both optical and tunneling experiments on Q Ds require, first, a calculation of the level structure. Various approaches have been developed to treat this problem, including effective mass-based models, with various degrees of band-mixing effects [50, 52, 54,73], and a more atomistic approach based on pseudopotentials ]69, 74]. Both approaches have been successfully applied to various nanocrystal systems [55, 56, 74—77]. In order to model the PLE data, it is necessary to calculate the oscillator strength of possible transitions, and to take into account the... 

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