Oscillator Strength Smakulas Formula

Let us now establish a way in which to relate / x p, or the transition probability given in Equation (5.14), with experimental measurements, such as the absorption spectrum. 

Considering our single two energy level center, it is easy to understand that the area under the absorption spectrum, /a co) dco, must be proportional to both /x and the density of absorbing centers, N. In order to build up this proportionality relationship, it is very common to use a dimensionless quantity, called the oscillator strength, f. This magnitude has already been introduced in the previous chapter (Section 4.3), when treating the classical Lorentz oscillator. It is defined as follows  

it can be demonstrated (see Appendix A4) that the area under the absorption spectrum is related to / and to the density of absorbing centers, N, by 

For ions in crystals of high symmetry, as in the case of our reference octahedral ABe center, the correction factor is Eioc/Eo = (n + 2)/3 (Fox, 2001), where n is the refractive index of the medium. Although this correction factor is not strictly valid for centers of low symmetry, it is often used even for these centers. Thus, assuming this local field correction and inserting numerical values for the different physical constants, expression (5.21) becomes 

The E center is an electron trapped at a negative Cl vacant site. These centers can be created in NaCl by irradiation or by additive coloration, as shown in the next chapter (Section 6.5). The band at 443 nm corresponds to a certain concentration, iV, of E centers that have been introduced by the irradiation process. The other band peaking at about 280 nm is related to other types of color center (which are formed by F center aggregation), beyond the scope of this example. 

---