Used to Describe the Interaction between Optical Centers and Their Surroundings

Models Used to Describe the Interaction between Optical Centers and Their Surroundings 

In this section we will first consider the configurational coordinate diagram 4,7) that describes the interaction of an optical center with its surroundings in the absence of center-center interaction. Later we will deal with the interaction between two centers that results in energy transfer (4,8). 

Let us consider a dopant ion in a host lattice and assume that it shows luminescence upon illumination. What we will have to discuss is the interaction of the dopant ion with the vibrations of the lattice. The environment of the dopant ion is not static the surrounding ions vibrate about some average positions, so that the crystalline field varies. The simplest model to account for the interaction between the dopant ion and the vibrating lattice is the single-configurational coordinate model (4, 7). 

In this model we consider only one vibrational mode, viz., the so-called breathing mode in which the surrounding lattice pulsates in and out around the dopant ion (symmetrical stretching mode). This mode is assumed to be described by the harmonic oscillator model. The configurational coordinate (Q) describes the vibration. In our approximation it represents the distance between the dopant ion and the surrounding ions. In ruby this Q would be the Cr -0 distance. 

If we plot energy vs. Q we obtain for the electronic states parabolas (harmonic approximation). This is presented in Fig. 3 for the electronic ground state g and one electronic excited state e. Further Qo presents 

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