A model for Raman scattering based on classical physics

A model for Raman scattering based on classical physics 

The electric field of the light wave varies with time. If a fixed molecule is irradiated with monochromatic radiation of frequency Vq, expressed in Hertz, which is plane polarised in the z direction, E as a function of time is given by 

Since depends on as well as E the properties of the molecule can change via a. In the present context a varies with time as a consequence of the vibrations of the molecule, since the ease with which electrons may be displaced by the electric field depends on how tightly they are bound to the nuclei, which in tirm depends on the intemuclear separation. The result of the time dependence of a and E on m can be seen by considering the simple example of a single diatomic molecule. 

For a diatomic molecule the difference from equilibrium in the intemuclear distance at time t, Ar t) can be written 

Using the postulate that the polarisabiHty of the diatomic molecule depends linearly on Ar, the component of a can be written  

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