Raman Wavefunction: Rayleigh & Raman Scattering Implications

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Regarding Rayleigh and Raman scattering:

I'm trying to understand the implications of the Raman wavefunction, being time independent. It certainly makes the derivation of the resonance Raman cross-section simple, but I'm struggling to understand the role of the imaginary component, especially in bound states.

And can anyone help me figure out which electronic transition is responsible for atmospheric Rayleigh in molecular nitrogen? My intuitions say it's the B3Pi -> A3Sigma, but I've found no literature sources for that yet.

Any insight is appreciated.
 
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Thanks! Raman scattering is an inelastic light scattering process, which occurs when light interacts with molecular vibrations and rotations. The incident light excites a molecule from its ground state to an excited state and the scattered light is shifted in energy, resulting in an observable change in wavelength. This phenomenon is known as a Raman shift. In bound states, the imaginary component of the wavefunction describes the probability of the system transitioning from one energy level to another. In the case of atmospheric Rayleigh scattering in molecular nitrogen, the main electronic transition responsible is the A2Σ+-->X2Σ+ transition. This transition involves the promotion of an electron from the ground state of the nitrogen molecule to its first electronically excited state. This transition is responsible for most of the Rayleigh scattering in the atmosphere.