All the resources I've seen on calculating refractive index of gases appear to give equations with various "magic constants", i.e. the equations are fits to experimental data. But I'd like to understand how refractive index of a gas can be calculated directly from the theory.

So, suppose molecular number density of a gas is fixed, and the gas consists of single species of molecules. How can its refractive index be calculated?

  • $\begingroup$ There are models in classical E&M in which atoms subject to a EM wave are treated as damped-driven oscillators, and from the parameters of the oscillators you should be able to get a indexes of refraction. All that remains (hah!) is to perform a complete, microscopic, quantum calculation (including emission) to give you the parameters of the oscillation... $\endgroup$ – dmckee --- ex-moderator kitten May 3 '19 at 22:54
  • $\begingroup$ @dmckee OK, suppose we do have these parameters. How are they combined to yield the refractive index of the gas? $\endgroup$ – Ruslan May 4 '19 at 12:00

The response of a gas is simply related to the atomic polarisability, inphase and out of phase. The polarisability can be obtained from atomic quantum chemical calculation. Take a look at cxro.lbl.gov to see how this is done for x-rays. Note that in the case of xrays the simple relation to atomic polarisability is even valid for solids and liquids.

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