Optical methods reflection angles and refraction are used to get RI of non ionized gas and slightly ionized gas. Strongly ionized gas loses transparency and must be evaluated by dispersion, scattering angles and intensities.
To my opinion Your case needs interferometric measurement due to small changes of gas index refraction even in the case of ionization. It is known that Releigh interferometer with two gas cell (initial and ionized) in interferometers sleeves will give You chance to record shift of interferometer pattern when You will ionize a gas in one of two cells.From regeistered shift under given wavelength You can calculate inde[ refraction of ionized gas. Details of this approach You can find in good optical books.
I agree with Dr.Eugene answer, where you can calculate refractive index for both (ionized and nonionized) gas in another way, where you can take the reflectance data vis range of wavelengths and after that by equation refractive index n=(1+R^0.5)/(1-R^0.5) , and you can plot between wavelengths and refractive index to get the average value or can you determined the optimum value at corresponding wavelength.