One-mode Raman spectrum example

Choose a vibrational Raman shift magnitude ${\tilde{\nu }}_v=1000\mathrm{c}{\mathrm{m}}^{-1}$, excitation vacuum wavelength ${\lambda }_0=532\mathrm{nm}$ and temperature $T=300\mathrm{K}$. These are original illustrative inputs, not a measured 1928 optical spectrum or a claim about a particular liquid. They giveTake reciprocal lengths in consistent units before converting to nanometres. At $300\mathrm{K}$, $r\simeq 0.00826337$ and $\overline{v}\simeq 0.00833222$. The predicted line-integrated radiant intensity ratio is $0.0126522$, whereas the ideal photon count-rate ratio is $0.0113740$. Thus the radiometric ratio is about $1.27$ percent, rather than the $0.826$ percent obtained by using the Boltzmann factor alone.