= Rayleigh attenuation from refractivity
{title2=$L_{\rm att}=3N\lambda^4/[32\pi^3(n-1)^2]$}
In a dilute nonmagnetic medium of isotropic independent polarizable particles, $n-1\simeq N\alpha/(2\epsilon_0)$ and the <Rayleigh scattering> cross-section is $8\pi^3\alpha^2/(3\epsilon_0^2\lambda^4)$. Eliminating <polarizability> and setting direct-beam attenuation coefficient to $N\sigma$ gives the title relation. It describes scattering out of a narrow beam, not absorption of all radiant <energy>. It assumes fixed <number density>, negligible <correlations>/local-field corrections and a scalar <polarizability>; molecular anisotropy, aerosols and stratification require additional information.
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