Opacity

The Einstein coefficients (Einstein 1917)ulProbability that atom will emit a quantumhν in time dt and solid angle dω is A uldt dωContribution of spontaneous emission coeff.j νis j νρ = N uA ulhν where N uis the number of atomsexcited to level u per unit volume.I νProbability for stimulated emission per atom giving quantum hνin time dt and solid angle dω is B ulI νdt dωI νulProbability for absorption by atom of quantum hνin time dt and solid angle dω is B luI νdt dωEnergy of radiation absorbed per unit pathlength and frequency, from beam withintensity I ν:κ ν ρ II ν ν = N lB lu II ν ν hν − N lB ul II ν ν hν