text: In cases of a discrete spectrum, the observed  at a particular frequency  can be treated as a sum of contributions from each transition, 
  where  is the contribution at  from the  transition,  is the absorption coefficient for the  transition, and  is a bandshape function (). Because eigenstates  and  depend on the applied external field, the value of  varies with field. It is frequently useful to compare this value to the absorption coefficient in the absence of an applied field, often denoted 
  When the Zeeman effect is small compared to zero-field state separations, line width, and  and when the line shape is independent of the applied external field , first-order perturbation theory can be applied to separate  into three contributing Faraday terms, called , , and . The subscript indicates the moment such that  contributes a derivative-shaped signal and  and  contribute regular absorptions. Additionally, a zero-field absorption term  is defined. The relationships between , , and these Faraday terms are 
  for external field strength , Boltzmann constant , temperature , and a proportionality constant . This expression requires assumptions that  is sufficiently high in energy that , and that the temperature of the sample is high enough that magnetic saturation does not produce nonlinear  term behavior. 
  Though one must pay attention to proportionality constants, there is a proportionality between  and molar extinction coefficient  and absorbance  for concentration  and path length . 
  These Faraday terms are the usual language in which MCD spectra are discussed. Their definitions from perturbation theory are 
  where  is the degeneracy of ground state ,  labels states other than  or ,  and  and  label the levels within states  and  and  (respectively),  is the energy of unperturbed state ,  is the  angular momentum operator,  is the  spin operator, and  indicates the real part of the expression.