In this expression, W c, v (E) represents the product of the Brillouin zone -averaged transition probability at the energy E with the joint density of states, J c, v (E) ; φ is a broadening function, representing the role of scattering in smearing out the energy levels. In general, the broadening is intermediate between Lorentzian and Gaussian ; for an alloy it is somewhat closer to Gaussian because of strong scattering from statistical fluctuations in the local composition on a nanometer scale.