The continuum radiation field is modified primarily by photoabsorption, for which the opacity, , is equal to the product of the ion abundance with the total photoionization cross section, summed over all levels.
A model is constructed by dividing the cloud into a set of concentric spherical shells. The radiation field incident on the innermost shell is the source spectrum. For each shell, starting with the innermost one, the ionization and temperature structure is calculated from the local balance equations using the radiation field incident on the inner surface. The attenuation of the incident radiation field by the shell is then calculated. The diffuse radiation emitted by the cloud is calculated using an expression of the formal solution if the equation of transfer:
where is the specific luminosity at the cloud boundary, is the optical depth from to the boundary, and is the emissivity at the radius . Since our models in general have two boundaries, we perform this calculation for radiation escaping at both the inner and outer cloud boundaries. This calculation is performed for each continuum energy bin, and separately for each line. In the case of the continuum, we construct a vector of emissivities, which includes contributions from the escaping fraction from all the levels which affect each energy. For the lines, the emissivity used in this equation is the escaping fraction for that line.