In the following discussion we use notation of Hauschildt (1992) and Paper I. The
basic framework and the methods used for the formal solution and the solution
of the scattering problem via operator splitting are discussed in detail in
paper I and will thus not be repeated here. We have extended the framework
to solve line transfer problems with a background continuum. The basic
approach is similar to that of Hauschildt (1993). In the simple case of a
2-level atom with background continuum we consider here as a test case,
we use a wavelength grid that covers the profile of the line including the
surrounding continuum. We then use the wavelength dependent mean intensities
and approximate operators
to compute the profile integrated
line mean intensities and
via

and

and are then used to compute an updated value for and the line source function

where is the line thermalization parameter ( for a purely absorptive line, for a purely scattering line). is the Planck function, , profile averaged over the line

via the standard iteration method

where . This equation is solved directly to get the new values of which is then used to compute the new source function for the next iteration cycle.

We construct the line directly from the wavelength dependent 's generated by the solution of the continuum transfer problems. For practical reasons, we use in this paper only the nearest neighbor discussed in paper I. Larger s require significantly more storage and small test cases indicate that they do not decrease the number of iterations enough to warrant their use as long as they are not much larger than the nearest neighbor .