Non-coherent scattering in subordinate line-V. Solutions of the transfer problem

We present several examples of the numerical solution of the radiative transfer in subordinate lines. Using a simplified physical model that yields the line source function analogous to the usual two-level-atom form modified by the presence of the redistribution function R_v in the scattering integral, we have solved the transfer problem for isothermal, plane-parallel atmospheres, both finite and semi-infinite. For finite atmospheres, we have found substantial differences between the solutions with R_v and those with complete redistribution. On the other hand, for semi-infinite atmospheres the complete redistribution appears to be a good approximation, at least for a_l{reversed tilde equals}a_u (damping parameters for the lower and upper levels, respectively). It is shown that the effect of R_v becomes more pronounced with increasing ratio a_u/a_l. Finally, it is demonstrated that an approximate form for R_v analogous to that of Kneer for R_II serves as a very good approximation for computing the line profiles, particularly in the line wings.