Radiation Transfer in the Cavity and Shell of Planetary Nebulae
  We develop an approximate analytical solution for the transfer of
line-averaged radiation in the hydrogen recombination lines for the ionized
cavity and molecular shell of a spherically symmetric planetary nebula. The
scattering problem is treated as a perturbation, using a mean intensity derived
from a scattering-free solution. The analytical function was fitted to Halpha
and Hbeta data from the planetary nebula NGC6537. The position of the maximum
in the intensity profile produced consistent values for the radius of the
cavity as a fraction of the radius of the dusty nebula: 0.21 for Halpha and
0.20 for Hbeta. Recovered optical depths were broadly consistent with observed
optical extinction in the nebula, but the range of fit parameters in this case
is evidence for a clumpy distribution of dust.
