Multiple scattering of solar resonance radiation in the nearby interstellar medium. I
The paper presents approximate solutions obtained for a radiative transfer problem that represents a highly-idealized description of the multiple scattering of solar resonance radiation in the nearby interstellar medium. The problem of a point source in the center of a spherically symmetric cavity imbedded in an infinite uniform medium is solved for a range of cavity radii. First and second-order scattering contributions are calculated, and the Eddington approximation is used to estimate the higher order components of the radiation field. It is shown that for coherent scattering at very large cavity radii, the backscattered intensity from the cavity approaches three times the value deduced from the optically thin solution, in agreement with previous work. It is concluded that an accurate analysis of sky background will require including not only the frequency redistribution, but also the correct spatial distribution of density.