SOLUTION OF THE TIME-DEPENDENT BOLTZMANN-EQUATION

The time-dependent Boltzmann equation, which describes the propagation of radiation from a point source in a random medium, is solved exactl y in Fourier space. An explicit expression in real space is given in t wo and four dimensions. In three dimensions an accurate interpolation formula is found. The average intensity at a large distance r from the source has two peaks, a ballistic peak at time t=r/c and a diffusion peak at t similar or equal to r(2)/D (With c the velocity and D the di ffusion coefficient). We find that forward scattering adds a tail to t he ballistic peak in two and three dimensions. proportional to(ct-r)(- 1/2) and proportional to-ln(ct-r), respectively. Expressions in the li terature do not contain this tail.