The gamma current intensity (flux) and the gamma emission (leakage) of a homogeneous, spherical medium are derived by inserting a source spectrum in the Boltzmann transport equation. In the range of photon energies from 0.5 Mev to 10.5 Mev, Compton scattering by electrons of the medium dominates the energy degradation of photons, so that one may use Klein-Nishina cross sections for the transfer kernel. Lumping the flux into energy groups permits an approximation of the transport equation as a matrix equation. Numerical solutions for the flux and leakage spectra, found by inverting the matrix equation, agree well with the results of previous theoretical studies.