  We consider the classical integral equation reformulation of the radiative
transport equation (RTE) in a heterogeneous medium, assuming isotropic
scattering. We prove an estimate for the norm of the integral operator in this
formulation which is explicit in the (variable) coefficients of the problem
(also known as the cross-sections). This result uses only elementary properties
of the transport operator and some classical functional analysis. As a
corollary, we obtain a bound on the convergence rate of source iteration (a
classical stationary iterative method for solving the RTE). We also obtain an
estimate for the solution of the RTE which is explicit in its dependence on the
cross-sections. The latter can be used to estimate the solution in certain
Bochner norms when the cross-sections are random fields. Finally we use our
results to give an elementary proof that the generalised eigenvalue problem
arising in nuclear reactor safety has only real and positive eigenvalues.
