Analytical Green’s function–based diffusion Monte Carlo (MC) methods have been applied earlier for simulation of reactor noise experiments for measuring the degree of subcriticality in accelerator-driven systems. In this method analytical solution of the diffusion equation is used to construct the probability distribution function for neutron absorption in a medium. This method has several advantages such as speed, elegance, and exactitude but was applicable to a rather restricted class of problems, such as an infinite or bare homogeneous medium.

In the present paper, we further develop the analytical Green’s function (analytical diffusion kernel) approach to demonstrate its utility in a wider class of problems like a heterogeneous medium with the same or different diffusion coefficients. We provide mathematical and numerical proofs of the validity of certain recipes that were proposed for heterogeneous systems. We also investigate whether and to what extent the diffusion theory–based MC can be improved to give results closer to transport theory, particularly in situations wherein diffusion theory methods are otherwise inapplicable.