# Article

**Keywords:**

spherical harmonics; transport of neutrons

**Summary:**

In this contribution, we will use the \textit{Maxwell-Cartesian spherical harmonics} (introduced in [1,2]}) to derive a system of partial differential equations governing transport of neutrons within an interacting medium. This system forms an alternative to the well known $P_N$ approximation, which is based on the expansion of the directional dependence into tesseral spherical harmonics ([3,p.197]). In comparison with this latter set of equations, the Maxwell-Cartesian system posesses a much more regular structure, which may be used for various simplifications that could be advantageous from computational point of view.