  In this paper, we investigate moment methods from a general point of view
using an operator notation. This theoretical approach lets us explore the
moment closure problem in more detail. This gives rise to a new idea, proposed
in [Levermore2005, Levermore2009], of how to improve the well-known Pn
approximations. We systematically develop a diffusive correction to the Pn
equations from the operator formulation - the so-called Dn approximation. We
validate the new approach with numerical examples in one and two dimensions.
