In a spherical harmonics expansion it is difficult to fulfil a vacuum boundary condition, e. g. a boundary at which neutrons are only going out but not entering the system. Even with high-order P, approximations such a condition can only be approximatively satisfied. The same thing applies to boundaries between media with very different cross-sections. A possible solution consists of expanding the angular — dependent flux density separately in the two half spaces. The procedure first proposed by Yvon is called double Pi and fulfils exactly the above-mentioned boundary conditions, but may lead to worse approximations in case of big homogeneous layers. Furthermore, it can only be applied to simple geometries (plane or spherical).