Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2021 / Module NE1 / 3 / b

For the prescribed homogeneous one-group model, number balance isUse steady state, $\partial n/\partial t=0$, and the diffusion approximation $\mathbf{J}=-D\nabla \varphi$. A spatially constant $D$ givesFor a spherically symmetric scalar field,Dividing by $D$ reproduces the requested radial equation. The assumptions are a steady source, spherical symmetry, homogeneous effective coefficients, a single energy-group description and a diffusion closure. In particular, replacing the general production term by the supplied $(\eta -1){\Sigma }_a\varphi$ is a model assumption, not a general identity for heterogeneous reactor materials.