Effect of lateral leakage on neutron waves

Abstract A mathematical description is given for a neutron wave propagating parallel to the surface of a semi-infinite medium or of a slab. Cercignani's method of singular eigenfunction expansions is applied under the assumption of one-speed isotropic scattering. Half-range orthogonality and closure relations for the eigenfunctions are derived, with the necessary precautions taken to account for the zeros of the dispersion function inside the area spectrum. The analog of the Milne problem is solved and the complex extrapolated endpoint evaluated. Several coefficients in an expansion of the latter quantity in terms of two characteristic parameters are computed. The results are used to derive an asymptotic solution of the slab problem, where a complex transverse buckling appears. For typical experiments on large assemblies Im(B2) is sufficiently small to be neglected.