Magnetic neutron scattering anti-Bragg solution

摘要

A new solution for the elastic spin magnetic scattering of slow neutrons by a N-electron target is obtained. The angular dependence of the differential cross section (DCS) has very unusual (anti-Bragg) shape for a target, which degenerate ground state has zero z -projection (M = 0) of the total spin. Contrary to usual assumption that neutron is scattered by each atomic spin independently, the scattering by the whole target spin system is considered. The many-electron many-determinant wave functions Ψ_a(x _1,...,x_N) (x_j ≡r_jσ _j) are used for analytical calculations of the scattering amplitude. The total spin square eigenfunctions Θ_(S0)(σ_1,...,σ_N) have been used for the spin part of Ψ_a. Explicit analytical expressions for the DCS are obtained and the initial and final neutron polarization effects are discussed. It is shown that the regular pattern of the anti-Bragg diffraction has no relation to the periodic magnetization of the target.