Multiple scattering theory for slow neutrons (from thermal to ultracold)

Abstract

The general theory of neutron scattering is presented, valid for the whole domain of slow neutrons from thermal to ultracold. Particular attention is given to multiple scattering which is the dominant process for ultracold neutrons (UCN). For thermal and cold neutrons, when the multiple scattering in the target can be neglected, the cross section is reduced to the known value. A new expression for inelastic scattering cross section for UCN is proposed. Dynamical processes in the target are taken into account and their influence on inelastic scattering of UCN is analyzed. PACS.28.20.-v Neutron physics, 61.12.Bt Theories of diffraction and scattering

Bulk effects in the coherent inelastic scattering of ultracold neutrons

“…It is clear, that the divergence at ε ′ → ε is integrable. This result for longitudinal thermo-diffusion and for fixed components k ⊥ and k of the initial neutron momentum was obtained in [14].…”

“…[12,13]) and, hence, does not imply rescattering. Strictly speaking, it may be applied only to thermal and cold neutrons (see also [14]). …”

“…Here β ν is the scattering length on the bound nucleus [14] (this quantity slightly differs from b ν ). Zero order amplitudes ψ(ν) = ψ(ρ ν ) in the continuous media approximation were found to satisfy the Schroedinger equation with the optical potential U (ρ) = 2πh 2 n(ρ)β c /m, where β c is the average ("coherent") scattering amplitude.…”

“…In our approach [14], the functions of zero approximation, ψ(k, ν) and ψ(k ′ , ν), are determined by optical potential with the imaginary part, defined only by radiative capture. At the same time, Eq.…”

“…Notice that in the paper [14] we have performed straightforward calculation of the total elastic cross section for a macroscopic plane sample and subbarier neutrons with the use of Eq. (2).…”