Neutron waveguides with finite repulsive potential in clad

Abstract

The interaction of an incoming slow neutron with a straight semi-infinite material waveguide (physically, a very lengthy one) located in vacuum (clad) in the infinite three-dimensional (3D) space is studied. The waveguide creates an attractive potential on the neutron. The physical quantum-mechanical wave phenomena are: (i) reflection and scattering of the neutron by the waveguide and (ii) its confined propagation along the latter, in specific propagation modes. The direct application of standard scattering integral equations meets several difficulties, arising mainly from the infinite length of the waveguide and (ii). New and more convenient 3D scattering integral equations are proposed and discussed, using suitable Green functions, adequate for the semi-infinite waveguide and accounting for (i) and the above difficulties. Approximate formulae for the probability amplitudes and fluxes for (i) and (ii) are given: in particular, the formulas for slow neutron confined propagation extend the ones given previously for optical waveguides. Some detailed applications and numerical computations for two-dimensional media and waveguides are presented.