Neutron fibres: a three-dimensional analysis of bending losses

The confined propagation of slow neutrons along waveguides of a small cross section (fibres), discussed theoretically some time ago and demonstrated e xperimentally by other authors later, is analysed further. Motivated by tho se experiments, a three-dimensional quantum-mechanical treatment of the ass ociated bending losses is presented. An approximate (two-parameter) formula is derived for the transmission coefficient Y of the curved fibre, which d isplays its explicit dependence on the curvature radius R-cu, for 0 < R-cu < +infinity. By adjusting one of the parameters (b), consistently with the theoretical analysis, and by fitting the other, the approximate formula des cribes all measured data for Y. The parameter b (which accounts for the exp erimental data for Y at large R-cu) allows the estimation of the number of effectively excited modes in the fibre.