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.