Calvo Padilla, María Luisa2023-06-202023-06-202000-07-210022-372710.1088/0022-3727/33/14/306https://hdl.handle.net/20.500.14352/59066© 2000 IOP Publishing Ltd. The author is grateful to Dr. W. M. Gibson (Center for X-ray Optics, State University of New York at Albany) for an interesting correspondence and comments regarding guided neutron beams, capillary optics and neutron fibres, and to Mr. Gabriel F. Calvo for some computational help when fitting the data. The constructive criticisms of the (anonymous) referees are acknowledged. This work is dedicated to the memory of Dr. Gustavo Torres-Cisneros.The confined propagation of slow neutrons along waveguides of a small cross section (fibres), discussed theoretically some time ago and demonstrated experimentally by other authors later, is analysed further. Motivated by those experiments, a three-dimensional quantum-mechanical treatment of the associated bending losses is presented. An approximate (two-parameter) formula is derived for the transmission coefficient Upsilon of the curved fibre, which displays its explicit dependence on the curvature radius Rcu, for 0<Rcu< + ∞. By adjusting one of the parameters (b), consistently with the theoretical analysis, and by fitting the other, the approximate formula describes all measured data for Upsilon. The parameter b (which accounts for the experimental data for Upsilon at large Rcu) allows the estimation of the number of effectively excited modes in the fibre.engjournal articlehttp://dx.doi.org/10.1088/0022-3727/33/14/306http://iopscience.iop.org/open access535OpticsÓptica (Física)2209.19 Óptica Física