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Advances in High Energy Physics
Volume 2014 (2014), Article ID 185414, 7 pages
http://dx.doi.org/10.1155/2014/185414
Research Article

Quantized Ultracold Neutrons in Rough Waveguides: GRANIT Experiments and Beyond

Department of Physics, University of Rhode Island, Kingston, RI 02881-0817, USA

Received 12 May 2014; Accepted 9 July 2014; Published 23 July 2014

Academic Editor: Stefan Baessler

Copyright © 2014 M. Escobar and A. E. Meyerovich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

We apply our general theory of transport in systems with random rough boundaries to gravitationally quantized ultracold neutrons in rough waveguides as in GRANIT experiments (ILL, Grenoble). We consider waveguides with roughness in both two and one dimensions (2D and 1D). In the biased diffusion approximation the depletion times for the gravitational quantum states can be easily expressed via each other irrespective of the system parameters. The calculation of the exit neutron count reduces to evaluation of a single constant which contains a complicated integral of the correlation function of surface roughness. In the case of 1D roughness (random grating) this constant is calculated analytically for common types of the correlation functions. The results obey simple scaling relations which are slightly different in 1D and 2D. We predict the exit neutron count for the new GRANIT cell.