Method for measuring the deviation from Lambert's cosine law in the diffuse reflection of ultracold neutrons from material walls

The simulation of the motion of ultracold neutrons is important for estimating their losses, accurately measuring their lifetimes, and describing other experiments. In material traps, it is necessary to take into account not only the specular reflection, but also the diffuse elastic reflection of ultracold neutrons from the walls of a trap. The angular distribution of diffusely reflected neutrons is usually described by Lambert's cosine law, which does not have a strict theoretical justification and is often violated. In this work, an experiment has been proposed to measure the deviation of the angular distribution of diffusely reflected ultracold neutrons from Lambert's cosine law. This deviation can be determined by the difference in the number of neutrons leaving a long, narrow trap for ultracold neutrons through its central and end windows. The performed Monte Carlo calculations corresponding to the proposed experiment have shown a significant effect for different shapes of the trap.