Loss rate of ultracold neutrons due to the absorption by trap walls in large material traps

Abstract: The most accurate neutron lifetime measurements now use the material or magnetic traps of ultracold neutrons (UCN). The precision of these experiments is determined by the accuracy of estimating the neutron loss rate. In material UCN traps the main source of neutron losses is the absorption by trap walls. In this paper we analyze the standard methods and their approximations for the calculation of UCN absorption rate by the walls of material traps. We emphasize the approximations used both in the standard analytical formulas and in the numerical Monte-Carlo simulations. For the two simplest trap geometries, rectangular and cylindrical, we obtain analytical formulas for this absorption rate provided the UCN velocity distribution is isotropic at trap bottom. Then we perform numerical calculations of UCN velocity distribution and absorption rate taking into account the diffuse elastic UCN reflections by trap walls obeying two different laws: Lambert`s cosine law and isotropic reflection. We compare the results with the standard estimation methods and discuss the differences. We indicate the difference between the UCN number and density velocity distribution. Our results may be useful to resolve the puzzling four-second discrepancy between the magnetic and material-trap measurements of neutron lifetime.