Effect of specular reflection on the storage time of ultracold neutrons in closed vessels

Confinement of ultracold neutrons in a unit radius sphere and in a unit radius infinite cylinder is considered. The neutron distribution is characterized by a function which presents the density of neutrons escaping from a point on a trap surface. It is shown that the time of confinement of ultracold neutrons in vessels is similarly expressed through the average absorption coefficient for all cases when the part of nonspecular reflection exceeds considerably the absorption at a single impact with a wall