Impact of a Reflecting Material on a Search for Neutron--Antineutron Oscillations using Ultracold Neutrons

We investigate neutron--antineutron oscillations of ultracold neutrons in a storage bottle represented by a one-dimensional potential. The experimental sensitivity is determined by the annihilation rate of antineutrons. Its dependence on the antineutron reflectivity and the relative phase shift between the neutron and the antineutron wavefunctions by a reflection from the wall is derived. Optimization of the antineutron pseudopotential was found crucial to maximize the sensitivity of the experiment. Furthermore, methods are discussed for determining the antineutron pseudopotential, which has only been studied indirectly thus far.