  We analyze the depolarization of ultracold neutrons confined in a magnetic
field configuration similar to those used in existing or proposed
magneto-gravitational storage experiments aiming at a precise measurement of
the neutron lifetime. We use an extension of the semi-classical Majorana
approach as well as an approximate quantum mechanical analysis, both pioneered
by Walstrom et al. [Nucl. Instr. Meth. Phys. Res. A 599, 82 (2009)]. In
contrast with this previous work we do not restrict the analysis to purely
vertical modes of neutron motion. The lateral motion is shown to cause the
predominant depolarization loss in a magnetic storage trap. The system studied
also allowed us to estimate the depolarization loss suffered by ultracold
neutrons totally reflected on a non-magnetic mirror immersed in a magnetic
field. This problem is of preeminent importance in polarized neutron decay
studies such as the measurement of the asymmetry parameter A using ultracold
neutrons, and it may limit the efficiency of ultracold neutron polarizers based
on passage through a high magnetic field.
