  The geometric phase (GP) acquired by a neutron passing through a uniform
magnetic field elucidates a subtle interplay between its spatial and spin
degrees of freedom. In the standard setup using thermal neutrons, the kinetic
energy is much larger than the typical Zeeman split. This causes the spin to
undergo nearly perfect precession around the axis of the magnetic field and the
GP becomes a function only of the corresponding cone angle. Here, we perform a
plane wave analysis of the GP of very slow neutrons, for which the precession
feature breaks down. Purely quantum-mechanical matter wave effects, such as
resonance, reflection, and tunneling, become relevant for the behavior of the
GP in this low energy scattering regime.
