Theoretical and conceptual analysis of the celebrated 4π-symmetry neutron interferometry experiments

In 1975, two experimental groups have independently observed the 4$\pi$-symmetry of neutrons' spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal (analogous to the Mach-Zehnder interferometer of light optics). In this article, we provide a complete analysis of the experiment, both from a theoretical and conceptual point of view. Firstly, we solve the Schr\"odinger equation in the weak potential approximation, to obtain the amplitude of the refracted and forward refracted beams, produced by the passage of neutrons through one of the three plates of the LLL interferometer. Secondly, we analyze their passage through a static magnetic field region. This allows us to find explicit expressions for the intensities of the four beams exiting the interferometer, two of which will be interfering and show a typical 4$\pi$-symmetry, when the strength of the magnetic field is varied. In the last part of the article, we provide a conceptual analysis of the experiment, showing a neutron's phase change, when passing through the magnetic field, is due to a longitudinal Stern-Gerlach effect, and not to a Larmor precession. We also emphasize that these experiments do not prove the observability of the sign change of the wave function, when a neutron is 2$\pi$ rotated, but strongly indicate that the latter, like any other elementary "particle," would be a genuinely non-spatial entity.