The neutron Berry phase

The neutron Berry phase is found from an exact analytic solution of the Shr$\ddot {\rm o}$dinger equation in a constant magnetic field $B_{0}$ and a perpendicular radiofrequency field $b$ rotating with an angular frequency $\omega$. The solution is found for arbitrary values of $B_{0}$, $b$, and $\omega$. The Berry phase is shown to be a linear approximation or the exact value in the parameter $\omega$/$B_{0}$ when this parameter is small.