Nonadiabatic spin transitions in an inhomogeneous magnetic field

Model calculations are presented for nonadiabatic passage of an oriented spin through a reversing solenoidal magnetic field; these are useful for comparison with experiments described elsewhere. The model corresponds closely to the well-known Landau-Zener-Stueckelberg model of a two-state curve crossing in molecular collision theory; various modifications appropriate to the Majorana problem are considered. The resulting transition amplitudes are discussed for the $F=1$ hyperfine component of the 2²S1/2 metastable state of atomic hydrogen as an example.