The Transverse Stern–gerlach Experiment

It is shown theoretically in this paper that if a beam of neutral spin Formula: see text particles incident along the z axis is passed through an inhomogeneous, time-dependent magnetic field of the formFormula: see textthe beam is split into two beams in the x–y plane when the resonance condition, ω = γH 0 , is satisfied. The properties of the beams are similar to those obtained in the ordinary Stern–Gerlach experiment. They represent spins in the two eigenstates of S x in a co-ordinate system rotating at the Larmor frequency about the s axis. For particles of angular momentum Formula: see text, the beam would be split into 2J + 1 beams. For atoms with unequally spaced energy levels E i and eigenfunctions ψ i in the field H 0 k, two beams are split off from the main beam when the resonance condition hω = E i –E j is satisfied. For an initially un-polarized beam, these two beams have eigenfunctions (1/√2)(ψ i ± ψ j ). Magnetic resonance measurements similar to those made using the Rabi modification of the Stern–Gerlach experiment may be performed with the transverse Stern–Gerlach experiment. For charged particles of spin Formula: see text the resonance frequency is γH 0 –ω c where ω c is the cyclotron frequency. The transverse Stern–Gerlach experiment may be used to measure the magnetic moments of charged particles and an experiment on free electrons is being carried out. Magnetic resonance spectroscopy of ions may be studied with this technique. Another interesting application is in the production of beams of polarized nuclei. Since this may be done with nuclei in ions, it may be possible to produce polarized beams of high intensity in a form useful to nuclear physics experiments.