# Stern-Gerlach with particles that are not electrically neutral. Can I "ignore" the Lorentz force?

Most realizations of Stern-Gerlach experiments that I'm aware of use electrically neutral particles (e.g. neutrons or silver atoms). In this way, the only deflection that the non-homogeneous magnetic field induces into the particles is the "vertical" deflection arising from the spin magnetic moment, i.e. there's no "horizontal" deflection arising from the Lorentz force $$\mathbf{F} = q (\mathbf{v \times B})$$.

Is there a way to use the same type of Stern-Gerlach apparatus (essentially a non-homogeneous magnetic field) for particles that are not electrically neutral? Couldn't I just ignore the "horizontal" deflection, and still take the "vertical" deflection as an indicator of the spin?

To this day I've never seen or heard of an experimental realization of a Stern-Gerlach with charged particles, so my guess is that there's some conceptual difficulties in "ignoring" the Lorentz force. Is it even correct to say that the deflection created by the Lorentz force is in a direction perpendicular to the direction of the deflection created by the spin interaction?

Stern Gerlach for charged particles is discussed in Gordon Baym's book, "Lectures on quantum mechanics.'' You cannot ignore the Lorentz force since $$\vec \nabla \cdot \vec B = 0$$ requires a field that changes in $$z$$ also change in $$x$$ or $$y$$. That leads to the result that Stern-Gerlach for electrons alone will not be able to resolve the two spots from the spins since the uncertainty in the momentum that causes the deflection from the Lorentz force causes a larger uncertainty in the deflection than the spin force deflection. Stern-Gerlach for ions whose mass is much larger with same electron magnetic moment is possible.