= Neutron Stern-Gerlach splitting
{title2=$F_z=\mu_z\partial_zB_z,\quad\mu_z=\pm\gamma_n\hbar/2$}
An electrically neutral <neutron> still has a <magnetic moment> $\boldsymbol\mu=\gamma_n\mathbf S$. A collimated beam passing through an inhomogeneous <magnetic field> experiences the force derived from $H=-\boldsymbol\mu\cdot\mathbf B$. In a region whose field axis is approximately fixed, a <spin one-half> neutron has two field-axis <spin eigenstates>, producing two allowed transverse forces and two separated beam components after a drift. A homogeneous field can cause <Larmor precession> but cannot separate positions through this force.
The neutron's negative <gyromagnetic ratio> interchanges which spin projection moves toward increasing field; it does not change the number of branches. An unpolarized beam gives equal ideal populations. A beam prepared in one field-axis eigenstate populates only one branch, so splitting into two observed spots presupposes both components and sufficient spatial resolution.
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