Substantial magnetic contribution to the neutron scattering length
Gadolinium has 7 spin-polarized electrons in the $f$ shell. Due to half-filling, the total orbital angular
momentum is zero ($S_{7/2}$ state).
For the Gd magnetic moment oriented along the z-axis and assuming that the scattering angle is small,
what is the total (nuclear + magnetic) scattering length for a neutron beam with its spin polarized
(a) along $+z$, (b) along $-z$, (c) along $+x$? In each case, what is the spin orientation of the scattered
neutrons?
