Neutron Scattering

ducing a complex component and were treated by Cayley and Klein (1897) [8] describing
the classical problem of a spinning top .
Classical mechanics shows that a torque exerted on a magnetic moment tî by a magnetic
field H inclined at an angle B relative to the magnetic moment causes the magnetic
moment of the neutron to precess about the direction of the field with the Larmor frequency
WL . The precession frequency is independent of the angle B . Different to the
motion of a spinning top in a gravity field the neutron's motion shows no nutation, its angular
momentum L - hS and its energy is a constant . S (- 2) denotes the spin quantum
number of the neutron and h is Planck's constant divided by 27r . The relation between
angular momentuni L and magnetic moment tî defines the gyromagnetic ratio y
An applied magnetic field will tend to align this magnetic moment and exerts a torque . No
force is exerted by a homogeneous field, so that the resulting equation of motion simply
says that the change of L in time is normal to L and H, i. e . a precession :
L = -yLxH-LXW L (4 .2)
with - yH = WLand y/27r - -2916 .4Hz/Oe .
A magnetic guide field defines a quantization axis and can bc used to maintain the
direction the spin and thus the polarization of the neutron beam, sec Fig . 4 .1 . The
neutron moments will align either parallel or anti-parallel . Guide fields are typically weak
so that the sample magnetization is net significantly influenced, but sufficiently stronger
than for instance the magnetic field of the earth or any other stray magnetic fields frein
the surrounding . Such a guide field may vary is space and two important limits are of
interest (sec Fig . 4 .2 and Fig . 4 .3) :
slow field change :
this so-called adiabatic case means that H slowly changes its
direction with a frequency that is small compared to the Larmor frequency, cW « WL,
such that a neutron moving with a velocity EN keeps its precession mode around the
spatially varying H . This cari be achieved by sufficiently long path fer the variation
of the field or by a sufficiently strong the field H (a WL) .
sudden field change : If the field direction changes suddenly, the polarization of the
neutron cannot follow . Two opposite guide fields can be separated by a current
4-2