MAGNETIC SCATTERING OF NEUTRONS - Rare Earth Magnetism: Structures and Excitations - page 180

may also be employed. In an actual experiment the directions and the
lengths of k and k are only defined with a limited degree of accuracy,
and the δ -functions occurring in (4.2.10-11) are broadened into peaks
with the shape of the instrumental resolution function ,whichtoagood
approximation is a Gaussian in the four-dimensional (

,ω )-space. If the
resolution function is known, it is possible to deconvolute the scattering
peaks obtained in constant q -scans from the broadening due to instru-
mental effects, and thereby determine the lifetimes of the excitations.
In this chapter, we have concentrated on the magnetic scattering of
neutrons, but they may also be scattered through the interaction, via
nuclear forces, with the nuclei in the sample. This interaction leads to
a cross-section of the same order of magnitude as in the magnetic case,
and it results in analogous phenomena to those discussed above, with
the positions of the atoms replacing the magnetic moments as the fluc-
tuating variables. The elastic Bragg scattering reveals the positions of
the atoms in the crystal, and the elementary excitations appearing in
the correlation functions are phonons. The fluctuations in the nuclear
cross-section, due to the different spin states of the nuclei, give rise to
an incoherent scattering, determined by the self-correlation of the indi-
vidual atoms, in contrast to the coherent scattering, which is governed
by the atomic pair-correlation function, in analogy with the magnetic
scattering discussed above. Incoherence can also be produced by differ-
ent isotopes of a particular element in a crystal, just as the variation of
the magnetic moments in disordered alloys leads to incoherent magnetic
scattering.
The magnetic scattering may be dicult to separate experimentally
from the nuclear component. One possibility is to utilize the different
temperature dependences of the two contributions, since the nuclear
scattering normally changes relatively slowly with temperature. If this
is not adequate, it may be necessary to perform polarized neutron scat-
tering, in which the spin states of the incoming and scattered neutrons
are determined, making it possible to isolate the scattering of purely
magnetic origin (Moon, Riste and Koehler 1969). For further details of
neutron scattering by nuclei in solids we refer to the texts mentioned at
the beginning of this chapter.

κ