Neutron Scattering

13 . Inelastic neutron scattering : phonons and
magnons
II.
Markus Brader
Physikalisches Institut, Universität zu Köln,
Zülpicher Str . 77, D-50937 Köln
bradenüph2.uni-koeln .de
13 .1 Interaction and scattering law
13 .1 .1 Basic concepts of scattering experiments
Scattering experiments are performed with almost all types of radiation on varions
systems (solids, liquids, gases, atoms, nuclei, . . . ) . 'T'he radiation with well defined initial
properties ( wavevector 1 ; energy E) hits the sample, gets scattered and may be detected
again with well defined final properties (wavevector k' ; energy E') in the angular segment
r2dQ, the schematic picture of the scattering arrangement is drawn in figure 1 . Aim of
any scattering experiment is to obtain information on the states of the sample by use of
the knowledge of the interaction between the radiation (for example neutrons) and the
particles forming the sample . In this chapter we deal with the inelastic neutron scattering
in solids which is till today the most efficient way to study dispersion relations of lattice
vibrations and magnetic excitations .
The initial and final states of the neutron may be denoted by Qz and Q', those of the
sample by ~z and A' . (7 z is characterized by the wavevector k and the energy E = 21rLk2, (7'
respectively. 'The momentum transferred to the sample crystal, Q, and the energy transfer,
E = hw, have to fulfill the conservation laws, Q = 1 - l' and ca = h( 27n, ) 2(k2 - k'2). 'T'he
probability to observe a scattered neutron in the angular segment dQ and in the energy
interval dE' is described by the partial differential cross section which may be obtained
within the Born-approximation, which is a perturbation theory of first order, i .e . one
considers the interaction between radiation and sample crystal to be small .
- (k 'lk)(m/2~)z ~ - a ;,Q; pa;pa i
13- 1