2.2 Experimental Methods
57
time taken to travel from moderator to sample (distance l 1 , time t 1 ), and the time
taken for the scattered neutron to travel from the sample to the detector (distance l f ,
time t 2 ). It therefore follows that
t tot =
l 1
v 1
+
l 2
v 2
=
l 1
2E i
m n
+
l 2
2E f
m n
(2.44)
In Eq. 2.44, E f , l 1 and l 2 are all fixed by the geometry of the instrument. Hence,
the time taken to travel to the detector uniquely defines the incident energy of the
neutron, and correspondingly, E tr .
2.2.2.3 Neutron Scattering
In a neutron scattering experiment, an incident beam of neutrons (neutral subatomic
particles with mass, m n , approximately equal to that of a proton) is scattered from a
sample. This scattering can be the result of magnetic interactions, or due to nuclear
interactions. Scattering due to magnetic interactions is outside the scope of this work,
and will not be discussed here; an introduction can be found in Ref. [72].
The total nuclear scattering is defined by the differential scattering cross section,
dσ
d
= b
2
=
σ t
4π
(2.45)
which describes the amount of total scattering, σ t into the elementary scattering cone
of solid angle d per unit time. This depends on the nuclear scattering length, b.
The scattering according to Eq. 2.45 forms the base for diffraction experiments.
As was discussed Sect. 2.1.2, INS is an inelastic process, and the detected neutrons
depend both on the solid angle at which they are scattered, and also on their energy.
This is captured in the partial differential cross-section for a system of N atoms,
which must therefore be considered as,
d
2
σ
dd E f
= b
2 k f
k i
N S( Q, ω)
(2.46)
where k =
2π
λ
is the wave vector for the incident (k i ) and final (k f ) neutron.
The term S( Q, ω) is the scattering function, and describes the probability that
the scattering process will change the energy of the system by an amount ω, and its
momentum by Q = k. Because both the energy and angle of the final scattered
neutron are fixed on TOSCA, this also fixes k f . The value of Q is therefore dependent
on E tr , and TOSCA probes a narrow stripe in (Q,ω) of kinematic space [70].
The scattering described in Eqs. 2.45 and 2.46 account for the elastic and inelastic
scattering processes. However, due to nuclear effects (isotope and spin effects), the
57
time taken to travel from moderator to sample (distance l 1 , time t 1 ), and the time
taken for the scattered neutron to travel from the sample to the detector (distance l f ,
time t 2 ). It therefore follows that
t tot =
l 1
v 1
+
l 2
v 2
=
l 1
2E i
m n
+
l 2
2E f
m n
(2.44)
In Eq. 2.44, E f , l 1 and l 2 are all fixed by the geometry of the instrument. Hence,
the time taken to travel to the detector uniquely defines the incident energy of the
neutron, and correspondingly, E tr .
2.2.2.3 Neutron Scattering
In a neutron scattering experiment, an incident beam of neutrons (neutral subatomic
particles with mass, m n , approximately equal to that of a proton) is scattered from a
sample. This scattering can be the result of magnetic interactions, or due to nuclear
interactions. Scattering due to magnetic interactions is outside the scope of this work,
and will not be discussed here; an introduction can be found in Ref. [72].
The total nuclear scattering is defined by the differential scattering cross section,
dσ
d
= b
2
=
σ t
4π
(2.45)
which describes the amount of total scattering, σ t into the elementary scattering cone
of solid angle d per unit time. This depends on the nuclear scattering length, b.
The scattering according to Eq. 2.45 forms the base for diffraction experiments.
As was discussed Sect. 2.1.2, INS is an inelastic process, and the detected neutrons
depend both on the solid angle at which they are scattered, and also on their energy.
This is captured in the partial differential cross-section for a system of N atoms,
which must therefore be considered as,
d
2
σ
dd E f
= b
2 k f
k i
N S( Q, ω)
(2.46)
where k =
2π
λ
is the wave vector for the incident (k i ) and final (k f ) neutron.
The term S( Q, ω) is the scattering function, and describes the probability that
the scattering process will change the energy of the system by an amount ω, and its
momentum by Q = k. Because both the energy and angle of the final scattered
neutron are fixed on TOSCA, this also fixes k f . The value of Q is therefore dependent
on E tr , and TOSCA probes a narrow stripe in (Q,ω) of kinematic space [70].
The scattering described in Eqs. 2.45 and 2.46 account for the elastic and inelastic
scattering processes. However, due to nuclear effects (isotope and spin effects), the