12.3. Neutron Spectroscopy 709
B.6 SpinEchoSpectrometer....................
All of the neutron spectroscopy techniques we have discussed so far demand use of
single-wavelength neutrons at a time. A typical reactor source of neutrons emits
neutrons having a broad energy spectrum. One then needs to use a monochromator
to select the neutrons of the right energy needed for the analysis. This is not very
convenient as the process greatly reduces the neutron flux, which is not a very
desirable effect. Spin echo spectrometry is a technique that does not require the
neutrons to be monochromatic for ensuring good energy resolution.
The idea behind spin echo spectrometry is graphically depicted in Fig.12.3.7.
The neutrons from the source are first selected by avelocity selector.Thevelocity
selector is not required to have a high resolution, as a wavelength spread of 10-15%
can be tolerated. The selected neutrons are then made to pass through a polarizer,
which aligns their spins in one direction. The next step is to flip the neutron spin
byπ/2 through aflipperusing externally applied magnetic field. This orients the
neutron spin perpendicular to the magnetic field. The neutrons then travel through
the magnetic field and as a result precess with an angular frequency that is given
by
ω=γB, (12.3.20)
whereγis the neutron’s gyromagnetic ratio andBis the applied magnetic field.ω
is generally known as Larmor frequency. The neutrons keep on precessing until they
reach the sample. We can determine the total precession angle by simply multiplying
the frequency by the time it takes them to reach the sample, that is
θ=ωt. (12.3.21)The timetcan be determined from
t=d
v, (12.3.22)
wheredis the distance traveled by the neutrons having velocityt. The total preces-
sion angle is then given by
θ=
γBd
v. (12.3.23)
Before the neutrons could interact with the sample, their spin is flipped by 180^0 by a
π-flipper. These neutrons then interact with the sample and undergo elastic, quasi-
elastic, and inelastic scatterings. The presence of the magnetic field after the sample
ensures that the neutron keeps on precessing. However now since their polarization
has been changed by 180^0 , they precess in opposite direction as compared to before
the sample. The total angle of precession swept by the neutrons after traveling a
distanced′in a magnetic fieldB′is given by
θ′=−
γB′d′
v′. (12.3.24)
wherev′is the velocity of the neutron after leaving the sample. Here the negative
sign simply signifies the fact that the precession is in the opposite direction. Now,
for simplicity assume that the magnetic field and the distance traveled before and