Physics and Engineering of Radiation Detection

710 Chapter 12. Radiation Spectroscopy

after the sample are equal, that is,B′=Bandd′=d. In this case the above
equation becomes

θ′=−

γBd

v′

(12.3.25)

This equation implies that in case of elastic scattering in which there is no change
in neutron’s velocity, that isv′=v, we will have

θ′=−θ, (12.3.26)

which is the so calledecho condition, hence the namespin echo spectroscopy.Ifthe
neutron undergoes inelastic scattering, it can either gain or loose energy. Let us
assume that the neutron looses some energy. In this casev′<vand consequently
|θ′|>|θ|. This shift in the angle of precession can be measured by detecting the
neutron polarization. However an easier way to do this is to vary the magnetic field
such that the echo condition gets satisfied. The magnitude of the magnetic field will
then be a measure of the change in neutron velocity. This echo condition according
to equations 12.3.23 and 12.3.24 can be written as

B′d′

v′

=

Bd

v

. (12.3.27)

And if the distances traveled by the neutrons before and after the sample are equal
then the magnetic field needed for echo condition will be give by

B′=B

v′

v

. (12.3.28)

The values ofBandvare known a priori while that ofB′is determined when
then the echo condition is satisfied. The final velocity of the neutrons can then be
determined from the above equation. Fig.12.3.7 shows the basic components of a
spin echo spectrometer.

π/2 Flipper πFlipper π/2 Flipper

Neutrons

Neutron Guide Polarizer

Velocity Selector Detector

Sample

Precession Chamber Precession Chamber

Sample

Chamber

Figure 12.3.7: Principle design of a spin echo neutron spectrometer.

12.4MassSpectroscopy

Mass spectroscopy is a methodology that is extensively used to determine properties
of charged particles. The basic principle of this technique is to dissociate the sample
into smaller fragments and then let them pass through a high magnetic field. The
charged particles get deflected in the magnetic field with the degree of deflection
proportional to their mass to charge ratio (m/e). These deflected particles are then
collected by a position sensitive detector, such as a microchannel PMT.