Physics and Engineering of Radiation Detection

692 Chapter 12. Radiation Spectroscopy

Example:

In an XDS experiment a first order diffraction peak was found to be at

2 θ=37^0. If the wavelength of the x-rays used in the study was 1.3 ̊A, find

the atomic plane spacing corresponding to the observed peak.

Solution:

A diffraction peak occurs when the Bragg condition 12.1.14 is satisfied, that

is

2 dsinθ=nλ.

This can be rearranged to give

d=

nλ

2sinθ

Substituting the given values ofn=1,λ=1. 3 × 10 −^10 m,andθ=37^0 /2=

18. 50 , in the above equation gives

d =

(1)

(

1. 3 × 10 −^10

)

(2) [sin (18. 50 )]

=2. 048 × 10 −^10 m

=2. 048 ̊A.

12.2SpectroscopyofChargedParticles

12.2.Aα-ParticleSpectroscopy

A large number of radionuclides emitα-particles of well defined energy. Since these
particles are emitted from the nucleus of the atom, their spectroscopic parameters
allow one to deduce information about the nuclear structure. This makesα-particle
spectroscopy a very valuable tool for nuclear physics. The usefulness of the spec-
troscopy has fueled a lot of research and development into not only the techniques
and methods but also the associated equipment.
Atypicalα-particle spectroscopy setup is shown in Fig.12.2.1. It consists of a
vacuumed enclosure for source and the detector, a pulse amplification system, and
a pulse analyzer. In the following we will look at these units individually.
A vacuumed enclosure for the source and the detector is absolutely necessary
to avoid parasitic absorption ofα-particles in the space between the source and the
detector. The reader might recall that the range ofα-particles emitted by radioactive
sources in air is very small, of the order of a centimeter. Even if the source and the
detector are placed very near to each other, there would still be some air between
them. Since the cross section of air molecules forα-particles is very high, there would
be significant absorption leading to loss of information and lowering of the signal to
noise ratio. The latter effect is due to the statistical nature ofα-particle interactions
leading to addition of a statistical noise term in the expression for the signal to noise
ratio. There are two ways to avoid the parasitic absorption ofα-particles. One is to
place the source inside the active volume of the detector, which would ensure total