Physics and Engineering of Radiation Detection

2.6. Interaction of Neutral Particles with Matter 141

radiation shields around neutron sources, such as nuclear reactors. Deeper penetra-
tion also carries advantages, though. For example, a neutron beam can be used for
non-destructive testing of materials.
Just like photons, a beam of neutrons passing through a material also suffers
exponential attenuation. The intensity of a neutron beam at a distancexfrom
origin can then be evaluated from

I=I 0 e−μnx, (2.6.6)

whereμnis the attenuation coefficient of neutrons. It depends on the type of material
as well as the neutron energy and is usually quoted in dimensions of inverse length.
We can define the mean free path of neutrons by substituting

λn=

1

μn

, (2.6.7)

andx=λnin the above exponential relation. This gives

I 0 −I

I 0

≈ 63 (2.6.8)

which implies thatλncorresponds to the depth of the material that attenuates about
63% of the neutrons.
The attenuation coefficient can also be written in terms of the total nuclear cross-
sectionσt,suchas
μn=Nσt, (2.6.9)

whereNis the number density of nuclei in the material, which can be computed
fromN=NAρ/A,whereNAis the Avogadro’s number,ρis the weight density of
the material, andAis its atomic weight. The attenuation coefficient can then be
computed from

μn=

NAρ

A

σt. (2.6.10)

The above relation is valid only for a single element. In case of a compound with
several elements or isotopes, generally an average attenuation coefficient is computed
by taking weighted mean of total nuclear interaction cross-sections of all the isotopes
present in the sample.

μavn(E)=ρn

[n

∑

i=1

wiσit(E)

]

(2.6.11)

Herewiis the fractional number ofithisotope in the sample ofnisotopes andρnis
thenumberdensity of the sample.

Equation 2.6.6 can be used to experimentally determine the attenuation coeffi-
cient for an elemental isotope since we can writeμnas

μn=

1

x

ln

(

I 0

I

)

. (2.6.12)

Such experiments are generally performed to determine the attenuation coefficients
for materials at specific neutron energies.