Nuclear Spectroscopy

E X P E R I M E N T 6
Absorption of Gammas by Materials
Figure 6.1. Gammas incident from the left interact with
electrons and nuclei in the absorbing material (crystal) by
Compton-scattering, photoeffect, and pair production, deflecting
many gammas from the original beam direction.
INTRODUCTION
As gammas pass through matter, they interact primarily
by the photoeffect, Compton scattering, and pair
production. If the gammas are traveling in a narrow
beam, any of these three interactions can cause a loss
of gammas from the beam either by deflecting them
along a different direction or by absorbing them.
This is shown schematically in Figure 6.1. The number
of gammas removed (-∆N) from the incident
beam(N o
) is proportional to the number of electrons
and nuclei along the path through the material. The
number of electrons and nuclei is proportional to the
atomic density (ρ) of the material (or the mass density)
and the path length traveled in the material
(∆x). This loss of gammas is expressed as
6.1
The solution to equation 6.1 gives
6.2
∆N =− N ( ρ ∆x)( µ / ρ)
Nx ( ) =
o
Ne o
−( ρ x) µ / ρ
N(x) is the number of gammas remaining after passing
through a thickness of material, x. The linear
attenuation coefficient, µ, is a constant of proportion-
ality in units of inverse centimeters, as indicated in
Figure 6.2. The exponential solution is to be expected,
for anything that grows or diminishes at a
fixed rate, grows or diminishes exponentially. Here
the rate of the diminution of gammas is µ. The ratio,
µ/ρ is called the mass absorption coefficient, where ρ
is the mass density. Corresponding to this definition,
the product ρx is also the thickness with typical units
of mg/cm 2 .
OBJECTIVE
The mass absorption coefficients for lead and aluminum
will be measured for two gamma energies, 661.6
keV and 121 keV. Other energies and absorbing
materials can be measured if there is enough time.
LINEAR ATTENUATION COEFFICIENTS (cm -1 )
1000
100
10
1
0.1
Compton
Photoelectric
Pair Production
Total
0.1 1
ENERGY (MeV)
Figure 6.2 The linear attenuation coefficient, µ,for lead.
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