Attenuation Coefficients & Buildup Factors for Various Materials in Gamma Shielding, Study Guides, Projects, Research of Advanced Physics

Information on the attenuation coefficients and buildup factors for different materials used in gamma radiation shielding. The concepts of attenuation coefficient, linear attenuation coefficient, buildup factor, and their significance in shielding materials. It also includes experimental data for lead, aluminum, and copper, and discusses the differences in attenuation coefficients obtained using collimation, sca window method, and multi-channel analyzer method.

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2011/2012

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BASIC DEFINITIONS
ATTENUATION COEFFICIENT
Since, it is known that electromagnetic radiations interact with the atoms of the absorbing
material mainly by three phenomena given as;
Photoelectric Effect Compton Scattering Pair Production
Here we define a parameter as; the probability of interaction per unit length in a given
material is called the linear attenuation coefficient µ of that material.
Thus theoretically it can be defined as follows:
Where τ, δc and k are the photoelectric, Compton scattering and pair production
probabilities respectively.
The intensity of gamma rays is attenuated by a shielding material according as:
( )
Where I0 is the intensity in the absence of shielding material and I(x) is the intensity
after the insertion of a shield of thickness x in a fixed source detector geometry.
The above equation can also be written as follows:
( ) ( )
This is the equation of a straight line with slope equal to -µ. It should be noted that the
last two equations are based on the assumption that the scattered photons are
completely removed from the gamma rays beam. The quantity I(x) then gives what is
called the uncollided intensity.
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BASIC DEFINITIONS

ATTENUATION COEFFICIENT

Since, it is known that electromagnetic radiations interact with the atoms of the absorbing

material mainly by three phenomena given as;

 Photoelectric Effect  Compton Scattering  Pair Production

Here we define a parameter as; the probability of interaction per unit length in a given

material is called the linear attenuation coefficient μ of that material.

Thus theoretically it can be defined as follows:

Where τ, δc and k are the photoelectric, Compton scattering and pair production

probabilities respectively.

The intensity of gamma rays is attenuated by a shielding material according as:

Where I0 is the intensity in the absence of shielding material and I(x) is the intensity

after the insertion of a shield of thickness x in a fixed source detector geometry.

The above equation can also be written as follows:

This is the equation of a straight line with slope equal to -μ. It should be noted that the

last two equations are based on the assumption that the scattered photons are

completely removed from the gamma rays beam. The quantity I(x) then gives what is

called the uncollided intensity.

BUILDUP FACTOR

For a relatively thin layer of shielding material, these equations result in good

approximation of the measured intensity because the probability that a scattered photon

will reach the observation point is small. Contrarily, if the shield is relatively thick, some

photons which have suffered multiple collisions within the shielding material may reach

the observation point. In this case the intensity at the observation point is more than the

uncollided intensity. The effect of these scattered radiations is included by means of

what us called build up factor, defined as:

Build up factor depends on the shield material, its thickness, geometry and energy of

gamma rays. It is generally expressed as a function of μx. Thus we have:

Experimentally, B can be determined by in turn forming the good geometry and bad

geometry in the experimental setup. B is simply the ratio of bad geometry counts and

good geometry counts from a gamma source shielded by a certain thickness of shield

material.

BAD & GOOD GEOMETRY

An arrangement of the source, shield and detector in which photons scattered in the

shield material are also able to reach the detector is called “bad geometry” and if only

those photons are counted which reach the detector without undergoing any collision in

the shield then this geometry is called “good geometry”.

CALCULATION AND RESULTS

GOOD GEOMETRY

MATERIAL Thickness

(cm)

GOOD GEOMETRY Atten.

Coeff. c1 c2 c3 mean LOG Slope

LEAD 0.8 27304 27405 27522 27410.33 4.437914 - 0.43317 0.
ALUMINIUM 0.65 55331 55997 55616 55648 4.74545 - 0.06882 0.
COPPER 1.3 31394 31063 30894 31117 4.492998 - 0.23718 0.

y = - 0.4332x + 4.

4

0 1 2 3

ln(N)

Thickness

LEAD

y = - 0.0688x + 4.

0 1 2 3

ln(N)

Thickness

ALUMINIUM

y = - 0.2372x + 4.

4

0 2 4 6

ln(N)

Thickness

COPPER

BAD GEOMETRY

MATERIAL Thickness

(cm)

BAD GEOMETRY BUILDUP
FACTOR

c1 c2 c3 mean LOG

LEAD 0.8 739452 722976 738955 733794.3 5.86557435 26.
ALUMINIUM 0.65 648908 646738 641452 645699.3 5.81003034 11.
COPPER 1.3 796397 791918 789173 792496 5.89899708 25.

20

70

0.5 1 1.5 2 2.

Build up Factor^ Thickness

LEAD B.Factor

10

12

14

16

0.5 1 1.5 2 2.

Build up Factor

Thickness

ALUMINIUM B.Factor

0

50

100

1 2 3 4

Build up Factor Thickness

COPPER B.Factor

BAD GEOMETRY

MATERIAL Thickness

(cm)

BAD GEOMETRY BUILDUP

c1 c2 c3 mean LOG

LEAD 0.9 363241 363223 363264 363242.6667 5.560197 3.
ALUMINIUM 0.65 689765 690033 690328 690042 5.838876 2.
COPPER 1.3 390245 390881 391351 390825.6667 5.591983 3.

3

8

13

0.8 1.3 1.8 2.3 2.

Build Up Factor

Thickness (cm)

LEAD Buildup factor

0.5 1 1.5 2

Build Up Factor

Thickness (cm)

Aluminium Buildup factor

0

5

10

15

1 2 3 4

Build up factor

Thickness (cm)

Copper Buildup factor

MULTI CHANNEL ANALYZER METHOD

GOOD GEOMETRY

MATERIAL Thickness

(cm)

GOOD GEOMETRY Atten

Coeff counts LOG Slope

LEAD 0.75 14968694 7.175184 - 0.44629 1.
ALUMINIUM 0.65 30032423 7.47759 - 0.08174 0.
COPPER 1.25 15402867 7.187602 - 0.26508 0.

y = - 0.4463x + 7.

6

7

0.5 1.5 2.

ln(N)

Thickness (cm)

Lead β Attenuation Coeff

y = - 0.0817x + 7.

0.5 1 1.5 2

ln(N)

Thickness (cm)

Aluminium β Attenuation Coeff

y = - 0.2651x + 7.

6

7

1 2 3 4

ln(N)

Thickness (cm)

Copper β Attenuation Coeff

RESULTS & DISCUSSION

Summarily, from the above data, it can be concluded that the attenuation coefficients for

each absorber used in this experiment are as follows:

ATTENUATION COEFFICIENTS μ (cm

-

MATERIAL
METHOD OF GEOMETRY
COLLIMATOR SCA MCA

Aluminum (^) 0.158462 0.225852 0.

Copper 0.546117 1.040876 0.

Lead 0.997407 1.726762 1.

Since the definition of attenuation coefficient μ is based originally on the assumption

that the gamma ray beam is collimated, its values calculated for the three materials

using good geometry method of collimation can be regarded as the standard results. It

can be seen that the values of μ obtained by using good geometry method of MCA are in

good agreement with the standard results obtained by collimation but in case of SCA,

the difference between the values obtained by using SCA good geometry method and the

standard results is significant. Its reason can be that counts corresponding to uncollided

gamma rays reaching up to the detector can be collected more accurately by using MCA

spectrum of gamma rays than using SCA because MCA channel window is much smaller

than that achievable in SCA and also the channel number corresponding to energy of

gamma rays coming from the source can be located in MCA spectrum.

The build up factor B was also calculated for different thicknesses of the three materials

in each of the three cases of good geometry by forming their corresponding bad

geometry arrangements. Then for each material, build up factor as a function of

thickness was plotted. From plots, it has been observed that B increases with thickness.

The reason is that by increasing thickness of the shield material, intensity of uncollided

gamma rays emerging from the shield decreases due to increasing probability of

interaction with the shield material atoms.

In case of collimation method, it has been noted from build up factor plots for the three

materials that B increases with thickness almost linearly but almost exponentially in

case of SCA.