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Introduction
Build Up Factor
The main objective of this work is to calculate the Build up factor build up factor for slabs of different shields of different materials such as Aluminum, Iron, Copper using Cs-137 Gamma rays source of energy 641KeV. Build up factor is defined as “The ratio of the intensity of the total radiation reaching a point, to the intensity of the primary radiation reaching the same point”.
The gamma ray build up factor represents a necessary correction factor in design calculation of radiation shielding. In laboratories where the shielding is an important principle to protection from nuclear radiation. As materials, used for shielding, because scatter radiation to reach the observation point and due to a number of scattered photons that reach to the observation point the measured intensity of radiation after passing a material is higher than that of expected. So build up factor is included in the calculation for measuring the correct intensity.
Attenuation
As x rays or gamma rays pass through different materials, some of the photons interact with the matter and their energy can be absorbed or scattered. This absorption and scattering is called attenuation. The linear attenuation coefficient (μ) of materials describes the fraction of a beam of x-rays or gamma rays that is absorbed or scattered per unit thickness of the absorber. It can also be defined as the fixed probability of absorbing or scattering of radiation per length of absorber. This probability depends upon the nature of atoms of absorber and as well as on its number density and the energy of the source.
Attenuation Mechanisms
Interaction between radiation and materials:
A large number of interaction mechanisms between the atoms of the absorbing material and gamma rays having energy between 20KeV and 10MeV have been found. The most significant of these are Photoelectric Effect, Compton Effect, Pair Production and Simple scattering (Rayleigh Scattering).
Simple Scatter (Rayleigh Scattering).
Rayleigh scattering (named after Lord Rayleigh) is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. It can occur when light travels in transparent solids and liquids, but is most prominently seen in gases. The incident photon energy is much less than the binding energy of the electron in an atom. The photon is scattered without change of energy. But Raleigh scattering is important for low energy photons and high Z material. It is the common practice to ignore the Rayleigh scattering in shielding calculation.
Figure1: Demonstration of Rayleigh scattering
Characteristic X-rays
When energy of the incident photon are high (wavelength is small as compare to the dimension of atom) as compare to the binding energy of the electron in an atom so it eject an electron from
Figure 3: Demonstration of Photo electric effect
Compton Scattering
When photon energy is much greater than the electron binding energy and only part of this is given up during the interaction with an outer valence electron (the binding of the valance electrons is relatively weak, hence the free).The photon is scattered with reduced energy and the energy of the electron is dissipated through ionization
Figure 4: Demonstration of Photo electric effect
This shows that the change in wavelength following a scattering event depends only on the scattering angle; it neither depends on the energy of the incident photon nor on the nature of the scatterer. As a consequence, a low-energy, long wavelength photon will lose a smaller percentage of its energy than a high-energy ,short-wavelength photon for the same scattering angle. Equation also shows that the electron cannot be scattered through an angle greater than 90 ◦. This scattered electron is of great importance in radiation dosimetry because it is the vehicle by means of which energy from the incident photon is transferred to an absorbing medium. The Compton electron dissipates its kinetic energy in the same manner as a beta particle and is one of the primary ionizing particles produced by gamma radiation (photons).
Pair Production.
Photon whose energy exceeds 1.02 MeV may, as it passes near a nucleus spontaneously disappear, and its energy reappears as a positron and an electron .Each of these two particles has a mass of m 0 c 2,^ or 0.51 MeV, and thetotal kinetic energy of the two particles is very nearly equal to E (gamma) – 2 m 0 c 2.This transformation of energy into mass must take place near a particle, such as a nucleus, for the momentum to be conserved. The kinetic energy of the recoiling nucleus is very small. This higher threshold energy is necessary because the recoil electron, which conserves momentum, must be projected back with a very high velocity, since its mass is the same as that of each of the newly created particles. The cross section, or the probability of the production of a positron–electron pair, is approximately proportional to Z^2 + Z and is therefore increasingly important as the atomic number of the absorber increases. The cross section increases slowly with increasing energy between the threshold of 1.02 MeV and about 5 MeV. For higher energies, the cross section is proportional to the logarithm of the quantum energy. This increasing cross section with increasing quantum energy above the 1.02-MeV threshold accounts for the increasing attenuation coefficient ,After production of a pair, the positron and electron are projected in a forward direction (relative to the direction of the photon) and each loses its kinetic energy by excitation, ionization, and bremsstrahlung, as with any other high- energy electron. When the positron has expended all of its kinetic energy, it combines with an electron and the masses of the two particles are converted to energy in the form of two quanta of 0.51 MeV each of annihilation radiation. Thus, a 10-MeV photon may ,in passing through a lead absorber, be converted into a positron–electron pair in which each particle has about 4 MeV of kinetic energy. This kinetic energy is then dissipated in the same manner as beta particles. The positron is then annihilated by combining with an electron in the absorber, and two photons of 0.51 MeV each may emerge from the absorber (or they may undergo Compton scattering or photoelectric absorption). The net result of the pair production interaction in this case was the conversion of a single 10-MeV photon into two photons of 0.51 MeV each and the dissipation of 8.98 MeV of energy.
Total Attenuation Coefficient
Total attenuation coefficient of a material can be written as the sum of all the individual
probabilities for attenuation of gamma rays by the various interactions, thus
μ = ζ + δc + k (1)
Where ζ, δc and k are the photoelectric, Compton scattering and pair production probabilities respectively.
Dependance of intensity of a radiation on thickness of a material
Let I is the intensity of gamma rays beam incident on a shield of thickness x, the change in the intensity dI over a thickness dx is
dI α I(x) (2)
dI α dx (3)
In equation form,
dI = -μI(x)dx (4)
The solution of the above equation is the general exponential law of radiation
I(x) = I 0 ି܍ μ ܠ^ (5)
Where I 0 is intensity in the absence of shielding material and I(x) is the intensity at thickness x of shielding material in a fixed source detector geometry. Here, μ is the linear coefficient of
attenuation. It is the function of atomic number of atoms of absorbing material and energy of
incident radiations.
Mass attenuation coefficient:
Sometimes another quantity, mass attenuation coefficient μm is defined as follows:
μ (^) m = μ ૉ
where ρ is density of the material.
Taking natural logarithm equation (5) on both sides, we get
ln ( I(x)) = ln (Io) - μx ------------------ (6)
This is equivalent to a linear equation of the form
y=mx+c --------------------(7)
where m (slope) = - μ and c (y-intercept) = ln (I (^) o )
Equation(1) and (2) are applicable only to a narrow collimated beam of Gamma rays and are
based on the assumption that the scattered photons are completely removed from the beam.
Where I(x) is called the Uncollided Intensity i.e. the intensity photons do not collide with the
particles within the shield. Equation(1) is valid for thin layer of shield material as the probability
of scattered photons to reach the observation plane is small and the measured intensity is the
Uncollided intensity
For a thick shield material ,photons suffer multiple collisions and may reach the observation
point. In this case some of the photons will be also counted in addition to Uncollided intensity .The effect of these scattered radiation is included by the mean which called Build Up F
Build up factor = B = ܡܜܑܛܖ܍ܜܖ ܑ ܌܍܌ܑܔܔܗ܋ܖܝା܌܍܌ܑܔܔܗ܋ ܡܜܑܛܖ܍ܜܖ ܑ ܌܍܌ܑܔܔܗ܋ܖܝ
Since equation (1) is a very useful and simple relation to find the intensity of a radiation in a
material of small thinness. But there is an important fact, which snatches the simplicity of the
relation. That fact becomes important when practical situations are dealt. Practically, the intensity of any radiation is measured by some sort of detector. In deriving the above relation, we
have given equal importance to absorbed and scattered parts of radiations. But if scattered
(backscattered or sideways scattered) radiations also reach the detector, most of the detectors
cannot differentiate between those radiations coming directly from source and those coming after
scattering or produced by other secondary photon emission mechanisms.
So a correction factor known as buildup factor is added in the equation (1) which changes it to
(4).
I(x) = B(x,Eγ) I 0 ି܍ μ ܠ^ --------------------- (8)
where B(x, Eγ) is the buildup factor. The values B(x, Eγ) for different material are available.
B(μx)=Ae -aμx^ –(1-A)e- bμx
Where A ,a,b are functions of material and Gamma energy
Methods for the measurement of attenuation Coefficient
and mass attenuation coefficient.
Good Geometry
In such an arrangement only those photons are allowed to reach the detector which suffer
no collision with the shield or the photons which suffer Compton scattering with the shield are
not counted.
Bad Geometry
It is an arrangement of source, shield and the detector in which scattered photons in the
shield are also able to reach the detector. Bad geometry counts are always greater than good
geometry counts.
Fig. Bad geometry arrangement
3.4.3 Formation of Good Geometries :
- Good geometry can be formed by using lead collimators. In such a way that the source, detector and
collimators all must be in a line. Collimator near the source provide us a narrow fine beam of Gamma
rays, while the collimator near the detector allow a rays coming directly from the first collimator without
collision with the shield.
- Good geometry can also be obtained by using SCA. In this case an electronic window is formed by
adjusting the lower and upper levels of SCA at a position that only full energy pulses can pass through it.
- In another method of good geometry formation by MCA. In this method the spectra of photons emitted
by a source is obtained on the MCA. In this way the integrated counts in the full energy peak gives us
Uncollided intensity.
Apparatus Of Experiment :
1.Gamma rays source Cs-
- Shielding material plates like Copper ,Aluminum ,Iron.
3.Collimators
4.Pre.Amplifier
5.Amplifier
6.Single Channel analyzer
7.Power supply
8.CRO
9.Delay amplifiers
10.Multi channel analyzer
NaI (Tl) detector theoretical background
1 .Sodium iodide is very important detector due to relatively high atomic number (Z = 53) of its iodine constituent ensures that photoelectric absorption is a important process and detection efficiency. In Sodium iodide radiation interact with detector where charges are produced and through the transmission of these charges an electronic signal is produced using electronics setup
2 .NaI(Tl) detector is consists of a single crystal of thallium activated sodium iodide optically coupled to the photocathode of a photomultiplier(PMT) tube. 3. Gamma rays in the detector causes the ionization of the sodium iodide. This creates excited states in the crystal that decay by emitting visible light photons this phenomena is called scintillation, so NaI(Tl) detector is a scintillation detector. 4. Basically the thallium doping of the crystal is for shifting the wavelength of the light photons into the sensitive range of the photocathode. 5 .No of visible-light photons produced in detector is directly proportional to energy deposited in the crystal by the gamma ray 6. After the process initiated, the intensity of the scintillation decays approximately exponentially in time, with a decay time constant of 250 ns. 7. At the photocathode, the scintillation photons release electrons via the photoelectric effect Photoelectrons increases by increasing the scintillation photons and also on energy deposited in the crystal by the gamma ray 8 .Photomultiplier tube consists of a series of dynodes enclosed in the evacuated glass tube. The each next dynode is biased to a higher voltage than previous dynode.
9. Since the first dynode is biased at a considerably more positive voltage than the photocathode, the photoelectrons are accelerated to the first dynode. As each electron strikes the first dynode the electron has acquired sufficient kinetic energy to knock out 2 to 5 secondary electrons. Thus, the dynode multiplies the number of electrons in the pulse of charge. The secondary electrons from each dynode are attracted to the next dynode by the more positive voltage on the next dynode. This multiplication process is repeated at each dynode, until the output of the last dynode is collected at the anode in form of charge avalanche. For the selected bias voltage,
10. Since it important to note that charge at the anode is directly proportional to energy deposited
by the gamma ray in the scintillator. 11. The preamplifier collects the charge from the anode on a capacitor, turning the charge into a voltage pulse 12 .. Then it transmits the voltage pulse sends to the supporting amplifier which is located at the output of the preamplifier .The pulse height is directly proportional to energy deposited in the scintillator by the detected gamma ray. 13. The Multichannel Analyzer (MCA) measures the pulse heights delivered by the supporting amplifier, and the energy spectrum produced by the NaI (Tl) detector located on the computer.
Pre amplifier
Preamplifier is used for obtaining the signal from the detector more effectively. Therefore, the
connection of the preamplifier with the detector will be fine, and the input circuits must match
the characteristics of the detector. Using preamplifier different pulse processing techniques are
available.
Figure: Left side source and detector, in mid apparatus to the right MCA
Figure: Set up of appratuse
Procedure for finding the Attenuation Coefficients
1. Method 1 using SCA
Before starting the experiment the apparatus is set according to the fig. 3. To find the
good geometry counts collimators are used in such a way that the source, collimator and the
detector are exactly in line. One collimator is placed in front of source and other before detector
in this way those photons will reach the detector which suffer no scattering with collimators.
Also lead shielding around the source is adjusted to reduce the dose rate below the maximum
permissible limit. Then serial numbers are marked on each plate and thickness of all the plates is
calculated. In this experiment 3 plates of each Aluminum, Copper, Iron plates were used.
Then the connections were made as in Fig. 3.
To carry on the experiment high power supply is turned on and voltage equal to the
operating voltage of detector is applied. Timer is fixed for 10 seconds, and then counts are
recorded first without placing any plate between the source and detector and then placing the
plates one by one until all the five plates. In this way three readings are taken for each plate and
then their average is evaluated.
(1):Calculation for Attenuation Coefficient
1.Good Geometry
Material : Copper (Cu)
Table No 1 : Table of peak counts to calculate the attenuation coefficient using different thickness
Fig 1 : Plot of thickness v/s ln(Counts) for Copper
Attenuation coefficient for Cu= Slope of straight line = 0.
No of Plates
Thickness ( cm)
Counts 01 Count02 Counts03 Average Counts
ln(Ave.Co unts) 1 0 41933 42073 41983 41981.33 10. 2 1.28 18491 18474 18500 18488.33 9. 3 2.54 8212 8298 8399 8300 9. 4 3.815 3835 3780 3821 3812 8. 5 5.07 1772 1764 1664 1733.33 7. 6 6.33 873 871 795 846.33 6.
Bad Geometry
Copper (Cu )
Table No 2 : Table of peak counts of bad geometry using different thickness
Build Up factor.
Copper (Cu)
No .of Plates Thickness
(c m)
Average Counts (Good Geometry) I (^) gg
Average Counts (Bad Geometry) I (^) bg
Buildup I (^) bg /Igg (x)
1 0 41981.33 892809 21.
2 1.28 18488.33 527254.33 28.
3 2.54 8300 255633.66 30.
4 3.815 3812 121885.66 31.
5 5.07 1733.33 57116.33 32.
6 6.33 846.33 26910.66 31.
Table No 3 : Table for to calculate build up factor for Copper
No of Plates Thickness ( cm)
Counts 01 Count02 Counts03 Average Counts 1 0 896812 891759 889856 892809 2 1.28 527651 527054 527058 527254. 3 2.54 256261 255263 255377 255633. 4 3.815 122127 122079 121451 121885. 5 5.07 57207 57200 56942 57116. 6 6.33 26802 26827 27103 26910.
