Experimental Determination of the Lineal Attenuation Coefficient of
Ground
icolás Larraguetaa*, Vanesa Sanza, MD. Luis Illanesa,b
a
Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La
Plata, 47 y 115, La Plata, Buenos Aires, Argentina.
b
Hospital Italiano, Avenida 51 entre 29 y 30, La Plata, Buenos Aires, Argentina.
Abstract. This work reports the measurement of the linear attenuation coefficient of ground in order to elaborate
a calculus memory for a nuclear medicine installation. The service is placed in the subsoil and the hot room is
surrounded by variable, higher than a meter, thicknesses of ground. Owing to the lack of bibliography about the
value of the linear attenuation coefficient of ground, we measured it and compared the result with that obtained
by the density correction method relative to concrete, using the linear attenuation coefficient value of this
material as derived from experimental measures of this material.
Measurements were made using a BaF2 scintillation detector and a 137Cs source, which was selected considering
the similitude between its energy and the energy of the radiopharmaceutical used in the service for the PET
studies, 22Na. Different increasing thicknesses of ground got from areas located near the service were placed as
absorbents. The work involves ten experimental points, interposing cumulatively 1.8cm thicknesses of ground
each time, between the detector and the source.
The results obtained from both methods do not present a significant difference, however, we have concluded that
the measured coefficient is more appropriate that the one estimated by the density correction method.
Consequently, for calculating the dose rates at different places of the service, the experimentally determined
value µ = 0.0884 cm-1 of the linear attenuation coefficient was used.
KEYWORDS: linear attenuation coefficient, ground, shielding.
1. Introduction
The elaboration of a calculus memory of a Nuclear Medicine Installation is used to evaluate the
received doses by external irradiation from the nuclides used in diagnostic and treatment. This
document, with character of sworn statement in Argentina, must verify that the calculated doses do not
exceed the recommended doses restrictions stipulated by the AR 8.2.4 normative: “Uso de Fuentes
radiactivas no selladas en instalaciones de Medicina Nuclear” of Autoridad Regulatoria Nuclear [1].
The Nuclear Medicine service analyzed has the following equipment: a double-head gamma camara
able to realize conventional gammagraphies and also tomographies studies (SPECT) and a diagnostic
equipment involving a complete ring of detectors, optimized for the positron emission tomography
(PET).
The room for treatment, fractionating and radiopharmaceutical preparation, from now on the hot room,
is placed in a subsoil and surrounded by variable, higher than one meter thicknesses of ground (Figure
1).
Owing to the lack of bibliography on the value of the linear attenuation coefficient of this material and
since its composition depends on its geographic localization, an experimental determination was made
and compared with the result obtained from the density correction method relative to concrete, widely
used to evaluate calculus memories. The value of the linear attenuation coefficient of concrete was
derived from the absorption data reported in the publication of Bibiloni et al [2].
The radionuclide used was 137Cs, of 30.1 years of half-life and with a gamma radiation of 662 keV, not
much different from the 511 keV of 22Na.
*
Presenting author, E-mail: [email protected]
1
Figure 1: Plane of the Nuclear Medicine installation.
1.1 Theoretical frame
When a monoenergetic beam of N photons is incident over the surface of a material of thickness (x),
the quantity of photons that interacts with it can be expressed in a differential form by [3]:
d = − µdx
(1)
where µ (cm-1) is the linear attenuation coefficient or probability of interaction by unit of path. This is
the product of the number of atoms per unit volume n (cm-3) inside the absorbent and the total cross
sections (cm2) or sum of probabilities of the different types of interaction, in our case by photoelectric
and Compton effects, since the photon energy used is smaller than the necessary for pair production
(1.022 MeV).
µ = n (φPhotoelectric + Z σ Compton )
(2)
where:
φPhotoelectric = 4α 4 2 Z 5
with α = 1
137
2
8π re
3
2
1
 
γ 
, the fine-structure constant
7/2
(3)
and
γ =
hν
, the normalized radiation energy
me c 2
and
1 + γ  2(1 + γ ) 1
 1
1 + 3γ 
− Ln(1 + 2γ ) +
Ln(1 + 2γ ) −

2 
γ
(1 + 2γ )2 
 2γ
 γ  1 + 2γ
σ Compton = 2πre 2 
(4)
In equations (3) and (4) the dependence of the cross sections on the energy and atomic number[2,4] can
be seen.
Integrating equation (1), one obtains:
( x ) = 0 e − µx
(5)
and in terms of intensity (number of photons by unit of time):
I ( x ) = I 0 e − µx
(6)
where I 0 and I (x ) are, respectively, the intensities before and after traversing the absorbent of
thickness x .
By measuring the intensity as a function of the different increasing absorbent thicknesses and fitting
the values to an exponential curve, the linear attenuation coefficient of the material can be obtained.
2. Experimental development: methods and materials
In order to perform the measurement of the linear attenuation coefficient of the ground, just a
superficial probe of this material was extracted of the neighborhood of the hot room in order to
minimize the variations in the composition owing to the geographic place. In fact, it must be into
account the variation in the composition of the ground with the depth. In the surface there is mainly
organic matter while more deeply, within the first meter, there is the so called clay soil, which
involves mainly silicon and ions like Fe+++, Al+++, Mg++ and Ba++, thus increasing the effective atomic
number of this material. This leads to an increase in the cross sections of the photoelectric and
Compton effect and consequently, to a higher linear attenuation coefficient.
At deeper layers as far as the 3 meters down, the composition is approximately constant but the
density is higher. Both the increases in the linear attenuation coefficient and in the density result in a
rise in the shielding capability. This is the reason why the extracted ground sample comes from the
superficial layer, in order to underestimate the shielding ability of the ground and so, keep a
conservative philosophy for the radioprotection criteria.
2.1 Experimental setup
For the experiment, a 137Cs source with 30.1 years of half-life that decays to an exciting state of 137Ba
(see figure 2) was used. A gamma electromagnetic radiation of hν =662 keV is emitted then to achieve
the ground state. This radionuclide was chosen due to the similitude of its energy with that of positron
annihilation (511 keV) of 22Na used for the PET studies. The little difference in energy once more
underestimates the shielding ability of the material, maintaining a conservative philosophy of
radioprotection.
3
Figure 2: Diagram of 137Cs decay.
The detector used (Figure 3) consists of a scintillating crystal (BaF2) optically connected to a
photomultiplier tube [5]. The generated radiations due to photoelectric and Compton effects of the
gamma radiation of 662 keV in the crystal excite and ionize its atoms and molecules, causing the
emission of an energy dependent- number of photons in the ultraviolet range of the electromagnetic
spectrum. These are directed to the photocathode of the photomultiplier tube, where they are converted
into a weak electron beam. The current pulse is then amplified by a dynode chain at increasing
voltages and finally measured with an analogical to digital converter connected to a computer. The
detector measures the quantity of pulses and from their highs, the energies of the photons that caused
them.
In the crystal, photons of energy ( hν − Bk ) and ( hν − E e − ) are produced by photoelectric and
Compton interactions, respectively.
Figure 3: Block diagram of the gamma spectrometer.
2.2 Procedure
Due to the natural background, a spectrum without the source was taken for an hour, to have good
statistics. The spectrum was properly normalized and subtracted from all spectra.
A set of ten empty Petri boxes of thickness 1.8 cm each were interposed between the source and the
detector. A starting spectrum was taken for 20 minutes to obtain the I 0 of equation (6). Then the first
box was filled with ground, as is shown in Figure 4.a, and again a spectrum was taken during the same
time. Then, the remaining boxes were filled with ground one by one and the corresponding nine
spectra were sequentially acquired.
4
3500
3500
3000
3000
3000
2500
2000
1500
Número de cuentas
3500
Número de cuentas
Número de cuentas
Figure 4
2500
2000
1500
2500
2000
1500
1000
1000
1000
500
500
500
0
0
0
200
400
600
800
1000
Canal
a. Experimental device and
spectrum corresponding to 1,8 cm
of ground (One Petri’s box)
0
0
200
400
600
800
1000
Canal
b. Experimental device and
spectrum corresponding to 10,8 cm
of ground (Six Petri’s box)
0
200
400
600
800
1000
Canal
c. Experimental
device
and
spectrum corresponding to 18 cm of
ground (Ten Petri’s box)
3. Analysis of results
From the acquired spectra, only the areas under the curve of the right half of the photopeak were
quantified, as is shown in the figure 5, owing to the fact that it does not take into account the Compton
contributions that come from the interactions outside the solid angle subtended by the source-detector
system. Hereby only photons interacting with the crystal and suffering photoelectric effect were
counted.
Figure 5: Observed phenomena.
5
From the obtained data, the area was plotted in terms of thickness, and an exponential fit was carried
out from which the value of the linear attenuation coefficient for the energy of 662 keV was obtained
(see Figure 6).
Figure 6: Exponential fit of the experimental data.
Experimental Data
Exponential decay fit
1,0
I (x ) = I 0 e − µx
Tansmission (I/I0)
0,8
R2
I0
0,6
µ
0.99919
191026 ± 4197
0.088 ± 0.004 cm-1
0,4
µ = 0,088 ± 0,004 cm
0,2
0
2
4
6
8
10
-1
12
14
16
18
Thickness (cm)
The result was compared with the data obtained from the density correction method using the
attenuation coefficient of the concrete measured by Bibiloni et al [2]. With this purpose, each box
filled with a known ground volume was weighted (scale precision = 1x10-6 gr) and then the density of
each absorbent and also the average was calculated, which resulted of 1.000 g/cm3. This experimental
value of the ground density and the density of concrete experimentally obtained from Bibiloni’s
measurement [2] allowed calculating the expression:
Cδ =
δ T 1.00
=
= 0.292
δ C 3.43
(7)
where δ T is the density of ground, and δ C the density of concrete.
The density correction method establishes:
δT x T = δ C x C
(8)
where xT and xC are the thicknesses of ground and concrete respectively.
Thus:
C δ = xC / xT
(9)
Since the same attenuation factor of concrete and ground is pretended:
6
e − µc xc = e − µT xT
(10)
µ c x c = µ T xT
(11)
And replacing the equation (9) in (11), one obtains:
µ c Cδ = µ T
(12)
Finally, replacing for the values given in previous equations, the linear attenuation coefficient of
ground was calculated as:
µT = 0.0736 cm −1
4. Conclusions
1. It has been possible to perform an accurate experimental determination of the lineal attenuation
coefficient of the ground surrounding the hot room of a Nuclear Medicine Service. The value
obtained is:
µ = 0.088 4 cm −1
2. From the comparison of the experimental result with that obtained by the density correction
method, it can be concluded that the last method has proved to be useful for a rough estimation of
the linear attenuation coefficient of ground. However, this result is lower than the experimentally
determined because this last one has been obtained sub-estimating the shielding capability of the
ground. Therefore, it is the experimental value that has been considered more appropriate and
thus, used for the elaboration of he calculus memory for the nuclear medicine installation.
Acknowledgements
The authors wish to thank Adrián Discacciatti (Autoridad Regulatoria Nuclear) and Cristina
Caracoche (Departamento de Física, Facultad de Ciencias Exactas, UNLP) for their collaboration in
revising this paper and we would like to thank especially to Professor A. G. Bibiloni for his
collaboration and guidance in the experiment.
REFERECES
[1]
[2]
[3]
[4]
[5]
NORMA AR 8.2.4, Use of not sealed radioactives sources in installations of Nuclear Medicine,
Autoridad Regulatoria Nuclear, Argentina. http://200.0.198.11/normas/8-2-4R1.PDF
BIBILONI, A. G. et al.; Determinación del coeficiente de atenuación total de un hormigón
pesado en el rango de energías gamma de un reactor nuclear, Revista del Hormigón 14, 431985.
EVANS D., The Atomic Nucleus, First edition, McGraw-Hill Book Company, New YorkToronto-London, 1955.
BIBILONI, A. G., CARACOCHE, M. C. et al, Atenuación de la radiación gamma en
hormigones pesados, Revista del Hormigón 8, 17-1982.
LEO W. R., Techniques for nuclear and particles physics experiments, 2nd Revised Edition,
Springer-Verlag, Berlin, 1994.
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