5. Example of gamma rays applications

### 5.1 Environmental gamma dosimetry

The thermoluminescence dating method (TL) requires a very accurate knowledge of the annual radiation doses deposited, in the minerals that are used, by the alpha, beta, gamma and cosmic rays [5, 6].

In the annual radiation doses, we can distinguish two components:


Gamma-ray dose-rate may be measured by a TL dosimeter. But as this dose is not valid for the dosimeter itself, corrections must be made to know the one corresponding to the soil.

These corrections are related to the complexity of the energy spectrum gamma radiation incidents; their origins are:


The correction factors had already been investigated theoretically [7] and experimentally [8, 9]. Below, we describe a theoretical evaluation method, for these factors, which does not require excessive computer time and so can be easily extended to a wide variety of site conditions.

lighter and less demanding procedure in computer time than the Monte-Carlo

Gamma Rays: Applications in Environmental Gamma Dosimetry and Determination Samples…

The ratio ε of the dose deposited in an encapsulated dosimeter by an incident gamma flux to that deposited in soil by the same flux can be evaluated using the

<sup>ϕ</sup>ð Þ <sup>E</sup> <sup>E</sup>μ<sup>a</sup>1:e�μa2<sup>t</sup>

where E is the photon energy: ϕ(E) is the incident γ-ray flux density (γ per unit area and unit time); μa1, μa2, μa3 are the total mass absorption coefficients for γ-rays,

In fact, formula Eq. (9) is only approximate and a more exact formulation is:

e�μ02<sup>t</sup> : <sup>σ</sup><sup>02</sup>

where μ<sup>02</sup> and σ<sup>02</sup> are, respectively the total and Compton mass attenuation coefficients for the encapsulating material; F(E, E') is the energy distribution of secondary γ-rays (energy E') from a Compton interaction induced by a photon of

dE

<sup>μ</sup><sup>02</sup> � �F E; <sup>E</sup><sup>0</sup> ð Þ<sup>ϕ</sup> <sup>E</sup><sup>0</sup> ð ÞdE<sup>0</sup>

<sup>ϕ</sup>ð Þ <sup>E</sup> <sup>E</sup>μ<sup>a</sup>3dE (10)

<sup>ϕ</sup>ð Þ <sup>E</sup> <sup>E</sup>μ<sup>a</sup>3dE (9)

� dE

5.1.2 Outline of the calculations of the dosimeter/soil dose ratio

ε ¼ Ð

<sup>E</sup>μ<sup>a</sup><sup>3</sup> <sup>ð</sup>1�e�μ02<sup>t</sup> <sup>f</sup> <sup>Þ</sup>ϕð Þþ <sup>E</sup> <sup>Ð</sup>

Ð

respectively in dosimeter, capsule walls, and soil; t is the capsule thickness.

Ð

method for a similar definition.

TL dosimeter irradiated by an incident γ-ray flux.

DOI: http://dx.doi.org/10.5772/intechopen.85503

expression:

Figure 3.

ε ¼ Ð

117

## 5.1.1 Environmental conditions

The calculations presented here refer to CaSO4: Dy as dosimeter, and two encapsulating materials, polyethylene and copper, of various thicknesses (Figure 3). However, the resulting computer programs can be easily extended to other materials.

Several kinds of soils were considered. For this case, we retained two extreme cases of real soils:


The relative energies and intensities of the lines taken into consideration are given in Table 1 [10]. For the uranium series, the contribution of uranium-235 and its descendants were taken into account.

The bulk of the calculation therefore comes down to a few dozen successive numerical integrations, with about 220 steps each time. It is therefore a much

Gamma Rays: Applications in Environmental Gamma Dosimetry and Determination Samples… DOI: http://dx.doi.org/10.5772/intechopen.85503

Figure 3. TL dosimeter irradiated by an incident γ-ray flux.

lighter and less demanding procedure in computer time than the Monte-Carlo method for a similar definition.

#### 5.1.2 Outline of the calculations of the dosimeter/soil dose ratio

The ratio ε of the dose deposited in an encapsulated dosimeter by an incident gamma flux to that deposited in soil by the same flux can be evaluated using the expression:

$$\varepsilon = \frac{\int \phi(E) E \mu\_{a1} \mathbf{e}^{-\mu\_{a2}t} dE}{\int \phi(E) E \mu\_{a3} dE} \tag{9}$$

where E is the photon energy: ϕ(E) is the incident γ-ray flux density (γ per unit area and unit time); μa1, μa2, μa3 are the total mass absorption coefficients for γ-rays, respectively in dosimeter, capsule walls, and soil; t is the capsule thickness.

In fact, formula Eq. (9) is only approximate and a more exact formulation is:

$$\varepsilon = \frac{\int E\mu\_{a3}\{ (\mathbf{1} - \mathbf{e}^{-\mu\_{02}t})\phi(E) + \int e^{-\mu\_{02}t} \cdot \begin{pmatrix} \frac{\sigma\_{02}}{\mu\_{02}} \Big| F(E, E')\phi(E')dE' \end{pmatrix} dE}{\int \phi(E)E\mu\_{a3}dE} \tag{10}$$

where μ<sup>02</sup> and σ<sup>02</sup> are, respectively the total and Compton mass attenuation coefficients for the encapsulating material; F(E, E') is the energy distribution of secondary γ-rays (energy E') from a Compton interaction induced by a photon of

5. Example of gamma rays applications

Use of Gamma Radiation Techniques in Peaceful Applications

The thermoluminescence dating method (TL) requires a very accurate knowledge of the annual radiation doses deposited, in the minerals that are used, by the

• internal dose: deposited by the radiations with a short range (alpha and beta)

• external dose: deposited by the long range radiations (gamma rays and cosmic)

Gamma-ray dose-rate may be measured by a TL dosimeter. But as this dose is

These corrections are related to the complexity of the energy spectrum gamma

• The difference in composition between TL dosimeter and the soil, resulting in absorption and therefore deposited different doses, especially for an energies

• The capsule enclosing the TL dosimeter induce absorptions of low energy

The correction factors had already been investigated theoretically [7] and experimentally [8, 9]. Below, we describe a theoretical evaluation method, for these factors, which does not require excessive computer time and so can be easily

The calculations presented here refer to CaSO4: Dy as dosimeter, and two encapsulating materials, polyethylene and copper, of various thicknesses

(Figure 3). However, the resulting computer programs can be easily extended to

• a siliceous soil of low <Z> (<Z> = 11.26), hereafter referred to as 'S soil';

• a very calcareous soil of high <Z> (<Z> = 14.07) referred to as 'C soil'.

The relative energies and intensities of the lines taken into consideration are given in Table 1 [10]. For the uranium series, the contribution of uranium-235 and

The bulk of the calculation therefore comes down to a few dozen successive numerical integrations, with about 220 steps each time. It is therefore a much

Several kinds of soils were considered. For this case, we retained two extreme

not valid for the dosimeter itself, corrections must be made to know the one

In the annual radiation doses, we can distinguish two components:

5.1 Environmental gamma dosimetry

alpha, beta, gamma and cosmic rays [5, 6].

coming out of the bulk of the sample.

corresponding to the soil.

less than 100 keV.

5.1.1 Environmental conditions

other materials.

cases of real soils:

116

gamma rays.

radiation incidents; their origins are:

extended to a wide variety of site conditions.

its descendants were taken into account.

coming out of the surroundings of the sample.


And the ratio of secondary to primary γ-rays is:

DOI: http://dx.doi.org/10.5772/intechopen.85503

Ni <sup>E</sup><sup>0</sup> ð Þ¼ <sup>ð</sup>

Figure 4 an example of various order spectra for 40K.

And the total spectrum will be:

energy carried.

medium involved.

Figure 4.

119

Q<sup>1</sup> ¼

Ð

Ð

N2(E), and in a more general manner the following recurrence relations hold:

Ni�1ð Þ E :

N Eð Þ¼ ∑

<sup>N</sup>0ð Þ <sup>E</sup> : <sup>σ</sup><sup>01</sup>

Gamma Rays: Applications in Environmental Gamma Dosimetry and Determination Samples…

In the same way, the spectrum of third generation γ-rays can be deduced from

∞ i¼1

Of course, there is a rapid decrease with i of the mean γ energy and of the total

Practically, the calculation will be stopped at a generation order i such that Q <sup>i</sup> ≪ 1. The condition Q <sup>i</sup> < 10�<sup>3</sup> was imposed, corresponding to i = 15–32 according to the

N(E) is the photon spectrum corresponding to the number of photons created per unit mass; to get ϕ(E), which is the number of incident photons per unit area,

<sup>ϕ</sup>ð Þ¼ <sup>E</sup> <sup>λ</sup>ð Þ <sup>E</sup> :N Eð Þ¼ <sup>∑</sup> Nið Þ <sup>E</sup>

μ<sup>01</sup>

the mean relaxation length λ(E) of photons must be taken into account:

Computed spectra of secondary γ-rays from 40K after 1, 2, 5, 10 Compton interactions [5].

σ01ð Þ E

<sup>μ</sup><sup>01</sup> � �:dE

<sup>N</sup>0ð Þ <sup>E</sup> :dE (12)

<sup>μ</sup>01ð Þ <sup>E</sup> F E; <sup>E</sup><sup>0</sup> ð ÞdE (13)

Nið Þ E (14)

(15)

#### Use of Gamma Radiation Techniques in Peaceful Applications

#### Table 1. U and Th series γ spectra.

energy E. F(E, E') can be obtained from the well-established Klein and Nishina cross-section for Compton effect [11].

For the use of these formulas, it is assumed that there is an electronic equilibrium, that is, the dimensions of the dosimeter are equal to or greater than the secondary electron range (of the order of a few mm). Murray [9] showed that this is verified if the dosimeter mass is greater than 100 mg.

In applying formula Eq. (9), the main difficulty lies in the calculation of the incident photon flux density ϕ(E). ϕ(E) includes not only the discrete primary emission spectrum of the considered γ source, but also the continuum spectrum of γ rays from successive Compton interactions.

#### 5.1.3 Infinite medium γ-ray spectrum

Here one assumes an infinite environment and homogeneous, in which the radioelements are evenly distributed. The interactions of gamma rays with the material taken into consideration are the photoelectric effect and the Compton effect; the pair production is considered negligible to the considered energies (<2.6 MeV).

Let N0(E) be the primary spectrum (number of photons per unit time and unit mass of soil). After one interaction, the energy spectrum of secondary γ-rays will be:

$$N\_1(E') = \int N\_0(E) \frac{\sigma\_{01}(E)}{\mu\_{01}(E)} F(E, E') dE \tag{11}$$

Gamma Rays: Applications in Environmental Gamma Dosimetry and Determination Samples… DOI: http://dx.doi.org/10.5772/intechopen.85503

And the ratio of secondary to primary γ-rays is:

$$Q\_1 = \frac{\int N\_0(E) \cdot \left(\frac{\sigma\_{01}}{\mu\_{01}}\right) dE}{\int N\_0(E) \, dE} \tag{12}$$

In the same way, the spectrum of third generation γ-rays can be deduced from N2(E), and in a more general manner the following recurrence relations hold:

$$N\_i(E') = \int N\_{i-1}(E) \frac{\sigma\_{01}(E)}{\mu\_{01}(E)} F(E, E') dE \tag{13}$$

And the total spectrum will be:

$$N(E) = \sum\_{i=1}^{\infty} N\_i(E) \tag{14}$$

Of course, there is a rapid decrease with i of the mean γ energy and of the total energy carried.

Figure 4 an example of various order spectra for 40K.

Practically, the calculation will be stopped at a generation order i such that Q <sup>i</sup> ≪ 1. The condition Q <sup>i</sup> < 10�<sup>3</sup> was imposed, corresponding to i = 15–32 according to the medium involved.

N(E) is the photon spectrum corresponding to the number of photons created per unit mass; to get ϕ(E), which is the number of incident photons per unit area, the mean relaxation length λ(E) of photons must be taken into account:

$$
\phi(E) = \lambda(E) N(E) = \sum \frac{N\_i(E)}{\mu\_{01}} \tag{15}
$$

Figure 4. Computed spectra of secondary γ-rays from 40K after 1, 2, 5, 10 Compton interactions [5].

energy E. F(E, E') can be obtained from the well-established Klein and Nishina

For the use of these formulas, it is assumed that there is an electronic equilibrium, that is, the dimensions of the dosimeter are equal to or greater than the secondary electron range (of the order of a few mm). Murray [9] showed that this is

Energy (keV) Intensity Energy (keV) Intensity

13 90 768 9 49 30 934 5 22 1120 17.5 14 1238 8 7 1377 8.6 10 1509 4.4 21 1764 23.3 40 2204 8.2

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 79 511 8.6 30 583 32.6 16 727 7.2 7 795 8.5 209 6 911 30 48 969 25.4 10 1588 11.6 16.4 2615 35.8

In applying formula Eq. (9), the main difficulty lies in the calculation of the incident photon flux density ϕ(E). ϕ(E) includes not only the discrete primary emission spectrum of the considered γ source, but also the continuum spectrum of γ

Here one assumes an infinite environment and homogeneous, in which the radioelements are evenly distributed. The interactions of gamma rays with the material taken into consideration are the photoelectric effect and the Compton effect; the pair

Let N0(E) be the primary spectrum (number of photons per unit time and unit mass of soil). After one interaction, the energy spectrum of secondary γ-rays will be:

> <sup>N</sup>0ð Þ <sup>E</sup> <sup>σ</sup>01ð Þ <sup>E</sup> μ01ð Þ E

F E; E<sup>0</sup> ð ÞdE (11)

production is considered negligible to the considered energies (<2.6 MeV).

ð

N<sup>1</sup> E<sup>0</sup> ð Þ¼

cross-section for Compton effect [11].

463 7

609 49

238U + 235U

232Th

Table 1.

118

U and Th series γ spectra.

verified if the dosimeter mass is greater than 100 mg.

rays from successive Compton interactions.

5.1.3 Infinite medium γ-ray spectrum

$$(\mathbf{With}): \lambda(E) = \frac{1}{\mu\_{01}}$$

The value of absorption or attenuation coefficients was obtained for the Compton effect from the Klein-Nishina formula.

For the photoelectric effect, they were deduced from the data of Hubbell [12]. Some typical spectra are shown in Figure 5 for 40K. The low energy cut-off is determined by photoelectric effect and occurs at higher energy for high-Z media. And for 232Th in pure water (Figure 6).

In the case of water, a "light" medium and a strong low energy ray contribution (below 100 keV) can be noticed. Similar features are also noticed for the more complex case of U and Th series.

These spectra show the overlapping of the primary ray spectrum and the degraded continuous spectrum, which carry most of the energy (60%).

There is a similarity in the degraded spectrum, even for two very different gamma sources (for example, thorium and potassim-40). On the other hand, the degraded spectrum is higher in energy as the <Z> of the medium is high: this is due to the increasing influence of the photoelectric effect which "cuts" the low gamma ray energy.

Our results are in good agreement with those obtained by G. Valladas [7] by the Monte-Carlo method for potassium-40 in siliceous medium.

5.1.4 Dosimeter to soil dose ratio for infinite homogeneous soils

• Copper, <Z > medium, frequently used

Computed energy spectra for 232Th in pure water [5].

DOI: http://dx.doi.org/10.5772/intechopen.85503

dose between the dosimeter and the soil is significant.

• Polyethylene, <Z > low

dosimeters and compositions.

the highest.

121

Figure 6.

types of 1 g/cm2 thick absorbers, sufficient to stop beta radiation.

The calculation of ε was done for the list of floors already cited (from the gamma ray energy spectra already calculated), for the three radiation sources and for two

Gamma Rays: Applications in Environmental Gamma Dosimetry and Determination Samples…

The results are given in Table 2. Calculations are performed here with, as a TL

It can be found that ε it may be less than or greater than 1; two antagonistic effects act: on the one hand, the absorption by the walls, which tends to decrease ε on the other hand, the difference in nature between soil and TL dosimeter which has the opposite effect, the coefficient of absorption of the dosimeter being

The dispersal of the value of ε is smaller between the different soil for a copper

capsule than for a polyethylene capsule. This can be explained by the fact that copper absorbs the lower part of the spectrum of energy for which the difference

dosimeter, CaSO4: Dy, but are readily feasible for any combination of known

Figure 5. Computed energy spectra for 40K in (a) dry C soil, (b) wet S soil, and (c) pure water [5].

Gamma Rays: Applications in Environmental Gamma Dosimetry and Determination Samples… DOI: http://dx.doi.org/10.5772/intechopen.85503

Figure 6. Computed energy spectra for 232Th in pure water [5].

#### 5.1.4 Dosimeter to soil dose ratio for infinite homogeneous soils

The calculation of ε was done for the list of floors already cited (from the gamma ray energy spectra already calculated), for the three radiation sources and for two types of 1 g/cm2 thick absorbers, sufficient to stop beta radiation.


The results are given in Table 2. Calculations are performed here with, as a TL dosimeter, CaSO4: Dy, but are readily feasible for any combination of known dosimeters and compositions.

It can be found that ε it may be less than or greater than 1; two antagonistic effects act: on the one hand, the absorption by the walls, which tends to decrease ε on the other hand, the difference in nature between soil and TL dosimeter which has the opposite effect, the coefficient of absorption of the dosimeter being the highest.

The dispersal of the value of ε is smaller between the different soil for a copper capsule than for a polyethylene capsule. This can be explained by the fact that copper absorbs the lower part of the spectrum of energy for which the difference dose between the dosimeter and the soil is significant.

ð Þ With : <sup>λ</sup>ð Þ¼ <sup>E</sup> <sup>1</sup>

For the photoelectric effect, they were deduced from the data of Hubbell [12]. Some typical spectra are shown in Figure 5 for 40K. The low energy cut-off is determined by photoelectric effect and occurs at higher energy for high-Z media.

In the case of water, a "light" medium and a strong low energy ray contribution

The value of absorption or attenuation coefficients was obtained for the

(below 100 keV) can be noticed. Similar features are also noticed for the more

These spectra show the overlapping of the primary ray spectrum and the

There is a similarity in the degraded spectrum, even for two very different gamma sources (for example, thorium and potassim-40). On the other hand, the degraded spectrum is higher in energy as the <Z> of the medium is high: this is due to the increasing influence of the photoelectric effect which "cuts" the low gamma

Our results are in good agreement with those obtained by G. Valladas [7] by the

degraded continuous spectrum, which carry most of the energy (60%).

Monte-Carlo method for potassium-40 in siliceous medium.

Computed energy spectra for 40K in (a) dry C soil, (b) wet S soil, and (c) pure water [5].

Compton effect from the Klein-Nishina formula.

Use of Gamma Radiation Techniques in Peaceful Applications

And for 232Th in pure water (Figure 6).

complex case of U and Th series.

ray energy.

Figure 5.

120

μ<sup>01</sup>


5.2 Calculation method adapted to the experimental conditions for determining

Gamma Rays: Applications in Environmental Gamma Dosimetry and Determination Samples…

The gamma radiation self-absorption coefficient is of great interest in activation analysis. Since it is difficult to measure this coefficient, various calculation methods

Measuring the self-absorption coefficient is not a simple thing. The physicists who have faced this problem, for a long time, have always used methods of statistical or non-statistical computation: Parallel beam methods, Monte-Carlo method and many other methods. For our part, we have developed an original technique calculating the self-absorption coefficient of multienergetic γ-radiations [13].

In this chapter, we are presenting a method that we have developed, this which

allows us control and calibrate the activation analysis experiments [13]. This method consists of simulating the interaction processes of gamma rays induced by neutron activation of various samples by using the Monte Carlo method adapted to

Different disk shaped red beet samples and standards were irradiated with 14 MeV neutrons. Standards were prepared by mixing pure graphite and high purity chemical compounds powders (NaCl, Na2HPO4 and K2CO3) [14]. The induced gamma activities on the sodium, potassium, chlorine and phosphorus elements have been experimentally measured by means of hyper-pure germanium

The analyzed beet samples and standards have a 23 mm diameter and a 6 mm

The different parameters of the nuclear reactions used (cross section, isotopic

After the irradiation (irradiation time = tirr) and cooling times (td), the number

ln 2 <sup>θ</sup>I<sup>γ</sup> <sup>1</sup> � <sup>e</sup>

Element θ (%) Nuclear reaction σ (mb) T E<sup>γ</sup> (keV) (I<sup>γ</sup> %) tirr (s) td (s) tm (s) Na 100 23Na(n, p)23Ne 43 � 5 38.0 s 440 (33%) 200 30 200 Cl 75.5 35Cl(n, 2n)34mCl 43 � 5 32.4 min 146.5 (45%) 600 30 600

K 93.1 39K(n, 2n)38gK 43 � 5 7.70 min 2167 (100%) 600 30 600

The produced nuclear reactions by irradiating the samples (standards) with 14 MeV neutrons.

is the half-life of the produced radionuclide, θ is the isotopic abundance of the studied element, Iγ, is the emitted gamma rays intensity and ϕ the neutron flux. To take into account the activity measuring time, relation Eq. (16) should be multiplied

where σ is the nuclear reaction cross section, N0 is the number of target nuclei, T

� ln<sup>2</sup> ð Þ <sup>T</sup> tirr : <sup>e</sup>

28Al 43 � 5 2.30 min 1779 (100%) 600 30 600

� ln<sup>2</sup> ð Þ <sup>T</sup> td (16)

TN0σϕ

samples γ-activities induced by 14 MeV neutrons

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5.2.2 Samples and standards induced gamma-activities

abundance, etc.) are summarized in Table 3.

� ln<sup>2</sup> ð Þ <sup>T</sup> tm .

N tð Þ¼ irr þ td

of produced radionuclides is given by:

5.2.1 Introduction

have been developed.

experimental conditions.

spectrometer.

by the term 1 � e

Table 3.

123

P 92.2 31P(p, α)

thickness.

#### Table 2.

Values of ε for infinite uniform medium with 1 g m<sup>2</sup> capsule wall thickness [5].

For a copper capsule, the difference of ε between dry a soil and moderately wet (e.g., less than 15% water) is negligible (less than 1%); therefore, it is not necessary in this case to know exactly the soil humidity to perform the correction, which is an advantage.

In practice, the limestone soil and the siliceous soil are two extreme cases, which make only a difference of 5% for copper on the value of ε, so only a coarse knowledge of the cashing medium is necessary for the calculation of e with an high accuracy.

The variations of ε for 40K with the absorber or medium are less important than for uranium or thorium. This is due to a smaller contribution of low energies to the 40K spectrum (no low energy lines).

An important consequence of the foregoing is that, for the experimenter, copper (or a close material) is well used when the composition (especially moisture) of the soil is not well known. The error made a priori on the value of ε will thus be reduced.

On the other hand, in most cases, the dispersion on ε related to the relative intensity of the three gamma radiation sources is insignificant. Indeed, the potassium-40, uranium and thorium series generally intervene for approximately 1/3 each, and significant deviations from this proportion are rare.

In general, it is difficult to determine the respective contribution of the potassium-40, uranium and thorium series to the total dose rate. However, in most cases, the contribution of these three radioelements does not exceed 60% and approximate values on the whole with acceptable dispersion may be proposed.

For example,


The results obtained with our program under the same conditions regarding the dosimeter, the surrounding environment, the capsules and the sources of the gamma rays are slightly superior to the theoretical results of G. Valladas [7]. This small difference (in the order of 3%) can be explained by the fact that the nominal values for capsule thickness have been used instead of the mean values which take into account geometry, also to a lesser extent by the fact that self-absorption has not been taken into account in our calculation. The effect of this last correction was estimated to be less than 1%.
