# P4: Photon Irradiation Facility

Loïc de Carlan, jean-marc bordy

► To cite this version:

Loïc de Carlan, jean-marc bordy. P4: Photon Irradiation Facility. International Workshop on Uncertainty Assessment in Computational Dosimetry, A Comparison of Approaches, Oct 2007, Bologna (ITALY), Italy. cea-05462591

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# P4 : Photon Irradiation Facility

Loïc de CARLAN & Jean-Marc BORDY

CEA-LIST, Laboratoire National Henri Becquerel, Gif sur Yvette F91191, France

**Abstract** – the problem presented in this paper deals with the determination of the uncertainty budget on air kerma value using a <sup>137</sup>Cs irradiation facility. A specific approach, described in this paper, was used to assess the whole uncertainty budget. Special aspects regarding the geometry of the source and collimator and their influence on the air kerma and the field penumbra were also proposed. The results of the authors and of the twelve participants to the comparison are presented and discussed.

## 1. Introduction

The problem is aimed at studying the uncertainty budget associated with the air kerma delivered by a calibration beam (<sup>137</sup>Cs) which could be used for radiotherapy and radiation protection. The design of the irradiator is based on the specifications of ISO 4037 part 1 [1], it is similar to those used in standard and accredited laboratories.

The problem is divided into 4 questions. The first one (the main one) is aimed at studying the uncertainty budget on the air kerma using a specific method described below. Questions 2, 3 and 4 are respectively dedicated to study special aspects of the geometry: influence of the source encapsulation, influence of the shape and materials of the collimator and finally influence of the volume of the chamber where the source is located. Additional data are required in these three last questions, in particular the spectral fluence where the air kerma is calculated and the beam profile in this plane. It was only mandatory to answer question 1. Questions 2 to 4 were proposed in order to help in understanding and quantifying the influence of the calibration facility components.

## 2. Description of the problem

### 2.1 Geometry

A cut view of the whole irradiator is given in figure 1.

<figure><img src="image_2.png" /><figcaption>**Figure 1:** Cut view of the <sup>137</sup>Cs irradiator. The origin is at the centre of the radioactive core located in the middle of the irradiation chamber. All dimensions are given in cm, there is no wall around the irradiator. Each ring of the collimator is 2 cm thick.</figcaption></figure>
## 2.2 Materials data

The materials used in this problem are listed in table 1 for the source and in table 2 for the irradiator.

<table><caption>**Table 1:** Isotopic composition of the sources' materials normalised to 100%.</caption><thead><tr><th></th><th>Density (g/cm³)</th><th>Cs</th><th>Cl</th><th>Fe</th><th>Al</th></tr></thead><tbody><tr><td>CsCl</td><td>4.00</td><td>50</td><td>50</td><td>-</td><td>-</td></tr><tr><td>Iron</td><td>7.87</td><td>-</td><td>-</td><td>100</td><td>-</td></tr><tr><td>Aluminium</td><td>2.70</td><td>-</td><td>-</td><td>-</td><td>100</td></tr></tbody></table>

<table><caption>**Table 2:** Isotopic composition of the irradiator materials.</caption><thead><tr><th></th><th>Density<br>(g/cm³)</th><th>C</th><th>O</th><th>N</th><th>Ar</th><th>Ni</th><th>Cu</th><th>Pb</th><th>W</th></tr></thead><tbody><tr><td>Dry Air (Wt Frac.)*</td><td>1.20484E-3</td><td>0.0124</td><td>23.1781</td><td>75.5267</td><td>1.2827</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Tungsten alloy (At<br>Frac)</td><td>16.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>6.0</td><td>4.0</td><td>-</td><td>90.0</td></tr><tr><td>Lead (At Frac)+</td><td>11.34</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>100</td><td>-</td></tr></tbody></table>

## 2.3 Nuclear data

$^{137}$Cs is a β⁻ emitter in equilibrium with its daughter $^{137}$Ba and it is recommended to simulate only the gamma ray at 661.66 keV of $^{137m}$Ba. Whole data are given as follow [3]:

* Electrons: 624.2 keV (8.07%), 656.0 keV (1.5%), 660.5 keV (0.35%)

* Betas (Energy max):514 keV (94.4%), 1175 keV (5.6%)

* X rays: 31.8 keV (1.9%); 32.2 keV (3.6%), 36.3 keV (1.0%)

* Gamma ray: 661.66 keV (85.2%)

Moreover, for calculating the air kerma value, it is recommended to calculate the fluence at the reference point and to use the conversion coefficients of ICRU 57 [4] given in table 3.

<table><caption>**Table 4:** Conversion coefficients for air kerma per unit fluence $K_a/\Phi$, of monoenergetic photons (ICRU 57 [4])</caption><thead><tr><th>E<br>(MeV)</th><th>K<sub>a</sub>/Φ<br>(pGy.cm<sup>2</sup>)</th><th>E<br>(MeV)</th><th>K<sub>a</sub>/Φ<br>(pGy.cm<sup>2</sup>)</th><th>E<br>(MeV)</th><th>K<sub>a</sub>/Φ<br>(pGy.cm<sup>2</sup>)</th><th>E<br>(MeV)</th><th>K<sub>a</sub>/Φ<br>(pGy.cm<sup>2</sup>)</th><th>E<br>(MeV)</th><th>K<sub>a</sub>/Φ<br>(pGy.cm<sup>2</sup>)</th></tr></thead><tbody><tr><td>0.010</td><td>7.43</td><td>0.050</td><td>0.323</td><td>0.200</td><td>0.856</td><td>0.800</td><td>3.69</td><td>4.000</td><td>12.1</td></tr><tr><td>0.015</td><td>3.12</td><td>0.060</td><td>0.289</td><td>0.300</td><td>1.38</td><td>1.000</td><td>4.47</td><td>5.000</td><td>14.1</td></tr><tr><td>0.020</td><td>1.68</td><td>0.080</td><td>0.307</td><td>0.400</td><td>1.89</td><td>1.500</td><td>6.14</td><td>6.000</td><td>16.1</td></tr><tr><td>0.030</td><td>0.721</td><td>0.100</td><td>0.371</td><td>0.500</td><td>2.38</td><td>2.000</td><td>7.55</td><td>8.000</td><td>20.1</td></tr><tr><td>0.040</td><td>0.429</td><td>0.150</td><td>0.599</td><td>0.600</td><td>2.84</td><td>3.000</td><td>9.96</td><td>10.000</td><td>24.0</td></tr></tbody></table>

## 2.4 Points of test and quantities

The point of test is defined at 50 cm from the source, along the axis of the irradiator. The origin is at the centre of the radioactive core of the source and it is located at the centre of the irradiation chamber; if a point source is used, the origin is taken from the centre of the irradiation chamber

The quantities of interest (i.e.: the spectral fluence distribution, the total air kerma and the air kerma profile for evaluating field penumbra) are specified for each question. Results are normalized to one history; additionally, results can be given per becquerel. For spectral fluence distribution, 14 bins are needed; the width of each bin being 50 keV.

<footnote>* For dry air, data taken from ICRU 49 [2]</footnote>
## 3. Questions to the participants

### 3.1 Question 0: reference air kerma value

This question was not asked in the initial version of the problem but it was in fact very useful for the comparison of the different solutions of the participants. It was proposed to provide the reference air kerma value at 50 cm from the source in the geometry given in figure 1. The whole goal of the exercise was not to calculate an absolute value but rather to study the variation with different conditions. Nevertheless, the reference value given by the participants allows detecting possible mistakes in the geometry, distances...

### 3.2 Question 1: uncertainty budget

This question was the only one to be mandatory in this problem. It was aimed at providing an uncertainty analysis of the calculation of the "reference" value of the air kerma at 50 cm from the centre of the source. The question is: Calculate the air kerma and its uncertainty budget at 50 cm from the source (see figure 1) by varying some parameters: source position, materials density, geometry...

The proposed approach to compute the uncertainty budget was to vary one parameter at a time. The main problem of this task was to be able to detect a very small variation of the air kerma due to a small variation of the parameter (e.g. the distance) without spending too much calculation time. The approach proposed in this exercise is given as follow (see table5 and figure 2):

1) Enlarge the variation of the parameters ($\Delta X$ instead of $dx$) to achieve results on which one could rely on without spending too much calculation time (column (1) table 5),

2) Calculate the slope of the kerma variation $\partial kair/\partial x$ (column (2) table 5) provided that $u_{MC}/\Delta kair < 0.1$: this criterion is very important. It means that the variation of the air kerma is ten time higher than the uncertainty associated to the calculation. In other words, it reflects that the influence of the uncertainty on kerma variation is low and consequently that the number of calculated histories (or the choice of $\Delta X$) is consistent. The calculation is made under the assumption that the variation is linear $\partial kair/\partial x=constant$ within the interval +/-$\Delta X$,

3) Calculate the estimated Standard uncertainty, $u$, (column (3) table 5), (depending on the case a gaussian, triangular or rectangular distribution is assumed, See ISO 13005 for details[5]) corresponding to the variation of the parameter $dx$ (eg 1mm) $u=2.dx/(2\sqrt{3})$ (rectangular distribution),

4) Calculate $\Delta kair = (\partial kair / \partial x) * u$.

Finally, it was asked to make a quadratic sum of the uncertainty of every parameters to calculate the combined uncertainty, $u_c$, (accounting or not for correlation between parameters). The variations of the parameters in calculation were proposed but it was up to the participants to modify them depending on the magnitude of the variation in air kerma that is found.

The method described above was only a proposal; participants were free to use a different method to estimate the standard uncertainty in terms of air kerma provided it is described.
<figure><img src="image_3.png" /><figcaption>**Figure 2:** Schematic view of the proposed method to calculate the uncertainty budget.</figcaption></figure>

<table><caption>**Table 5:** Example for the presentation of the results</caption><thead><tr><th rowspan="2">Parameter identification<br>X</th><th colspan="3">Parameter variation in the<br>calculation</th><th rowspan="2">Reported<br>uncertainty in<br>parameters *</th><th colspan="2">Standard uncertainty of<br>experimental parameter</th></tr><tr><th>(1) ΔX</th><th>(∂ k<sub>air</sub> / ∂x) (∂ k<sub>air</sub> / ∂x) ΔX</th><th>(2) CC mGy</th><th>u (3)</th><th>(4) Δ k<sub>air</sub></th></tr></thead><tbody><tr><td>Position of the source<br>(throw off centre)</td><td>+ ΔX/2</td><td></td><td></td><td>+0.05 cm</td><td>0.1 / 2√3</td><td>CC<br>ΔX<br>u</td></tr><tr><td>Source chamber (depth)</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.2 cm</td><td>0.4 / 2√3</td><td></td></tr><tr><td>Rings collimator<br>(diameter)</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.05 cm</td><td>0.1 / 2√3</td><td></td></tr><tr><td>tungsten alloy density</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.2 g/cm<sup>3</sup></td><td>0.4 / 2√3</td><td></td></tr><tr><td>Density of CsCL</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.2 g/cm<sup>3</sup></td><td>0.4 / 2√3</td><td></td></tr><tr><td colspan="7">Parameters below are not mandatory</td></tr><tr><td>Position of the source<br>(depth)</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.1 cm</td><td>0.2 / 2√3</td><td></td></tr><tr><td>Source chamber (diameter)</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.05 cm</td><td>0.1 / 2√3</td><td></td></tr><tr><td>Length of the rings of the<br>collimator</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.05 cm</td><td>0.1 / 2√3</td><td></td></tr><tr><td>Density of aluminium</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.05 g/cm<sup>3</sup></td><td>0.1 / 2√3</td><td></td></tr><tr><td>Density of iron</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.05 g/cm<sup>3</sup></td><td>0.1 / 2√3</td><td></td></tr><tr><td>Density of Lead</td><td>+/- (ΔX/2)</td><td></td><td></td><td>+/-0.1 g/cm<sup>3</sup></td><td>0.2 / 2√3</td><td></td></tr><tr><td>Energy cut off *</td><td>+/- (ΔX/2)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cross section and physics<br>models **</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<footnote>* Uncertainty on the parameter taken from literature, log books, schemes, ...</footnote>

<footnote>** Parameter which could introduce a bias.</footnote>
### 3.3 Question 2: Influence of the source encapsulation

This question was **not mandatory** but was recommended because in many circumstances, the assumption of a point source is made assuming that it will be quite correct. It can be seen through the results to this question that this assumption is somewhat questionable. It was asked to calculate the air kerma, the spectral fluence distribution and the air kerma profile at 50 cm from the source. Four configurations were proposed in this case:

a - Point source in air,

b - Volume source in air without material (no self absorption) and without encapsulation,

c - Volume source with material (to account for self absorption) but without iron encapsulation,

d - Volume source with material (to account for self absorption) and with iron encapsulation.

It has to be noticed that the collimator is made only of lead. For geometries (b) to (d) the centre of the active part of the source is positioned at the place of the point source in geometry (a).

<figure><img src="image_4.png" /><figcaption>**Figure 3:** Cut view of the irradiator; the source is a point or a cylinder; all dimensions are given in cm; there is no wall around the irradiator.</figcaption></figure>

### 3.4 Question 3: Influence of the collimator

This question was **not mandatory**. Five geometries (figures 4a to 4d and figure 3) were proposed. They allow studying the collimator influence by adding the rings progressively (in 5 steps). It was asked to calculate the air kerma, the spectral fluence distribution and the air kerma profile at 50 cm and 100 cm from the source.
<figure><img src="image_5.png" /><figcaption>**Figure 4a:** Cut view of the irradiator, all dimensions are given in cm, there is no wall around the irradiator</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 4b:** Cut view of the irradiator, all dimensions are given in cm, there is no wall around the irradiator</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 4c:** Cut view of the irradiator, all dimensions are given in cm, there is no wall around the irradiator</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 4d:** Cut view of the irradiator, all dimensions are given in cm, there is no wall around the irradiator</figcaption></figure>

7.5

7.5

**3.5 Question 3: Influence of the source chamber dimensions**

As questions 2 and 3, this question was **not mandatory**. It was asked to calculate the air kerma and the spectral fluence distribution at 50 cm (see figure 5).

7.5

7.5
<figure><img src="image_9.png" /><figcaption>**Figure 5:** Cut view of the irradiator, all dimensions are given in cm, there is no wall around the irradiator</figcaption></figure>

**4. Solution of the authors**

The authors used MCNP version 4c2 [6] to solve the problem. Different possibilities were studied to calculate the spectral fluence and then the air kerma value. The tallies F2 (average fluence on a surface), F4 (average fluence on a cell, volume) and F5 (point detector) were compared in a simple geometry case (also a hand calculation of the fluence was performed to check the geometry and the parameterization). It was shown that a difference of less than 0.1% was found between the three approaches. Since tally F5 is much faster than the other ones and since the goal of the whole exercise was not to provide an absolute value but rather a relative uncertainty, tally F5 was chosen for the whole problem. No PERT card was used (this card allows getting two solutions for one particular tally by varying a parameter, eg the density) because it is not possible with tally F5.

In order to calculate the air kerma value, the DE-DF card was used. It allows multiplying the tally by each energy bin by using interpolated data. A LOG-LOG interpolation of the conversion coefficients listed in table 4 was chosen.

The physical parameters of the simulation are included in the PHYS card of MCNP. It was decided to use the default parameters in order to include the bremsstrahlung X-rays coming from the secondary electrons created in the irradiator. Secondary electrons were not transported (MODE P): a calculation with the MODE P,E showed no significant difference with the MODE P, which is faster. The computing time was limited to about 840 minutes for each calculation on a 3.2 GHz (1 Go RAM) Dell computer. The authors' solution was not considered as the reference one but included in the comparison with other participants. For the reference geometry, the calculated air kerma value was 8.17660.10⁻⁵ (+/- 0.01 %) pGy/ emitted particle.

**5. Participants and Q0 answer**

It should be mentioned that it was not possible to present all the results in details for all the questions of this problem. Authors decided to present the more interesting results.

**5.1 Participants and codes used**

For this problem, 12 institutes of 10 countries were represented: United Kingdom (1), Czech Republic (1), USA (2), Russia (1), Germany (1), Poland (1), Spain (1), Switzerland (2), Portugal (1), France (2). The codes used to solve this problem are mainly from the MCNP-MCNPX family as it can be seen on figure 6a. It should be noticed that also two home made codes were used. Moreover, figure 6b shows the distribution of the answers for each parameter and each question (the mandatory questions are plotted in red). Most of the participants proposed only a solution of the mandatory questions. This can be explained by the fact the calculation time is long.

It should be noticed that this exercise is not a comparison of different codes, but the comparison of the association code+user. For this reason, results (referenced as participant number + calculation code) do not necessarily reflect the capability of a code to simulate such or such configuration of this problem.
<figure><img src="image_10.png" /><figcaption>**Figure 6a-b:** Codes used to solve the problem and answers of the participants per question.</figcaption></figure>

## 5.2 Reference air kerma value for each participant

In order to have a first overview of the answers of the participants, it was proposed to summarize the reference air kerma value. The results are not plotted as absolute values but by showing the relative shift to the mean expressed in percent (figure 7). By excluding participant b), the relative standard deviation is about 1.4% that is really satisfactory and shows that in a first approach, one can consider that the geometry and the simulation parameters are correct. Further investigations showed that participant b) made a mistake when sampling the source. Indeed, the cylinder of the source and the cylinder of the sampling points were not oriented on the same axis.

<figure><img src="image_11.png" /><figcaption>**Figure 7:** Relative reference air kerma value.</figcaption></figure>

# 6. Answers to question 1

## 6.1 Calculation of the variation of the kerma

Question 1 was solved by all of the participants. In order to be able to compare the results, the analysis was made step by step. The first comparison was made on the value listed in column (2) of table 5 (dair
For each parameter and each participant. The results are shown in figure 8 (the lines joining dots have no physical meaning but are used as guide). We can see that there is a satisfactory agreement for some participants but for others, data can differ of two orders of magnitude, that is really surprising when one considers the good agreement of question 0.

To calculate the slope of the kerma variation, some participants decided not to use only two points but to fit a curve as function of the value of the parameter that is studied. It is for example the case for participant f) as it can be seen on figure 9.

In order to better understand the differences between the participants, it was decided to compare the values of uMC/ΔK.

<figure><img src="image_12.png" /><figcaption>**Figure 8:** $\partial kair/\partial x$ values for all the parameters and all the participants.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 9:** Air kerma value versus source chamber depth, participant f).</figcaption></figure>
## 6.2 $u_{MC}/\Delta K$ for all the participants

As explained in § 3.2, the ratio $u_{MC}/\Delta K$ is a good estimator for the reliability of a simulation. This ratio allows to compare the variation of the air kerma and the uncertainty related to the simulation. Figure 10 shows the values of this ratio. It should be observed that about half of the calculated values did not pass this calculation criterion. It means that for half of the values, the uncertainty is too high to conclude on the reliability of the results. This can be explained by the fact that calculation time is rather long and there are many parameters to study. This may explain why the discrepancies in figure 8 are so high. Moreover it means that the uncertainty budget can not be properly calculated for the data that are not in agreement with the criterion.

<figure><img src="image_14.png" /><figcaption>Figure 10: $u_{MC}/\Delta K$ versus the studied parameters.</figcaption></figure>

## 6.3 Uncertainty budget for question 1

Figure 11 shows the relative variation of the air kerma for each parameter relative to the reference air kerma value, expressed in percent. It can be seen on this figure that the higher contribution to the uncertainty on the air kerma is given by the density of the source and its position (depth). On the other hand, the chamber depth, the density of aluminium, the density of lead and particularly the chamber diameter have a very little influence on the variation of the kerma. The total uncertainty budget is about 0.7 % (k=1) for the authors' solution which is mainly due to the source density: 0.6 % (+/- 0.2 g cm⁻³) due to the self absorption of the source and the distance: 0.3 % (+/- 1 mm). Other parameters can be considered as negligible.

Participant d) used an approach consisting in implementing directly in the simulation the variation of the following parameters : source chamber depth, rings diameter, alloy density and source density. The final uncertainty was found to be 0.8% (uniform distribution) that is consistent with the other method. The same calculation was made using a Gaussian distribution that leads to a relative uncertainty of 0.5% that is also consistent.
<figure><img src="image_15.png" /><figcaption>**Figure 10:** Relative contribution to the uncertainty on air kerma for each parameter</figcaption></figure>

As already mentioned, participants were free to study parameters other than those proposed in table 5. Some participants studied the following parameters:

- air density variation. Participant f) considered a standard deviation of 0.5% of the reference air density that leads to a relative air kerma variation of about 0.001%

- interpolation of conversion coefficients. Participant j) made the comparison of the calculation of air kerma in LOG-LOG interpolation and with the Origin® software. Differences are not significant (they are included in the uncertainties). An other calculation was made using a LOG(E)-LIN(coefficient) interpolation. In this case the difference is of 0.7%.

**Remark :** The method proposed can lead to the fact that some contributions to the relative uncertainty can be lower than the relative uncertainty on the reference value of the calculated air kerma. The question arising is to know if this contribution is significant regarding to the MC uncertainties. The answer is yes, provided that the criterion uMC/ΔK is lower than 0.1. It means that the variation of the air kerma is significant regarding to the uncertainty of the calculation.

# 7. Answers to question 2

Question 2 was dedicated to the study of the influence of the source encapsulation (and self absorption) on the air kerma and the penumbra.

## 7.1 Air kerma, air kerma profile and spectral fluence for configuration a).

As an example, figure 11 shows the reference air kerma value for the configuration a): point source in air. One can see a good agreement of the values with a relative standard deviation of 0.7%.
<figure><img src="image_16.png" /><figcaption>**Figure 11:** Relative reference air kerma value for configuration 2a.</figcaption></figure>

Figure 12 shows the air kerma profile for configuration 2a. The agreement is very good for all the participants except for participant g). After discussion with the participant it appeared that there was a small mistake in the source positioning that led to a smaller source-point of test distance implying a bigger field size (it was then corrected). In some cases, the number of calculations was not enough in the region where the gradient is very high to provide a precise profile.

<figure><img src="image_17.png" /><figcaption>**Figure 12:** Air kerma profile for configuration 2a.</figcaption></figure>

The last comparison for configuration 2a deals with the spectral fluence. Figure 13 shows the spectral fluence at 50 cm from the source.
<figure><img src="image_18.png" /><figcaption>**Figure 13:** Spectral fluence for configuration 2a.</figcaption></figure>

There is a rather good agreement between participants for the whole energy spectrum. In the low energy part, at about 80 keV, the peaks are due to the X-ray fluorescence in lead. It seems that the BRAND code does not take it into account. At about 180 keV, one can see the backscattering peak in lead. In the Compton scattering region, there are some spurious scatterings that look like oscillations for participant g). In a first approach, it was attributed to the physics of the code which could use a special scattering model. In fact the reason was not the model, but the geometry. Indeed, it was discovered that this participant took the same geometry as in question 1: collimator made of rings instead a full lead collimator. The multi-scattering peaks, that disappeared when using volume source in the configuration b) to d), could not have been detected when participants provided the fluence in question 1. These special scatterings could be explained by the fact that the rings and the point source lead to particular scattering angles.

## 7.2 Air kerma profile for all the configurations

A comparison of the profiles for the 4 configurations of question 2 is shown in figure 14, provided by participant a). It is representative for the answer of all participants. One can see that there is an important difference of the penumbra between the point source and the volume sources. Nevertheless, it is more surprising that there is no significant difference of profile for all the volume sources. The penumbra (defined as the distance of the 20-80% kerma value) is about 4 mm for the point source and 2 cm for the volume sources.
<figure><img src="image_19.png" /><figcaption>**Figure 14:** Air kerma profile for the 4 configurations of question 2 for participant a).</figcaption></figure>

**7.3 Spectral fluence and relative air kerma for all the configurations of question 2**

Figure 15 shows the spectral fluence for the 4 configurations. In the case of the point source in air, the Compton edge is sharp. This is not the case for a volume source in air. When the real source is used especially when the self absorption occurs, the fluence is largely affected by multiple scattering. Furthermore, the efficiency of the peak at 661.66 keV is reduced, leading to a decrease of the air kerma value (figure 16). The decrease is of about 20 % between the source in air and the real source with the self-absorption. It means that the assumption sometimes made to calculate a rough value of the air kerma using the activity of the source is not correct.

<figure><img src="image_20.png" /><figcaption>**Figure 15:** Spectral fluence for question 2, participant f).</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>**Figure 16:** Relative air kerma value for question 2, averaged values of all the participants.</figcaption></figure>

**8. Answers to question 3**

Question 3 was dedicated to the study of the influence of the collimator by reducing step by step the number of the rings and by replacing them by full lead. The reference configuration (question 1) has to be modified according to the one of question 2. No special comments can be made on this question since the change in the collimator shape and material has no particular influence neither on the spectral fluence (and then on the air kerma) nor, more surprisingly, on the air kerma profile (see figure 17). In fact to see an effect, it would have been necessary to reduce the length of the collimator with the number of the rings.

<figure><img src="image_22.png" /><figcaption>**Figure 17a-b:** Spectral fluence and air kerma profile for question 3, participant f).</figcaption></figure>

**9. Answers to question 4**

The goal of this question was to look at the influence of the chamber volume. The comparison of the air kerma showed no significant differences with the results of the question Q0. Nevertheless one can compare the spectral fluence for both configurations (Q4 & Q0, fig. 18). The figure is zoomed to see better
the influence of the chamber. It has a very low effect on the fluence except for the backscattering peak which is a little bit less pronounced due to the fact that the distance from the wall of the chamber to the rear of the source is bigger and then the probability for the backscattered photons to reach the point of test is lower. For the same reason one can see that the K and L X-rays of lead have a lower intensity.

<figure><img src="image_23.png" /><figcaption>**Figure 18:** Comparison of spectral fluence for question 4 and question Q0 (participant m).</figcaption></figure>

**10. Special aspects treated by the authors : the whole beta and photon spectrum**

In the exercise, participants were encouraged to simulate only the gamma ray line of 661.66 keV from
¹³³Ba. Authors performed some simulations to study the influence of the whole photon spectrum and also the
electrons and β emission of the source.

- Influence of the whole photon spectrum.

The three X rays of the spectrum : 31.8 keV (1.9%); 32.2 keV (3.6%), 36.3 keV(1.0%) were added to
the main gamma line (figure 19). The rest of the spectrum was not changed. Figure 19 shows that there is
only a very low effect of the whole photon spectrum on the fluence that has no influence on the air kerma.

<figure><img src="image_24.png" /><figcaption>**figure 19 :** Influence of the whole photon spectrum on spectral fluence.</figcaption></figure>
- Influence of β and electrons emissions

The first test consisted in switching off the TTB (Thick Target Bremsstrahlung) that was used to take into account the secondary photons due to slowing down of electrons created by photoelectric or Compton interactions. To do that, the IDES parameter in the PHYS:P card was switched to 1. Calculations showed a small difference with the reference calculation (0.12% of reduction compared to the reference value).

To go further in assessing the contribution of β radiation, it was decided to implement the electron and β spectra. It was done using the β spectra coming from the MIRD [7] data in which the two β spectra are implemented. In order to implement the whole spectrum with the electrons, data were added to the previous spectra by taking care of the emission probabilities since the electrons are discrete lines and β radiation is calculated with different energy binning. Finally the used spectrum is shown in figure 20.

<figure><img src="image_25.png" /><figcaption>**figure 20** : Spectrum of electrons + β contribution of <sup>137</sup>Cs in equilibrium with <sup>137</sup>Ba (energy binning is not linear; the electrons lines are in red).</figcaption></figure>

The second problem that was encountered was how to handle this spectrum (β radiation) to calculate the contribution to the air kerma (due to photon radiation) since in MCNP the tally F5:p can only score the contribution from initial photons. In the same way, if the P (or P,E) mode is used, the contribution due to initial photons is only scored, since MCNP will automatically consider that the source is made of photons. To overcome this problem, the mode P, E and F5:p was kept but the PAR parameter in the source card (SDEF) was changed to “3” to simulate initial electrons. Different tests were made to ensure that the simulation worked correctly. The final value of the air kerma due to the whole β radiations was 9.9353·10<sup>-8</sup> (+/- 0.6%) pGy/equivalent gamma line of 661.66 keV. It is expressed in order to compare with the reference kerma value obtained. This kerma represent 0.12% of the reference kerma value.

**11. Conclusion**

The goal of this exercise was to assess the uncertainty budget related to the determination of the air kerma value by simulating a realistic <sup>137</sup>Cs irradiator. The exercise proposed also to study the influence of the source geometry, the collimator shape and the chamber volume in which the source is located. A specific approach was proposed to calculate the uncertainty budget by studying each parameter contributing to the uncertainty budget. Each parameter was treated separately, assuming no correlation, and the overall uncertainty was calculated by using the contribution of each parameter.

The number of participants (12 institutes and 10 countries and 7 different codes) shows the interest of the proposed exercise even if only a few participants answered to the whole exercise. Indeed, it represents a lot of calculations with different geometries and configurations. The results given by the participants showed a very good agreement of the reference air kerma value even if it was not the purpose of the work. Considering the assessment of the uncertainty budget of question 1, some discrepancies were found between
the participants. This is partially due to the fact that the sensitivity of the air kerma value is very low with
respect to most of the studied parameters. Indeed when the sensitivity was higher, a rather good agreement
was obtained. Calculation time was probably not sufficient to obtain reliable results in some cases, the
criterion $u_{MC}/\Delta$ kair < 0.1 being not always fulfilled. The overall uncertainty budget considering most of the
parameters led to a standard uncertainty of about 0.7% that is mostly dominated by the source density
(0.6%; +/- 0.2 g cm$^{-3}$) and source to point of measurement position (0.1%; +/- 1 mm), the rest being
considered as negligible.

The influence of the source (geometry and self absorption) was studied and results showed an
important influence of the geometry of the source on field penumbra that starts from 4 mm for a point source
to about 2 cm for a realistic source. Moreover, the self-absorption of the source was estimated to be about 20
%, that is very important. For this question the results of the participants were in a good agreement.

The collimator shape and the used materials were studied to see their influence on the air kerma. No
significant difference was found between a ring collimator made of tungsten alloy and a full lead collimator.
Finally, the volume of the chamber containing the source was studied but no difference was found with the
reference geometry except for a very small difference in fluorescence X-rays that has no influence on the air
kerma.

To conclude, the authors would like to thank the participants to this exercise for their contributions and
for the work they performed in this problem.

This problem was proposed by H. Vincke, C. Hranitsky and J.-M. Bordy.

References

[1] ISO 4037-1. X and gamma reference radiation for calibrating dosemeters and doserate meters and for determining their response as a function of photon energy -- Part 1: Radiation characteristics and production methods (1996)

[2] International Commission on Radiation Units and Measurements. *Stopping Powers and Ranges for Protons and Alpha Particles*, ICRU Report 49 (Bethesda, MD: ICRU Publications) (1993)

[3] http://www.nucleide.org/DDEP_WG/Nuclides/Cs-137_tables.pdf

[4] International Commission on Radiation Units and Measurements. *Conversion Coefficients for use in Radiological Protection Against External Radiation*, ICRU Report 57 (Bethesda, MD: ICRU Publications) (1998)

[5] BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, *Guide for the Expression of Uncertainty in Measurement* (GUM), ISBN 92-67-10188-9 (1995)

[6] J. F. Briesmeister. (Ed.) MCNP - *A General Monte Carlo N-Particle Transport Code, Version 4C*. Los Alamos National Laboratory (LANL), Technical Report LA-13709-M (2000)

[7] K.F. Eckerman, R.J. Westfall, J.C. Ryman, M. Cristy, *Availability of nuclear decay data in electronic form, including beta spectra not previously published*. Health Phys. 67, 338-345 (1994)