Commissioning of the Radiation Monitor Calibration Laboratory (LabCal) of IDQBRN for cesium-137 irradiation system

The provision for the Brazilian Army of equipment that provides reliable and safe measurements, enabling decision-making based on radioprotection parameters, leads to the need to investigate the metrology of the calibration system used in the Radiation Monitor Calibration Laboratory (LabCal) of the Institute of Chemical, Biological, Radiological and Nuclear Defense (IDQBRN). To this end, the commissioning in cesium-137 is of primary importance in this process. In order to check the conformity of the radiator system, in this work, the ambient dose equivalent rate, H * (10) ̇ , was obtained experimentally for several configurations to compare them with the appropriate theoretical concepts. For this, the distance between the source of cesium-137 (36.9 GBq in 01/22/2015) and the ionization chamber was varied from 500 to 3000 mm at 250mm intervals. To obtain lower ambient dose equivalent rates, 15 and 32 mm thick lead attenuators were used. The mathematical model that best fit the experimental values was analyzed. In all cases, the potential function offers better fit, since the coefficients of determination obtained are approximately equal to 1, obeying the Law of the Inverse Square of the Distance, according to theoretical foundation. Moreover, it was evaluated that the relative deviations are below the limits established by the relevant


INTRODUCTION
The Aiming to meet the needs of the Army's Chemical, Biological, Radiological and Nuclear Defense System (Sistema de Defesa Química, Biológica, Radiológica e Nuclear do Exército -SisDQBRNEx) in expanding the EB's operational capacity to act in the protection of society, the aim is to provide radiological monitors and identifiers with reliable and safe measurements [2] for prompt use in prevention and security actions against terrorist threats; illegal storage; use, transfer and trafficking of radioactive and nuclear substances and materials [3].
As a preliminary way to guarantee the quality of calibration tests at the magnitude of the ambient dose equivalent rate, H * (10), this study seeks to detail and validate the commissioning of the LabCal cesium-137 source irradiator system. Arrangements involving distance variations between the detector and the radiation source and the use (or not) of lead attenuators were proposed to provide an extensive continuous range of the magnitude under study. To validate this commissioning, the mathematical treatment of the experimental data, the comparison with the related theoretical basis and, finally, the analysis of the conformity of the system according to the set of standards of ISO 4037-1, which deals with radiological protection, is envisaged for reference gamma radiation for calibrating dosimeters and dose rate meters [4].

Commissioning
Commissioning is the process of ensuring that the system and components of a facility or industrial unit are designed, installed, tested, operated, and maintained in accordance with the appropriate operational requirements. That is, the commissioning aims to verify its conformity with the design characteristics and performance criteria [5]. It can be used both in new ventures and in units and systems in the process of expansion, modernization or adequacy [6]. In practice, commissioning is defined as the integrated application of a set of techniques and procedures to verify, inspect and test the system under analysis [7].
As an integral part of commissioning, this study carried out a conference on the conformity of the cesium-137 radiator system, which aims to analyze whether the variation in the ambient dose equivalent rate is in accordance with the theoretical behavior believed with minor variations than the normative upper limit [4].

Inverse Square Law
The Inverse Square Law (ISL) is a mathematical law commonly applicable in wide areas of knowledge and refers to the behavior of a magnitude, proportional to the emission of a beam equally in all directions by a point source, measured (or estimated) at different distances from the issuing source and the detector [8]. In the area of ionizing radiation, this Law applies, without restrictions, to cases of point radioactive sources emitting isotropically in the vacuum [9].
For a point source emitting radiation in all directions, the flow is inversely proportional to the square of this distance. It should be noted that this mathematical model is only true for a point source, a punctiform detector and negligible absorption between the source and the detector [10].
Applied to the ambient dose equivalent operational quantity, the ISL is expressed by Equation 1: * (10) 1 * (10) 2 = where H * (10)1 is the ambient dose equivalent at distance r1 of the source and H * (10)2, at distance r2 of the source.
Through mathematical manipulations and making the distance r1 = 1 m. So, H * (10)1 represents the ambient dose equivalent at a point away from one meter from the source. Thus, we obtain Equation 2. * (10) 2 = * (10) 1 Since H * (10)2 can be the equivalent of the ambient dose at any point whose distance from the source is r and that H * (10)1 is equal to a constant B, we can generalize to Equation 3: * (10) 2 = 2 where B is the ambient dose equivalent at a point 1 m away from the radioactive source.
In specific cases of real sources with small dimensions in relation to detector distance, the ISL lacks experimental approval [11], as will be developed in this study.

Correction for air temperature and pressure variation for an unsealed ionization chamber
For adverse environmental conditions, it is necessary to introduce a correction factor for air temperature and atmospheric pressure (Equation 4) between the measurement and the reference calibration conditions [12]: where p is atmospheric pressure during the test in in kPa; T is the ambient temperature during the test in K; p0 is the reference atmospheric pressure (101.3 kPa) and T0 is the reference ambient temperature (293.15 K).

Air kerma and ambient dose equivalent quantities
Radioprotection is a set of legal, technical and administrative measures that aim to reduce the exposure of living beings to ionizing radiation, to levels as low as reasonably achievable. In this area, the fundamental magnitude on which national gamma radiation standards are calibrated is air kerma, Ka [in Gray = Gy =J kg -1 ]. In theoretical terms, the air kerma is the dEtr quotient per dm, where dEtr is the sum of all the initial kinetic energies of all charged particles released by neutral particles or photons, incident on a dm mass of air [6].
According to CNEN NN 3.01-2011 [13], for strongly penetrating external radiation, the magnitude adopted for defined area monitoring is the ambient dose equivalent, H * (10) [in Sievert = Sv = J Kg-1], in a tissue equivalent phantom known as the ICRU sphere (International Commission on Radiation Units & Measurements). This magnitude refers to the value of the dose equivalent that would be produced by the corresponding expanded field and aligned in the ICRU sphere at depth d, in the radius that opposes the aligned field [5]. The recommended depth is 10 mm [9].
From the air kerma it is possible to determine all the operational quantities of current use in radioprotection, whose definitions and conversion factors are found in the literature. According to ISO 4037-3, the ambient dose equivalent rate, H * (10) , is measured indirectly and calculated from the air kerma rate, ̇, according to Equation 5 [14]. * (10) = ℎ * (10) × ̇ Specifically for a monoenergetic beam of cesium-137 (whose main gamma energy is defined as 662 keV) [4], the conversion factor h * K(10) is equal to 1.21 Sv/Gy [14].

Time correction of quantities
Similar to the exponential decay of the activity of a radioactive source [9], the air kerma rate (and hence the ambient dose equivalent rate) must be corrected according to the lapse of time between the date of the initial measurement and the reference date (Equation 6). For comparative purposes in this study, the reference date was set as 04/06/2021, performing the radioactive decay between the original test date and the reference date: where K a 0 the initially measured air kerma rate, ̇ the corrected air kerma rate after a period ∆ between the reference date and the start date and t1/2 the half-life time of Cs-137 (11018.3 days) [15].

Materials
To perform the experimental analyses, a reference set previously calibrated in a competent laboratory was used, consisting of:

Measurement chamber assembly
The measure set (ionization chamber and electrometer) must be calibrated by a competent laboratory linked to the Brazilian Calibration Network (Rede Brasileira de Calibração -RBC).
The ionization chamber is one of the main dosimeters used for precision measurements, being considered a reference instrument for radiometric survey. They consist of a volume filled with an electrical and radiation-sensitive insulating gas and two collecting electrodes. The radiation incident in the chamber ionizes atoms in the sensitive volume of gas creating electrons and ions pairs. The electric field attracts these charged particles, generating a deposited electrical charge. Thus, the resulting electric current (related to the intensity of incident radiation) is measured by means of an electrical measurement device (electrometer) [17].
The electrometer quantifies the integrated electrical load during a certain period of irradiation of the ionization chamber [18]. Specifically, at LabCal, these devices are pre-programmed to account for the electrical charge over a period of 60 s.
The reference set used in this study was calibrated at the National Laboratory of Ionizing Radiation Metrology (Laboratório Nacional de Metrologia das Radiações Ionizantes -LNMRI) on 10/26/2020, resulting in an air kerma calibration factor (NK) equal to 2.4987E+04 (Gy/C), obtained with average energy photons corresponding to cesium-137 [19].

Temperature, humidity and pressure meter
The equipment has thermometer, hygrometer and barometer integrated as measuring instruments for the control environmental conditions (temperature, relative humidity and atmospheric pressure, respectively). The parameters obtained in the meter are used to correct the test conditions (temperature and air pressure) in relation to the reference conditions. The equipment is periodically calibrated at each of these quantities by a laboratory designated by RBC [20].

Methods
Initially, the ionization chamber was fixed to the irradiation table at the reference point. In LabCal, the default position is 2000 mm distance between the dosimeter and the radioactive source ( Figure 2).
In possession of the average corrected current value ( ̅ ), the respective air kerma rates explained in Equation 8 [9] are calculated, using the NK value of the reference assembly [16], and the corresponding ambient dose equivalent rates, using the conversion factor (Equation 5) [11].
For comparative purposes, the air kerma rates and the corresponding ambient dose equivalent rates for the reference date are corrected using radioactive decay (Equation 6).

Finally, it is mathematically treated the numerical values obtained experimentally in order to
investigate if the real behavior resembles the ISL, thus being able to be validated the adopted premises [6]. In addition, there is the reproducibility of commissioning in accordance with normative instructions [4].

Calculation of air kerma rate and ambient dose equivalent rate
For better exemplifying and understanding, the experimental measurements performed at 500 mm from the radiative source without the use of attenuator (A0) in Table 1 and the respective calculations of the air kerma rate and the ambient dose equivalent rate were explained in this study. Similarly, the same detailed procedure was performed for the other test points selected with exposures without attenuator. Data from 500 to 3000 mm with attenuator A0 are expressed in Table 2. Similarly, the same procedure was performed with A15 and A32 for distance from 500 mm to 3000 mm, whose data are presented in Tables 3 and 4, respectively.

Plot of graphics
With tables 2, 3 and 4, and with the help of Excel software, in Figures 3, 4 and 5 are qualitatively represented the results referring to the methodology adopted in this study, in order to define the mathematical model that best describes the behavior of LabCal's cesium-137 irradiator system.   .
The coefficient of determination (R 2 ), which represents the measure of fit of a generalized linear statistical model, such as simple or multiple linear regression to the observed values, is also explained next to each graph mentioned above. Indeed , the mathematical models proved to be adequate to the experimental data, to the extent that the higher the R 2 , the more explanatory the model adopted. The It is also emphasized that, in all cases, the coefficients A obtained for the power functions (Equation 9) are approximately equal to -2, It is reiterated that the experiments performed are appropriate to the Law of the Square of the Inverse of distance; since the power functions significantly represent reality and have exponents close to -2, similar to Equation 3 for point sources [5]. That is, it is evident that the dimensions of the source geometry are despicable compared to the dimensions of the radiation field.

Irradiator system conformity check
Taking as reference the positioning at 2000 mm between the Source of cesium-137 and the ionization chamber, the LabCal conformity in this commissioning was investigated. To this goal, the calculated theoretical values and their respective values measured experimentally of the magnitude of the ambient dose equivalent rate were compared.
According to ISO 4037-1 [4], standard on radiological protection for dosimeter calibration and dose rate meters in gamma radiation, the measurements of the air kerma rate and, consequently, the ambient dose equivalent rate should be proportional within 5% of the respective theoretical values predicted through the ISL for various test points along the main axial axis. The distances of 1000 and With the data collected from Tables 2, 3 and 4, Table 5 shows the relative deviation, in percentage, between the rate of ambient dose equivalent measured experimentally and the theoretical ambient dose equivalent rate, calculated by ISL (Equation 2), which represents the conventional true value.
It is emphasized that the relative deviations are less than 5% for all combinations of attenuators and selected distances. Thus, the conformity conference of LabCal's cesium-137 irradiator system was demonstrated in the light of ISO 4037-1 [4]

CONCLUSIONS
The research objective was achieved by checking between experimental values, mathematical models and theoretical foundation. in conformity with the Law of the Square of the Inverse of distance and that the geometric dimensions of the radiative source are despicable compared to the dimensions of the studied radiation field, in accordance with the expected theoretical behavior.
The work also allowed contributing in future time to the determination, through mathematical devices, of the necessary laboratory parameters (distance and attenuator) to exposure at a certain rate of normative environment ambient dose equivalent. This can be seen in Tables 2, 3 and 4 and in the graphs of Figures 3, 4 and 5 of this study. Therefore, it is perceived that this methodology (configuration determination) is essential to structure the calibration tests for gamma radiation monitors.
As a result of the results described in Table 5, it is possible to positively assess the conformity of LabCal's cesium-137 irradiator system, since the relative deviations obtained were within the normative limit of 5% in all cases evaluated.
Finally, in the continuation of the qualification of the Laboratory of Calibration of Gamma Radiation Monitors, the main objective of this work, the aim is to carry out other tests to compose the commissioning of the LabCal irradiator system, such as: influence of scattered radiation, uniformity radiation beam, field size, and head radiation leakage. In addition, concepts, studies and evaluations of uncertainties associated with the commissioning process and, consequently, with the calibration process will be inserted in the future.

ACKNOWLEDGMENT
The team thanks the IDQBRN, the Military Institute of Engineering (Instituto Militar de Engenharia -IME) and the Institute of Radiation Protection and Dosimetry (Instituto de Radioproteção e Dosimetria -IRD) of the National Nuclear Energy Commission (Comissão Nacional de Energia Nuclear -CNEN) for all support for the development of this study.