Evaluation of the calibration factors of neutron dose rate meters in a ²⁴¹Am-Be neutron field

Evaluation of the calibration factors of neutron dose rate meters in a 241 Am-Be neutron field 1 corresp first-author lnthiem@vinatom.gov.vn lnthiem@vinatom.gov.vn lnthiem@vinatom.gov.vn 2 1 2 corresp tranhoainam4@dtu.edu.vn tranhoainam4@dtu.edu.vn tranhoainam4@dtu.edu.vn Institute for Nuclear Science and Technology, VINATOM, 179 Hoang Quoc Viet, Hanoi, Vietnam Institute for Nuclear Science and Technology, VINATOM, 179 Hoang Quoc Viet, Hanoi, Vietnam Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City, Vietnam Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City, Vietnam Calibrations were performed for three types of neutron ambient dose equivalent rate meters, i.e., Aloka TPS-451C (Hitachi), KSAR1U.06 (Baltic Scientific Instruments) and Model 12-4 (Ludlum), using a standard field of a 241 Am-Be source. The measured total neutron ambient dose equivalent rates, <math id="M1"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> , were analyzed to obtain the direct neutron ambient dose equivalent rates, <math id="M2"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> , using the ISO 8529-2 recommended the generalized-fit method (GFM), semi-empirical fit method (SEM), and reduced-fitting method (RFM) fit methods. The calibration factor (CF), defined as the ratio between the conventional true value of the neutron ambient dose equivalent rates in a free field, <math id="M3"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>FF</mtext></mrow></msub><mo>'</mo></mrow></math> , and <math id="M4"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> , was evaluated as one of the important characteristics of the neutron meters in the present work. The fitting results show that the <math id="M5"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> values of the meters are in good agreement within the theoretical data within 4%. The averaged CFs of the three neutron meters were evaluated as 0.99 ± 0.01, 1.00 ± 0.03 and 0.99 ± 0.08, respectively. The largest standard uncertainty of these values was determined to be approximately 18.47% ( k =1). The standard uncertainty of the CFs obtained using the RFM method was less than 4.23% ( k =1), which is the smallest uncertainty among the three methods. Neutron meter Calibration factor 241 Am-Be source 1 Introduction 1 The reading of a neutron dose equivalent rate meter in a neutron field is attributable to both neutrons that arrive directly from the source to the meter and neutrons scattered from air, concrete walls, and other objects in the calibration room. The scattered component depends on the source type, room materials and configuration, calibration distance, and also the shape and the material composition of the neutron meters [ 1 1 ]. However, different neutron meters could yield different readings for the same total neutron field. Thus, an appropriate calibration process is necessary before this instrument can be used for radiation protection assessment. In the calibration process, the calibration factor (CF) of the neutron meter is evaluated as one of the important characteristics. The CF is defined as the ratio between the conventional true value of the neutron ambient dose equivalent rate in a free field (denoted as <math id="M6"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>FF</mtext></mrow></msub><mo>'</mo></mrow></math> ) and the direct component of the neutron ambient dose equivalent rate as measured by the neutron meter (denoted as <math id="M7"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> ). H * (10) FF can be calculated analytically and H * (10) dir can be obtained by analyzing the readings of the neutron meters. To obtain the value of <math id="M8"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> , the scattered component must be extracted from the total neutron ambient dose equivalent rate (denoted as <math id="M9"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> ). Various methods are available for this purpose, such as the well-known shadow-cone technique and the ISO 8529-2 recommended fit methods. To apply the shadow-cone technique, it is necessary that the geometry of the shadow-cone should be amenable to that of the source and the neutron meter. Regarding the fit methods, three methods are recommended including the generalized-fit method (GFM), semi-empirical fit method (SEM), and reduced-fitting method (RFM) [ 2 2 ]. In the present work, calibrations were performed for three types of neutron meters, i.e. Aloka TPS-451C (Hitachi), KSAR1U.06 (Baltic Scientific Instruments), and Model 12-4 (Ludlum), in the standard calibration field with a 241 Am-Be source at the Institute for Nuclear Science and Technology (Hanoi, Vietnam). The neutron meters were used to measure the values of <math id="M10"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> at various distances from the source. Give that a suitable shadow-cone for the 241 Am-Be source and the neutron meters is not available, the GFM, SEM, and RFM fit methods were used to obtain the values of <math id="M11"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> for the neutron meters. The <math id="M12"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> values of each meter obtained using the three fit methods were compared to confirm the reliability of these approaches. Once the <math id="M13"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> values of the meters are available, the CFs can be evaluated. A comparison of the CFs of the neutron meters and the uncertainties among the three methods was also performed. The most suitable fit method for the calibration routine is discussed in this work. 2 Instruments and methods 1 2.1 Neutron calibration field property 2 A neutron calibration room was constructed with inner dimensions of 7.0×7.0×7.0 m 3 [ 3 3 ] and a radionuclide neutron 241 Am-Be source of X14 type encapsulation supplied by Hopewell Designs, Inc., USA, was installed in a container at the center of the floor base. The initial source strength was determined at NIST (USA) on January 23, 2015, to have a value of 1.299 × 10 7 s -1 with the expanded uncertainty of 2.9% ( k =2). A detailed description of the neutron calibration room and the 241 Am-Be source can be found in previous works [ 3 3 , 4 4 ]. The source anisotropy correction factor is 1.030, which was evaluated at a distance of 100 cm from the source and in a direction perpendicular to the cylindrical source axis using the MCNP5 simulation [ 4 4 ]. This anisotropy correction factor is consistent with the values of 1.027 - 1.030 for similar 241 Am-Be sources as reported by other laboratories [ 5 5 , 6 6 ]. 2.2 Neutron meters 2 In the measurements, three portable neutron meters were used as shown in Fig. 1 Fig. 1 . The Aloka-TPS-451C meter that is made by the Hitachi group consists of a cylindrical proportional counter with a length of 15.5 cm and a diameter of 2.5 cm and filled with 5 atm 3 He gas at 20 o C. The counter is covered by a cylindrical moderator of high-density polyethylene ( ρ =0.95 g/cm 3 ) with a length of 23.0 cm and a diameter of 21.0 cm. The counter has cylindrical effective dimensions of 7.0 cm in length and 2.4 cm in diameter. The Aloka-TPS-451C meter can be used to measure neutrons in the energy range from 25×10 -9 to 15 MeV with a dose equivalent rate up to 10 mSv/h. In general, the meter is not sensitive to photons [ 7 7 ]. The KSAR1U.06 meter that is made by Baltic Scientific Instruments (BSI) enterprise has three cylindrical 3 He proportional counters with a diameter of 3.2 cm and a length of 2.0 cm and is filled with 2.7 atm pressure assembled to form a neutron sensitive detector and a photon sensitive Geiger Muller counter. The meter allows for measurement of the ambient dose equivalent rate in the range from 0.28 μ Sv/h to 700 μ Sv/h for neutrons and from 0.14 μ Sv/h to 1400 μ Sv/h for photons. The KSAR1U.06 meter is produced in compliance with IAEA recommendations and requirements [ 8 8 ]. The outer dimensions of the meter are 30 cm×16 cm×13 cm [ 9 9 ]. The Model 12-4 meter is made by Ludlum Incorporation and consists of a cylindrical proportional counter 3 He with a diameter of 1.6 cm and a length of 2.5 cm surrounded by a 22.9 cm diameter cadmium loaded polyethylene sphere. The meter rejects photons up to 100 mSv/h and facilitates the measurement of neutrons from thermal through 7 MeV sources. It provides response up to 12 MeV with a neutron ambient dose equivalent rate up to 100 mSv/h. The meter generates an energy response for an appropriate inverse radiation protection guide curve for neutrons [ 10 10 ]. 2.3 Measurements of total neutron ambient dose equivalent rates 2 In the experiments, the effective points of the neutron meters were placed at the reference point of the neutron field such that the central axis of the Aloka TPS-451C meter was parallel to the base floor and perpendicular to the central beamline at the effective point. The appropriate settings were applied to the other two neutron meters during the measurements. The KSAR1U.06 meter was irradiated from the front side, whereas the Model 12-4 meter was irradiated from the side with the needle analog display facing upwards. Then the values of <math id="M14"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> were measured using each neutron meter at various distances ranging from 60 cm to 250 cm away from the source. In general, the neutron meters based on the 3 He gas proportional counters as thermal neutron detectors can detect neutrons by the reaction 3 He(n,p) 3 H ( Q = 0.76 MeV) and are not sensitive to photons due to the suitably applied discrimination level [ 11 11 ]. Therefore, the influence of photons on the <math id="M15"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> readings is negligible. In this work, the low sensitivity to photons of the Aloka-TPS 451C and Model 12-4 meters was confirmed by irradiation at the photon ambient dose equivalent rate of the 137 Cs OB6 Buchlor standard source at 100 μ Sv/h. The photon sensitivity of the KSAR1U.06 meter was not confirmed because it is integrated with a photon sensitive Geiger Muller counter. However, the influence of photons to the KSAR1U.06 meter can also be neglected due to its low contribution in the neutron standard field, which is confirmed in a previous work [ 12 12 ]. 2.4 Fit methods 2 To obtain the <math id="M16"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> for the neutron meter’s total reading, the scattered component must be extracted from the <math id="M17"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> measured by the meter. Three ISO recommended fit methods, i.e. GFM, SEM, and RFM methods were used with the assumption that the linearity of the neutron meter is unity. The GFM method describes <math id="M18"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> as a function of the distance from the source as follows: [ 2 2 , 13 13 ] <math display="block" id="M19"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo><mo stretchy="false">(</mo><mi>l</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mi>k</mi><mrow><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac><mo>×</mo><mrow><mo>[</mo><mrow><mfrac><mrow><mn>1</mn><mo>+</mo><mi>δ</mi><mo>×</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>r</mi><mtext>D</mtext></msub></mrow><mrow><mn>2</mn><mi>l</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mn>1</mn><mo>+</mo><mover accent="true"><mi>Σ</mi><mo stretchy="true">¯</mo></mover><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo><mo>×</mo><mi>l</mi></mrow></mfrac><mo>+</mo><msup><mi>A</mi><mo>′</mo></msup><mo>×</mo><mi>l</mi><mo>+</mo><mi>s</mi><mo>×</mo><msup><mi>l</mi><mn>2</mn></msup></mrow><mo>]</mo></mrow><mn>,</mn></mrow></math> where, k is the characteristic constant; l is the distance from the center of the source to the device center; A’ is the air in-scatter component; s is the factor that accounts for the contribution of all other in-scattered neutrons; r D is the detector radius of the spherical meter or it is considered as half of the minimum dimension for a non-spherical meter; δ = 0.5 is the neutron effectiveness parameter and <math id="M20"><mrow><mover accent="true"><mo>∑</mo><mo stretchy="true">¯</mo></mover><mo stretchy="false">(</mo><mi>E</mi><msup><mrow><mo stretchy="false">)</mo><mo>=</mo><mn>890</mn><mo>×</mo><mn>10</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow></math> cm -1 . In Eq. (1), k , A’ and s are free parameters obtained during the fitting process. The SEM method proposed by Eisenhauer et al. [ 5 5 , 6 6 ] was summarized in ISO 8529-2:2001 [ 2 2 ]. The SEM is based on the assumption that the air-scattered component decreases linearly with distance from the source while the room-scattered component is independent of the distance. Therefore, the <math id="M21"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> can be fitted as a function of the distance from the source center ( l ) and the detector radius ( r D ) as follows: <math display="block" id="M22"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo><mo stretchy="false">(</mo><mi>l</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mi>k</mi><mrow><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac><mo>×</mo><mrow><mo>[</mo><mrow><mn>1</mn><mo>+</mo><mi>δ</mi><mo>×</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>r</mi><mtext>D</mtext></msub></mrow><mrow><mn>2</mn><mi>l</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mo>]</mo></mrow><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>A</mi><mo>×</mo><mi>l</mi><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>R</mi><mo>×</mo><msup><mi>l</mi><mn>2</mn></msup><mo stretchy="false">)</mo><mn>,</mn></mrow></math> where, A is the net air-scatter effect (in-scatter minus out-scatter) which may appear to be similar to the A’ factor in Eq. (1); R is the room scattered component which is similar to the factor s in Eq. (1). The other parameters such as δ , r D , and k have the same meanings as those in Eq. (1). In the SEM method, k , A and R are free parameters obtained via a fitting process. It is indicated in Ref. [ 15 15 ] that the SEM is well applied in small and intermediate size rooms. It is therefore suggested that the SEM will be useful for the neutron calibration room in this work. The RFM method is applicable if the measured distance l is greater than or equal to approximately 1.5 times the largest dimension of the meter [ 16 16 ]. Given that in the present work, the measurements were conducted at distances greater than 60 cm, the RFM method is applicable. Based on this assumption, it is considered that the neutron ambient dose equivalent rate due to the room-scattered component, denoted as R sct , is dominant at most calibration points and is constant in the space of the calibration room. Thus, the <math id="M23"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> can be rewritten as [ 2 2 ]: <math display="block" id="M24"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo><mo stretchy="false">(</mo><mi>l</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mi>k</mi><mrow><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac><mo>+</mo><msub><mi>R</mi><mrow><mtext>sct</mtext></mrow></msub><mn>.</mn></mrow></math> In Eq. (3), the term k/l 2 is an important factor which determines the corresponding direct component <math id="M25"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> rate at the distance l from the source. 3 Results and discussion 1 3.1 Conventional true value of <math id="M26"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>FF</mtext></mrow></msub><mo>'</mo></mrow></math> 2 The values of <math id="M27"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>FF</mtext></mrow></msub><mo>'</mo><mo stretchy="false">(</mo><mi>l</mi><mo stretchy="false">)</mo></mrow></math> at the distance l can be theoretically determined by the Eq. (4) [ 2 2 ]: <math display="block" id="M28"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>FF</mtext></mrow></msub><mo>'</mo><mo stretchy="false">(</mo><mi>l</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi>B</mi><mo>×</mo><msub><mi>F</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo></mrow><mrow><mn>4</mn><mi>π</mi><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac><mo>×</mo><msub><mi>h</mi><mi>ϕ</mi></msub><mn>,</mn></mrow></math> where B is the neutron source strength; F 1 ( θ ) is the source anisotropy correction factor which is 1.030 at 1.0 m as reported in a previous work [ 4 4 ]. For the purpose of this work, <math id="M29"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>FF</mtext></mrow></msub><mo>'</mo></mrow></math> at 1.0 m is considered as the conventional true value to determine the CFs of the neutron meters. 3.2 Neutron ambient dose equivalent rates measured by neutron meters 2 The results of measurements of <math id="M30"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> using the neutron meters Aloka TPS-451C (Hitachi), KSAR1U.06 (BSI), and Model 12-4 (Ludlum) in the distance range from 60 cm to 250 cm are shown in Fig. 2 Fig. 2 . All values of the <math id="M31"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> were normalized to the same time point. In the measurements, the statistical deviation of the H * (10) tot measured using the Aloka TPS-451C meter, and KSAR1U.06 meter are estimated within 5%. The value for the Model 12-4 meter is estimated within 10% given that it uses a needle analog display. It is evident from Fig. 2 Fig. 2 that the readings of KSAR1U.06 show a higher response than that of the others. This is ascribed to the intrinsic response of the KSAR1U.06 meter. 3.3 Fitting parameters 2 The <math id="M32"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> measured by the three neutron meters in the distance range from 60 cm to 250 cm were fitted according to Eqs. (1)–(3) with the application of the instrumental weighting method in the Levenberg Marquardt iteration algorithm, in which the weighting factors were set as <math id="M33"><mrow><mn>1</mn><mo>/</mo><msqrt><mrow><msub><mi>R</mi><mtext>d</mtext></msub></mrow></msqrt></mrow></math> , where R d is the <math id="M34"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>'</mo></mrow></math> measured by the neutron meters. As a result of the fitting process, the free parameters corresponding to each methods are obtained (i.e. k , A’ and s in GFM; k , A and R in SEM; k and R sct in RFM) as shown in Table 1 Table 1 . From Table 1 Table 1 , it is evident that the deviations of k obtained from the fit methods are less than 20%, which could contribute to the uncertainty budgets of the CFs. 1 1 Method 1 1 Fitting parameters 3 1 Neutron dose equivalent rate meter 1 1   1 1 1 1 Aloka TPS-451C, Hitachi 1 1 KSAR1U.06, BSI 1 1 Model 12-4, Ludlum 1 1 GFM 1 1 k 1 1 1535750 ± 34790 1 1 1508230 ± 105050 1 1 1506720± 277450 1 1   1 1 A’ (× 10 -4 ) 1 1 0.243 ± 2.985 1 1 0.000 ± 0.001 1 1 9.918± 0.004 1 1   1 1 s (× 10 -6 ) 1 1 9.025 ± 0.729 1 1 32.631 ± 1.581 1 1 0.000 ± 0.144 1 1 SEM 1 1 k 1 1 1528160± 28760 1 1 1475300 ± 98120 1 1 1516850 ± 214160 1 1   1 1 A (× 10 -4 ) 1 1 0.002 ± 3.024 1 1 6.211± 0.002 1 1 7.855 ± 0.003 1 1   1 1 R (× 10 -6 ) 1 1 8.875 ± 1.465 1 1 26.912± 15.630 1 1 0.001 ± 9.009 1 1 RFM 1 1 k 1 1 1530730± 6130 1 1 1500560± 20690 1 1 1506560 ± 60140 1 1   1 1 R sct 1 1 13.521± 0.195 1 1 48.753± 0.888 1 1 10.500 ± 3.535 3.4 Calibration factors and uncertainties 2 From the definition of CF, the equation of H * (10) FF (Eq. (4)) and the direct term k/l 2 in the fitting process, the CF can be expressed as: <math display="block" id="M35"><mrow><mi>C</mi><mi>F</mi><mo>=</mo><mfrac><mrow><mi>B</mi><mo>×</mo><msub><mi>F</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo></mrow><mrow><mn>4</mn><mi>π</mi><mi>k</mi></mrow></mfrac><mo>×</mo><msub><mi>h</mi><mi>ϕ</mi></msub><mn>.</mn></mrow></math> The standard uncertainty of the CF (denoted as u CF ) can be calculated by applying the uncertainty propagation principle. The uncertainty budgets of the CFs due to type A uncertainty of the fitting characteristic constant ( u k ) and type B uncertainty of the source strength ( u B ) are summarized and shown in the Table 2 Table 2 , together with the u CF values. The CFs of each neutron meter corresponding to the three fit methods are in agreement and close to unity (see Fig. 3 Fig. 3 ), even at different levels of u CF (see Table 2 Table 2 ). The averaged CFs of the three neutron meters are 0.99 ± 0.01, 1.00 ± 0.03 and 0.99 ± 0.08, respectively. The largest difference in the CFs due to different fit methods is approximately 4.0% and was obtained with the KSAR1U.06 meter using the GFM and SEM methods. For the other cases, the CF of each meter is consistent within 2.0%. This means that the calibration process is reliable. The CFs satisfy the ISO criteria [ 2 2 ] as a unique property of the neutron measuring device and is independent of the characteristics of the facilities and the calibration techniques. The largest uncertainty of the CFs was determined for the Model 12-4 meter, which can be seen in Table 2 Table 2 . It is also evident that the CF uncertainties due to the RFM fit method are the smallest (in the range from 1.50% to 4.23%) compared to that obtained using the two other methods. This is described as a simple form of the fitting equation (Eq. (3)), where the constant R sct is consistent with the statement of uniform scattered component as noted by Vega-Carrillo et al. [ 17 17 , 18 18 ]. 1 1 Method 4 1 Uncertainty budget 3 1 u CF (%) 1 1 2 1 u k (%) 2 1 u B (%) 1 1 1 1 1 1 1 1 1 1 Aloka TPS-451C 1 1 KSAR1U.06 1 1 Model 12-4 1 1 Source strength 1 1 Aloka TPS-451C 1 1 KSAR1U.06 1 1 Model 12-4 1 1 GFM 1 1 2.27 1 1 7.00 1 1 18.41 1 1 1.45 1 1 2.69 1 1 7.14 1 1 18.47 1 1 SEM 1 1 1.88 1 1 6.65 1 1 14.12 1 1 1.45 1 1 2.38 1 1 6.81 1 1 14.19 1 1 RFM 1 1 0.40 1 1 1.38 1 1 3.99 1 1 1.45 1 1 1.50 1 1 2.00 1 1 4.23 4 Conclusion 1 Calibrations were performed for three types of neutron ambient dose equivalent rate meters, i.e. Aloka TPS-451C, KSAR1U.06, and Model 12-4, using the GFM, SEM and RFM fit methods. The direct component of the neutron ambient dose equivalent rate, <math id="M36"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>dir</mtext></mrow></msub><mo>'</mo></mrow></math> , obtained using the three meters were analyzed in addition to the conventional true values of the free field, <math id="M37"><mrow><msup><mi>H</mi><mo>*</mo></msup><msub><mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow><mrow><mtext>FF</mtext></mrow></msub><mo>'</mo></mrow></math> , to evaluate the CFs of the meters. The results show that the CFs of the three neutron meters obtained based on the three methods are close to unity with a deviation of less than 4%. The average values of the CFs of the meters are 0.99 ± 0.01, 1.00 ± 0.03 and 0.99 ± 0.08, respectively. The standard uncertainties of the CFs obtained via the different methods are in the range from 1.50% to 18.47% depending on the neutron meter and fit method that was utilized. By comparing the three fit methods, it was determined that the uncertainty obtained with the RFM method is the smallest (less than 4.23%). This means that this method is the most suitable for routine calibration. References S.M. Jun , B.H. Kim , J.L. Kim , J.K. Lee , Calibration of spherical neutron measuring devices with a 252Cf source in the neutron calibration room of the KAERI . Journal of Nuclear Science and Technology , Supplement 5 , 286 - 289 ( 2008 ). Calibration of spherical neutron measuring devices with a 252Cf source in the neutron calibration room of the KAERI ISO 8529-2:2001 (E), Reference Neutron Radiations- Part 2: Calibration Fundamentals of Radiation Protection Devices Related to the Basic Quantities Characterizing the Radiation Field . Switzerland ( 2000 ). Le, T.N. , Tran, H.N. , Nguyen, K.T. , Trinh, G.V ., Neutron calibration field of a bare 252Cf source in vietnam . Nuclear Engineering and Technology 49 , 277 - 284 ( 2017 ). doi: 10.1016/j.net.2016.07.011 http://doi.org/10.1016/j.net.2016.07.011 Neutron calibration field of a bare 252Cf source in vietnam Le, T.N. , Tran, H.N. , Nguyen, Q.N. , Trinh, G.V. , Nguyen, K.T ., Characterization of a neutron calibration field with 241Am-Be source using bonner sphere spectrometer . journalApplied Radiation and Isotopes 133 , 68 - 74 ( 2018 ). doi: 10.1016/j.apradiso.2017.12.012 http://doi.org/10.1016/j.apradiso.2017.12.012 Characterization of a neutron calibration field with 241Am-Be source using bonner sphere spectrometer Loreti, S. , Pietropaolo, A ., 2015 . Assessment of the neutron emission anisotropy factor of a sealed Am-Be source by means of measurements and Monte Carlo simulations . Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 797 , 201 - 205 . doi: 10.1016/j.nima.2015.06.047 http://doi.org/10.1016/j.nima.2015.06.047 Assessment of the neutron emission anisotropy factor of a sealed Am-Be source by means of measurements and Monte Carlo simulations Mazrou, H. , Sidahmed, T. , Allab, M ., 2010 . Neutron field characterisation of the OB26 CRNA irradiator in view of its use for calibration purposes . Radiation Protection Dosimetry 141 , 114 - 126 . doi: 10.1093/rpd/ncq166 http://doi.org/10.1093/rpd/ncq166 Neutron field characterisation of the OB26 CRNA irradiator in view of its use for calibration purposes Aloka TPS-451C-Hitachi, Neutron Survey Meter TPS-451C . http://www.hitachi.com/businesses/healthcare/products-support/radiation/surveymeter/tps451c/index.html http://www.hitachi.com/businesses/healthcare/products-support/radiation/surveymeter/tps451c/index.html . Aloka TPS-451C-Hitachi, Neutron Survey Meter TPS-451C IAEA Nuclear Security Series No. 1, Technical and functional specifications for border monitoring equipment . International Atomic Energy Agency , ( 2006 ). IAEA Nuclear Security Series No. 1, Technical and functional specifications for border monitoring equipment KSAR1U.06-BSI, Neutron Search Detector KSAR1U.06 . http://bsi.lv/en/products/neutron-search-detectors-infrare/neutron-search-detector-ksar1u06/ http://bsi.lv/en/products/neutron-search-detectors-infrare/neutron-search-detector-ksar1u06/ . KSAR1U.06-BSI, Neutron Search Detector KSAR1U.06 Model 12-4-Ludlum, titleNeutron Dose Ratemeter - Model 12-4 . https://ludlums.com/products/all-products/product/model-12-4 https://ludlums.com/products/all-products/product/model-12-4 . Model 12-4-Ludlum, titleNeutron Dose Ratemeter - Model 12-4 G.F. Knoll , Radiation detection and measurement . 4 th edition ed., Wiley ( 2010 ). Radiation detection and measurement T.N. Le , H.N. Tran , T.D. Duong , Q.N. Nguyen , T.Q. Ho , G.V. Trinh , K.T. Nguyen , Evaluation of gamma contribution in a neutron calibration field of 241Am-Be source . journalApplied Radiation and Isotopes volume 133 , 117 - 120 ( 2018 ). doi: 10.1016/j.apradiso.2018.01.001 http://doi.org/10.1016/j.apradiso.2018.01.001 Evaluation of gamma contribution in a neutron calibration field of 241Am-Be source H. Kluge , K. Weise , J.B. Hunt , Calibration of neutron sensitive spherical devices with bare and D2O-moderated 252Cf sources in rooms of different sizes . Radiation Protection Dosimetry 32 , 233 - 244 ( 1990 ). doi: 10.1093/oxfordjournals.rpd.a080738 http://doi.org/10.1093/oxfordjournals.rpd.a080738 Calibration of neutron sensitive spherical devices with bare and D2O-moderated 252Cf sources in rooms of different sizes C.M. Eisenhauer , Review of scattering corrections for calibration of neutron instruments . Radiation Protection Dosimetry 28 , 253 - 262 ( 1989 ). doi: 10.1093/oxfordjournals.rpd.a080514 http://doi.org/10.1093/oxfordjournals.rpd.a080514 Review of scattering corrections for calibration of neutron instruments C.M. Eisenhauer , J.B. Hunt , R. Schwartz , Calibration techniques for neutron personal dosimetry . Radiation Protection Dosimetry 10 , 43 - 57 ( 1985 ). doi: 10.1093/oxfordjournals.rpd.a079410 http://doi.org/10.1093/oxfordjournals.rpd.a079410 Calibration techniques for neutron personal dosimetry H. Schraube , F. Grünauer , G. Burger , Calibration problems with neutron moderator detectors , In Proceeding of Symposium on Neutron Monitoring for Radiation Protection Purposes , pp. 453 - 464 ( 1972 ). Calibration problems with neutron moderator detectors H.R. Vega-Carrillo , E. Manzanares-Acuña , Pilar Iñiguez, M. , E. Gallego , A. Lorente , Spectrum of isotopic neutron sources inside concrete wall spherical cavities . Radiation Measurements 42 , 1373 - 1379 ( 2007 ). doi: 10.1016/j.radmeas.2007.06.006 http://doi.org/10.1016/j.radmeas.2007.06.006 Spectrum of isotopic neutron sources inside concrete wall spherical cavities H.R. Vega-Carrillo , E. Manzanares-Acuña , M. Pilar Iñiguez , E. Gallego , A. Lorente , Study of room-return neutrons . Radiation Measurements 42 , 413 - 419 ( 2007 ). doi: 10.1016/j.radmeas.2007.01.036 http://doi.org/10.1016/j.radmeas.2007.01.036 Study of room-return neutrons 10.1007/s41365-019-0654-7 This work was supported by the Ministry of Science and Technology of Vietnam under Grant 07/HÐ/ÐTCB. 2019-03-16 2019-04-15 2019-05-09 2019-08-10 2019-09-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2019 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-019-0654-7 http://dx.doi.org/10.1007/s41365-019-0654-7 . 2019 Nuclear Science and Techniques 09 30