Xác định hoạt độ các nguyên tố phóng xạ bằng phương pháp phổ kế gamma kết hợp LabSOCS và mô phỏng monte – carlo GEANT4

ĐẠI HỌC QUỐC GIA HÀ NỘI TRƯỜNG ĐẠI HỌC KHOA HỌC TỰ NHIÊN - Lê Quốc Việt XÁC ĐỊNH HOẠT ĐỘ CÁC NGUYÊN TỐ PHÓNG XẠ BẰNG PHƯƠNG PHÁP PHỔ KẾ GAMMA KẾT HỢP LABSOCS VÀ MÔ PHỎNG MONTE-CARLO GEANT4 Chuyên ngành: Vật lý nguyên tử hạt nhân Mã số: 8440130.04 LUẬN VĂN THẠC SĨ KHOA HỌC NGƯỜI HƯỚNG DẪN KHOA HỌC: TS Phan Việt Cương PGS TS Bùi Văn Loát Hà Nội - 2019 LỜI CẢM ƠN Trước tiên xin gửi lời cảm ơn đến ban lãnh đạo Viện Công nghệ Xạ hiếm, ban lãnh đạo Trung tâm Phân tích – Viện Cơng nghệ Xạ tạo điều kiện cho tơi tham gia khóa đào tạo sau đại học Trường Đại học Khoa học Tự nhiên, với ThS Đồn Thanh Sơn cán Trung tâm Phân tích – Viện Công nghệ Xạ giúp đỡ công tác nghiên cứu sử dụng dụng cụ, trang thiết bị Trung tâm Tiếp theo, xin gửi lời cảm ơn đến Văn phòng Khoa Vật lý, Bộ mơn Vật lý Hạt nhân nhiệt tình giúp đỡ thời gian khóa đào tạo Xin gửi lời cảm ơn đến PGS.TS Bùi Văn Loát, ThS Nguyễn Thế Nghĩa, TS Hà Thụy Long ThS Somsavath giúp đỡ nhiều q trình học tập hồn thành luận văn Cuối cùng, xin chân thành cảm ơn TS Phan Việt Cương, ThS Lê Tuấn Anh đồng nghiệp Viện Vật lý – Viện Hàn lâm Khoa học Việt Nam hướng dẫn, góp ý, bổ sung giúp tơi hồn thiện luận văn CHÂN THÀNH CẢM ƠN i MỤC LỤC LỜI CẢM ƠN i MỤC LỤC ii DANH MỤC CÁC KÍ HIỆU, VIẾT TẮT iv LỜI NÓI ĐẦU v CHƯƠNG 1: TỔNG QUAN 1.1 Phân rã phóng xạ nguồn gốc xạ gamma 1.2 Phương trình tốn học biểu diễn q trình phân rã 1.3 Tương tác xạ gamma với vật chất 1.3.1 Hiệu ứng quang điện 1.3.2 Hiệu ứng tán xạ Compton 1.3.3 Hiệu ứng tạo cặp 1.4 Độ suy giảm cường độ chùm gamma qua lớp vật chất 1.4.1 Hệ số suy giảm tuyến tính 1.4.2 Hệ số suy giảm khối 1.5 Hệ số tự hấp thụ nguồn thể tích 1.5.1 Xác định hệ số tự hấp thụ 1.5.2 Xác định hệ số suy giảm tuyến tính 10 1.6 Cơ sở vật lý phương pháp gamma xác định hoạt động phóng xạ đồng vị 12 1.6.1 Phân tích định tính 12 1.6.2 Phân tích định lượng 14 ii CHƯƠNG 2: PHƯƠNG PHÁP MÔ PHỎNG MONTE – CARLO GEANT4 VÀ PHẦN MỀM LABSOCS 18 2.1 Phương pháp mô Monte-Carlo GEANT4 18 2.2 Phần mềm LabSOCS 21 2.2.1 Giới thiệu phần mềm LabSOCS 21 2.2.2 Sử dụng phần mềm LabSOCS 23 2.2.3 Khảo sát sai số khác biệt thành phần mẫu mật độ khối LabSOCS 29 CHƯƠNG 3: KẾT QUẢ THỰC NGHIỆM 32 3.1 Kết phân tích mẫu chuẩn 32 3.1.1 Mô tả mẫu thực nghiệm 32 3.1.2 Kết tính tốn với mẫu đất 32 3.1.3 Kết tính tốn với mẫu thực vật 35 3.1.4 Kết tính tốn với mẫu nước 36 3.2 Kết so sánh đối chứng 38 KẾT LUẬN 40 TÀI LIỆU THAM KHẢO 42 PHỤ LỤC 45 Các mẫu cấu hình hộp đo có sẵn LabSOCS 45 Thông tin loại vật liệu có sẵn thư viện LabSOCS 47 Hình ảnh số mẫu chuẩn 49 Bài báo 49 iii DANH MỤC CÁC KÍ HIỆU, VIẾT TẮT ANGLE Ứng dụng tính tốn hiệu suất ghi tiên tiến dành cho HPGe NaI detector ISOCS In-Situ Sourceless Calibration Software: Phần mềm hiệu chuẩn không dùng nguồn trường LabSOCS Laboratory Sourceless Calibration Software: Phần mềm hiệu chuẩn khơng dùng nguồn phòng thí nghiệm HPGe High Purity Germanium: Germanium siêu tinh khiết REXX Restructured Extended Executor: loại ngơn ngữ lập trình cấp cao phát triển Mike Cowlishaw PC Personal Computer: máy tính cá nhân NIST National Institute of Standards and Technology: Viện Tiêu chuẩn Công nghệ Quốc gia (Mỹ) MCNP Monte Carlo N-Particle: gói phần mềm mơ trình hạt nhân GEANT4 Geometry and Tracking 4: công cụ mô đường hạt qua vật chất sử dụng phương pháp Monte-Carlo CERN Conseil Européen pour la Recherche Nucléaire: Tổ chức nghiên cứu hạt nhân Châu Âu LPM Landau – Pomeranchuk – Migdal: hiệu ứng vật lý lượng cao làm giảm tiết diện hiệu ứng xạ hãm hiệu ứng tạo cặp lượng cao mật độ vật chất lớn EUR Euro: Đồng tiền chung Châu Âu VND Việt Nam Đồng iv LỜI NÓI ĐẦU Trong phương pháp xác định hoạt độ nguyên tố phóng xạ, phương pháp phổ gamma phương pháp sử dụng rộng rãi Phương pháp phổ gamma phương pháp không phá hủy không cần phải chuẩn bị mẫu Hệ phổ kế gamma độ phân giải cao dựa detector bán dẫn sử dụng nhiều lĩnh vực nghiên cứu cơng nghiệp Nó cho phép phân tích định tính định lượng đồng vị phóng xạ bên vật liệu Giống tất kĩ thuật phân tích khác, để phân tích định lượng, phương pháp phổ gamma yêu cầu mẫu chuẩn để thiết lập đường chuẩn hiệu suất thực nghiệm Các mẫu chuẩn có giá thành đắt, vận chuyển lâu không khả dụng độ phức tạp mẫu cần đo Mẫu chuẩn cần thay sau thời gian định (nhất đồng vị có chu kì bán rã ngắn) Cũng có khó khăn để xây dựng đường chuẩn hiệu suất sử dụng mẫu chuẩn yêu cầu cần phải biết mật độ khối, thành phần cấu tạo để hiệu chỉnh hệ số tự hấp thụ, đặc biệt nguồn thể tích Để vượt qua khó khăn này, nhiều nhà khoa học đưa chương trình cho phép tính tốn, mơ phỏng, dự đốn đường chuẩn hiệu suất (ANGLE, ISOCS/LabSOCS,…) Các chương trình cho phép mơ đường cong hiệu suất cho nhiều loại detector khác khoảng lượng từ 59-1836 keV, so sánh thực nghiệm với nguồn chuẩn nhiều cấu hình đo khác Để xây dựng đường chuẩn hiệu suất mà không cần nguồn chuẩn, chương trình cần cung cấp thơng tin cấu hình đo (loại hình dạng detector, hình dạng mẫu, vị trí tương đối mẫu detector, …) thông tin thành phần mật độ khối mẫu đo [13] v Trong khuôn khổ luận văn này, tơi tóm tắt tổng quan xạ gamma, tương tác chúng với vật chất, phương pháp phổ gamma phần mềm LabSOCS khảo sát sử dụng phần mềm LabSOCS, yếu tố ảnh hưởng đến sai số phương pháp phổ gamma ứng dụng LABSOCS tính tốn hoạt độ nguyên tố phóng xạ cho mẫu chuẩn IAEA, so sánh với phương pháp mô Monte-Carlo GEANT4 kết hợp đo hệ số truyền qua Qua ứng dụng phần mềm LabSOCS để nâng cao độ xác, rút ngắn thời gian giảm giá thành cho phương pháp phổ gamma công tác phân tích dịch vụ vi CHƯƠNG 1: TỔNG QUAN 1.1 Phân rã phóng xạ nguồn gốc xạ gamma Những nghiên cứu chất tượng phóng xạ chứng tỏ rằng: hạt nhân ngun tử khơng bền tự phân rã phát hạt khác hạt alpha (α), beta (β-), positron (β+) thường kèm theo xạ điện từ hay xạ gamma (ɣ) Hình 1: Sơ đồ 60Co phân rã hạt nhân 60Ni Bình thường bên hạt nhân, nucleon chiếm đầy mức lượng thấp hạt nhân trạng thái Giả sử lý đó, nucleon từ mức lượng bên nhận lượng từ bên nhảy lên mức lượng bên cao Mức lượng bên có lỗ trống tương ứng với hạt nhân trạng thái kích thích Trạng thái kích thích hạt nhân trạng thái khơng bền, nucleon mức lượng tử có lượng cao giải phóng lượng dư có giá trị hiệu hai mức lượng để nhảy vào lấp chỗ trống lớp Tùy theo cách giải phóng lượng dạng xạ điện từ hay giải phóng lượng dư cách truyền lượng dư cho electron quỹ đạo có xạ gamma electron biến hoán nội phát [2] 1.2 Phương trình tốn học biểu diễn q trình phân rã Q trình phân rã phóng xạ q trình thống kê Khi phân rã phóng xạ, số hạt nhân phóng xạ bị suy giảm theo thời gian 𝐻 = 𝜆 𝑁 = 𝐻0 𝑒 −𝜆.𝑡 = 𝜆 𝑁0 𝑒 −𝜆.𝑡 (1) đó: H0 N0 hoạt độ số hạt nhân phóng xạ thời điểm ban đầu H N hoạt độ số hạt nhân phóng xạ lại sau thời gian t 𝜆= 𝑙𝑛2 𝑇1/2 số phân rã hạt nhân phóng xạ T1/2 chu kì bán rã hạt nhân phóng xạ Hình 2: Quy luật suy giảm số hạt nhân phóng xạ theo thời gian 1.3 Tương tác xạ gamma với vật chất Khi vào môi trường vật chất, xạ gamma khơng gây ion hóa trực tiếp hạt tích điện mà thơng qua tương tác với electron hạt nhân nguyên tử Có ba tương tác xạ gamma với nguyên tử là: hiệu ứng quang điện, hiệu ứng tán xạ Compton hiệu ứng tạo cặp 1.3.1 Hiệu ứng quang điện Bức xạ gamma có lượng lớn lượng liên kết electron lớp vỏ nguyên tử môi trường, tương tác với electron đó, xạ gamma truyền tồn lượng để giải phóng electron khỏi nguyên tử, electron gọi electron quang điện Động electron quang điện 𝑇𝑒 = 𝐸𝛾 − 𝐸𝑛 hiệu lượng xạ gamma tới lượng liên kết electron quỹ đạo n Hiệu ứng quang điện có xác suất xảy cao electron lớp vỏ bên nguyên tử, electron lớp nguyên tử giải phóng bên ngồi, electron lớp vỏ bên ngồi nhảy xuống chỗ phát xạ tia X đặc trưng độ chênh lệch lượng liên kết electron hai lớp vỏ ngun tử Hình 3: Mơ tả hiệu ứng quang điện [2] Xác suất xảy hiệu ứng quang điện nguyên tử: 𝜎𝑞đ ~ 𝑍5 𝐸𝛾 7/2 𝑘ℎ𝑖 𝐸𝛾 𝑛ℎỏ 𝑣à 𝑍5 𝜎𝑞đ ~ 𝑘ℎ𝑖 𝐸𝛾 ≫ 𝑚𝑒 𝑐 𝐸𝛾 [1] L.T Anh, P.V Cuong, N.C Tam et al Nuclear Inst and Methods in Physics Research, A 941 (2019) 162305 Table The energies and emission probabilities of the 𝛾-peaks used in this work [3] Energy (keV) 226 295.224 351.932 609.312 1120.287 1764.494 2204.21 228 228 Ra 19.3 37.6 46.1 15.1 15.4 5.08 214 (2) (4) (5) (2) (2) (4) 𝑃𝑏 𝑃𝑏 214 𝐵𝑖 214 𝐵𝑖 214 𝐵𝑖 214 𝐵𝑖 214 43.3 (2) 84.5 (7) 12.42 (10) 1.49 (3) 99 212 𝑃 𝑏 11.27 (19) 4.25 (7) 25.8 (4) 15.8 (3) 228 208 𝑇𝑙 𝑇𝑙 212 𝐵𝑖 208 𝑇𝑙 208 group 338.321 794.947 911.204 968.971 Based on these criteria, RGK-1 could be a good candidate because this reference material contains mainly 40 K radionuclide [9] And 40 K emits only one measurable gamma ray with an energy of 1460.83 keV [3], which can be treated as E∗ in Eq (4) The diagram shown in Fig describes the method using separative 40 K reference sample Briefly, the activities of radionuclides in an analyzed sample are determined by this method as the following steps: Emitter Th group 238.632 583.191 860.564 1620.50 2614.533 Fig The diagram of the method for determining the radioactivity using only one absolute efficiency value and an intrinsic efficiency curve Emission probability Ra group 𝐴𝑐 228 𝐴𝑐 228 𝐴𝑐 228 𝐴𝑐 rays emitted from those samples were detected by high-resolution HPGe gamma-ray spectroscopy system at Center for Nuclear physics, Institute of Physics, VAST The system includes a GEM series p-type HPGe (GEM20P4-70) manufactured by Ortec-AMETEK The detector energy resolution and relative efficiency at 1.332.5 keV of 60 Co are 1.80 keV and 20% respectively, peak to Compton ratio corresponding to 60 Co is 52:1 The detector is surrounded by the clean lead shielding chamber with the internal surface covered by super clean tin and copper The data acquisition was performed using software Maestro-32-v.6.08 Data analysis was performed using ROOT data analysis framework [19] • Step 1: The intrinsic efficiency curve for radionuclide T is derived from 𝛾-spectrum of environmental sample • Step 2: The absolute efficiency, 𝜀𝑟𝑒𝑓 at 1460.83 keV is calculated from 𝛾-spectrum of RGK-1 • Step 3: Calculation of relative self-absorption factor, C, at 1460.83 keV This step could be skipped in some certain cases (see in Section 5) • Step 4: Activities of 𝛾-emitters in environmental sample are determined by using Eqs (4)–(6) Data analysis and results Since photo-peaks corresponding to the gamma-rays emitted from and 226 Ra decay series appeared dominantly in the gamma spectra of Sample-1 and Sample-2, it would be convenient to construct intrinsic efficiency function based on these gamma-rays Activity concentrations of radionuclides were derived from the measured gamma-spectra using the method described in Section Validation experiment 228 Th Two samples having been prepared based on reference materials [9, 16,17], called Sample-1 and Sample-2, and other five soil samples were used to validate the method • Sample-1 is directly RGTh-1 materials • Sample-2 is secondary reference material based on the mixture of RGU-1 (12.00 ± 0.01 g), RGTh-1 (12.10 ± 0.01 g) and RGK-1 (12.60 ± 0.01 g), SiO2 (57.35 ± 0.01 g), CaCO3 (57.35 ± 0.01 g), MgO (19.10 ± 0.01 g) and TiO (9.50 ± 0.01 g) The activity concentrations of the three radionuclides (226 Ra, 228 Th and 228 Ra) in this sample were computed from the available isotopic data [16,17] and shown in Table • Soil samples: Five soil samples, which were collected in Savannakhet, Laos (see Table 4), were used to test how the method described in Section deals with real environmental samples 4.1 Calculate absolute efficiency and relative self-absorption factor at 1460.83 keV Only one gamma-ray with the energy of 1460.83 keV is emitted by [3] In the environmental sample, the 1460.83 keV peak is interfered by 1459.138 keV peak of 228 Ac But in the case of RGK-1, this interference is ignorable [9] The result was found to be 𝜀𝑟𝑒𝑓 (1460.83 keV) = (0.532 ± 0.003)% (Fig 9) This value will be used in Eq (2a) to calculate absolute efficiency 𝜀∗ for Sample-1, Sample-2, and soil samples Since the densities of Sample-1, Sample-2 and Sample-Ref are equal to each other ( 1.3 g/cm3 ) The relative self-absorption correction factors for (Sample-1, Sample-Ref) pair and (Sample-2, Sample-Ref) pair and (soil sample, Sample-Ref) pairs are safely considered as a unity However, to check this hypothesis, another experiment was performed using a transmission method proposed by Cutshall et al [5] The C(1460.83 keV) = 1.001 ± 0.001 was found between Sample-1 and Sample-Ref, while C(1460.83 keV) = 1.003 ± 0.001 was for (Sample-2, Sample-Ref) pair (Fig 10) For (soil sample,Sample-Ref) pairs, geant4 code [7] and labSOCS [20] are used to evaluate relative self-absorption correction factors (see in Section 5) 40 K These samples were each held in a polyethylene cylindrical box of 7.6 cm × cm (diameter × height) Each sample has a mass of 180 g A commercial press (CrushIR-Digital Hydraulic Press) was used to ensure all sample having the same density They all were sealed for more than weeks to establish secular equilibrium [18] before measurements Another polyethylene cylindrical box filled with RGK-1 material labeled as Sample-Ref was considered as reference material to calculate 𝜀𝑟𝑒𝑓 The dimension and mass of Sample-Ref are exactly the same as Sample-1 and Sample-2 The samples were placed directly on the surface of the detector One day measurement was carried out for Sample-1, Sample-Ref, and background while half of a day is for Sample-2 The characteristic gamma L.T Anh, P.V Cuong, N.C Tam et al Nuclear Inst and Methods in Physics Research, A 941 (2019) 162305 Fig The intrinsic efficiency curve of 228 Ra in Sample-1 obtained by using Eq (10) which contains F𝑇 ℎ228 (E) The only free parameter in the fit is p4 shown in the box The black square symbol presents the experimental data The red line is the fit curve The error bars are not seen because of being smaller than the size of symbols Fig The intrinsic efficiency curve of 228 Th in Sample-1 The circles present the experimental data Meanwhile, two lines are fit curves: the red one is for the case of using 1620.74 keV, and the dash, the green one is corresponding to the case of not using 1620.74 keV The arrow shows the position of 1460.83 keV The error bars are not seen because of being smaller than the size of symbols 4.2 Gamma-rays of 226 Ra and 228 Th decay series for constructing F𝑇 (E) In general, the gamma-rays emitted directly by 228 Th cannot be measured by gamma spectroscopy because of low emission probability 226 Ra has a detectable gamma-ray with the energy of 186.211 keV, but this peak is totally overlapped by 185.712 keV peak of 235 U Luckily, the short-lived daughters of these isotopes emit intense gamma-rays measurable by gamma spectroscopy By sealing the sample container long enough for establishing secular equilibrium between the short-lived daughters and their parent, one obtains: (7) 𝐴𝑅𝑎226 = 𝐴𝑃 𝑏214 = 𝐴𝐵𝑖214 𝐴𝑇 ℎ228 = 𝐴𝑃 𝑏212 = 𝐴𝐵𝑖212 𝐴 = 𝑇 𝑙208 𝑝 (8) where A𝑅𝑎226 , A𝑇 ℎ228 , , denote the corresponding activities at the time of measurement, while p = 0.3594 is the decay branching probability of the decay of 212 Bi to 208 Tl Let F𝑅𝑎226 (E) and F𝑇 ℎ228 (E) be the intrinsic efficiency calibration curves corresponding to 226 Ra, 228 Th, respectively Because 1460.83 keV of 40 K in RGK-1 reference material is chosen to calculate 𝜀∗ , the peaks used to build F𝑅𝑎226 (E), F𝑇 ℎ228 (E) have to distribute in a range of energy which 1460.83 keV is located within Table listed the energies and their emission probability which were used in this paper Fig The intrinsic efficiency curve of 226 Ra in Sample-1 obtained in the same way as F𝑅𝑎228 (E) The black square symbol presents the experimental data The red line is the fit curve The error bars are not seen because of being smaller than the size of symbols Table Results for Sample-1 All the results were expressed with 95% confidence intervals Radionuclide Activity (this work) (Bq/kg) Activity (Ref [16]) (Bq/kg) Deviation (%) 228 3236 ± 76 3268 ± 77 76.00 ± 1.78 3250 ± 88 3250 ± 88 78 ± −0.43 0.55 −1.6 𝑇 ℎ = 212 𝑃 𝑏 = 212 𝐵𝑖 = 208 𝑇 𝑙∕𝑝 𝑅𝑎 = 228 𝐴𝑐 226 𝑅𝑎 = 214 𝑃 𝑏 = 214 𝐵𝑖 4.3 Calculate activity of radionuclides in Sample-1 228 The 𝑛𝑗 ∕𝐼𝛾𝑗 ratios can be fitted with a mathematical model or a physical model Within the scope of this paper, only the mathematical model is considered The following mathematical form is proposed to describe F𝑇 (E) functions [14]: ( ) 𝐹𝑇 (𝐸) = 𝐸𝑥𝑝 𝑝0 + 𝑝1 𝑙𝑛(𝐸) + 𝑝2 𝑙𝑛(𝐸)2 + 𝑝3 𝑙𝑛(𝐸)3 (9) spectrum of the environmental sample After F𝑇 ℎ228 (E) is determined, the result A𝑇 ℎ228 = A𝑃 𝑏212 = A𝐵𝑖212 = A𝑇 𝑙208∕𝑝 is found and shown in Table The A𝑇 ℎ228 with the use of 1620.74 keV was closer to reference data The small boxes on the right of Fig showed the fit parameters: the upper one is for the case of using 1620.74 keV, the lower one is when not using 1620.74 keV 4.3.1 228 Th The F𝑇 ℎ228 (E) was obtained by fitting the Eq (9) to the 𝑛𝑗 ∕𝐼𝛾𝑗 ratios at 238.832 keV of 212 Pb, 1620.74 keV of 212 Bi and 583.191, 860.564, 2614.533 keV of 208 Tl Since the emission probability of 1620.74 keV is rather small in comparison with other gamma-rays (see Table 1), and the distance between 860.564 and 2614.533 keV is large, it is worth testing that how well F𝑇 ℎ228 (E) behaves with or without using 𝑛𝑗 ∕𝐼𝛾𝑗 ratio at 1620.74 keV in the fit The results of this check are in reality meaningful where 1620.74 keV peak is not always seen in the gamma 4.3.2 228 Ra and 226 Ra The activity of 228 Ra was derived through the gamma-rays of 228 Ac due to secular equilibrium The four measurable gamma-rays of 228 Ac were 338.32, 794.947, 911.204, 968.971 keV It is easily seen that 1460.83 keV is far away out of this energy range Hence, if fitting directly Eq (9) to 𝑛∕𝐼𝛾 ratios at these energies, the value of F𝑅𝑎228 (E) at 1460.83 keV would fluctuate very strongly and suffer high uncertainty L.T Anh, P.V Cuong, N.C Tam et al Nuclear Inst and Methods in Physics Research, A 941 (2019) 162305 Table Results for Sample-2 All the results were expressed with 95% confidence intervals Radionuclide Activity (this work) (Bq/kg) Activity (Ref data) (Bq/kg) Deviation (%) = 212 𝑃 𝑏 = 212 𝐵𝑖 = 208 𝑇 𝑙∕𝑝 𝑅𝑎 = 228 𝐴𝑐 226 𝑅𝑎 = 214 𝑃 𝑏 = 214 𝐵𝑖 216.2 ± 8.4 218.2 ± 8.5 329.8 ± 6.4 218.5 ± 6.0 218.5 ± 6.0 329.3 ± 2.0 −1.05 −0.14 0.15 228 𝑇 ℎ 228 Table Sampling locations of soil samples Samples ID Location name M106 M108 M122 M125 M134 Na Thad, Uthomphone, Savannakhet, Laos Non Vi Lay, Uthomphone, Savannakhet, Laos Nong Hai, Cong Kon, Savannakhet, Laos Na Vang, Cong Kon, Savannakhet, Laos Na Jan, Cham Phone, Savannakhet, Laos Table Results for M125 All the results were expressed with 95% confidence intervals Radionuclides 228 𝑇 ℎ = 212 𝑃 𝑏 = 212 𝐵𝑖 = 208 𝑇 𝑙∕𝑝 𝑅𝑎 = 228 𝐴𝑐 226 𝑅𝑎 = 214 𝑃 𝑏 = 214 𝐵𝑖 228 Activity [Bq/kg] Updated method FEPEC method (Eq (2b)) 25.2 ± 1.0 25.6 ± 1.0 23.8 ± 0.5 25.6 ± 1.4 27.4 ± 1.6 23.6 ± 0.8 Fig The intrinsic efficiency curve of 226 Ra in Sample-2 The black symbol presents the experimental data The red line is the fit curve The arrow shows the position of 1460.83 keV The error bars are not seen because of being smaller than the size of triangles In this case, Eq (5) was used to overcome this difficulty More clearly, the following function is dedicated to extracting F𝑅𝑎228 (E): 𝐹𝑅𝑎228 (𝐸) = 𝑝4 𝐸𝑥𝑝(15.1 − 3.9𝑙𝑛(𝐸) + 0.393𝑙𝑛(𝐸)2 − 0.0166𝑙𝑛(𝐸)3 ) (10) where all the numbers in Eq (10) were corresponding to fit parameters p0, p1, p2, p3 of F𝑇 ℎ228 (E) (see the upper box on Fig 2) Looking at the box on the upper right of Fig 3, the uncertainties of p0, p1, p2, p3 are zero This implied that these values were fixed in the fit The parameters p4 is equal to R in Eq (5), hence from Eq (6), A𝑅𝑎228 is determined as : 𝐴𝑅𝑎228 = 𝑝4 𝐴𝑇 ℎ228 (11) F𝑅𝑎226 (E) and A𝑅𝑎226 in Sample-1 would be determined exactly in the same way as F𝑅𝑎228 (E) and A𝑅𝑎228 , but at 351.931, 609.312 keV Fig shows the intrinsic efficiency curve for 226 Ra in Sample-1 The results for A𝑅𝑎226 and A𝑅𝑎228 in Sample-1 are listed in Table Compared to reference data, our results gave a good agreement 4.4 Calculate the activity of radionuclides in Sample-2 Fig The intrinsic efficiency curve of 226 Ra in sample M125 The black symbol presents the experimental data The red line is the fit curve The arrow shows the position of 1460.83 keV In the gamma-spectrum of Sample-2, only 226 Ra had enough number of photo-peaks which had high statistic for building F𝑇 (E) function Fig presents the F𝑅𝑎226 (E) curve The red smooth line is obtained by fitting the Eq (9) to 𝑛∕𝐼𝛾 ratios at 295.224, 351.932 keV of 214 Pb and 609.312, 1120.287, 1764.494, 2204.21 keV of 214 Bi The activities A𝑇 ℎ228 and A𝑅𝑎228 were determined through F𝑅𝑎226 (𝐸) by using Eq (6): 𝑛583 keV ∕𝐼𝛾583 keV 𝐴 0.3594𝐹𝑅𝑎226 (583 keV) 𝑅𝑎226 𝑛911 keV ∕𝐼𝛾911 keV = 𝐴 𝐹𝑅𝑎226 (911 keV) 𝑅𝑎226 𝐴𝑇 ℎ228 = (12) 𝐴𝑅𝑎228 (13) was then put into a polyethylene cylindrical box Two methods are used to calculate the radioactivity in these samples: the updated method and the FEPEC method The objective of this work is to compare the results obtained by the widely-used method and the method developed in this work In principle, a F𝑇 (E) function ought to be constructed for each sample But, these five soil samples can be considered to have the same density and chemical components Therefore, it is possible to use one F𝑇 (E) function for all five samples The gamma-spectrum of sample M125 was chosen to construct F𝑇 (E) function because it has high statistics peaks After subtracting background, the 𝑛∕𝐼𝛾 ratios at 295.224, 351.932 keV of 214 Pb and 609.312, 1120.287, 1764.494 of 214 Bi are fitted with Eq (9) to obtain F𝑅𝑎266 (E) for sample M125 (see Fig 6) Eq (4) was used to determine the activity of 226 Ra in sample M125 The other radionuclides concentration in this sample and the rest Table listed the results for A𝑇 ℎ228 , A𝑅𝑎228 and A𝑅𝑎226 in Sample-2 The results were in good agreement with reference data 4.5 Apply the updated method for soil samples Five soil samples, which were collected in Laos (see in Table 4), were dried in a temperature-controlled furnace for 24 h After being dried, soil samples were sieved through a 0.2 mm mesh to gain homogeneous and fine-sized particles Each sample with the mass of 180 g L.T Anh, P.V Cuong, N.C Tam et al Nuclear Inst and Methods in Physics Research, A 941 (2019) 162305 Table Results for M106 All the results were expressed with 95% confidence intervals Radionuclides Activity [Bq/kg] 228 𝑇 ℎ = 212 𝑃 𝑏 = 212 𝐵𝑖 = 208 𝑇 𝑙∕𝑝 𝑅𝑎 = 228 𝐴𝑐 226 𝑅𝑎 = 214 𝑃 𝑏 = 214 𝐵𝑖 228 Updated method FEPEC method (Eq (2b)) 11.9 ± 1.0 12.0 ± 1.1 14.8 ± 0.7 12.3 ± 1.0 12.8 ± 1.1 14.7 ± 0.7 Table Results for M108 All the results were expressed with 95% confidence intervals Radionuclides Activity [Bq/kg] 228 𝑇 ℎ = 212 𝑃 𝑏 = 212 𝐵𝑖 = 208 𝑇 𝑙∕𝑝 𝑅𝑎 = 228 𝐴𝑐 226 𝑅𝑎 = 214 𝑃 𝑏 = 214 𝐵𝑖 228 Updated method FEPEC method (Eq (2b)) 7.2 ± 0.7 12.2 ± 0.8 13.2 ± 0.5 7.4 ± 0.7 13.0 ± 0.8 13.2 ± 0.5 Fig The full-energy peak efficiency curve was derived from gamma-spectrum of 180 g RGU-1 for detector system described in Section The black squares present the experimental data, while the red line is the fit curve The error bars are not seen because of being smaller than the size of square symbols Table Results for M122 All the results were expressed with 95% confidence intervals Radionuclides Activity [Bq/kg] 228 𝑇 ℎ = 212 𝑃 𝑏 = 212 𝐵𝑖 = 208 𝑇 𝑙∕𝑝 𝑅𝑎 = 228 𝐴𝑐 226 𝑅𝑎 = 214 𝑃 𝑏 = 214 𝐵𝑖 228 Updated method FEPEC method (Eq (2b)) 29.7 ± 2.0 32.9 ± 2.3 27.7 ± 1.2 30.5 ± 2.0 35.0 ± 2.3 27.6 ± 1.1 Table Results for M134 All the results were expressed with 95% confidence intervals Radionuclides Activity [Bq/kg] 228 𝑇 ℎ = 212 𝑃 𝑏 = 212 𝐵𝑖 = 208 𝑇 𝑙∕𝑝 = 228 𝐴𝑐 226 𝑅𝑎 = 214 𝑃 𝑏 = 214 𝐵𝑖 228 𝑅𝑎 Updated method FEPEC method (Eq (2b)) 18.0 ± 1.4 18.8 ± 1.6 18.7 ± 0.8 18.5 ± 1.5 20.0 ± 1.6 18.6 ± 0.8 Fig The full-energy peak efficiency at 1460.83 keV for various environmental samples The red circles present the values calculated by Geant4, except the experimental value at RGK-1 (Exp) The black smooth line shows the value determined experimentally for RGK-1 The two purple dash lines are corresponding to ±1% deviation of experimental value samples were calculated based on intrinsic calibration curve for 226 Ra in sample M125 The results are listed in Tables to The activity of 228 Th was estimated at 583.191 keV of 208 Tl, while the activity of 228 Ra was determined at 911.204 keV of 228 Ac The 𝑛∕𝐼𝛾 ratio at 609.312 keV of 214 Bi was used to calculate the activity of 226 Ra in the rest four samples The details of the calculation are: 𝐴𝑇 ℎ228 = 𝐴𝑅𝑎228 𝑛583 keV ∕𝐼𝛾583 keV 𝐴 0.3594𝐹𝑅𝑎226∕𝑀125 (583 keV) 𝑅𝑎226−𝑂𝑓 −𝑀125 𝑛911 keV ∕𝐼𝛾911 keV = 𝐴 𝐹𝑅𝑎226∕𝑀125 (911 keV) 𝑅𝑎226−𝑂𝑓 −𝑀125 𝑛609 keV ∕𝐼𝛾609 keV = 𝐴 𝐹𝑅𝑎226∕𝑀125 (609 keV) 𝑅𝑎226−𝑂𝑓 −𝑀125 The influence of density and chemical composition on fullenergy peak efficiency and relative self-absorption correction factor at the energy of 1460.83 keV (14) (15) where A𝑅𝑎226−𝑂𝑓 −𝑀125 is the activity of 226 Ra in sample M125, F𝑅𝑎226∕𝑀125 is intrinsic calibration curve for 226 Ra in sample M125 The results obtained by updated method for these five samples were directly compared to ones deduced by FEPEC method Fig presents the full-energy peak efficiency curve of the detector system A Geant4 code, see [7], was implemented for studying the variation of full-energy peak efficiency on the chemical composition of environmental samples and the density of RGK-1 reference material Fig shows the efficiency of the detector system at 1460.83 keV for various typical environmental samples Their chemical compositions were described in Table 10 The density and volume of simulated samples are the same as those of Sample-Ref The agreement between experimental data and the simulated ones for RGK-1 implies that the geant4 code is reliable Let 𝛥 be defined as: 4.6 Uncertainty calculation 𝛥= 𝐴𝑅𝑎226 (16) 𝜀(1460.83 keV)for Env sample − 𝜀(1460.83 keV)RGK-1, 𝜀(1460.83 keV)RGK-1, Exp 100% (17) Exp It is easily seen in Fig that 𝛥 for simulated samples lies within ±1% (region marked by two purple dash-lines) This means the chemical composition for some typical environmental samples affects insignificantly on the efficiency at 1460.83 keV Therefore, the efficiency value calculated from Sample-ref can be safely applied for various types of environmental samples without correction for self-absorption, as long as the densities and volumes are identical The uncertainties of results came from all the quantities appearing in the equations used to calculate activity, they were: the statistics uncertainty of peak areas in the spectra, the uncertainty of the emission probabilities 𝐼𝛾 , the uncertainty of the fit The total uncertainty was calculated by uncertainty propagation equation [21] A 95% confidence interval, corresponding to the coverage factor of t = 1.96, was used in the calculation of the uncertainty L.T Anh, P.V Cuong, N.C Tam et al Nuclear Inst and Methods in Physics Research, A 941 (2019) 162305 Table 10 Principal components in ash (seaweed, vegetable, fish, rice), sea sediment [22] and soil [20] samples Environmental samples Seaweed (Undaria pinnatifida) Vegetable (Brassica oleracea) Fish (Trachurus trachurus) Rice Sea sediment Dry soil Elemental composition (%) C O Na P Cl K Ca H Mg Al Si Fe Ti 11 20 36 28 0 0 0 13 32 40 36 0 0 0 40 18 21 15 0 0 0 29 2.14 34 48 49.62 0 0.84 18 0 0 19 2.37 11 4.21 0 0.36 1.6 11 7.1 24 27.38 4.04 0 0.34 Fig The full-energy peak efficiency at 1460.83 keV, 𝜀𝑟𝑒𝑓 varies with the density of RGK-1 The open green circles present the values calculated by Geant4 The simulated data were fitted with function 𝜀𝑟𝑒𝑓 (𝜌) = a*𝜌+b The two black dash lines are corresponding to the values 𝜀𝑟𝑒𝑓 (1460.83 keV, 1.3 g/cm3 ) [1 ± 0.03] Fig 10 The dependence of C on density for 7.6 cm × cm cylindrical samples The results for Soil/Sample-Ref and Cellulose/Sample-Ref pairs were calculated by LabSOCS [20], while ones for Sample-1/Sample-Ref and Sample-2/Sample-Ref pairs were determined experimentally through Cutshall’s method [5] The two black dash line are corresponding to 𝐶 = ± 0.03 lines, while the smooth black line is for C = Fig shows the dependence of full-energy peak efficiency, 𝜀𝑟𝑒𝑓 , at 1460.83 keV on density The open green circles present values obtained by simulation with Geant4, only one value marked with the red square symbol is experimental datum The simulation was conducted with the same geometry setup as the experiment, only density corresponding to RGK-1 was varied in Geant4 code The two dash lines shows the 3% of 𝜀𝑟𝑒𝑓 (1460.83 keV) = (0.532 ± 3%) region In practical work, if samples having wide density range are analyzed, one can consider 𝜀𝑟𝑒𝑓 (1460.83 keV) in 3% region (𝜌 ≈ 0.8–1.7 g/cm3 ) unchanged and use value 𝜀𝑟𝑒𝑓 (1460.83 keV) = (0.532 ± 0.003) for radioactivity calculation, as long as all samples have the same shape with Sample-Ref This will be time-saving because one does not have to re-prepare Sample-Ref with different density Similarly, for Soil and Cellulose, there also exists a 3% region, in which the relative absorption correction factor can be considered unchanged and equal to (see two dash lines in Fig 10) The results for Soil and Cellulose were obtained by using LabSOCS It is easily seen in Fig 10, even with cellulose composition, there is a density range (𝜌 ≈ 0.9–1.6g/cm3 ) which C lies in 3% region radionuclides in other samples can be determined without constructing their own intrinsic efficiency curves The intrinsic efficiency function can be improved by constructing from gamma lines of all radionuclides in the measured sample In this paper, gamma-rays from 228 Th or 226 Ra series were used for building intrinsic efficiency function, F𝑇 (E) Some gamma-lines can encounter true coincidence summing effect Correction factors can be determined by Geant4 simulation In environmental measurements, however, acceptable counting uncertainties are usually high and consequently coincident summing corrections might be ignored [23,24] IAEA-RGK-1 was chosen as a perfect candidate for determining 𝜀∗ because it fulfills the criteria mentioned in Section The accuracy of results derived from this method depends on the precision of the value of intrinsic efficiency function and the absolute efficiency at the energy of 1460.84 keV corresponding to 𝛾-ray of 40 K IAEA-RGK-1 was used in separation to investigated samples, therefore making our work differ from the work proposed by Felsmann and Denk [15], where reference material KCl was blended uniformly into investigated samples The absolute efficiency at 1460.83 keV varies insignificantly with the chemical composition of typical environmental samples (Fig 8) This implies that the relative self-absorption correction factor at 1460.83 keV can be ignored as long as analyzed samples have the same density, volume and container’s shape as the Sample-Ref Even in the case of different densities, one can safely remove relative selfabsorption correction factor within the suitable density range (Fig 10) The absolute efficiency at 1460.83 keV depends linearly on the density of RGK-1 reference material However there exists a density Concluding remarks A development for determining the radio-activities in environmental samples using only one value of detector full-energy peak efficiency was presented The ‘‘holy grail’’ of this method is to build an intrinsic efficiency calibration from experimental 𝑛∕𝐼𝛾 ratios of the same radionuclide in the same spectrum This is also the limitation of this method However, if a set of samples are analyzed and from one of their 𝛾-spectra, an intrinsic efficiency function is derived, then the L.T Anh, P.V Cuong, N.C Tam et al Nuclear Inst and Methods in Physics Research, A 941 (2019) 162305 range that this efficiency value can be considered as unchanged with acceptable deviation (±3%) compared to value for 𝜌 = 1.3 g/cm3 (Fig 9) Besides being used in activity determination, another application of this method is to use for constructing full-energy peak efficiency function using only RGK-1 reference and an unknown-activity environmental sample The accuracy of F𝑇 (E) function depends on the statistical uncertainties of the areas of peaks which are used for calculating 𝐼𝑛 ratios In 𝛾 practical work, for time-saving, when plenty of samples are analyzed, only one sample should be measured for a long span of time for getting high statistic at interested peaks The intrinsic efficiency of this sample will be applied for other samples as in Section 4.5 The results obtained in our work were confirmed by environmental reference materials (Sample-1, Sample-2) Five soil samples were also be used to test how this method works for real environmental samples It can be concluded that the method described in this paper can be a reliable alternative for radioactivity determination of environmental samples In this paper, only activities of radionuclides which emit measurable gamma-line with energy from 238 keV–3000 keV can be determined In future work, the F𝑇 (E) function will be extended for energy below 238 keV [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] References [1] P.P Povinec, et al., Radioactivity in the Environment, Volume 11: Analysis of Environmental Radionuclide, Elsevier, 2008 [2] M.F L’Annunziatta, Handbook of Radioactivity Analysis, third ed., Academic Press, 2012 http://nucleardata.nuclear.lu.se/toi/radSearch.asp https://www.nndc.bnl.gov/nudat2/indx_adopted.jsp N.H Cutshall, et al., Nucl Instrum Methods 206 (1983) 309–312 G Cinelli, et al., J Environ Radioact 155–156 (2016) 31–37 S Agostinelli, et al., Nucl Instrum Methods A 506 (2003) 250–303 http://www.fluka.org/fluka.php https://nucleus.iaea.org/rpst/referenceproducts/referencematerials/ radionuclides/IAEA-RGK-1.htm MGA++ Software User’s Manual Software Version 1.03, EG & G ORTEC R Gunnink, et al., MGAU: a new analysis code for measuring U-235 enrichments in arbitrary samples, UCRL-JC-114713 (1994) C.T Nguyen, et al., Nucl Instrum Methods Phys Res B 243 (2006) 187 J Zsigrai, et al., Nucl Instrum Methods Phys Res B 359 (2015) 137–144 T.A Le, et al., Appl Radiat Isot 142 (2018) 220–226 M Felsmann, H.J Denk, J Radioanal Nucl Chem 157 (1992) 47–55 https://nucleus.iaea.org/rpst/referenceproducts/referencematerials/ radionuclides/IAEA-RGTh-1.htm https://nucleus.iaea.org/rpst/referenceproducts/referencematerials/ radionuclides/IAEA-RGU-1.htm G.R Gilmore, Practical Gamma-Ray Spectrometry, second ed., John Wiley & Sons, 2008 https://root.cern.ch Model S574 LabSOCS Calibration Software, available from Canberra Industries, Meriden CT, USA P.R Bevington, D.K Robinson, Data reduction and error analysis for the physical sciences, 3rd ed., McGraw-Hill Higher Education K Satoh, et al., J Radioanal Nucl Chem 84 (1984) 431–440 M Garcia-Talavera, et al., J Radiat Isot 54 (2001) 769–776 K.P Maphoto, Determination of Natural Radioactivity Concentrations in Soil: A Comparative Study of Windows and Full Spectrum Analysis (M.Sc degree Thesis in Physics), The University of the Western Cape, South Africa, 2004 ... Trong phương pháp xác định hoạt độ nguyên tố phóng xạ, phương pháp phổ gamma phương pháp sử dụng rộng rãi Phương pháp phổ gamma phương pháp không phá hủy không cần phải chuẩn bị mẫu Hệ phổ kế gamma. .. số phương pháp phổ gamma ứng dụng LABSOCS tính tốn hoạt độ ngun tố phóng xạ cho mẫu chuẩn IAEA, so sánh với phương pháp mô Monte- Carlo GEANT4 kết hợp đo hệ số truyền qua Qua ứng dụng phần mềm LabSOCS. .. suất ghi detector, Eɣ lượng xạ gamma, hệ số làm khớp 17 CHƯƠNG 2: PHƯƠNG PHÁP MÔ PHỎNG MONTE – CARLO GEANT4 VÀ PHẦN MỀM LABSOCS 2.1 Phương pháp mô Monte- Carlo GEANT4 Geant4 phát triển dựa ngôn