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Theoretical calculation of irradiation time was obtained based on neutron flux distribution at different channels and locations.. INTRODUCTION 99Mo can be produced in nuclear reactors b

NGHIÊN CỨU TÍNH TOÁN VÀ MÔ PHỎNG QUÁ TRÌNH SẢN XUẤT 99m Tc BẰNG

N.M QUACH 1 , V.T NGUYEN 1, *, M.D DO 2 , H SUEMATSU 2

1 Department of Nuclear Engineering and Environmental Physics, School of Engineering Physics, Hanoi University of Science and Technology (HUST)

2 Department of Nuclear System Safety Engineering, Extreme Energy-Density Research Institute,

Nagaoka University of Technology

* E-mail: thai.nguyenvan@hust.edu.vn

Tóm tắt: Đồng vị phóng xạ Technitium-99m (99m Tc), sản phẩm phân rã β  của 99 Mo được sử dụng phổ biến nhất trong y tế,

có thể được tạo ra trong các lò phản ứng hạt nhân bằng hai phương pháp cơ bản: phản ứng phân hạch của 235 U làm giàu cao

và phản ứng bắt nơtron của 98 Mo Mặc dù phương pháp phân hạch có thể tạo ra đồng vị 99 Mo có hoạt độ rất cao nhưng lại gây ra những lo ngại về an ninh hạt nhân Phương pháp (n, γ) có quy trình đơn giản với nhiều ưu điểm, tuy nhiên, vẫn có một số hạn chế như năng suất thấp cả về hoạt độ và hàm lượng do quá trình chiết xuất phức tạp Rất nhiều giải pháp đã được

đề xuất để đơn giản hóa các kỹ thuật chiết xuất cũng như nâng cao hiệu quả thu hồi của 99 Mo Bia MoO 3 cấu trúc xốp với diện tích tiếp xúc bề mặt lớn sau khi được chiếu xạ có thể tạo ra 99 Mo với khả năng hòa tan cao và có thể thu hồi lại bằng nước một cách đơn giản Bài báo trình bày kết quả nghiên cứu điều kiện chiếu xạ thích hợp đối với dây MoO 3 có cấu trúc xốp trong điều kiện Lò phản ứng nghiên cứu hạt nhân Đà Lạt Tính toán lý thuyết về thời gian chiếu xạ được thực hiện dựa trên

sự phân bố thông lượng neutron tại các vị trí khác nhau trong các kênh Ngoài ra, quá trình kích hoạt neutron 98 Mo trong dây MoO 3 xốp được mô phỏng bằng phần mềm MCNPX để kiểm tra tương tác giữa các hạt Kết quả tính toán, phân tích và thảo luận trong bài báo sẽ được sử dụng trong quá trình thiết kế và thực hiện thí nghiệm tại Lò phản ứng nghiên cứu hạt nhân Đà Lạt

Từ khoá: 99 Mo/ 99m Tc, chiếu xạ, tính toán lý thuyết, mô phỏng MCNPX

Abstract: The most widely used medical radioisotope, Technitium-99m (99m Tc), is a daughter product of β the decay of

99 Mo which can be produced in nuclear reactors by two basic methods: fission reaction of highly enriched 235 U and neutron capture reaction of 98 Mo Although the first method can produce very high specific activity obtainable of 99 Mo, it causes nuclear security concerns The (n, γ) method uses a simple procedure with many advantages, however, there are some limitations such as lower productivity at both activity and quantity due to the complex extraction process A lot of efforts have been carried out to simplify the extraction techniques as well as improve the recovery efficiency of 99 Mo after the irradiation process Porous MoO 3 target structure with a large surface area can provide high solubility of 99 Mo/ 99m Tc after being irradiated and it is possible to recover 99 Mo/ 99m Tc simply by pouring water This paper presents an investigation

of appropriate irradiation conditions for MoO 3 wire with porous structure in Dalat Nuclear Research Reactor Theoretical calculation of irradiation time was obtained based on neutron flux distribution at different channels and locations Also, the neutron activation process of 98 Mo in porous MoO 3 wire was simulated with MCNPX code to examine the interactions between the particles Results were analyzed, discussed, and will be further applied in experiments at Dalat Nuclear Research Reactor

Keywords: 99 Mo/ 99m Tc, irradiation, theoretical calculation, MCNPX simulation

1 INTRODUCTION

99Mo can be produced in nuclear reactors by two basic methods: fission reaction of highly enriched

235U and neutron capture reaction of 98Mo The fission method causes nuclear security concerns such as generating large quantities of radioactive waste and reprocessing of the unused uranium targets due to proliferation concerns [1] Although the simple method with neutron capture reaction (n, γ) is being developed to replace, there are some limitations of low yields in both activity and quantity [2] Solutions were proposed to overcome these burdens, such as using a high density of MoO3 pellet or using solutions with extremely adsorptive However they are limited at laboratory scale for 99

Mo production due to the complicated extraction process [3] With the purpose to improve the recovery 99mTc from 99Mo, Seki [4] used α-MoO3 powder which was irradiated in an experimental reactor and then dispersed in water After the separation and precipitation process, the concentration of 99Mo in water is higher than the solubility limit It is probable that 99Mo isotopes can behave as “hot atoms”, and water can be used to recover 99Mo

the irradiation experiment Porous target containing many pores (voids) with large surface area Moreover, when using wire instead of powder to create a porous structure, the unreacted components are fixed avoiding contamination of the recovery solution Therefore, porous 98MoO3 target can provide high solubility of 99Mo/99mTc after being irradiated and it is possible to recover 99Mo/99mTc simply by pouring water 98MoO3 wire will be heated in the electric furnace to form a porous structure and then irradiated in DNRR to produce 99Mo This paper presents preliminary calculations by theory and MCNPX simulation to investigate appropriate irradiation conditions for MoO3 wire with porous structure in DNRR

2 METHODOLOGY

2.1 Theoretical background

99Mo decays into a meta-stable isomer of 99Tc through the emission of a beta particle with a half-life time of 66 hours Technetium-99m then (a half-life time of 6 hours) decays into 99Tc, which is also unstable but has a long half-life time (2.13x105 years) Fig 1 shown the decay scheme of 99Mo and 99mTc The nuclear properties of 99mTc are ideal for medical imaging as it emits readily available photon energy (~140 keV) that is sufficient to determine the exact molecular structure of the coordination compounds by scintillation instruments such as gamma cameras [5] The data collected by the gamma camera are analyzed

to produce detailed structural and functional images of certain human organs that are otherwise difficult or impossible to image In the neutron capture process, 99Mo is produced by irradiation of molybdenum (98Mo) in thermal neutron flux, {98Mo (n,𝛾)99Mo}

The thermal (~ 0.025 eV) or epithermal (0.025–1.0 eV) neutrons produced by the fission of uranium

in a nuclear reactor can be used to attack stable 98Mo target material installed in a nuclear reactor In this process, the 98Mo nuclei capture a neutron and transform into a 99Mo isotope as shown in Figure 2

Reaction cross-sections depict how the probability of a particular reaction occurrence changes with respect to projectile energy (in the case of neutron energy, see Figure 3) It can be divided into a number of

Figure 3 Cross-sections of the 98 Mo (n, γ) 99 Mo reaction

As with the thermal fission case, the amount of 99Mo produced from this reaction is dependent on the thermal neutron flux 𝜑[n.cm-2

.s-1], the number of 98Mo atoms initial condition 𝑁𝑀𝑜#$%,0 [𝑛], and the irradiation time t [s] Since some amount of 98Mo will be consumed by the capture reaction, it is necessary

to establish the variation of 98Mo concentration Since 98Mo is stable and is not being produced by other reactions, the change in its population is due entirely to thermal neutron capture Therefore, the amount of

98

Mo present in the system at time t is determined as:

𝑁𝑀𝑜−98 = 𝑁𝑀𝑜−98,0𝑒(−𝜑𝜎𝑀𝑜−98 )𝑡 (1)

99Mo is produced only through the neutron capture of 98Mo but also lost through radioactive decay or further neutron capture:

𝑁𝑀𝑜−99 = 𝜑𝜎𝑀𝑜−98𝑁𝑀𝑜−98,0

𝜆𝑀𝑜−99+ 𝜑(𝜎𝑀𝑜−99− 𝜎𝑀𝑜−98)[𝑒(−𝜑𝜎𝑀𝑜−98 )𝑡− 𝑒−(𝜆𝑀𝑜−99 +𝜑𝜎𝑀𝑜−99)𝑡] (2)

where the decay constant for 99Mo is determined by 𝜆 = 𝑙𝑛2

𝑇1/2 [s-1]

If secondary absorptions are neglected, the solution gives the 99Mo activity (Bq) produced after irradiation period t as follows:

𝐴𝑡ℎ[𝐵𝑞/𝑔] = 𝜆𝑀𝑜−99𝑁𝑀𝑜−99= 𝜑𝜎𝑀𝑜−98𝑁𝑀𝑜−98,0[1 − 𝑒−𝜆𝑀𝑜−99 𝑡] (3)

2.2 MCNPX code simulation

Dalat reactor and its parameters: The DNRR was rebuilt and upgraded from the USA TRIGA MARK

II reactor, which was 500 kW pool - typed, light water - cooled, and moderated Radioisotope manufacturing, neutron activation analysis, fundamental and applied research, and workforce training are all now possible with the reactor in operation In the working configuration of DNRR, the neutron trap was designed to have maximum thermal neutron flux in the reactor core Neutron trap is a water cylinder surrounded by Beryllium blocks located in the center of the core which has 6.5cm in diameter and about 2050cm3 in volume MCNPX code was used to determine the neutron flux distribution at the neutron trap position and reaction rate of neutron activation The MCNPX has been being officially used for core management of DNRR with ENDF/B 7.0 library [7] The calculation model for DNRR using MCNPX computer code is shown in Figure 4 The parameters of 98Mo wire is listed in Table 1

Figure 4 Calculation model of DNRR using MCNP5 computer code

Table 1 Summary description of the sample

Diameter Outer diameter: 1.5cm

Inner diameter: 1.25 cm Diameter: 0.5 cm

Component 100% Aluminum 75% of mass 98 Mo, 25% of mass 16 O

Estimates of 99Mo yield from neutron capture on 98Mo may be produced by integrating the total capture cross-section and neutron flux at the energy ranging from 10-11 to 20-1 MeV The thermal neutron flux and neutron absorption cross-section is divided into corresponding bins according to the energy For small quantities of 98Mo (N98), where self-shielding and target burn-out effects are negligible, the 99

Mo production rate can be approximated by

𝑑𝑁99

𝑑𝑡 = −𝜆𝑁99+ ∑ 𝜎̅𝑗𝜙̅𝑗𝑁98

𝑗

(1)

where t is irradiation time, 𝜆 is the 99Mo decay constant (𝜆 = 𝑙𝑛2/ 𝑇1/2), 𝜎̅𝑗 is the energy group

j-averaged (n,) cross – section, and 𝜙̅𝑗 the energy group-averaged neutron flux which calculated by MCNPX The transmutation of the 99Mo product has been neglected—its inclusion would simply introduce

a modification to 𝜆 in Equation 5 that is of the order of the uncertainty of itself

The solution of Equation 5 gives the 99Mo activity (Bq) produced after irradiation period t according to:

𝑗

(2)

where the 98Mo in equation (5) is the number of 98Mo atoms of course calculated from the mass of target molybdenum oxide MoO3

On the other hand, using the FM card in MCNPX code, the tally 4 printout will indicate the number

of 99Mo (atoms/ cm3 ) produced as a result of (n, 𝛾) capture with 98

Mo The number of reactions was calculated by equation (7) below:

where 𝜙(𝐸): Neutron flux (neutrons/cm2

.s), 𝜎(𝐸): Microscopic cross section (barn), C: Normalization constant (atoms/barn.cm)

(5 )

where 𝜌𝑥: Density (g/cm3), 0.6022: Result of product of the Avogadro’s Number and equivalence between barn unit and cm-2 (atoms/mol), 𝜀𝑀𝑜7): MoO3 in the material, 𝑀𝑀𝑜7): Molecular weight of the MoO3 (g/mol)

Fig 5 Input card in MCNPX code

In this way, the 99Mo activity (Bq) produced after irradiation was calculated according to:

𝐴𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑟𝑎𝑡𝑒[𝐵𝑞/𝑔] =𝑄 [

𝑎𝑡𝑜𝑚𝑠

𝑐𝑚3 ] × 𝑉𝑐𝑒𝑙𝑙[𝑐𝑚3] × 𝜆 [1𝑠]

𝜌 [𝑐𝑚𝑔3] × 𝑉𝑐𝑒𝑙𝑙[𝑐𝑚3]

(6)

3 RESULTS AND DISCUSSION

Neutron spectra were divided into 3 energy groups Neutron spectra obtained from calculated at the neutron trap are shown in Table 2 This result of input has not updated the burn of the fuel

Table 2 Neutron flux of the neutron trap using MCNPX

(n/cm2.s)

Relative Error (%)

The Fig 6 shows that the maximum thermal neutron flux value is located 20cm away from the core bottom The sample was inserted into the neutron trap at the position where have maximum thermal neutron flux The shift of maximum flux is mainly affected by the control rod position

Figure 6 Thermal neutron distribution at neutron capture

a) Thermal neutron distribution in radial direction b)Thermal neutron distribution in axial direction

The decay constant for 99Mo (66h half-life) is determined by 𝜆 = 2.9167 × 10-6 𝑠-1.The thermal neutron absorb cross-section for 98Mo(n, 𝛾)99Mo is approximately 0.13barn so that 𝜎 = 0.13𝑏 = 1.3 × 10-25

𝑐𝑚2, thermal neutron flux of DNRR take from the result simulated by MCNPX code is 1.48x1011 n/cm2.s

So the result theoretical calculation of 99Mo activity (Bq) produced after irradiation is 8922 [Bq/g.s] With the MCNPX code, the cross-section and thermal neutron flux were divided into eighty-eight bins based on energy see (Fig 7) Substituted back into Equation (5), the short-time production rate which calculated using the average group is 8811[Bq/g.s] By using the FM card in tally F4, the number of 99Mo produced as a result of (n, 𝛾) capture with 98

Mo is 1.295x1010 atoms/cm3 Substituted back into Equation (9), 99Mo activity (Bq) produced after irradiation is 8056 [Bq/g.s]

To begin with compare between the theoretical calculation and the calculation using the average group In the theoretical calculation using the average thermal neutron absorption cross-section of 98Mo multiplied directly by the thermal neutron flux of DNRR which take from the result of MCNPX On the other hand, in the calculation using the average group, the cross- section of 98Mo and neutron flux are subdivided according to the energy, calculating each group's average value After that multiply the cross-section with the corresponding neutron and the calculated sum of them This is the reason for the small difference between the two values above (1.24%) Secondly, compare between the theoretical calculation and the calculation using the FM card of tally F4 In MCNPX the calculation considers additional factors such as self- shielding, target burned effects, or scattering between materials which theoretical calculations are negligible This is the reason for the difference between the theoretical calculation and the calculation using the FM card (9.71%)

0.90

0.92

0.94

0.96

0.98

1.00

Position[cm]

0.0 0.2 0.4 0.6 0.8 1.0

Position[cm]

1E-11 1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10 1E-6

1E-5 1E-4 0.001 0.01 0.1 1 10 100 1000 10000 100000 1000000 1E7 1E8 1E9 1E10

-2 s

-1 )

Neutron Flux Cross section Group AVG

1E-4 0.001 0.01 0.1 1 10 100 1000 10000

Figure 8 The number 99 Mo present at coressponding time

The 99Mo activity was calculated as a function of time Based on Fig 8, the time to the number of

99

Mo became saturated can be determined At that time, the number of 99Mo produced by neutron capture

of 98Mo was equal to the number of 99Mo lost by decay With this result, after synthesizing the porous sample, measure the parameter of the sample, and determine the specific activity at least essential of 99Mo, the position insert sample and time irradiation can be calculated In the DNRR, besides neutron traps, the configuration has two other positions where can insert the sample such as wet channels 1-4 and dry channels 13-2, 1- 7 Therefore, in the future, the research will continue to be studied at the two above positions

4 CONCLUSION

The growing demand for 99mTc and the inherent problem associated with 99Mo production from fission products has increased the interest for economically feasible alternative sources of 99Mo Production of 99Mo via the neutron capture method can be a feasible alternative to fission- derived 99Mo This report proposes the porous MoO3 target made from Mo wire together with the investigation of specific activity also reaction rate of the irradiation process by MCNPX with the conditions of the Da Lat Nuclear Research Reactor Therefore, simplifies the separation of 99Mo/99mTc as well as improves the performance of 99Mo

ACKNOWLEDGMENTS

This research was funded by the scholarship from the Global Academic-Industry Consortium for Collaborative Education Program (GAICCE), the AUN/SEED-Net project that is supported by the Japanese Government through JICA for the Double Degree Program at Hanoi University of Science and Technology (HUST), Vietnam and Nagaoka University of Technology, Japan

REFERENCES

[1] Lyra M, et al., “Alternative production methods to face global molybdenum-99 supply shortage,” National Library

of Medicine, 49-55, 2011

[2] RE Boyd, “Molybdenum-99: Technetium-99m generator” , National Center for Biotechnology Information,

123-145, 1982

[3] A.Kimura, et al., “Development of 99m Tc Extraction Techniques from 99 Mo by (n, 𝛾) Reaction”, JEAE Review, 2010-053, 2010

[4] M Seki, (2017), “Development of water nuclide separation method for medical 99 Mo 99mTc generator develop-ment”, Nagaoka University of Technology

[5] CG Whipple, “Medical isotope production without highly enriched uranium,”Science Engineering Medicine,

2009

[6] 2012, “Báo cáo phân tích an toàn lò phản ứng hạt nhân Đà Lạt,” Viện Nghiên cứu hạt nhân Đà Lạt

[7] MB Chadwick et al., “ENDF/B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Science and

Technology,” Nuclear DataSheets, 2006

0E+00 1E+06 2E+06 3E+06 4E+06 5E+06 6E+06 7E+06 0.0E+00

2.0E+14 4.0E+14 6.0E+14 8.0E+14 1.0E+15 1.2E+15

Time(s)

Theoretical Average Group MCNPX code