Exploration of Adiabatic Resonance Crossing Through Neutron Activator Design for Thermal and Epithermal Neutron Formation in 99 Mo Production and BNCT Applications

Abstract

A feasibility study was performed to design thermal and epithermal neutron sources for radioisotope production and boron neutron capture therapy (BNCT) by moderating fast neutrons. The neutrons were emitted from the reaction between ⁹Be, ¹⁸¹Ta, and ¹⁸⁴W targets and 30 MeV protons accelerated by a small cyclotron at 300 μA. In this study, the adiabatic resonance crossing (ARC) method was investigated by means of ²⁰⁷Pb and ²⁰⁸Pb moderators, graphite reflector, and boron absorber around the moderator region. Thermal/epithermal flux, energy, and cross section of accumulated neutrons in the activator were examined through diverse thicknesses of the specified regions. Simulation results revealed that the ¹⁸¹Ta target had the highest neutron yield, and also tungsten was found to have the highest values in both surface and volumetric flux ratio. Transmutation in the ⁹⁸Mo sample through radiative capture was investigated for the natural lead moderator. When the sample radial distance from the target was increased inside the graphite region, the production yield had the greatest value of activity. The potential of the ARC method is a replacement or complements the current reactor-based supply sources of BNCT purposes.

Highlights

• A feasibility study was performed to design thermal and epithermal neutron sources.

• Neutrons were emitted from three targets and 30 MeV protons through a small cyclotron.

• Adiabatic resonance crossing method studied by lead moderator in radioisotope production and boron neutron capture therapy purposes.

• An alternative production method of ⁹⁹Mo using accelerators was developed.

• Cheaper and safer way suggested in medical radiochemistry applications.

Introduction

There are essentially three processes that can be modeled in accelerator-driven systems for neutron radioisotope production and also for boron neutron capture therapy (BNCT) applications: neutron production, moderation, and capture or collimation.^1

–6 In this study, the authors consider low-current proton sources incident on an appropriate target to produce neutrons for driving the neutron activator.

Moderation is the process of slowing neutrons down through interactions with the nuclei of a material. When neutrons collide with nuclei, they lose momentum and slow down until they are in epithermal and thermal equilibrium with the medium they are moving through.^7,8 The adiabatic resonance crossing (ARC) technique has been proposed by Rubbia in 1997⁹ for element activation and waste transmutation by neutron capture.^10
–12

An accelerator-driven neutron activator that is based on the ARC method has been simulated in the frame of the Karaj cyclotron (Cyclon30; IBA, Belgium) in Iran. The investigation was made with the aim of efficiently utilizing ion-beam-generated neutrons for production of thermal and epithermal neutrons in the lead storage region. MCNPX (Monte Carlo N-Particle version ×2.7.0)¹³ simulations were carried out to optimize the scheme of the activator, which is based on neutron production from an incident low-energy proton, lead moderator and dispersal, graphite reflector, and boron absorber. The framework has been divided into investigating low-energy proton, target design, moderator, and reflector material.

Yonai et al.¹⁴ and Tahara et al.¹⁵ investigated a neutron source using spallation reactions that occur for 30–50 MeV protons incident on a tantalum target. Tahara et al. showed that the epithermal neutron field required by BNCT is 1 mA for 30 MeV incident protons. Energy amplifier systems consist of a subcritical fast neutron core driven by a proton accelerator, and Kadi,¹⁶ Bak,¹⁷ Schwenk-Ferrero,¹⁸ and Hong¹⁹ demonstrated transmutation capabilities through fission and transuranic elements presently produced by nuclear reactors. Meanwhile, Kadi and Revol²⁰ have proposed an accelerator-driven system for the destruction of nuclear waste and testing minimal cost long-lived fission fragments using the concept of the ARC method.

Furthermore, BNCT is a technique that was designed to selectively target high-LET heavy charged particle radiation to tumors at the cellular level. ¹⁰B absorbs a thermal neutron in a (n,α) reaction. The energetic emitted α particle and the recoiling ⁷Li ion result in locally deposited energy averaging about 2.33 MeV. About 94% of the time, the recoiling ⁷Li ion is produced in an excited state and de-excites in flight, emitting a 477 keV γ ray. In the remaining events, ⁷Li is emitted in the ground state with no γ ray emission, which can be ignored from a dosimetry perspective, although they are frequently utilized for ¹⁰B analysis purposes.^21
–23 In this project, the authors have shown that an epithermal and thermal neutron field required by BNCT and radioisotope production, respectively, can be realized when a proton of 300 μA at 30 MeV by cyclotron is used.

Methods and Materials

Neutron generator system by proton reaction through target design

Design and development of a target design for radioisotope production or BNCT require making a balance among neutronic, mechanical, and thermal considerations. The target must produce a sufficient number of neutrons when irradiated by a suitable proton beam. The charged particle beam striking the target should also be as large as possible to spread the heat load, but must still remain small enough to limit the loss of those neutrons generated near the edges of the target. Since the charged particle beam generates heat when it is stopped by the target material, a target heat removal system must be designed to keep the target cool and mechanically stable. This entire target and cooling assembly must be integrated into the moderator/reflector assembly without adversely affecting the neutron field either by reducing the flux or by altering the desired neutron energy spectrum. The low-energy proton beam with 0.5 cm radius in 30 MeV at 1 μA current has produced 30 J/second on the target area.

The target was designed in a cylindrical shape with 0.83 cm radius and 1 cm length. Moreover, the target was equipped with a cooling system and water was used as its coolant. Beryllium, tungsten, and tantalum are considered as target materials because they possess a high melting point equal to 1287°C, 3422°C, and 3017°C, respectively, and also fine mechanical properties with a density of 1.85, 19.3, and 16.4 g/cm³, respectively. Equation 1 demonstrates the produced neutron source per volume per second inside × thickness of target as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}S = Nj \ \sigma x \tag{{ \rm Equation} \ 1}\end{align*} \end{document}

where N (nucleus/cm³) is the density of target nuclide, j (proton/cm²/s) is beam intensity, and σ (cm²) is the microscopic cross section. Then, the authors can calculate the S/j ratio as neutron yield: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \frac { S } { j } = N \ \sigma \ \int_0^ { E_0 } \frac { dE } { dE / dx } = N \ \sigma\ R = \frac { R } { \lambda} \tag { { \rm Equation } \ 2 } \end{align*} \end{document}

where dE/dx is stopping power (MeV/cm), R is reaction rate, and λ is mean free path of the incident proton. Moreover, the differential thick target neutron yield is given as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \begin{split} \frac {d^2Y \ ( E_0 )} {dEd \Omega} & = N \int_0^X \frac {d^2 \sigma \big ( E_0 - \int_0^x \big ( \frac{dE} {dx} \big) dx \big )} {dEd \Omega} \\ & \quad \times e ^{ - N \sigma_{nonel} \big ( E_0 - \int_0^x ( \frac{dE} {dx} ) dx \big ) x}dx \quad ( n / MeV / Sr / projectile )\end{split} \tag{{ \rm Equation \ 3}}\end{align*} \end{document}

where E₀ is the incident particle energy (MeV), X is thickness of the target (cm), and σ_nonel is the nonelastic cross section (cm²). In this study, absorption, elastic, and capture cross sections of neutrons were considered from the ENDF/B-VII.1 libraries.²⁴

Moderator and reflector designs

MCNP code is widely used for neutron transport and also for simulating moderation and reflection. The MCNPX version 2.7.0 will be used with a 30 MeV proton source to test varying moderator and reflector setups. In this study, the materials used were tested in the code and the final flux and energy spectra were compared. For each test, the same setup is used for several radiuses' sphere of material with a spherical detector layer at a radius of 2.2, 5, 7, and 20 cm inside the material that allows for backscattering.

Neutron physics characteristics of some light moderators (hydrogen, deuterium, graphite, and oxygen) and heavy materials (natural lead and lead isotope ²⁰⁸Pb) are presented in Table 1. Elastic cross sections of natural lead and ²⁰⁸Pb do not differ significantly from the others, being between the corresponding values for hydrogen and other light nuclides. Slowing down of neutrons from 0.1 MeV to 0.5 eV requires from 12 to 102 elastic collisions with light nuclides, whereas slowing down of the same neutrons requires about 1270 elastic collisions with natural lead or ²⁰⁸Pb. The reason is the high atomic mass of lead compared to the other light nuclides. From this point of view, neither natural lead nor ²⁰⁸Pb is an effective neutron moderator.^25

–28 Taking into account that capture cross section at thermal energy and capture resonance integral of natural lead are much larger than the corresponding values of most of the light nuclides, it is safe to say that neutrons are captured during the slowing down process in natural lead with a higher probability compared to the slowing down process in light materials. Therefore, only a small part of neutrons will slow down to thermal energy. This means that thermal neutron flux in natural lead will be much lower than in the light materials. At the same time, the nucleus of ²⁰⁸Pb is a double magic nucleus with closed proton and neutron shells. Thanks to this, the capture cross section at thermal energy and capture resonance integral of ²⁰⁸Pb are much lower than the corresponding values of lighter nuclides. The authors can, therefore, expect that even with multiple scattering of neutrons on ²⁰⁸Pb during the process of their slowing down, they will be slowed down to thermal energy with a high probability and thus will create a high thermal neutron flux.

Table 1.

Neutron Moderator Physical Properties of Some Materials

Nuclide	σ_elastic (barn)	Number of collisions (0.1 MeV to 0.5 eV)	\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\sigma_{ ( n , \gamma ) }^{th}$$ \end{document} (mbarn)
¹H	30.1	12	332
²D	4.2	17	0.55
_12C	4.9	77	3.9
_16O	4.0	102	0.19
Natural Pb	11.3	1269	174
²⁰⁷Pb	11.51	1263	620
²⁰⁸Pb	11.46	1274	0.23

The effective material for reflection of neutrons would be very useful as it would increase the chances of capture or collimation. Graphite is used in nuclear reactors to reflect neutrons back into uranium to cause more fission.²⁹ A good reflector material has a high probability of scattering neutrons backward at a range of energies.

In this study, an evaluation of ARC in accelerator-driven systems has been simulated by the MCNPX code. The assembly of simulation in a neutron activator and bulk storage of epithermal neutrons are shown in Figure 1. Lead moderator assembly with 30 cm radius is surrounded by a spherical graphite reflector, which is radially 35 cm thick. The third layer is a 5 cm thick boron as a neutron absorber. In the simulation of lead moderator, both ²⁰⁷Pb and ²⁰⁸Pb have been considered to estimate thermal and epithermal neutron flux.

FIG. 1.

The schematic of neutron storage, including neutron generator and moderator, is surrounded by spherical reflector and absorber.

⁹⁸Mo sample position inside the activator for ⁹⁹Mo production

The target was surrounded by a moderator assembly. Transmutation was prepared in lead moderator and graphite reflector regions. Figure 1 shows ⁹⁸Mo locations at diverse regions, which were settled in the direction of the beam axis. The beam axis is perpendicular to the base of the cylindrical target as well as the target places in origin. Induced neutrons slowed down inside the moderator region at first. Then, the graphite reflector, which had a 35 cm thickness around the moderator assembly, saved the derived neutrons. Graphite was preferred as a reflector because of its high elastic scattering cross section and low-absorption cross section to store the neutrons in a superior flux. Moreover, boron with a 5 cm thickness was used as the absorbent matter to enclose the reflector.

⁹⁸Mo samples were spheres with a 1 cm radius and were arranged at distances of 15 and 25 cm from the target inside the lead moderator region and at 38 and 45 cm inside the graphite reflector region. The ⁹⁹Mo production yield related to the neutron flux in the thermal range must be proper to achieve gains. Therefore, the use of a desirable system and location of samples inside lead or graphite regions for production yield is very important.

Conceptual design for BNCT purposes

The induced neutron source from the target in the activator region needed to be amassed in the lead region and then guided to the beam port with the reflector material. The schematic of the neutron activator and storage space of neutrons is shown in Figure 2. The reflector was designed in an arc shape around the lead buffer to prevent neutron waste. Heading the appropriate beam components for epithermal neutrons in the direction of the head phantom necessitates a collimator and filter assemblies. The collimator is made up of two layers of boron carbide (B₄C) and Bi materials. The internal layer of the collimator acts as an absorber that should eliminate the dispersed neutrons. The external layer works as a γ shield, which is supposes to reduce hard γ rays. The filtered beam facilities support of the proper flux of epithermal neutrons within air with the order of 1E+9 n/cm²/s, and likewise IAEA-TECDOC-1223²³ has recommended beam quality parameters and corresponding neutron beam energy limits in BNCT. The epithermal energy group is between 1 eV and 10 keV. The scalp–skull–brain phantom consisting of homogeneous regions of bone- or brain-equivalent material was simulated to assess the dosimetric effect in the brain. Table 2 gives the elemental composition of the biological tissues used in the Monte Carlo simulations according to the International Commission on Radiation Units and Measurements (ICRU) report 46 (ICRU 1992). The geometry of the phantom was defined as a spherical shape, and the 1 cm seated tumor in the head phantom was compounded at 7.14% ¹H, 57.14% ¹⁶O, and 35.72% ¹⁰B with the density of this segment calculated as 1.77 g/cm³.

FIG. 2.

The proposed design in boron neutron capture therapy and the thicknesses are as follows: (1) typical target with 0.83 cm radius, (2) 30 cm in radius natural lead moderator, (3) 25 cm in thickness graphite reflector, (4) Fluental moderator, (5) first Fe filter, (6) 0.5 cm Li filter, (7) Bi filter, (8) second Fe filter, (9) B₄C frustum 65 cm gateway radius and 4 cm end of cone radius, (10) Bi frustum 68 cm entrance radius and 5 cm egress radius, (11) 0.2 cm scalp, (12) 2 cm skull, (13) 10 cm in radius of brain, (14) 1 cm in radius of tumor at depth of 1 cm inside brain region, and (15) lead shield.

Table 2.

Weight Fraction (%) of Elemental Compositions Used in Monte Carlo Simulations According to ICRU Report 46 (ICRU 1992)

Element	Brain (1.040 g/cm³)	Skull (1.610 g/cm³)	Scalp (1.090 g/cm³)
¹H	10.70	5.00	10.00
¹⁶O	71.20	43.50	64.50
¹²C	14.50	21.20	20.40
¹⁴N	2.20	4.00	4.20
²³Na	0.20	0.10	0.20
³¹P	0.40	8.10	0.10
³²S	0.20	0.30	0.20
³⁵Cl	0.30	—	0.30
³⁹K	0.30	—	0.10
²⁴Mg	—	0.20	—
⁴⁰Ca	—	17.60	—

ICRU, International Commission on Radiation Units and Measurements.

Epithermal neutrons can pass through the scalp, temporal muscle, and the cranial bone and convert to thermal neutrons in the tissue. Therefore, epithermal neutrons would improve the number of thermal neutrons delivered to deep-seated lesions. Subsequently, it was determined that for deep-seated brain tumors, a beam of epithermal neutrons, defined as neutrons with energies between 0.5 eV and 10 keV, was preferable to a beam of thermal neutrons.²³

Results and Discussion

Neutron yield from diverse targets

A conceptual design for neutron source is proposed for low-energy protons in ⁹Be, ¹⁸⁴W, and ¹⁸¹Ta targets. Three targets were simulated in air and lead mediums encircling the target for incident protons with energy of 30 MeV and current of 300 μA, as well as the beam axis is perpendicular to the base of the cylindrical target.

Interaction of the proton beam in the target results in target disintegration because of the proton energy range and target characteristics. The projected range in ⁹Be, ¹⁸⁴W, and ¹⁸¹Ta targets was calculated as 0.580, 0.103, and 0.120 cm, respectively, for 30 MeV energy of incident protons. The values of the total number of neutrons per second and per microampere in these three targets produced by incident protons were 0.0192, 0.0182, and 0.0208, respectively. Meanwhile, the neutron yields were simulated at 300 μA equal to 3.60E+13, 3.41E+13, and 3.89E+13 n/s, respectively. The simulated results revealed that the tantalum target had the highest value in the neutron-to-proton (n/p) ratio equal to 0.0208 for 1 μA of proton beam, and then the ¹⁸¹Ta target had the highest neutron yield. The formula of Rubbia 1997⁹ has exposed the total of neutrons produced by the proton reaction.

The generated neutrons from proton interactions are spread around the target. Analysis of neutron dispersion is related to property of the target, in addition, neutron flux reduces exponentially with increase in distance from the target. Neutronic surface flux ratio to neutron yield at 5 cm distance of spherical geometry around the target in air medium was 0.086, 0.106, and 0.042 for ⁹Be, ¹⁸⁴W, and ¹⁸¹Ta, respectively. Meanwhile, neutron flux in a spherical volume to volumetric neutron yield was simulated at 7 cm distance from diverse targets in the air in which these ratios were 0.032, 0.050, and 0.046 for ⁹Be, ¹⁸⁴W, and ¹⁸¹Ta, respectively, and also tungsten indicated the highest values.

Flux of accumulated neutrons through ²⁰⁷Pb and ²⁰⁸Pb moderators

During the interaction of incipient proton with diverse targets, the generated neutrons disperse in the surrounding lead. The generated neutrons in various angles were simulated in ²⁰⁷Pb and ²⁰⁸Pb moderators from the target through F2 tally in Monte Carlo simulations. Figure 3 reveals surface flux in terms of angle of the generated neutrons from the center of the cylindrical target for the ²⁰⁸Pb moderator at 2.2, 5, and 20 cm distances. The angle between 20° and 30° at 2.2 cm distance from the surface of ⁹Be target had the curve peak by means of the ²⁰⁸Pb moderator. Meanwhile, the flux was drawn at r = 2.2 cm distance inside the ²⁰⁷Pb region for three targets. When the distance from the target increased, the peak of the surface flux curve in the lead buffer decreased. At this time, the maximum point shifted to lesser angles. Comparison of the flux at 2.2 cm distance inside ²⁰⁷Pb and ²⁰⁸Pb showed that the ⁹Be target in 22° contains the maximum surface flux, and the ²⁰⁸Pb moderator revealed a higher value than the ²⁰⁷Pb moderator. ¹⁸¹Ta and ¹⁸⁴W targets had the maximum surface flux in 30° into the beam axis, and the ¹⁸¹Ta target in the ²⁰⁸Pb moderator showed higher values than others.

FIG. 3.

Surface flux from three targets at different distances in terms of angle of generated neutrons inside ²⁰⁸Pb moderator and at 2.2 cm distance inside ²⁰⁷Pb moderator.

Exploration of volume flux in different thicknesses of lead moderator and graphite reflector

The scheme was simulated in different thicknesses of lead moderator and graphite reflector. The thickness of boron absorber was chosen 5 cm around the reflector. The F4 tally in MCNP, which was used, is a track length tally, which sums the distances traveled by a particular type of particle in a defined volume. The unit of a volume and time-normalized F4 tally is particle · cm/cm³/s. Table 3 shows the simulated results of the neutron volumetric flux in thermal, epithermal, and fast ranges, plus total flux within the last column in the ²⁰⁷Pb moderator. Thermal and epithermal flux in ²⁰⁷Pb were in the order of 1E+9 and 1E+10 n/cm²/s, respectively, except ⁹Be in thermal range with 25 and 40 cm in ²⁰⁷Pb and graphite thicknesses, respectively. Some results of simulation in thermal and epithermal ranges were shown in italic/bold with higher/highest flux values, for instance ⁹Be and ¹⁸¹Ta targets with ²⁰⁷Pb thickness of 25 cm and graphite thickness of 40 cm had greater flux values, as well as the ¹⁸⁴W target with moderator and reflector thicknesses of 35 cm had a superior value in the thermal neutron range. Moreover, in the epithermal neutron range, the ⁹Be target with moderator thickness of 25 cm had a maximum value in neutron flux between 0.1 eV and 5 keV energy of reduced neutron energy.

Table 3.

Volumetric Flux of Neutrons (n/cm ² /s) Derived from Three Targets in ²⁰⁷ Pb Moderator and Graphite Reflector with Different Thicknesses

Target	²⁰⁷Pb thickness	Graphite thickness	Thermal (0–0.1 eV)	Epithermal (0.1 eV–5 keV)	Fast (5 keV–1 MeV)	Total (0–30 MeV)
⁹Be		30	9.52E+09	3.75E+10	1.07E+11	1.55E+11
	25	35	9.78E+09	3.93E+10	1.09E+11	1.58E+11
		40	1.01E+10	3.94E+10	1.10E+11	1.61E+11
		30	6.11E+09	2.89E+10	8.61E+10	1.21E+11
	30	35	6.48E+09	2.93E+10	8.73E+10	1.26E+11
		40	6.68E+09	2.96E+10	8.70E+10	1.29E+11
		30	4.02E+09	2.20E+10	7.00E+10	9.66E+10
	35	35	4.20E+09	2.19E+10	6.99E+10	9.68E+10
		40	4.40E+09	2.26E+10	7.03E+10	9.73E+10
¹⁸¹Ta		30	7.14E+09	3.08E+10	8.84E+10	1.26E+11
	25	35	7.10E+09	2.93E+10	8.61E+10	1.28E+11
		40	7.51E+09	3.00E+10	8.67E+10	1.29E+11
		30	4.27E+09	2.04E+10	6.38E+10	8.86E+10
	30	35	4.73E+09	2.09E+10	6.44E+10	9.02E+10
		40	4.90E+09	2.21E+10	6.72E+10	9.44E+10
		30	2.74E+09	1.55E+10	5.27E+10	7.10E+10
	35	35	2.85E+09	1.56E+10	5.22E+10	7.11E+10
		40	3.04E+09	1.57E+10	5.25E+10	7.12E+10
¹⁸⁴W		30	6.60E+09	2.76E+10	8.04E+10	1.15E+11
	25	35	6.49E+09	2.75E+10	8.12E+10	1.16E+11
		40	7.25E+09	2.98E+10	8.36E+10	1.21E+11
		30	4.16E+09	1.99E+10	6.29E+10	8.72E+10
	30	35	4.33E+09	2.07E+10	6.41E+10	8.92E+10
		40	4.71E+09	2.08E+10	6.45E+10	9.05E+10
		30	2.61E+09	1.43E+10	4.87E+10	6.58E+10
	35	35	7.70E+09	1.47E+10	5.07E+10	7.33E+10
		40	2.94E+09	1.53E+10	5.04E+10	6.89E+10

The values in italic show higher flux for the distinct targets, while the value in bold indicates the highest flux for the distinct targets.

The results of changing in ²⁰⁸Pb and graphite thicknesses are demonstrated in Table 4. In the ²⁰⁸Pb moderator, both thermal and epithermal ranges were in the order of 1E+10 n/cm²/s. The maximum flux in the thermal range for ⁹Be and ¹⁸¹Ta is with ²⁰⁸Pb thickness of 25 cm, but that for the ¹⁸⁴W target is with ²⁰⁸Pb thickness of 35 cm. The epithermal neutrons derived from the ⁹Be target with ²⁰⁸P thickness of 25 cm had greater values among the two other thicknesses of ²⁰⁸P. Hence, on the basis of these simulations, it is very important to develop an alternative production method of ⁹⁹Mo using accelerators because of the economic advantages. This method was founded on the production and collimation with respect to the standard nuclear reactor route, which will be completely weighed up. For this reason, the result of thermal and epithermal energy and flux can be suitable for production of some radioisotopes and BNCT applications.

Table 4.

Volumetric Flux of Neutrons (n/cm ² /s) Derived from Three Targets in ²⁰⁸ Pb Moderator and Graphite Reflector with Different Thicknesses

Target	²⁰⁸Pb thickness	Graphite thickness	Thermal (0–0.1 eV)	Epithermal (0.1 eV–5 keV)	Fast (5 keV–1 MeV)	Total (0–30 MeV)
⁹Be		30	5.51E+10	8.97E+10	1.44E+11	2.90E+11
	25	35	6.07E+10	9.56E+10	1.50E+11	3.06E+11
		40	6.40E+10	9.87E+10	1.52E+11	3.18E+11
		30	4.83E+10	7.57E+10	1.19E+11	2.47E+11
	30	35	5.14E+10	7.93E+10	1.22E+11	2.55E+11
		40	5.56E+10	8.40E+10	1.27E+11	2.67E+11
		30	4.15E+10	6.45E+10	9.94E+10	2.05E+11
	35	35	4.45E+10	6.78E+10	1.03E+11	2.18E+11
		40	4.65E+10	6.99E+10	1.04E+11	2.23E+11
¹⁸¹Ta		30	4.13E+10	6.75E+10	1.15E+11	2.25E+11
	25	35	3.98E+10	6.71E+10	1.15E+11	2.22E+11
		40	4.76E+10	7.36E+10	1.20E+11	2.43E+11
		30	3.27E+10	5.30E+10	8.94E+10	1.78E+11
	30	35	3.64E+10	5.68E+10	9.38E+10	1.87E+11
		40	3.90E+10	5.98E+10	9.67E+10	1.97E+11
		30	2.87E+10	4.54E+10	7.52E+10	1.49E+11
	35	35	3.20E+10	5.07E+10	8.08E+10	1.66E+11
		40	3.36E+10	5.10E+10	8.05E+10	1.67E+11
¹⁸⁴W		30	3.84E+10	6.38E+10	1.09E+11	2.11E+11
	25	35	4.35E+10	6.84E+10	1.15E+11	2.28E+11
		40	4.58E+10	7.23E+10	1.17E+11	2.35E+11
		30	3.35E+10	5.25E+10	8.71E+10	1.75E+11
	30	35	3.65E+10	5.63E+10	9.08E+10	1.86E+11
		40	3.75E+10	5.72E+10	9.24E+10	1.88E+11
		30	2.80E+10	4.41E+10	7.26E+10	1.45E+11
	35	35	7.99E+10	4.63E+10	7.47E+10	2.02E+11
		40	3.21E+10	4.88E+10	7.70E+10	1.59E+11

The values in italic show higher flux for the distinct targets, while the value in bold indicates the highest flux for the distinct targets.

Radioisotope production and BNCT process are related to the proper neutron flux in thermal and epithermal ranges to achieve gains. Therefore, using this scheme, positioning of samples for activation yields in the lead or graphite region is very important for radioisotope production. Meanwhile, in the BNCT route, location of the collimator gate from lead or graphite is insignificant to realize dose values in the tumor. Thus, investigation into the volumetric flux of neutrons in thermal and epithermal ranges was simulated in three parts of this scheme, including moderator, reflector, and absorber for different ranges of neutron energy from three targets, and is also tabulated in Tables 5 and 6 for ²⁰⁷Pb and ²⁰⁸Pb moderators, respectively. In these simulations, the flux of neutrons derived from three targets was considered in the lead moderators with thickness of 30 cm and graphite reflector with thickness of 35 cm surrounded by 5 cm boron.

Table 5.

Volumetric Neutron Flux (n/cm ² /s) for Three Targets in ²⁰⁷ Pb Moderator, Graphite Reflector, and Boron Absorber

Target	Material	Thermal (0–0.1 eV)	Epithermal (0.1 eV–5 keV)	Fast (5 keV–1 MeV)	Total (0–30 MeV)
⁹Be	²⁰⁷Pb	6.48E+09	2.93E+10	8.73E+10	1.26E+11
	Graphite	1.38E+10	2.06E+10	2.30E+10	5.75E+10
	Boron	2.35E+09	2.71E+09	2.72E+09	7.79E+09
¹⁸¹Ta	²⁰⁷Pb	4.73E+09	2.09E+10	6.44E+10	9.02E+10
	Graphite	9.43E+09	1.42E+10	1.57E+10	3.95E+10
	Boron	1.54E+09	1.81E+09	1.81E+09	5.16E+09
¹⁸⁴W	²⁰⁷Pb	4.33E+09	2.07E+10	6.41E+10	8.29E+10
	Graphite	9.22E+09	1.38E+10	1.53E+10	3.83E+10
	Boron	1.52E+09	1.75E+09	1.75E+09	5.05E+09

The values in italic show higher flux for the distinct targets.

Table 6.

Volumetric Neutron Flux (n/cm ² /s) for Three Targets in ²⁰⁸ Pb Moderator, Graphite Reflector, and Boron Absorber

Target	Material	Thermal (0–0.1 eV)	Epithermal (0.1 eV–5 keV)	Fast (5 keV–1 MeV)	Total (0–30 MeV)
⁹Be	²⁰⁸Pb	5.14E+10	7.93E+10	1.22E+11	2.55E+11
	Graphite	2.60E+10	3.43E+10	3.70E+10	9.75E+10
	Boron	3.61E+09	4.19E+09	4.21E+09	1.20E+10
¹⁸¹Ta	²⁰⁸Pb	3.64E+10	5.68E+10	9.38E+10	1.87E+11
	Graphite	1.77E+10	2.35E+10	2.52E+10	6.67E+10
	Boron	2.46E+09	2.83E+09	2.83E+09	8.13E+09
¹⁸⁴W	²⁰⁸Pb	3.65E+10	5.63E+10	9.08E+10	1.86E+11
	Graphite	1.70E+10	2.25E+10	2.42E+10	6.39E+10
	Boron	2.53E+09	2.88E+09	2.89E+09	8.30E+09

The values in italic show higher flux for the distinct targets.

The comparison between ²⁰⁷Pb and ²⁰⁸Pb moderators demonstrated that the ²⁰⁸Pb moderator had greater values of neutron flux in both the thermal and epithermal ranges. According to Table 5, flux of thermal neutrons for all targets in the graphite region is higher than in the ²⁰⁷Pb and boron regions; as for the epithermal range, higher flux takes place in the ²⁰⁷Pb region. Furthermore, the use of the ²⁰⁸Pb moderator is significantly different from that of the ²⁰⁷Pb moderator. Table 6 demonstrates that all thermal neutron fluxes in ²⁰⁸Pb and graphite regions are in the order of 1E+10 n/cm²/s, and higher values of flux occur in the ²⁰⁸Pb region for both thermal and epithermal ranges. These simulations indicate that the use of ²⁰⁸Pb moderator could be compatible with medical applications to accumulated neutrons in a specified region for two ranges of neutron energies. Moreover, gathering thermal or epithermal neutrons in a region is related to target and moderator properties, in addition to thickness of the reflector. The ⁹Be target revealed greater values of flux in both thermal and epithermal ranges using ²⁰⁷Pb and also ²⁰⁸Pb moderators.

Total flux of accumulated epithermal and thermal neutrons in diverse regions relies on velocity of neutrons, and also the regional storage in lead or graphite volume alters the flux of collected neutrons. Figure 4a and b reveal the neutronic flux in terms of n/s/cm²/MeV/particle using ²⁰⁷Pb and ²⁰⁸Pb procedures, and also ²⁰⁸Pb shows higher total flux than ²⁰⁷Pb. Furthermore, the gathered neutrons in thermal and epithermal ranges inside the graphite region were considerably more than the lead region with order of 1E+10 n/cm²/s.

FIG. 4.

(A) Total flux of neutrons derived from Ta target inside ²⁰⁷Pb (solid histogram) and graphite (dash histogram) regions. (B) Total flux of neutrons derived from Ta target inside ²⁰⁸Pb (solid histogram) and graphite (dash histogram) regions.

Radiative capture yield in ⁹⁹Mo production

The ⁹⁹Mo activity per gram and ⁹⁸Mo placement from the three targets for lead moderator were investigated. When the sample radial distance from the ⁹Be target was 38 cm inside the graphite region, the production yield had the greatest value of activity equal to 249.25 MBq/g. The activities generated in molybdenum samples are tabulated in Table 7 for the three targets using the natural lead moderator. When the material changed from lead to graphite, the activity increased, this increase for the ⁹Be target was greater than the increase for the ¹⁸¹Ta and ¹⁸⁴W targets. The energy threshold of ⁹⁸Mo(n,γ)⁹⁹Mo reaction was 480 eV with the cross section of activated molybdenum 0.72 barns, in which the radiative capture resonances happened in thermal ranges of neutron energies.^13,24 Frequently, ⁹⁹Mo is produced by the neutron fission of enriched uranium. Assuming a specific in the fissium with an atomic fraction λ and the exposure time t_exp equal to one half-life of compound, the initial activity for 1 kg of activated sample is 2.5 × 10⁻¹⁰ S₀λη_f (GBq/kg), in which S₀ is the neutronic source (n/s) and η_f is fissium efficiency (kg ⁻¹). If the target is 20% enriched metallic uranium of a mass of 33 kg, and the exposure time is set to 10 days, the asymptotic yield is calculated to 51.3 GBq/kg^9,18
–20

Table 7.

Emitted Photons Through (n,γ) Reaction in Thermal Range of Neutron Energy and Photon Number per Second (MBq/g) in ⁹⁸ Mo Samples at Various Distances

⁹⁸Mo radial distance from target (cm)	Region	Radiation capture yield (MBq/g)
		⁹Be	¹⁸¹Ta	¹⁸⁴W
15	Natural lead	137.64	241.71	105.09
25		202.46	219.13	181.01
38	Graphite	249.25	233.88	197.15
45		209.69	122.97	118.70

Neutron flux analysis in BNCT applications

In BNCT, the epithermal-to-fast flux ratio and the epithermal-to-thermal flux ratio must be larger than 20 and 100, respectively.²³ Table 8 demonstrates surface flux of derived neutrons at the end of the collimator (in air) from thickness changing in Fluental and the first Fe filters. The thicknesses of Fluental and first Fe filters were considered between 1.4–5.4 and 3–7 cm, respectively, and thicknesses of second Fe, Bi, and Li filters were kept constant at 1, 5, and 0.5 cm, respectively. The minimum flux of fast and thermal neutrons occurred in 5.4 and 4.4 cm Fluental, respectively. The greatest amount of epithermal neutron flux occurred at 4.4 cm Fluental and 4 cm first Fe. At the same time, the fast and thermal fluxes were 2.62E+8 and 1.63E+7 n/cm²/s, respectively. Table 9 shows the surface neutronic flux in different thicknesses of second Fe and Bi filters at the end of the collimator (in air), when the thicknesses of Fluental, first Fe, and Li filters were kept constant at 2.4, 6, and 0.5 cm, respectively. Using 5.2 cm Bi and 0.8 cm second Fe filters, the maximum epithermal neutron flux was equal to 8.39E+9 n/cm²/s. Table 10 exhibits the surface neutronic flux with different thicknesses of filters (7.4 cm Fluental, 4 cm Fe, 0.5 cm Li, and 3 cm Bi), exclusive of second Fe filter in diverse regions. In the proposed work, the epithermal-to-thermal neutron flux ratio was higher than that recommended by IAEA. In that case, to reach the IAEA recommended level, the authors had to increase the neutronic epithermal flux against the fast flux using different filters and diverse thicknesses. Neutron and photon dose values at the epithermal range in three regions of the phantom were tabulated in terms of Gy/h/#/cm²/s, where # is the number of neutrons or photons per particle. The value of quality factor for neutron radiation is energy dependent and this value in the epithermal range amounts to 5. Photon dose decreased in scalp, tumor, and brain regions, respectively.

Table 8.

Surface Neutronic Flux (n/cm ² /s) in Different Thicknesses of Fluental and First Fe at the End of the Collimator for ⁹ Be Target, When the Thicknesses of Second Fe, Bi, and Li Filters Were 1, 5, and 0.5 cm, Respectively

Fluental thickness (cm)	First Fe thickness (cm)	Thermal (0–1 eV)	Epithermal (1 eV–10 keV)	Fast 10 keV–1 MeV)
1.4	7	4.21E+07	8.23E+09	2.78E+08
2.4	6	1.98E+07	7.61E+09	2.51E+08
3.4	5	2.90E+07	8.62E+09	2.47E+08
4.4	4	1.63E+07	9.33E+09	2.62E+08
5.4	3	2.36E+07	8.71E+09	2.33E+08

Table 9.

Surface Neutronic Flux (n/cm ² /s) in Different Thicknesses of Second Fe and Bi at the End of the Collimator for ⁹ Be Target, When the Thicknesses of Fluental, First Fe, and Li Filters Were 2.4, 6, and 0.5 cm, Respectively

Bi thickness (cm)	Second Fe thickness (cm)	Thermal (0–1 eV)	Epithermal (1 eV–10 keV)	Fast (10 keV–1 MeV)
5.4	0.6	2.01E+07	7.88E+09	2.78E+08
5.3	0.7	2.27E+07	7.85E+09	2.62E+08
5.2	0.8	2.81E+07	8.39E+09	2.84E+08
5.1	0.9	1.98E+07	7.88E+09	2.77E+08
5	1	1.98E+07	7.61E+09	2.51E+08
4.9	1.1	1.76E+07	8.07E+09	2.34E+08
4.8	1.2	1.93E+07	7.85E+09	2.36E+08
4.7	1.3	1.93E+07	8.13E+09	2.45E+08
4.6	1.4	1.43E+07	7.18E+09	2.42E+08
4.5	1.5	1.94E+07	5.38E+09	1.99E+08
4.4	1.6	1.35E+07	4.83E+09	1.99E+08

Table 10.

Simulated Neutron Flux and Dose Component in Epithermal Range on Beryllium Target With 7.4 cm Fluental, 4 cm Fe, 0.5 cm Li, and 3 cm Bi Filters Without Second Fe Filter

	Surface neutron flux (n/cm²/s)
Material	Thermal (0–1 eV)	Epithermal (1 eV–10 keV)	Fast (10 keV–1 MeV)	ϕ _epi /ϕ_fast	ϕ _epi /ϕ _thermal
Air	1.67E+07	1.98E+09	1.12E+08	17.68	118.56

				Dose in epithermal range (Gy/h)/(#/cm²/s)
				Neutrons	γ
Scalp	9.18E+07	1.44E+09	8.11E+08	8.54E−11	2.09E−12
Tumor	4.16E+07	1.09E+09	2.78E+08	9.09E−11	5.09E−13
Brain	1.01E+07	6.12E+08	2.90E+08	3.64E−12	5.83E−13

Cross-section properties

The high atomic mass of lead causes mounting neutron energy loss through the elastic scattering procedure, and its high transparency to fast neutron results in a long storage time inside the activator, provided that the lead volume is large enough to minimize neutron escape from the system. This should allow exploitation of the resonance peaks in the thermal and epithermal energy ranges of neutrons in the cross-section chart for radioisotope production or BNCT submissions. Total cross section of neutrons in the ²⁰⁷Pb region is compared with elastic cross section in Figure 5a, and also this comparison is carried out in the²⁰⁸Pb region as shown in Figure 5b. The significant resonances in the ²⁰⁷Pb material are raised between 0.01 and 1 MeV of neutron energy, but these peaks in the ²⁰⁸Pb material happened between 0.1 and 1 MeV. Maximum peaks of cross section occurred between 10 and 100 barn for both ²⁰⁷Pb and ²⁰⁸Pb moderators. Elastic cross section of neutrons in the ²⁰⁷Pb region had lesser values rather than in the ²⁰⁸Pb region between 1E−11 and 1E−5 MeV.

FIG. 5.

(A) Total (solid line) and elastic (dash line) cross sections of neutrons in ²⁰⁷Pb region. (B) Total (solid line) and elastic (dash line) cross sections of neutrons in ²⁰⁸Pb region.

Absorption and elastic cross sections in ²⁰⁷Pb and ²⁰⁸Pb volumes are compared in Figure 6a and b, respectively, because of greater elastic characteristics in absorption than in other moderators, with the exception of ¹H, as explained in Table 1. Although the ²⁰⁷Pb material indicated some resonances between 0.001 and 0.1 MeV with higher absorption resonances than in the²⁰⁸Pb material, the ²⁰⁸Pb material showed resonances between 0.1 and 1 MeV of neutron energy. The ²⁰⁸Pb material has distinct characteristics such as immense elastic than absorption cross sections at thermal and epithermal ranges and also high transparency to fast neutrons. Then, these properties of the ²⁰⁸Pb choose it as a good moderator in the neutron storage purposes. Figure 7 indicates the elastic cross section in the ²⁰⁸Pb moderator and graphite reflector, as well as in graphite that shows less significant elastic properties than ²⁰⁸Pb between 1E−8 and 30 MeV.

FIG. 6.

(A) Absorption (solid line) and elastic (dash line) cross sections of neutrons in ²⁰⁷Pb region. (B) Absorption (solid line) and elastic (dash line) cross sections of neutrons in ²⁰⁸Pb region.

FIG. 7.

Elastic cross section of neutrons in ²⁰⁸Pb region (solid line) and graphite region (dash line).

Transport of fast neutrons in the moderator with a short mean free path and low energy loss per collision decelerates the fast neutrons, and in addition, (n,2n) and (n,3n) interactions transpire in the moderator. Fast neutrons can have interactions with the moderator to produce induction neutrons related to the reaction's Q value. The Q value of (n,2n) and (n,3n) interactions with the ²⁰⁷Pb moderator was about 7 and 17 MeV, respectively, and also these reactions with the ²⁰⁸Pb moderator extracted about 8 and 15 MeV, respectively, as shown in Figure 8a and b. The cross section of the activated molybdenum sample is shown in Figure 9, in which the radiative capture resonances happen in thermal ranges of neutron energies.

FIG. 8.

(A) (n,2n) and (n,3n) Cross sections of neutrons in ²⁰⁷Pb region with solid and dash lines, respectively. (B) (n,2n) and (n,3n) Cross sections of neutrons in ²⁰⁸Pb region with solid and dash lines, respectively.

FIG. 9.

(n,γ) Cross section inside the ⁹⁸Mo sample.

Figure 10 specifies the absorption cross section of neutrons in the graphite buffer and boron absorber. At the thermal range, graphite absorbed neutrons less than boron, but at the epithermal range, this action was vice versa.

FIG. 10.

Absorption cross section of neutrons in boron region (solid line) and graphite region (dash line).

Figure 11 shows (n,α) cross section inside the brain and tumor, and (n,α) cross section in the tumor region had higher values than the region inside the brain. In addition, in the lower energy of neutrons, the neutron capture had highly enhanced cross-section values. Figure 12 shows (n,γ) cross sections in the bismuth filter and lead region. Bi had higher (n,γ) cross-section values in the lower neutron energies into lead, and this property selected the Bi as the γ filter.

FIG. 11.

(n,α) Cross section in brain (solid line) and in tumor (dash line) regions.

FIG. 12.

(n, γ) Cross section in Bi material (solid line) and in lead buffer (dash line).

Discussion

To generate epithermal and thermal neutrons for radioisotope production and BNCT, the authors proposed a review of moderating fast neutrons, which are emitted from the reactions between diverse targets and low energy and current protons accelerated by a small cyclotron. The ARC method has been investigated in this study, by means of lead moderator and graphite reflector for assessment of energy and cross section of accumulated neutrons in the lead storage.

The performance of an accelerator-driven system is conditioned by the optimization of the geometrical coupling between the accelerator and intended assembly. The aim of this review is to investigate some parameters (neutron yield, target property, neutron flux, and cross section) for a low-energy accelerator configuration. Neutrons produced in the nuclear reactions mentioned before are generally at energies above the resonance peaks in a sample and need to be moderated to reach more useful energies for capturing in radioisotope production. Using the flux and energy spectrum of neutrons exiting the moderator, the authors can estimate how much a specified radioisotope is produced through capture. They can therefore expect that even with multiple scattering of neutrons on ²⁰⁸Pb during the process of their slowing down, they will be slowed down to thermal energy with a high probability and thus create a high thermal neutron flux.

The ARC method was investigated through slowing down of neutrons from their original energy to the final thermal energy through collisions with the nuclei of the moderator. This collision and energy loss simulated as a continuous process that is valid if the neutron energy loss is for radioisotope production through the inserted “father radioisotope” inside the activator. In the standard ARC scheme, natural lead is used as both a spallation target and moderator, its moderating inefficiency being an important feature for the ARC process; but in this study, the ARC method was explored through three targets. Neutronic flux around the target goes with 1/r inside the lead moderator instead of 1/r² inside air (for bare target) that is the power of ARC, and that it is “amplifying geometrically” the neutron source strength in the lead as a heavy nuclei. Meanwhile, transport of fast neutrons in the lead moderator by a short mean free path and low energy loss per collision decelerates the fast neutrons, and in addition to (n,2n) and (n,3n), interactions transpire in the moderator. Fast neutrons can have interactions with the moderator to produce induction neutrons related to the reaction's Q value. Moreover, capture cross section at thermal energy and capture resonance integral of natural lead are much larger than the corresponding values of most of the light nuclides, therefore it is safe to say that neutrons are captured during the slowing down process in natural lead with a higher probability than the slowing down process in light materials. Therefore, only a small part of neutrons will slow down to thermal energy. This means that thermal neutron flux in natural lead will be much lower than in light materials.

Simulation results revealed that the ¹⁸¹Ta target had the highest neutron yield, and tungsten had the highest values in both surface and volumetric ratios. Comparison of the maximum surface flux at 2.2 cm distance inside ²⁰⁷Pb and ²⁰⁸Pb schemes demonstrated that ²⁰⁸Pb led to a higher value than ²⁰⁷Pb. ⁹Be in 22° and also ¹⁸¹Ta and ¹⁸⁴W in 30° into the beam axis had the maximum surface flux, and ¹⁸¹Ta through ²⁰⁸Pb showed a higher value than others.

The epithermal neutrons derived from ⁹Be target with ²⁰⁸Pb thickness of 25 cm had higher flux value than the two other thicknesses of ²⁰⁸Pb. Hence, on the basis of these simulations, the authors can suggest an experimental production of this plan. The economic advantages of an accelerator founded upon production and collimation with respect to the standard nuclear reactor route will be fully evaluated. For this reason, the result of thermal and epithermal energy and flux can be suitable for some radioisotope production and BNCT applications.

In this study, the neutron activator has included graphite reflector and boron absorber. Comparison between utilizing ²⁰⁷Pb and ²⁰⁸Pb moderators demonstrated that the ²⁰⁸Pb moderator had greater values of neutron flux in both thermal and epithermal ranges in the moderator, reflector, and absorber regions. Flux of thermal neutrons for all targets using ²⁰⁷Pb and ²⁰⁸Pb systems had higher values in graphite and ²⁰⁸Pb regions, respectively. However, greater values of flux for epithermal neutrons were revealed in the lead buffer; consequently using this system in BNCT application, the collimator gate must be set about the lead buffer, not through the graphite region. These investigations indicated that the use of the ⁹Be target and the ²⁰⁸Pb moderator could be compatible with medical applications to accumulated neutrons in a specified region for two ranges of neutron energies. The potential of the ARC method is a replacement or complements the current reactor-based supply sources of BNCT purposes. When the epithermal neutron flux inside air before the phantom is in order of 1E+9 n/cm²/s, BNCT using the ARC method will be very attainable.

In this study, the authors have shown that a 30 MeV proton cyclotron can be used to generate useful quantities of ⁹⁹Mo and can be used as a source of epithermal neutrons for BNCT.

Conclusions

The ARC method is well known with respect to the field of minor actinides transmutation, therefore assessment in the neutron activator opens new perspectives regarding the use of ion-beam-generated neutrons for production of medical radioisotopes that are currently produced in nuclear reactors. Hence, it is very important to develop an alternative production method of ⁹⁹Mo-^99mTc and BNCT applications using small accelerators.

Footnotes

Acknowledgments

The author thankfully acknowledges the spiritual and financial maintenance from Gerashian people who have constructed and supplied the Gerash University of Medical and Paramedical Sciences, Amir-Al-Momenin Hospital, Medical Laboratories, Home residence, and requirements in Fars province, especially Sheikh-Ahmad Ansari, Gerash charity institution, and social support with low governmental provision rate in regional public welfare and health promotion.

Disclosure Statement

No competing financial interests exist.

References

Abbas

, Buono

, Burgio

, et al. Development of an accelerator driven neutron activator for medical radioisotope production. Nucl Instrum Methods Phys Res A, 2009; 601:223.

Brett

, Owen

, Gill

. Resonant neutron capture for radioisotope production. Interim Report, University of Manchester, 2010.

Froment

, Tilquin

, Cogneau

, et al. The production of radioisotopes for medical applications by the adiabatic resonance crossing (ARC) technique. Nucl Instrum Methods Phys Res A, 2002; 493:165.

Kadi

, Herrera-Martinez

. Energy amplifier systems: Simulation and experiments in the field. Nucl Instrum Methods Phys Res A, 2006; 562:573.

Tanaka

, Sakurai

, Suzuki

, et al. Improvement of dose distribution in phantom by using epithermal neutron source based on the Be(p,n) reaction using a 30MeV proton cyclotron accelerator. Appl Radiat Isot, 2009; 67:258.

Blue

, Yanch

, Neuro

. Accelerator-based epithermal neutron sources for boron neutron capture therapy of brain tumors. Oncol., 2003; 62:19.

Atchison

. Spallation and Fission in Heavy Metal Nuclei Under Medium Energy Proton Bombardment. Proceedings of the Meeting on Targets for Neutron Beam Spallation Source, Julich, 1979, Kernforschungsanlage Julich GmbH, Germany, 1980).

Tolstov

. Some aspects of accelerator breeding. JINR Preprint, 18-89-778, Dubna, Russia, 1989.

Rubbia

. Resonance Enhanced Neutron Captures for Element Activation and Waste Transmutation. CERN-LHC/97-0040EET, 1997.

10.

TARC collaboration, Neutron-Driven Nuclear Transmutation by Adiabatic Resonance Crossing. CERN-SL-99-036EET, 1999.

11.

Abanades

, Aleixandre

, Andriamonje

, et al. Results from the TARC experiment: Spallation neutron phenomenology in lead and neutron driven nuclear transmutation by adiabatic resonance crossing. Nucl Instrum Methods Phys Res A, 2002; 487:577.

12.

Khorshidi

, Sadeghi

, Pazirandeh

, et al. Radioanalytical prediction of radiative capture in ⁹⁹Mo production via transmutation adiabatic resonance crossing by cyclotron. J Radioanal Nucl Chem, 2014; 299:303.

13.

Monte Carlo Team, MCNPX User's Manual Version 2.7.0, LA-UR-11-02295, Los Alamos National Laboratory, LANL, 2011.

14.

Yonai

, Aoki

, Nakamura

, et al. Feasibility study on epithermal neutron field for cyclotron-based boron neutron capture therapy. Med Phys, 2003; 30:2021.

15.

Tahara

, Oda

, Shiraki

, et al. Engineering design of a spallation reaction-based neutron generator for Boron Neutron Capture Therapy. J Nucl Sci Technol, 2006; 43:9.

16.

Kadi

. Transmutation capabilities of the CERN Energy Amplifier System. Prog Nucl Energy, 2007; 49:606.

17.

Bak

, Hong

, Kadi

, et al. Simulation of transmutation of long-lived fission products. Master's Degree Thesis, Sungkyunkwan University, 2011.

18.

Schwenk-Ferrero

. German spent nuclear fuel legacy: Characteristics and high-level waste management issues. Sci Technol Nucl Ins, 2013; 2013:1.

19.

Hong

. Research Status of ADS in Korea. In: Presentation in the 9th Workshop on ADS and Nuclear Transmutation Technology, Hengyang, China, 2011.

20.

Kadi

, Revol

. Design of an accelerator-driven system for the destruction of nuclear waste. In: Workshop on Hybrid Nuclear Systems for Energy Production: Utilisation of Actinides and Transmutation of Long-Lived Radioactive Waste, Trieste, 2001.

21.

Cerullo

, Daquino

, Muzi

. An overview on the developments and improvements of a treatment planning system for BNCT. IEEE Trans Nucl Sci, 2006; 53:1333.

22.

Cerullo

, Daquino

, Muzi

, et al. Development of a treatment planning system for BNCT based on positron emission tomography data: Preliminar results. Nucl Instrum Methods Phys Res B, 2004; 213:637.

23.

International Atomic Energy Agency. Current Status of Neutron Capture Therapy, IAEA-TECDOC-1223, IAEA, 2001.

24.

ENDF/B-VII.1 U.S. Evaluated Nuclear Data Library, https://www-nds.iaea.org/exfor/endf.htm, 2011.

25.

Shmelev

, Kulikov

, Apse

, et al. Radiowaste Transmutation in Nuclear Reactors. Proceedings of Specialist Meeting: Use of Fast Reactors for Actinide Transmutation, Obninsk, Russia, 1992 (IAEA TECHDOC, 693, 77, 1993).

26.

Khorasanov

, Blokhin

. Development of weak activated lead coolant with isotopic enrichment for innovative nuclear power plants, Series: Nuclear constants, 1, Nuclear science and technology issues, 2001.

27.

Khorasanov

, Korobeinikov

, Ivanov

, et al. Minimization of Uranium-Plutonium Load of the Fast Reactor by Using Low-Capturing Enriched ²⁰⁸Pb as a Coolant. Proceedings of the XII International scientific conference: Physical and chemical processes in atomic and molecular selection in laser, plasma and nanotechnologies, Zvenigorod, Russia, 2008.

28.

Shibata

, Iwamoto

, Nakagawa

, et al. JENDL-4.0: A new library for nuclear science and engineering. J Nucl Sci Technol, 2011; 48:1.

29.

Doe Fundamentals Handbook, Material Science, Volume 2 of 2, U.S. Department of Energy, Washington D.C., 1993, page 72.

Exploration of Adiabatic Resonance Crossing Through Neutron Activator Design for Thermal and Epithermal Neutron Formation in 99 Mo Production and BNCT Applications

Abstract

Highlights

Introduction

Methods and Materials

Neutron generator system by proton reaction through target design

Moderator and reflector designs

98Mo sample position inside the activator for 99Mo production

Conceptual design for BNCT purposes

Results and Discussion

Neutron yield from diverse targets

Flux of accumulated neutrons through 207Pb and 208Pb moderators

Exploration of volume flux in different thicknesses of lead moderator and graphite reflector

Radiative capture yield in 99Mo production

Neutron flux analysis in BNCT applications

Cross-section properties

Discussion

Conclusions

Footnotes

Acknowledgments

Disclosure Statement

References

⁹⁸Mo sample position inside the activator for ⁹⁹Mo production

Flux of accumulated neutrons through ²⁰⁷Pb and ²⁰⁸Pb moderators

Radiative capture yield in ⁹⁹Mo production