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Reaction cross sections (σR) for 24–38Mg on C targets at the energies of around 240 MeV/nucleon have been measured precisely at RIBF, RIKEN for the purpose of obtaining the crucial information on the changes of nuclear structure in unstable nuclei, especially around the so-called “island of inversion” region. In the island of inversion region, which includes neutron-rich Ne, Na, and Mg isotopes, the vanishing of the N = 20 magic number for neutrons have been discussed along with nuclear deformation. The present result suggest deformation features of Mg isotopes and shows a large cross section of weakly-bound nucleus 37Mg, which could be caused by a neutron halo formation.

The total reaction cross sections of Mg isotopes on a 12C target at 240 MeV/nucleon have been analyzed with a fully microscopic framework, i.e., the double folding model with the density calculated by antisymmetrized molecular dynamics. Our results well reproduce the latest experimental data except 37Mg as a new candidate for a deformed halo nucleus.

Neutron-nucleus cross sections calculated by macroscopic potentials are compared with a microscopic one to study the performance for long-lived fission products. The macroscopic potentials show a good agreement with the microscopic one at higher energies, where neutron experimental data are scarce. Besides it, analyses of differential elastic cross sections at low energies also suggest that the macroscopic potentials are still effective and applicable enough for the long-lived fission products.

We aim for fully microscopic understanding of many-body nuclear reactions starting from two- and three-nucleon forces based on chiral effective field theory (Ch-EFT). We first construct a g-matrix with the nuclear forces based on Ch-EFT using Brueckner-Hartree-Fock theory, in which the three-nucleon force effects are represented through the density dependence of the g-matrix. Then, the folding model and microscopic coupled-channels method with the g-matrix are applied to nucleon-nucleus and nucleus-nucleus scattering at intermediate incident energies. This new microscopic framework well describes the elastic and inelastic cross sections with no ad-hoc parameters. In addition, the three-nucleon force and coupled-channels effects on many-body nuclear reactions are clarified.

We investigate breakup dynamics in 6Li elastic scattering on heavy targets (T = 209Bi or 208Pb) near the Coulomb barrier energy. Since the subsystem of 6Li has a bound state as deuteron (n + p = d), a four-body channel (6Li + T → n + p + α + T) and a three-body channel (6Li + T → d + α + T) get entangled during scattering as a breakup channel. Both channels are precisely treated with the four-body version of the continuum-discretized coupled-channels method (four-body CDCC). Four-body CDCC well reproduces measured elastic cross sections with no adjustable parameter. We then estimate the channel coupling effects by dividing the breakup channel into fourand three-body channels. It is found that 6Li breakup is mainly induced by a three-body channel.

Some recent activities with the microscopic effective reaction theory (MERT) on elastic, inelastic, breakup, transfer, and knockout processes are reviewed briefly. As a possible alternative to MERT, a description of elastic and inelastic scattering with the continuum particle-vibration coupling (cPVC) method is also discussed.

Understanding radioactive Cs contamination has been a central issue at Fukushima Daiichi and other nuclear legacy sites; however, atomic-scale characterization of radioactive Cs in environmental samples has never been achieved. Here we report, for the first time, the direct imaging of radioactive Cs atoms using high-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). In Cs-rich microparticles collected from Japan, we document inclusions that contain 27 - 36 wt% of Cs (reported as Cs 2 O) in a zeolite: pollucite. The compositions of three pollucite inclusions are (Cs 1.86 K 0.11 Rb 0.19 Ba 0.22 ) 2.4 (Fe 0.85 Zn 0.84 X 0.31 ) 2.0 Si 4.1 O 12 , (Cs 1.19 K 0.05 Rb 0.19 Ba 0.22 ) 1.7 (Fe 0.66 Zn 0.32 X 0.41 ) 1.4 Si 4.6 O 12 , and (Cs 1.27 K 0.21 Rb 0.29 Ba 0.15 ) 1.9 (Fe 0.60 Zn 0.32 X 0.69 ) 1.6 Si 4.4 O 12 (X includes other cations). HAADF-STEM imaging of pollucite, viewed along the [111] zone axis, revealed an array of Cs atoms, which is consistent with a simulated image using the multi-slice method. The occurrence of pollucite indicates that locally enriched Cs reacted with siliceous substances during the Fukushima meltdowns, presumably through volatilization and condensation. Beta radiation doses from the incorporated Cs are estimated to reach 10 6 - 10 7 Gy, which is more than three orders of magnitude less than typical amorphization dose of zeolite. The atomic-resolution imaging of radioactive Cs is an important advance for better understanding the fate of radioactive Cs inside and outside of nuclear reactors damaged by meltdown events., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Radioactive particles often contain very high radioactivity concentrations and are widespread. They pose a potential risk to human health and the environment. Their detection, quantification, and characterization are crucial if we are to understand their impact. Here, we present the use of a real-time autoradiography gaseous detector (using parallel ionization multiplier) to expedite and improve the accuracy of radioactive particle screening in complex environmental samples. First, standard particles were used to assess the detector capabilities (spatial resolution, spectrometry, and artefact contributions), then, we applied the technique to more complex and environmentally relevant samples. The real-time autoradiography technique provides data with a spatial resolution (≲100 µm) suitable for particle analysis in complex samples. Further, it can differentiate between particles predominantly emitting alpha and beta radiation. Here, the technique is applied to radioactive cesium-rich microparticles collected from the Fukushima Daiichi nuclear exclusion zone, showing their accurate detection, and demonstrating the viability of real-time autoradiography in environmental scenarios. Indeed, for more complex samples (radioactive particles in a less radioactive heterogeneous background mix of minerals), the technique permits relatively high selectivity for radioactive particle screening (up to 61.2% success rate) with low false positive percentages (~ 1%)., (© 2024. The Author(s).)

Radioactive Cs-rich microparticles (CsMPs) released from the Fukushima Daiichi Nuclear Power Plant (FDNPP) are a potential health risk through inhalation. Little has been documented on the occurrence of CsMPs, particularly their occurrence inside buildings. In this study, we quantitatively analyze the distribution and number of CsMPs in indoor dust samples collected from an elementary school located 2.8 km to the southwest of FDNPP. The school had remained deserted until 2016. Then, using a modified version of the autoradiography-based "quantifying CsMPs (mQCP) method," we collected samples and determined the number of CsMPs and Cs radioactive fraction (RF) values of the microparticles (defined as total Cs activity from CsMPs/bulk Cs activity of the entire sample). The numbers of CsMPs ranged from 653 to 2570 particles/(g dust) and 296-1273 particles/(g dust) on the first and second floors of the school, respectively. The corresponding RFs ranged between 6.85 - 38.9% and 4.48-6.61%, respectively. The number of CsMPs and RF values in additional outdoor samples collected near the school building were 23-63 particles/(g dust or soil) and 1.14-1.61%, respectively. The CsMPs were most abundant on the school's first floor near to the entrance, and the relative abundance was higher near the stairs on the second floor, indicating a likely CsMP dispersion path through the building. Additional wetting of the indoor samples combined with autoradiography revealed that indoor dusts had a distinct absence of intrinsic, soluble Cs species, such as CsOH. These combined observations indicate that a significant amount of poorly soluble CsMPs were likely contained in initial radioactive airmass plumes from the FDNPP and that the microparticles penetrated buildings. CsMPs could still be abundant at the location, with locally high Cs activity in indoor environments near to openings., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

Boron carbide control rods remain in the fuel debris of the damaged reactors in the Fukushima Daiichi Nuclear Power Plant, potentially preventing re-criticality; however, the state and stability of the control rods remain unknown. Sensitive high-resolution ion microprobe analyses have revealed B-Li isotopic signatures in radioactive Cs-rich microparticles (CsMPs) that formed by volatilization and condensation of Si-oxides during the meltdowns. The CsMPs contain 1518-6733 mg kg -1 of 10+11 B and 11.99-1213 mg kg -1 of 7 Li. The 11 B/ 10 B (4.15-4.21) and 7 Li/ 6 Li (213-406) isotopic ratios are greater than natural abundances (~4.05 and ~12.5, respectively), indicating that 10 B(n,α) 7 Li reactions occurred in B 4 C prior to the meltdowns. The total amount of B released with CsMPs was estimated to be 0.024-62 g, suggesting that essentially all B remains in reactor Units 2 and/or 3 and is enough to prevent re-criticality; however, the heterogeneous distribution of B needs to be considered during decommissioning., (Copyright © 2022 Elsevier B.V. All rights reserved.)

We investigated mass loading and the spatial distribution of volatile methylsiloxanes (VMSs) including four cyclic VMSs (D3-D6; cVMSs, the number refers to the number of SiO bonds) and three linear VMSs (L3-L5; lVMSs) in Tokyo Bay, Japan, which is one of the most industrialized, urbanized, and populated areas in the world. Based on the VMS concentrations determined in eight main inflow rivers to the bay, the mass loading of VMSs via inflow rivers and sewage treatment plants located in Tokyo Bay was estimated at 2500 kg/y for total VMSs. Elevated mass loadings of VMSs were found in three of the rivers, inflowing to the inner west of Tokyo Bay. The distribution and deposition characteristics of VMSs were observed depending on the estuarine condition. Estuarine sediments were found to be efficient and effective traps for VMSs and the salting-out effect is one possible mechanism to explain this phenomenon. The overall profiles of D4, D5, and D6 in surface water and sediment were observed across Tokyo Bay; elevated concentrations were identified in the inner west bay with dispersed low concentrations in the outer bay, except for one hotspot of D4 in the sediment, indicating a major emission route of VMSs via inflow rivers. Additionally, the historical pollution profiles of VMSs in Tokyo Bay were reconstructed based on the VMS concentrations determined in a dated sediment core. VMSs were identified throughout the upper 40 cm of the sediment core (representing the mid 1980s); the profiles correspond with the historical use of VMSs in wash-off personal care-products. The noted decreasing trend of D4 might be a reflection of the early 2000s replacement of D4 with D5 in such products. The elevated VMS concentrations in the estuarine sediment raise concerns about the impact on the aquatic environment., Competing Interests: Declaration of competing interest To the best of our knowledge, the named authors have no conflict of interest, financial or otherwise., (Copyright © 2021 Elsevier B.V. All rights reserved.)

The large production volume of methylsiloxanes (MSs), combined with their high mobility/volatility and persistence, is a matter of concern from the atmospheric pollution perspective. Therefore, we evaluated of the concentrations and emission sources of MSs, including 7 cyclic methylsiloxanes (D3-D9; CMSs, the number refers to the number of Si-O bonds) and 13 linear methylsiloxanes (L3-L15; LMSs) in ambient air collected from Saitama, Japan. This is a first study regarding the evaluation of 20 methylsiloxanes in the Japanese atmosphere. We improved the air sampling methodology by determination the stability of D5 during a 7-d air sampling and arbitrary sample storage period using polystyrene-divinyl benzene copolymer sorbent (Sep-Pak plus PS-2). We analyzed air samples for MSs seasonally collected from nine locations in Saitama, including urban, suburban, rural, and mountainous areas. The mean CMS and LMS concentrations were 358 ng m -3 and 13.4 ng m -3 , respectively. The D5 concentrations were distributed widely, with high concentrations in urban/suburban populous areas and dispersed at low concentrations in surrounding areas (north and mountainous areas). We analyzed 7-d air samples collected every week over a year and found apparent seasonal and periodic trends in the CMS concentrations. In the diurnal sampling campaign, we observed periodic fluctuations in ambient CMSs, with an inverse relationship with the atmospheric boundary layer development during the day. Backward trajectories and the prevailing wind direction during the sampling period indicated that the specific profiles of D4 observed in fall/winter weeks and north of Saitama could be ascribed to northwestward air-mass advection. We employed a novel approach in estimating CMSs emission sources and source apportionment by using non-negative matrix factorization (NMF). The concentration matrix was divided successfully into two factors (emission sources) namely, personal care and household products and industrial activities., Competing Interests: Declaration of competing interest The authors have no conflict of interest, financial or otherwise., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Wastewater, aeration gas, dewatered sludge, and incineration ash and flue gas (from dewatered sludge) were collected from 9 sewage treatment plants (STPs) located in Saitama Prefecture, Japan, and analyzed for seven cyclic and linear volatile methylsiloxanes (VMSs) namely, D3, D4, D5, D6, L3, L4, and L5. The mass loadings and distribution of VMSs in STPs were estimated based on measured concentrations in liquid, solid, and gaseous samples, including incinerated dewatered sludge. Mass loading of ΣVMS varied widely from 21 kg y -1 to 3740 kg y -1 , depending on the volume of wastewater treated in each STP. Mass % of ΣVMS distributed in aeration gas was 15% and that in activated sludge was 78%. Approximately 6.6% of ΣVMS remained in the final effluent. Overall, partitioning onto the activated sludge was the dominant removal mechanism for D4, D5, and D6, whereas volatilization was also an important removal mechanism for D4. Incineration was effective to degrade VMSs in dewatered sludge, with a reduction rate of >99%. Activated carbon treatment removed >99% of VMSs from the aeration gas. In Saitama Prefecture, total emission of ΣVMS via STPs was estimated at 434 kg y -1 , 86 kg y -1 , and 0.065 kg y -1 , to aquatic, atmospheric, and terrestrial environments, respectively, which accounted for 83%, 17%, and 0.01% of the total environmental emissions. Our results indicate that majority of VMSs in dewatered sludge can be removed by incineration and emission of VMSs through incineration ash landfill is negligible., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

Bulk (wet and dry) deposition samples were collected in Saitama Prefecture, Japan throughout a year (February 8, 2012 to February 7, 2013) to estimate the influence of dioxins emitting from waste incinerators on river water quality. The annual deposition flux of dioxins was 3.3ng-toxic equivalent (TEQ)/m 2 /year. Source identification using indicative congeners estimated that 82% of dioxin TEQ in the bulk deposition (2.7ng-TEQ/m 2 /year) was combustion-originated, indicating that most of the dioxins in the deposition were derived from waste incinerators. In Saitama prefecture the annual flux of combustion-originated dioxins in depositions was apparently consistent with that of dioxin emission into the air from waste incinerators. The TEQ of combustion-originated dioxins in the deposition per rainfall was 2.4pg-TEQ/L on annual average, exceeding the environmental quality standard (EQS) for water in Japan of 1pg-TEQ/L. This suggests there is a possibility that dioxins in atmospheric deposition have a significant influence on the water quality of urban rivers which rainwater directly flows into because of many paved areas in the basins. The influence of combustion-originated dioxin in the deposition on the water quality of Ayase River, an urban river heavily polluted with dioxins, was estimated at 0.29pg-TEQ/L on annual average in 2015. It seems that dioxins in atmospheric deposition from waste incinerators have a significant influence on water quality of some urban rivers via rainwater though the dioxins in the ambient air have achieved the EQS for atmosphere at all monitoring sites in Japan., (Copyright © 2017. Published by Elsevier B.V.)

Surface waters including river water and effluent from sewage treatment plants (STPs) were collected from Tokyo Bay watershed, Japan, and analyzed for seven cyclic and linear volatile methylsiloxanes (VMSs), i.e., D3, D4, D5, D6, L3, L4, and L5 by an optimized purge and trap extraction method. The total concentrations of seven VMSs (ΣVMS) in river water ranged from <4.9 to 1700ng/L (mean: 220ng/L). The individual mean concentrations of cyclic VMSs in surface waters were; 10ng/L for D3, 13ng/L for D4, 180ng/L for D5, and 18ng/L for D6. The concentrations of ΣVMS determined in STP effluents varied widely from 99 to 2500ng/L and the individual mean concentrations were 21ng/L for D3, 27ng/L for D4, 540ng/L for D5, and 45ng/L for D6. D5, which is widely used in personal-care products, was found to be the most abundant compound in both river water and STP effluent. Linear VMSs were detected at much lower frequency and concentrations than those of cyclic VMSs. The measured concentrations of D4 were below the no-observed effect concentration (NOEC). The annual emission of ΣVMS through STPs into Tokyo Bay watershed was estimated at 2300kg. Our results indicate widespread distribution of VMSs in Tokyo Bay watershed and the influence of domestic wastewater discharges as a source of VMSs in the aquatic environment., (Copyright © 2017 Elsevier B.V. All rights reserved.)

We perform the first quantitative analysis of the reaction cross sections of {28-32}Ne by {12}C at 240  MeV/nucleon, using the double-folding model with the Melbourne g matrix and the deformed projectile density calculated by antisymmetrized molecular dynamics. To describe the tail of the last neutron of {31}Ne, we adopt the resonating group method combined with antisymmetrized molecular dynamics. The theoretical prediction excellently reproduces the measured cross sections of {28-32}Ne with no adjustable parameters. The ground state properties of {31}Ne, i.e., strong deformation and a halo structure with spin parity 3/2{-}, are clarified.

Distribution, characteristics, and global inventory of dioxins (polychlorinated dibenzo-p-dioxins [PCDDs] and dibenzofurans [PCDFs] and dioxin like polychlorinated biphenyls) in kaolin clays collected from 10 countries were investigated. Dioxins were found in all kaolin clay samples analyzed, at total concentrations ranging from 1.2 pg/g (Brazil) to 520,000 pg/g (USA). Dioxin concentrations in kaolin clays from a few countries (e.g., Brazil and UK) were lower than those reported for background soils in Japan. Dioxin profiles in kaolin clays were characterized by the domination of the congener octachlorodibenzo-p-dioxin (OCDD), and the concentrations of other congeners decreased in the order of reduction in the levels of chlorination. Furthermore, specific distribution of congeners, with predominant proportions of 1,4,6,9-substituted PCDDs within each homologue group, was found in most clay samples. The ratios of concentrations of PCDD to PCDF and 1,2,3,7,8,9-HxCDD to 1,2,3,6,7,8-HxCDD indicated differences in the profiles found for anthropogenic sources (including pentachlorophenol) and kaolin clays. Concentrations of PCDD/Fs in kaolin clays, except for American ball clays, did not exceed the environmental criteria set by the Law Concerning Special Measures against Dioxins in Japan. Based on the average concentrations measured in our study, inventories of PCDD/Fs from the production/usage of ball clays on a global scale were estimated to be 650 kg/yr; the corresponding value on a TEQ basis is 2400 g-TEQ/yr. More than 480 kg of OCDD is estimated to be released annually from the production of kaolin clays worldwide, suggesting that kaolin clays can be a major contributor for additional source of dioxins, especially OCDD, in the environment.

In Japan, Ayase River is one of the most polluted rivers by PCDDs, PCDFs and dioxin-like PCBs, which are referred to as dioxins in this paper. The water samples of the river were collected once per month for a year, and dioxins were analyzed to examine the dioxin sources and their contributions to toxic equivalent (TEQ). The WHO-2006 TEQs ranged from 0.26 to 7.0 pg-TEQL(-1) and the average was 2.7 pg-TEQL(-1); eight of 12 samples exceeded the environmental quality standard in Japan (1.0 pg-TEQL(-1)). The TEQ value was high during the irrigation period from May to August. The most part of the dioxins in the river water existed in suspended solids (SS) and it seemed that the river received water with highly-dioxin-contaminated SS in the irrigation period. The homologue profiles of the water samples suggested that the dioxins were influenced by pentachlorophenol (PCP) and chlornitrofen (CNP) formulations which were widely used as herbicides for the paddy fields in Japan. According to TEQ apportionment estimated by using indicative congeners, the TEQ was mainly contributed by PCP. Moreover, it was also shown that the TEQ contributions of PCP and CNP formulations increased along with the increase of the total TEQ and the TEQ contribution was dominated by these herbicides during the irrigation period. Therefore, it was concluded that the herbicides-originated dioxins run off from the paddy fields into the river during the irrigation period and increased the dioxins level in the river water. The result from the principal component analysis was consistent with these conclusions., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Polychlorinated dibenzo-p-dioxins (PCDDs), polychlorinated dibenzofurans (PCDFs), and dioxin-like polychlorinated biphenyls (DL-PCBs) contained in the smoke generated from rice straw burning in post-harvest paddy fields in Japan were analyzed to determine their congener profiles. Both the apportionment of toxic equivalent (TEQ) by using indicative congeners and the comparison of the homolog profiles showed that the PCDDs/PCDFs/DL-PCBs present in the rice-straw smoke were greatly influenced by those present as impurities in pentachlorophenol (PCP) and chlornitrofen (CNP, 4-nitrophenyl-2,4,6-trichlorophenyl ether) formulations that had been widely used as herbicides in paddy fields in Japan. Further, in order to investigate the effects of paddy-field soil on the PCDDs/PCDFs/DL-PCBs present in rice-straw smoke, PCDD/PCDF/DL-PCB homolog profiles of rice straw, rice-straw smoke and paddy-field soil were compared. Rice-straw smoke was generated by burning rice straw on a stainless-steel tray in a laboratory. The results suggested that the herbicides-originated PCDDs/PCDFs/DL-PCBs and the atmospheric PCDDs/PCDFs/DL-PCBs contributed predominantly to the presence of PCDDs/PCDFs/DL-PCBs in the rice-straw smoke while the contribution of PCDDs/PCDFs/DL-PCBs formed during rice straw burning was relatively minimal. The major sources of the PCDDs/PCDFs/DL-PCBs found in the rice-straw smoke were attributed primarily to the paddy-field soil adhered to the rice straw surface and secondarily to the air taken by the rice straw. The principal component analysis supported these conclusions. It is concluded that rice straw burning at paddy fields acts as a driving force in the transfer of PCDDs/PCDFs/DL-PCBs from paddy-field soil to the atmosphere., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Here, we proposed a simplified determination method for dioxin (polychlorinated dibenzo-p-dioxins, polychlorinated dibenzofurans, and dioxin-like polychlorinated biphenyls (PCBs)) toxic equivalency (TEQ; based on the World Health Organization-2006 toxicity equivalent factor) in environmental samples collected in Japan. This method has estimated the total TEQ from the concentrations of only five indicative congeners, namely, 2,3,4,7,8-pentachlorodibenzofuran; 1,2,3,4,6,7,8-heptachlorodibenzo-p-dioxin; 1,2,3,7,8-pentachlorodibenzo-p-dioxin; and PCBs of IUPAC Nos. #126 and #105, which were obtained from a single GC/MS measurement using a combination of columns of 10-meter-long DB-5ms (injector side) and 20-meter-long DB-17ms (detector side). Applying this simplified determination method to various environmental samples (ambient air, river water, river sediment, and soil) showed that the estimated TEQ was in good agreement with TEQ obtained by the corresponding official methods. Moreover, this method could estimate the TEQ contributions of the four major dioxin sources in Japan: combustion by-products, pentachlorophenol formulations, chlornitrofen formulations and PCB products.

The major sources of dioxins (polychlorinated dibenzo-p-dioxins (PCDDs), polychlorinated dibenzofurans (PCDFs), and dioxin-like polychlorinated biphenyls (DL-PCBs)) in the environment in Japan have been considered to be combustion by-products, pentachlorophenol (PCP) formulations, chlornitrofen (CNP, 4-nitrophenyl-2,4,6-trichlorophenyl ether) formulations, and PCB products. Data on PCDDs, PCDFs and DL-PCBs from the four sources were analyzed, and indicative congeners whose concentrations were highly correlated with WHO-2006 toxic equivalencies (TEQs) were identified for each source sample. The indicative congeners for combustion by-products, PCP formulations, and CNP formulations were 2,3,4,7,8-pentachlorodibenzofuran, 1,2,3,4,6,7,8-heptachlorodibenzo-p-dioxin, and 1,2,3,7,8-pentachlorodibenzo-p-dioxin, respectively; for PCB products, the indicative congeners were IUPAC Nos. #126- and #105-pentachlorobiphenyls. Moreover, using the data on PCDDs, PCDFs and DL-PCBs, we developed a set of equations for estimating the apportionment of TEQs from the four sources by using only the concentrations of the above-mentioned five indicative congeners. The equations were used along with the analysis results of different types of environmental samples collected from Japan, to determine the TEQ contributions of the four sources. The obtained values of TEQ contributions seemed to be reasonable. The estimation method was developed by using the data on major dioxin sources in Japan, and therefore, it is generally adaptable to environmental samples from any part of Japan. The method may be usable for regions outside Japan if source identification is carried out and the estimation equations are modified appropriately., (Copyright © 2010 Elsevier Ltd. All rights reserved.)