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論文

$$^{137}$$Cs contamination of Japanese mustard spinach by resuspended particles in areas with different contamination conditions

辰野 宇大*; 吉村 和也; 二瓶 直登*

Journal of Radioanalytical and Nuclear Chemistry, 8 Pages, 2024/00

 被引用回数:0 パーセンタイル:0.18(Chemistry, Analytical)

Resuspended matters occur the secondary radioactive contamination of the crops in Fukushima Prefecture. We investigated the Cs-137 contamination derived from the resuspended matters to Japanese mustard spinaches in the multiple sites. In the less contaminated site, because Cs-137 of the surface ground soil was low, contamination of crops by the soil particles might be small. In the highly contaminated area, Cs-137 deposition of the soil particles might increase. However, the soil particles had no significant effect on Cs-137 contamination to crops. This was because the grown crop might cover the soil and reduce the Cs-137 deposition on the soil.

論文

福島県木造家屋内外の空間線量率の分布調査; 線量低減係数の実態

Kim, M.; Malins, A.*; 町田 昌彦; 吉村 和也; 斎藤 公明; 吉田 浩子*

日本原子力学会和文論文誌(インターネット), 22(4), p.156 - 169, 2023/11

福島県木造家屋内外の空間線量率分布の特徴を明らかにすることを目的に、空間線量率の連続測定が可能な$$gamma$$プロッター等を用いて実測調査を行った。その結果、舗装面と非舗装面で空間線量率が明確に異なりまた、家屋近辺は家屋から離れた場所に対して低い空間線量率を示すことが分かった。また、家屋内の空間線量率は屋外に比べて空間線量率のバラツキが小さいことが分かった。

論文

Thirty-year prediction of $$^{137}$$Cs supply from rivers to coastal waters off Fukushima considering human activities

池之上 翼; 嶋寺 光*; 中西 貴宏; 近藤 明*

Water (Internet), 15(15), p.2734_1 - 2734_18, 2023/08

 被引用回数:0 パーセンタイル:0(Environmental Sciences)

福島第一原子力発電所事故は沿岸海域における堆積物への$$^{137}$$Csの蓄積を引き起こした。また、河川から海洋への$$^{137}$$Csの供給は沿岸海域における堆積物中の$$^{137}$$Csの長期的な挙動に影響を与える可能性がある。福島沿岸の河川流域には大規模な除染地域や避難指示地域が含まれているため、除染作業や農業再開を考慮することは$$^{137}$$Csの供給量を予測する上で重要である。そこで本研究は、これらの人間活動の影響を考慮した分布型放射性セシウム予測モデルを用いて、福島沿岸河川から海洋への$$^{137}$$Cs供給量の30年間の予測を実施した。結果として、除染地域と避難指示地域のある河川流域では人間活動により、農地、市街地、森林から河川への$$^{137}$$Csの流出量は5.0%、海洋への$$^{137}$$Cs供給量は6.0%それぞれ減少すると推定された。これらの結果は、人間活動が$$^{137}$$Csの流出と供給に与える影響は小さかったことを示している。事故の影響を受けた河川から海底堆積物への$$^{137}$$Cs供給量は、事故初期の沿岸海域における堆積物中の$$^{137}$$Csの存在量に対して11%から36%に相当すると推定された。したがって、沿岸海域における堆積物中の$$^{137}$$Csの長期的な挙動には河川から海洋への$$^{137}$$Cs供給が重要なプロセスであることが示唆された。

論文

$$^{137}$$Cs transfer from soils contaminated by resuspended particles to Japanese mustard spinach in difficult-to-return zone of Fukushima

辰野 宇大*; 二瓶 直登*; 吉村 和也; 大手 信人*

Journal of Radioanalytical and Nuclear Chemistry, 332(6), p.1677 - 1686, 2023/06

 被引用回数:1 パーセンタイル:72.91(Chemistry, Analytical)

This study investigated the transfer of $$^{137}$$Cs to crops and soil contamination by resuspended particles derived from airborne and ground surface. We conducted the cultivation test of a Japanese mustard spinach in pot placed at study fields. The soil in pots might be mainly contaminated by soil particles derived from the ground surface, and $$^{137}$$Cs transferred to the spinaches was observed. However, the proportion of water-exchangeable and organic fractions of $$^{137}$$Cs in the resuspended particles derived from airborne was greater than that from ground surface, resulting in the greater $$^{137}$$Cs transfer factor. Therefore, it is important to grasp the source of resuspended particles.

論文

A New application technique of a position-sensitive liquid light guide Cerenkov counter for the simultaneous position detection of $$^{90}$$Sr/$$^{90}$$Y and $$^{137}$$Cs radioactivity

寺阪 祐太; 瓜谷 章*

Nuclear Instruments and Methods in Physics Research A, 1049, p.168071_1 - 168071_7, 2023/04

 被引用回数:1 パーセンタイル:0.02(Instruments & Instrumentation)

A new application of a position-sensitive liquid light guide Cerenkov counter for the simultaneous position detection of $$^{90}$$Sr/$$^{90}$$Y and $$^{137}$$Cs radioactivity in a gamma-ray-dominant environment is proposed. $$beta$$-emitting $$^{90}$$Sr/$$^{90}$$Y and $$gamma$$-emitting $$^{137}$$Cs radioactive point sources were measured using a position-sensitive liquid light guide based on the time-of-flight (TOF) method. We found a clear difference in the count rate ratio between the source position peak and reflection peak of the position histogram. Moreover, simultaneous measurements of the radioactive point sources were performed. The results suggest that the source position and activity of $$^{90}$$Sr/$$^{90}$$Y and $$^{137}$$Cs can be simultaneously determined based on the count rate ratio of the source position peak and the reflection peak.

論文

Effect of radioactive cesium-rich microparticles on radioactive cesium concentration and distribution coefficient in rivers flowing through the watersheds with different contaminated condition in Fukushima

辰野 宇大*; 脇 嘉理*; 角間 海七渡*; 二瓶 直登*; 高瀬 つぎ子*; 和田 敏裕*; 吉村 和也; 中西 貴宏; 大手 信人*

Journal of Environmental Management, 329, p.116983_1 - 116983_13, 2023/03

 被引用回数:1 パーセンタイル:14.8(Environmental Sciences)

This study investigated the effect of radioactive cesium-rich microparticles (CsMPs) on the radiocesium (RCs) concentration and distribution coefficient (Kd) in two rivers, Takase River and Kami-Oguni River, flowing in the watersheds with different radioactive contaminated conditions in Fukushima Prefecture. Unlike RCs adsorbed on to the suspended solids (SS), there was no correlation between the RCs concentration derived from CsMPs and the SS concentration in both rivers. Inflow of CsMPs to the targeted rivers was contingent. CsMPs were detected only in some samples during rainfall. Furthermore, the proportion of RCs concentration derived from CsMPs in the average RCs concentrations per unit mass of SS in both rivers during rainfall were not large, which were 10% or less. As a results, CsMPs did not significantly increase particulate RCs concentration and had little effect on Kd in both river water flowing the watershed with different RCs contaminated condition.

論文

A New approach to extracting biofilm from environmental plastics using ultrasound-assisted syringe treatment for isotopic analyses

Battulga, B.; 安藤 麻里子; 中西 貴宏; 小嵐 淳

Science of the Total Environment, 849, p.157758_1 - 157758_11, 2022/11

 被引用回数:3 パーセンタイル:43.07(Environmental Sciences)

本研究では、マイクロプラスチックの表面に形成されるバイオフィルム(有機付着物)の特性を明らかにするための第一ステップとして、バイオフィルムを分離回収する手法を開発した。茨城県内の河川において、大きさ,色,組成の異なる様々なマイクロプラスチック試料を採取した。それらの試料に超音波処理を行った後、シリンジを用いた方法により有機付着物を溶液として分離回収した。バイオフィルム由来の有機物から放射性セシウムが検出され、マイクロプラスチックが河川生態系における放射性核種の輸送媒体としての役割を果たすことが示唆された。また、有機物の安定炭素・窒素同位体の分析にも成功した。本手法は、マイクロプラスチックの状態や環境中における物質循環への寄与を解明するために有効である。

論文

Cesium-rich microparticles runoff during rainfall; A Case study in the Takase River

辰野 宇大*; 脇 嘉理*; 角間 海七渡*; 二瓶 直登*; 和田 敏裕*; 吉村 和也; 中西 貴宏; 大手 信人*

Radiation Protection Dosimetry, 198(13-15), p.1052 - 1057, 2022/09

 被引用回数:1 パーセンタイル:31.61(Environmental Sciences)

Cesium-rich microparticles (CsMPs) with high cesium-137 ($$^{137}$$Cs) concentrations were released and deposited in surface soil after the Fukushima Daiichi Nuclear Power Plant accident. Radioactive materials on the soil surface layer enter rivers owing to soil erosion during rainfall. In this study, we investigated CsMPs runoff through the river via soil erosion during rainfall in the Takase River watershed in Namie Town, Fukushima Prefecture, Japan. CsMPs were rarely detected in suspended solids (SS) in water samples collected during four rainfalls between February and July 2021. Furthermore, the proportion of $$^{137}$$Cs concentration derived from CsMPs to $$^{137}$$Cs concentration in the form of SS (particulate $$^{137}$$Cs) in the water was $$sim$$6% on average, which suggests that $$^{137}$$Cs runoff in the form of CsMPs from the forest to the Takase River was not large.

論文

Radiation monitoring in the residential environment; Time dependencies of air dose rate and $$^{137}$$Cs inventory

吉村 和也; 中間 茂雄; 藤原 健壮

Journal of Radiation Protection and Research, 47(1), p.30 - 38, 2022/03

To better understand the radiation environment in urban area, this study investigated temporal changes in air dose rate as well as $$^{137}$$Cs inventories (Bq m$$^{-2}$$) in both residential areas and agricultural fields. The air dose rate decreased faster in residential areas than in agricultural fields. It was also observed that the $$^{137}$$Cs inventory on paved surfaces decreased with time due to horizontal wash-off, while the permeable surfaces showed no significant temporal changes unless decontamination. Our results suggest that the horizontal wash-off of $$^{137}$$Cs on the paved surfaces facilitated the decrease in air dose rate in urban areas to a greater extent compared with agricultural fields, of which air dose rate was decreased due to vertical migration of $$^{137}$$Cs.

論文

Air dose rates and cesium-137 in urban areas; Deposition, migration, and time dependencies after nuclear power plant accidents

吉村 和也

Journal of Nuclear Science and Technology, 59(1), p.25 - 33, 2022/01

 被引用回数:6 パーセンタイル:72.21(Nuclear Science & Technology)

Our goal is to review and synthesize knowledge obtained after the Fukushima Dai-ichi and Chernobyl Nuclear Power Plant accidents to provide important information to better understand environmental radiation in urban areas. As was reported in Europe, the cesium-137 ($$^{137}$$Cs) inventory (Bq m$$^{-2}$$) was high on soil grounds but relatively low on impermeable surfaces such as roads and roofs because of the high initial runoff and wash-off of $$^{137}$$Cs from surfaces. The air dose rate in urban areas decreased faster than that in other land uses owing to large $$^{137}$$Cs wash-off on pavements and anthropogenic effects, such as decontamination. Thus, environmental recovery in urban area was thought to be facilitated by human activities and $$^{137}$$Cs wash-off, reducing radiation risk of local residents comparing to the other land uses.

論文

Impacts of freeze-thaw processes and subsequent runoff on $$^{137}$$Cs washoff from bare land in Fukushima

五十嵐 康記*; 恩田 裕一*; 脇山 義史*; 吉村 和也; 加藤 弘亮*; 小塚 翔平*; 馬目 凌*

Science of the Total Environment, 769, p.144706_1 - 144706_9, 2021/05

 被引用回数:2 パーセンタイル:13.39(Environmental Sciences)

The impact of freeze-thaw processes and subsequent runoff affecting the Cs-137 ($$^{137}$$Cs) flux and concentration in sediment discharge were revealed in bareland erosion plot following the Fukushima Nuclear Power Plant accident by detailed monitoring and laser scanner measurement on the soil surface. We found that surface topographic changes due to the frost-heaving during the winter- spring period, and rill formation during the summer. We also found the evident seasonal changes in $$^{137}$$Cs concentration; high during the early spring and gradually decreased thereafter, then surface runoff from the plot frequently occurred during spring and autumn when rainfall was high and reached a maximum in summer.

論文

Calculations for ambient dose equivalent rates in nine forests in eastern Japan from $$^{134}$$Cs and $$^{137}$$Cs radioactivity measurements

Malins, A.; 今村 直広*; 新里 忠史; 高橋 純子*; Kim, M.; 佐久間 一幸; 篠宮 佳樹*; 三浦 覚*; 町田 昌彦

Journal of Environmental Radioactivity, 226, p.106456_1 - 106456_12, 2021/01

 被引用回数:6 パーセンタイル:35.21(Environmental Sciences)

Understanding the relationship between the distribution of radioactive $textsuperscript{134}$Cs and $textsuperscript{137}$Cs in forests and ambient dose equivalent rates ($textit{.{H}}$*(10)) in the air is important for researching forests in eastern Japan affected by the Fukushima Dai-ichi Nuclear Power Plant (FDNPP) accident. This study used a large number of measurements from forest samples, including $$^{134}$$Cs and $textsuperscript{137}$Cs radioactivity concentrations, densities and moisture contents, to perform Monte Carlo radiation transport simulations for $textit{.{H}}$*(10) between 2011 and 2017. Calculated $textit{.{H}}$*(10) at 0.1 and 1 m above the ground had mean residual errors of 19% and 16%, respectively, from measurements taken with handheld NaI(Tl) scintillator survey meters. Setting aside the contributions from natural background radiation, $textsuperscript{134}$Cs and $textsuperscript{137}$Cs in the organic layer and the top 5 cm of forest soil generally made the largest contributions to calculated $textit{.{H}}$*(10). The contributions from $textsuperscript{134}$Cs and $textsuperscript{137}$Cs in the forest canopy were calculated to be largest in the first two years following the accident. Uncertainties were evaluated in the simulation results due to the measurement uncertainties in the model inputs by assuming Gaussian measurement errors. The mean uncertainty (relative standard deviation) of the simulated $textit{.{H}}$*(10) at 1 m height was 11%. The main contributors to the total uncertainty in the simulation results were the accuracies to which the $textsuperscript{134}$Cs and $textsuperscript{137}$Cs radioactivities of the organic layer and top 5 cm of soil, and the vertical distribution of $textsuperscript{134}$Cs and $textsuperscript{137}$Cs within the 5 cm soil layers, were known. Radioactive cesium located in the top 5 cm of soil was the main contributor to $textit{.{H}}$*(10) at 1 m by 2016 or 2017 in the calculation results for all sites.

論文

Simulation analysis of the Compton-to-peak method for quantifying radiocesium deposition quantities

Malins, A.; 越智 康太郎; 町田 昌彦; 眞田 幸尚

Proceedings of Joint International Conference on Supercomputing in Nuclear Applications + Monte Carlo 2020 (SNA + MC 2020), p.147 - 154, 2020/10

Compton-to-peak analysis is a method for selecting suitable coefficients to convert count rates measured with in situ gamma ray spectrometry to radioactivity concentrations of $$^{134}$$Cs & $$^{137}$$Cs in the environment. The Compton-to-peak method is based on the count rate ratio of the spectral regions containing Compton scattered gamma rays to that with the primary $$^{134}$$Cs & $$^{137}$$Cs photopeaks. This is known as the Compton-to-peak ratio (RCP). RCP changes as a function of the vertical distribution of $$^{134}$$Cs & $$^{137}$$Cs within the ground. Inferring this distribution enables the selection of appropriate count rate to activity concentration conversion coefficients. In this study, the PHITS Monte Carlo radiation transport code was used to simulate the dependency of RCP on different vertical distributions of $$^{134}$$Cs & $$^{137}$$Cs within the ground. A model was created of a LaBr$$_3$$(Ce) detector used in drone helicopter aerial surveys in Fukushima Prefecture. The model was verified by comparing simulated gamma ray spectra to measurements from test sources. Simulations were performed for the infinite half-space geometry to calculate the dependency of RCP on the mass depth distribution (exponential or uniform) of $$^{134}$$Cs & $$^{137}$$Cs within the ground, and on the altitude of the detector above the ground. The calculations suggest that the sensitivity of the Compton-to-peak method is greatest for the initial period following nuclear fallout when $$^{134}$$Cs & $$^{137}$$Cs are located close to the ground surface, and for aerial surveys conducted at low altitudes. This is because the relative differences calculated between RCP with respect to changes in the mass depth distribution were largest for these two cases. Data on the measurement height above and on the $$^{134}$$Cs & $$^{137}$$Cs activity ratio is necessary for applying the Compton-to-peak method to determine the distribution and radioactivity concentration of $$^{134}$$Cs & $$^{137}$$Cs in the ground.

論文

Measurement of cesium isotopic ratio by thermal ionization mass spectrometry for neutron capture reaction studies on $$^{135}$$Cs

芝原 雄司*; 中村 詔司; 上原 章寛*; 藤井 俊行*; 福谷 哲*; 木村 敦; 岩本 修

Journal of Radioanalytical and Nuclear Chemistry, 325(1), p.155 - 165, 2020/07

 被引用回数:8 パーセンタイル:71.58(Chemistry, Analytical)

$$^{135}$$Csの断面積を測定するために用いる放射性Cs試料について、熱イオン化マススペクトロメトリーによって同位体比を測定した。分析において高強度、および安定ビームを得るために、Cs試料に加える添加剤の効果を調べた。本研究で、シリコンタングステンが、添加剤の中で一番高いイオン化効率を示したが、一方で多原子イオンの高い同重体干渉も示した。$$^{135}$$Cs/$$^{137}$$Cs比の測定で要求される精度を達成するのに、添加剤:酸化タンタルないしグルコースを用いた場合で、僅か2$$times$$10$$^{-13}$$gのCs試料で十分達成できることを実証した。バリウム核種による干渉効果などの分析条件を調べた後、2種類の放射性Cs試料の同位体比測定を行い、同位体比によりどのくらい$$^{135}$$Csの中性子捕獲断面積に影響を及ぼすかを議論した。

論文

Vertical and horizontal distributions of $$^{137}$$Cs on paved surfaces affected by the Fukushima Dai-ichi Nuclear Power Plant accident

吉村 和也; 渡辺 貴善; 操上 広志

Journal of Environmental Radioactivity, 217, p.106213_1 - 106213_6, 2020/06

 被引用回数:5 パーセンタイル:25.07(Environmental Sciences)

To obtain the important information and parameter for the measurement of $$^{137}$$Cs activity per unit area on paved ground, this study evaluated their vertical and horizontal distributions. This study showed that $$^{137}$$Cs was retained in extremely surface layer with mass depth less than 0.5 cm$$^{-2}$$. This study also demonstrated the horizontal variations of $$^{137}$$Cs activity and the relation of the variation with grid size.

論文

Measurements of thermal-neutron capture cross-section of cesium-135 by applying mass spectrometry

中村 詔司; 芝原 雄司*; 木村 敦; 岩本 修; 上原 章寛*; 藤井 俊行*

Journal of Nuclear Science and Technology, 57(4), p.388 - 400, 2020/04

 被引用回数:3 パーセンタイル:31.89(Nuclear Science & Technology)

$$^{135}$$Cs(n,$$gamma$$)$$^{136}$$Cs反応の熱中性子捕獲断面積($$sigma_{0}$$)及び共鳴積分(I$$_{0}$$)を、ガンマ線及びマススペクトロメトリーにより測定した。我々は、$$^{137}$$Cs標準溶液に不純物として含まれている$$^{135}$$Csを利用した。$$^{137}$$Cs溶液中の$$^{135}$$Csを定量するために、$$^{135}$$Csと$$^{137}$$Csの同位対比をマススぺクトロメトリーにより求めた。分析した$$^{137}$$Cs試料を、京都大学複合原子力科学研究所の研究炉の水圧輸送管を用いて中性子照射を行った。照射位置の中性子成分を求めるために、Co/AlとAu/Alモニタも一緒に照射した。$$sigma_{0}$$を求めるために、Gdフィルターを用いて、中性子カットオフエネルギーを0.133eVに設定した。$$^{137}$$Cs, $$^{136}$$Csとモニタの放射能をガンマ線スペクトロメトリーにより測定した。Westcottコンベンションに基づき、$$sigma_{0}$$とI$$_{0}$$を、それぞれ8.57$$pm$$0.25barn及び45.3$$pm$$3.2barnと導出した。今回得られた$$sigma_{0}$$は、過去の測定値8.3$$pm$$0.3barnと誤差の範囲で一致した。

論文

Land use types control solid wash-off rate and entrainment coefficient of Fukushima-derived $$^{137}$$Cs, and their time dependence

脇山 義史*; 恩田 裕一*; 吉村 和也; 五十嵐 康記*; 加藤 弘亮*

Journal of Environmental Radioactivity, 210, p.105990_1 - 105990_12, 2019/12

 被引用回数:21 パーセンタイル:67.06(Environmental Sciences)

This study provides the results of observations of plot-scale $$^{137}$$Cs wash-off from various land uses (two uncultivated farmlands, two cultivated farmlands, three grasslands and one forest) from 2011 to 2014. Annual $$^{137}$$Cs wash-off rate ranged from 0.0026 to 7.5% per year, and more vegetation cover resulted in lower sediment discharge. $$^{137}$$Cs concentration observed in uncultivated farmland plot decreased with time and the rate was lower than those of riverine, suggesting that contributions of $$^{137}$$Cs from the upslope area may be insignificant to that in riverine. A negative relationship between $$^{137}$$Cs concentration normalized by initial deposition amount and sediment concentration in runoff water was found. Cultivation appeared to cause enhanced soil erosion and resulted in constant relatively low $$^{137}$$Cs concentration. A contribution of coarse organic matter to $$^{137}$$Cs wash-off was suggested in the forest, which had relatively high $$^{137}$$Cs concentration and low sediment discharge.

論文

Activation measurement for thermal-neutron capture cross-section of Cesium-135

中村 詔司; 木村 敦; 岩本 修; 芝原 雄司*; 上原 章寛*; 藤井 俊行*

KURNS Progress Report 2018, P. 106, 2019/08

核変換による高レベル放射性廃棄物の大幅な低減化、資源化を目指した革新的研究開発推進プログラム(ImPACT)において、長寿命核分裂生成核種$$^{135}$$Csの中性子捕獲断面積測定研究を京都大学複合原子力科学研究所にて行った。本論文は、京大原子炉(KUR)を用いた$$^{135}$$Csの熱中性子捕獲断面積の測定について報告するものである。

論文

Modelling the effect of mechanical remediation on dose rates above radiocesium contaminated land

Malins, A.; 操上 広志; 北村 哲浩; 町田 昌彦

Remediation Measures for Radioactively Contaminated Areas, p.259 - 272, 2019/00

Mechanical strategies for remediating radiocesium contaminated soils, e.g. at farms, schoolyards, gardens or parks, lower air dose rates in one of two characteristic ways. The first is to physically remove radiocesium from the environment, for example by stripping topsoil and sending it for disposal. The second is to redistribute the radiocesium deeper within the ground, e.g. by mixing the topsoil or switching the positions of different soil layers, in order that soil attenuates radiocesium gamma rays before they reach the surface. The amount that air dose rates reduce because of remediation can be calculated using radiation transport methods. This chapter summarizes modelling results for the effect of topsoil removal (with and without recovering with a clean soil layer), topsoil mixing, and soil layer interchange on dose rates. Using measurements of the depth profile of $$^{134}$$Cs and $$^{137}$$Cs activity in soil at un-remediated sites across North East Japan, the potential effectiveness of remediation work was estimated considering remediation to different soil depths and different time lags after the accident. The results show that remediation performance would have been essentially constant irrespective of the time at which it was undertaken in the initial five year period following the fallout.

論文

Analysis of $$^{135}$$Cs/$$^{137}$$Cs isotopic ratio for samples used for neutron capture cross section measurement project by thermal ionization mass spectrometry

芝原 雄司*; 上原 章寛*; 藤井 俊行*; 中村 詔司; 木村 敦; Hales, B. P.; 岩本 修

JAEA-Conf 2018-001, p.205 - 210, 2018/12

ImPACT事業の中性子捕獲断面積研究において、$$^{135}$$Cs中性子捕獲断面積測定に使用する試料として$$^{137}$$Cs標準溶液中に含まれる$$^{135}$$Csの利用を考えた。$$^{135}$$Cs試料を定量するためには、$$^{135}$$Csと$$^{137}$$Csの同位体比を高精度で分析する必要がある。そこで、熱イオン化質量分析器(TIMS)を用いて、最初のサンプルとして$$^{137}$$Cs標準溶液の質量分析試験を行なった。分析試験の結果、わずか10Bq(pgオーダー)の$$^{137}$$Cs標準溶液でも$$^{135}$$Csと$$^{137}$$Csの同位体比を0.5%の高精度で導出することができた。

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