JAEA-Research2024-002
DOI:10.11484/jaea-research-2024-002

Analysis of the Relationship Between
Operational Quantity Used for Area Monitoring andProtection Quantity for External Exposure
Akira ENDO

Sector of Nuclear Science Research

May 2024
Japan Atomic Energy Agency

日本原子力研究開発機構

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JAEA-Research 2024-002

Analysis of the Relationship Between Operational Quantity Used for
Area Monitoring and Protection Quantity for External Exposure
Akira ENDO
Sector of Nuclear Science Research
Japan Atomic Energy Agency
Tokai-mura, Naka-gun, Ibaraki-ken(Received January 16, 2024)
This report presents a comprehensive analysis of the relationship between three quantities used for area
∗ , and ambient dose 𝐻𝐻 ∗monitoring — ambient dose equivalent 𝐻𝐻 ∗ (10), maximum dose equivalent 𝐻𝐻max— and eﬀective dose for external irradiation by photons, neutrons, electrons, positrons, protons, muons,pions, and helium ions. For the analysis, calculations were performed using PHITS (Particle and Heavy∗
can
Ion Transport code System) and the ICRU sphere. The analysis result shows that 𝐻𝐻 ∗ (10) and 𝐻𝐻max
induce large diﬀerences in the estimation of eﬀective dose over a wide energy range for various particle
types covered by ICRP Publication 116 while 𝐻𝐻 ∗ can conservatively estimate eﬀective dose within the∗have limitations in estimating
acceptable range for area monitoring. In other words, 𝐻𝐻 ∗ (10) and 𝐻𝐻max∗
eﬀective dose, and using 𝐻𝐻 is recommended as a more appropriate quantity for the purpose. Thisconclusion supports the proposal of ICRU Report 95 to use 𝐻𝐻 ∗ for estimating eﬀective dose in various
external exposure situations. The use of ambient dose 𝐻𝐻 ∗ is particularly important in situations where
various types of radiation are encountered, such as the use of radiation in the medical and academic
ﬁelds and exposure in aviation and can meet the evolving requirements of radiation monitoring for the
expansion of the ﬁeld of radiological protection.
Keywords: External Radiation, Operational Quantity, Protection Quantity, ICRU Report 95,
Area Monitoring, Ambient Dose Equivalent, Maximum Dose Equivalent,
Ambient Dose, Eﬀective Dosei

JAEA-Research 2024-002

外部被ばくに対するエリアモニタリングに使われる実用量と防護量の関係の分析

日本原子力研究開発機構
遠藤

原子力科学研究部門

章(2024 年 1 月 16 日 受理)
本報告書は，光子，中性子，電子，陽電子，陽子，ミューオン，パイ中間子及びヘリウムイオンによる外部被ばくについて，エリアモニタリングに用いられる 3 つの量である周辺線量当量 𝐻𝐻 ∗ (10) ，∗
最大線量当量 𝐻𝐻max
及び周辺線量 𝐻𝐻 ∗ と実効線量との関係を包括的に分析した結果を示す。分析のための計算は，PHITS (Particle and Heavy Ion Transport code System) と ICRU 球を用いて行った。

その結果，ICRP Publication 116 で対象としている幅広いエネルギー範囲における外部被ばくに対∗して，𝐻𝐻 ∗ (10) と 𝐻𝐻max
は実効線量の評価に大きな差を生じる場合がある一方，𝐻𝐻 ∗ はエリアモニタ

リングに許容される範囲で実効線量を保守的に評価できることが分かった。すなわち，実効線量を∗評価するために，𝐻𝐻 ∗ (10) と 𝐻𝐻maxには限界があり，より適切な量として 𝐻𝐻 ∗ の使用が推奨される。

この結論は，多様な被ばく状況における実効線量の評価に 𝐻𝐻 ∗ を導入した ICRU Report 95 の提案を支持するものである。周辺線量 𝐻𝐻 ∗ の利用は，医療や学術研究における放射線利用や航空機搭乗時の被ばく等の様々な種類の放射線により被ばくする状況で特に重要であり，放射線防護の対象の拡大に伴う放射線モニタリングの新たなニーズに応えることができる。

—————————————————————————————————————————–
原子力科学研究所：〒 319–1195 茨城県那珂郡東海村大字白方 2 番地 4ii

JAEA-Research 2024-002

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Deﬁnitions of quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Radiation transport code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Calculation model and method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Validation of calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Comparison of ℎ∗ (10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Comparison of ℎ∗max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Overview of 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄
3.3 Comparison of 𝐻𝐻 ∗ (10) and 𝐸𝐸 max . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
∗and 𝐸𝐸 max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Comparison of 𝐻𝐻max∗
3.5 Comparison of 𝐻𝐻 and 𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸
3.6 Discussion on appropriate quantity for use in area monitoring for assessment of eﬀective
dose from external radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1
2

3

4
謝

序

目

次

論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

研究方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 量の定義 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 放射線輸送計算コード . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 計算モデル及び方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

結果と考察 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 計算の検証 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 ℎ∗ (10) の比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 ℎ∗max の比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 𝑑𝑑 ∗ (10), ℎ∗ (10) 及び 𝑄𝑄 の概要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 𝐻𝐻 ∗ (10) と 𝐸𝐸 max の比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
∗と 𝐸𝐸 max の比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 𝐻𝐻max∗
3.5 𝐻𝐻 と 𝐸𝐸 の比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 外部放射線に対する実効線量評価のためのエリアモニタリングに用いる適切な量の検討 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

辞. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

参考文献 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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JAEA-Research 2024-002

List of Tables
Table 1
Table 2
Table 3
Table 4
Table 5
Table 6
Table 7
Table 8
Table 9
Table 10
Table 11

Particles and energy ranges for calculation of dose coeﬃcients. . . . . . . . . . .
Photons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . . . . . .
Neutrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . . . . . .
Electrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . . . . . .
Positrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . . . . . .
Protons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . . . . . . .
Negative muons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . .
Positive muons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . . .
Negative pions: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . . .
Positive pions: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . . .
Helium ions: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values. . . . . . . . . . . . . . . .

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List of Figures
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26

Quality factor, 𝑄𝑄, as a function of linear energy transfer, 𝐿𝐿. . . . . . . . . . . . .
Model used for calculation of 𝐷𝐷 ∗ (𝑑𝑑) and 𝐻𝐻 ∗ (𝑑𝑑). . . . . . . . . . . . . . . . . .
Distributions of dose equivalent in the ICRU sphere irradiated by photons. . . . .
Comparison of ℎ∗ (10) for photons. . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗ (10) for neutrons. . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗ (10) for electrons. . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗ (10) for positrons. . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗ (10) for protons. . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗ (10) for negative muons. . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗ (10) for positive muons. . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗ (10) for negative pions. . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗ (10) for positive pions. . . . . . . . . . . . . . . . . . . . . .
Comparison of 𝑑𝑑 ∗ (10) and ℎ∗ (10) for photons calculated by FLUKA and PHITS.
Comparison of ℎ∗max for photons. . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗max for neutrons. . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗max for electrons. . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗max for positrons. . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗max for protons. . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗max for negative muons. . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗max for positive muons. . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗max for negative pions. . . . . . . . . . . . . . . . . . . . . . .
Comparison of ℎ∗max for positive pions. . . . . . . . . . . . . . . . . . . . . . .
Absorbed dose distribution in the frontal region of the ICRU sphere. . . . . . . .
Eﬀect of radius of the scoring region on ℎ∗max . . . . . . . . . . . . . . . . . . . .
Photons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . . . . . .
Neutrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . . . . . .

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Figure 27
Figure 28
Figure 29
Figure 30
Figure 31
Figure 32
Figure 33
Figure 34
Figure 35
Figure 36
Figure 37
Figure 38
Figure 39
Figure 40
Figure 41
Figure 42
Figure 43
Figure 44
Figure 45
Figure 46
Figure 47
Figure 48
Figure 49
Figure 50
Figure 51
Figure 52
Figure 53
Figure 54
Figure 55
Figure 56
Figure 57
Figure 58
Figure 59
Figure 60
Figure 61
Figure 62
Figure 63
Figure 64
Figure 65

Electrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . . . . . .
Positrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . . . . . .
Protons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . . . . . . .
Negative muons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . .
Positive muons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . . .
Negative pions: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . . .
Positive pions: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . . .
Helium ions: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄. . . . . . . . . . . . . . . . . . . . . . . .
LET distributions of charged particles in the ICRU sphere irradiated by protons. .
Photons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . .
Neutrons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . .
Electrons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . .
Positrons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . .
Protons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . .
Negative muons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . .
Positive muons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . .
Negative pions: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . . .
Positive pions: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . . .
Helium ions: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max . . . . . . . . . . . . . . . . . . . .
Photons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . . . .
Neutrons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . . . .
Electrons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . . . .
Positrons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . . . .
Protons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . . . . .
Negative muons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . .
Positive muons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . .
Negative pions: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . .
Positive pions: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . .
Helium ions: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max . . . . . . . . . . . . . . . . . . . . . .
Photons: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neutrons: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electrons: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Positrons: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Protons: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Negative muons: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Positive muons: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Negative pions: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Positive pions: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Helium ions: 𝑒𝑒 and ℎ∗ /𝑒𝑒. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

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JAEA-Research 2024-002

1 Introduction

1

Introduction

Protection against the health eﬀects of ionizing radiation requires preventing tissue reactions (deterministic eﬀects) and limiting cancer risks and hereditary eﬀects (stochastic eﬀects). The International
Commission on Radiological Protection (ICRP) developed risk-related dosimetric quantities called “protection quantities” to meet these requirements1–3) . The most recent deﬁnitions of protection quantities,
given in the 2007 Recommendations of ICRP3) , include the mean absorbed dose in an organ or tissue,
the equivalent dose in an organ or tissue, and the eﬀective dose.
The body-related protection quantities are not measurable in practice; therefore, they cannot be useddirectly as quantities in radiation monitoring. The International Commission on Radiation Units andMeasurements (ICRU) has developed a set of “operational quantities” to assess equivalent and eﬀective
doses via a series of reports4–8) . The operational quantities are intended to provide a reasonable, generally
conservative, estimate of protection quantity values associated with an exposure or a potential exposureof persons under various irradiation conditions3) .
The relationship between the protection quantities and the operational quantities is established using
dose coeﬃcients which relate the operational and protection quantities to physical quantities describing
the radiation ﬁeld. ICRU Reports 435) and 476) , and ICRP Publication 749) /ICRU Report 5710) reported
sets of dose coeﬃcients to these quantities from radiometric and dosimetric quantities.
The currently used operational quantities were deﬁned in the 1980s and have been implemented inpractice in many countries under radiation protection directives and regulations during the last 30 years.
Nevertheless, the existing system of operational quantities has limitations and needs further improvement
to consider changes in the application of protection and operational quantities3, 11–13) . The types andenergy range of particles used in medical diagnostics and therapy and scientiﬁc research have been
expanded. The ICRP Recommendations include natural radiation sources2) ; aircraft crews are one of themost exposed occupational groups, and the radiation ﬁeld at ﬂight altitudes includes a large componentof high-energy particles from cosmic radiation.
To meet the evolving requirements for the expansion of the ﬁeld of radiological protection, ICRP
developed dose coeﬃcients of the protection quantities that extend particle types and energy ranges tohigher regions and published the dataset of dose coeﬃcients in Publication 11614) together with ICRU.
The dataset of ICRP Publication 116 superseded those of ICRP Publication 74 and ICRU Report 57.
However, ICRP Publication 116 highlighted that the operational quantities deﬁned in ICRU Reports 394)
and 517) are not always close estimates of the protection quantities in higher energy ﬁelds14) . Thus, ICRU
established the Report Committee 26 in 2010 to address these issues. The Report Committee 26 reviewed
the shortcomings and limitations of the existing system of operational quantities, considering an extensionof the range of particle types and energies of the dose coeﬃcients in ICRP Publication 116. As a result ofextensive discussion, the Report Committee 26 decided to introduce new operational quantities deﬁned
using the dose coeﬃcient values of the protection quantities for external exposures. The deﬁnitions of
the operational quantities and a set of dose coeﬃcients were published in ICRU Report 9515) .
ICRU Report 95 provided a comparison of the dose coeﬃcients for area monitoring deﬁned in Reports
39 and 51 and those newly proposed in Report 95 to indicate the limitations of the existing system deﬁned
in Reports 39 and 51. The comparisons were limited for photons, neutrons, electrons, positrons, andprotons, and they were provided in graphical form only.
To gain a deeper understanding of the background of motivation for introducing new operational
quantities by ICRU, the present report analyzes the limitations of the existing system by comparing-1-

JAEA-Research 2024-002

several quantities used for area monitoring with eﬀective dose. The analysis result validates the decisionof the Report Committee 26 and shows the advantages of the new operational quantities.

2 Materials and methods
2 Materials and methods
2.1

Deﬁnitions of quantities

This section provides deﬁnitions for three quantities used in area monitoring and eﬀective dose, which
are the subjects being compared in this report.
1) Ambient dose equivalent
The ambient dose equivalent, 𝐻𝐻 ∗ (𝑑𝑑), at a point in a radiation ﬁeld, is the dose equivalent that would
be produced by the corresponding expanded and aligned ﬁeld in the ICRU sphere at a depth, 𝑑𝑑, on theradius opposing the direction of the aligned ﬁeld7) . The unit of the ambient dose equivalent is J kg−1
and has the special name sievert (Sv). For strongly penetrating radiation, a depth of 10 mm is currently
recommended. The ambient dose equivalent for this depth is then denoted by 𝐻𝐻 ∗ (10).
A quantity analogous to ambient dose equivalent can be deﬁned in terms of absorbed dose, known as
the ambient absorbed dose, 𝐷𝐷 ∗ (𝑑𝑑). Its unit is J kg−1 and has the special name gray (Gy).
The dose equivalent, 𝐻𝐻, is the product of 𝑄𝑄 and 𝐷𝐷 at a point in a tissue, where 𝑄𝑄 is the quality factor
and 𝐷𝐷 is the absorbed dose at that point; thus, 𝐻𝐻 = 𝑄𝑄𝑄𝑄. Consequently, in this report, a value of 𝐻𝐻 ∗ (10)is derived from 𝑄𝑄 at 10-mm depth and 𝐷𝐷 ∗ (10) of the ICRU sphere.
𝑄𝑄 is deﬁned in ICRP Publication 602) as a function of the unrestricted linear energy transfer (LET), 𝐿𝐿,
in water at the point of interest, as follows.
𝑄𝑄(𝐿𝐿) = 1
𝑄𝑄(𝐿𝐿) = 0.32𝐿𝐿 − 2.2√
𝑄𝑄(𝐿𝐿) = 300/ 𝐿𝐿(𝐿𝐿 𝐿 10 keV 𝜇𝜇m−1 )(1)(10 ≤ 𝐿𝐿 ≤ 100 keV 𝜇𝜇m )−1(𝐿𝐿 > 100 keV 𝜇𝜇m )
−1

(2)
(3)

Figure 1 illustrates the relationship between 𝑄𝑄 and 𝐿𝐿 deﬁned by Equations (1)–(3).
2) Maximum dose equivalent∗ , represents the maximum value of the dose equivalent that would
The maximum dose equivalent, 𝐻𝐻max
be produced by the corresponding expanded and aligned ﬁeld in the ICRU sphere on the radius opposing
the direction of the aligned ﬁeld. The unit of the maximum dose equivalent is J kg−1 and has the specialname sievert (Sv).
∗ , used in this report is diﬀerent from
Note that the deﬁnition of the maximum dose equivalent, 𝐻𝐻max
the maximum dose equivalent in an irradiated body (MADE)16) and the dose equivalent index17, 18) .
Furthermore, as stated in Appendix B of ICRU Report 435) , the maximum dose equivalent in a 30 cm
diameter sphere exposed to a unidirectional beam may not occur exactly on the central axis. However, in
this study, the focus is on examining the maximum dose equivalent value along the central axis within
the ICRU sphere to facilitate comparison with previous research19) .

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3) Ambient dose
The ambient dose, 𝐻𝐻 ∗ , at a point in a radiation ﬁeld, is the product of the particle ﬂuence at that point,𝛷𝛷, and dose coeﬃcient, ℎ∗ , which relates the particle ﬂuence to the maximum value of eﬀective dose,
𝐸𝐸 max , for various irradiation conditions15) ; therefore, 𝐻𝐻 ∗ = 𝛷𝛷𝛷∗ . The unit of the ambient dose is J kg−1
and has the special name sievert (Sv).
For a speciﬁc particle type 𝑖𝑖 with kinetic energy 𝐸𝐸 p , the dose coeﬃcient
Sv cm2ℎ∗𝑖𝑖 (𝐸𝐸 p ) = 𝐸𝐸 max,𝑖𝑖 (𝐸𝐸 p )/𝛷𝛷i (𝐸𝐸 p )

(4)
(5)

= 𝑒𝑒 max,𝑖𝑖 (𝐸𝐸 p )is calculated for the exposure of the ICRP/ICRU adult reference phantoms20) for broad uniform parallel
beams of the incident radiation ﬁeld. The irradiation geometries are antero–posterior (AP), postero–anterior (PA), left lateral (LLAT), right lateral (RLAT), rotational (ROT), isotropic (ISO), superior
hemisphere semi-isotropic (SS-ISO), and inferior hemisphere semi-isotropic (IS-ISO) ﬁelds for photons,
neutrons, and protons; AP, PA, ISO, SS-ISO, and IS-ISO ﬁelds for electrons, positrons, muons, and pions;and AP, PA, and ISO for helium ions. The eﬀective dose coeﬃcients for these irradiation geometries arepresented in ICRP Publication 11614) .
4) Eﬀective dose
The eﬀective dose, 𝐸𝐸, is the tissue-weighted sum of the equivalent doses in all speciﬁed organs andtissues of the body and is given by the expression
𝐸𝐸 =

∑
T

𝑤𝑤 T

∑

𝑤𝑤 R 𝐷𝐷 T,R =R∑

𝑤𝑤 T 𝐻𝐻T(6)

T

where 𝐻𝐻T is the equivalent dose in an organ or tissue T, 𝐷𝐷 T,R is the mean absorbed dose in an organ or
tissue T from radiation of type R, and 𝑤𝑤 T is the tissue weighting factor3) . This sum is made over organs
and tissues considered to be sensitive to the induction of stochastic eﬀects. The unit of the eﬀective dose
is J kg−1 and has the special name sievert (Sv).

2.2

Radiation transport code

The calculation of 𝐷𝐷 ∗ (𝑑𝑑) and 𝐻𝐻 ∗ (𝑑𝑑) was performed using PHITS (Particle and Heavy Ion Transport
code System)21) . PHITS is a versatile Monte Carlo code that enables the simulation of the transport andinteraction of hadrons, leptons, and heavy ions in arbitrary three-dimensional geometries. It uses several
nuclear reaction models and data libraries. PHITS version 3.32 was used for the calculation. The models
and parameters used in the calculation are described in detail below.
The dynamic stage of hadron-induced nuclear reactions was simulated using the intranuclear cascade
models JAM22) /INCL4.623) , while nuclei-induced reactions were simulated using an improved versionof the quantum molecular dynamics model, JQMD24) . To simulate nucleus–nucleus reactions exceeding
3 GeV n−1 , a hybrid method integrating JAM and JQMD, called JAMQMD, was applied. The generalized
evaporation and ﬁssion model GEM25) was used to simulate the static stage of these reactions.

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JAEA-Research 2024-002

The ATIMA algorithm26) using the continuous slowing down approximation was used to calculate
the energy loss of charged particles, excluding electrons and positrons. The transport of neutrons withenergies ≤ 20 MeV was simulated using evaluated neutron data libraries; speciﬁcally, JENDL-4.027) wasused in this calculation. For the scattering of low-energy neutrons, the eﬀect of chemical bonding ofhydrogen was considered using S(𝛼𝛼𝛼 𝛼𝛼) data for hydrogen in water.
The transport of photons, electrons, and positrons was modeled using an algorithm of the EGS5 code28)
integrated with PHITS. JAM and JQMD were used to simulate photonuclear reactions29) . Furthermore,
the models for muon-induced nuclear reactions were integrated, including virtual photonuclear reactions
and the negative muon capture reaction following muonic atom formation30) .
𝐻𝐻 ∗ (𝑑𝑑) was determined using the PHITS t-deposit tally. The t-deposit tally calculates the dose equivalent
𝐻𝐻 based on the quality factor 𝑄𝑄, which is a function of the LET of charged particles recommended in
ICRP Publication 6031) .
Additional validation calculations were performed for photons with the FLUKA code, speciﬁcallyusing FLUKA201132) . Within FLUKA, while users have the ﬂexibility to specify models and parameters
for calculations, predeﬁned parameter sets optimized for simulations are also available. The parameterset designated as “PRECISIOn” was used for the calculations presented in this report. In particular,“PRECISIOn” is tailored for precise simulations and allows the activation of processes important forparticle transport and interaction over a wide energy range.

2.3

Calculation model and method

Figure 2 illustrates the geometry used to calculate 𝐷𝐷 ∗ (𝑑𝑑) and 𝐻𝐻 ∗ (𝑑𝑑), following a previous study by
Ferrari and Pelliccioni33) . The ICRU sphere was irradiated with a monoenergetic parallel particle beam
uniformly expanded over its front surface. The ICRU sphere is a tissue-equivalent sphere with a densityof 1 g cm−3 , diameter of 30 cm, and a mass composition of 76.2 % oxygen, 11.1 % carbon, 10.1 %hydrogen, and 2.6 % nitrogen34) . The space between the particle source and ICRU sphere was assumed
to be vacuum.
To obtain the depth dose distributions along the central axis of the sphere, the deposited energy wasevaluated using a series of cylindrical structures aligned along the central axis of the sphere, as shown in
Figure 2. Diﬀerent grids were used depending on the depth: 0.2 cm-long longitudinal grids were used
up to 1.7 cm, 0.3 cm for a depth of 1.7–2.0 cm, and 1.0 cm for beyond 2.0 cm, with a cylinder radius of
0.5 cm.
The 𝐷𝐷 ∗ (𝑑𝑑) values were derived from the energy deposited per unit mass within the cylindrical regions.
𝐻𝐻 ∗ (10) was calculated from the value of 𝑄𝑄 as a function of LET in water, as determined by the t-deposit
tally in PHITS. Speciﬁcally, 𝐷𝐷 ∗ (10) and 𝐻𝐻 ∗ (10) were determined for the cylindrical region with a depth∗of 0.9–1.1 cm and a radius of 0.5 cm. This region is called the 10-mm depth region in this report. 𝐻𝐻max
was obtained from the maximum value of 𝐻𝐻 ∗ (𝑑𝑑).
∗are normalized to the incident particle ﬂuence, 𝛷𝛷, and are
The values of 𝐷𝐷 ∗ (10), 𝐻𝐻 ∗ (10), and 𝐻𝐻max
2
2
presented in units of Gy cm and Sv cm as
𝑑𝑑 ∗ (10) = 𝐷𝐷 ∗ (10)/𝛷𝛷∗∗ℎ (10) = 𝐻𝐻 (10)/𝛷𝛷∗ℎ∗max = 𝐻𝐻max
/𝛷𝛷

-4-

Gy cm2

(7)

2

(8)

Sv cm2(9)

Sv cm

JAEA-Research 2024-002

Table 1 summarizes particle types and energy ranges considered for the calculations of 𝑑𝑑 ∗ (10), ℎ∗ (10),and ℎ∗max in this report. These were determined with reference to the conditions employed for calculating
the dose coeﬃcients for the protection quantities given in ICRP Publication 11614) . Note that the lower
energy limits for electrons, positrons, protons, and helium ions are higher than those reported in ICRP
Publication 116. These particles with the energies below the lower energy limits have extremely shortranges in the ICRU sphere. Furthermore, considering secondary particles produced by the low-energy
particles’ interactions in the ICRU sphere, an enormous amount of computational time is required togive a statistically signiﬁcant energy to the 10-mm depth region in the ICRU sphere. Therefore, these
low-energy particles were excluded from the dose coeﬃcient calculation. Note that the exclusion of these
extremely low-energy particles is expected to have no signiﬁcant eﬀect on area monitoring because theircontribution to doses is small.
The total number of incident particles was suﬃciently large to maintain the standard deviation of ℎ∗ (10)typically below 3 %.

3 Results and discussion
3 Results and discussion
Tables 2–11 present the numerical values of the dose coeﬃcients from particle ﬂuence to ambient
absorbed dose, 𝑑𝑑 ∗ (10), ambient dose equivalent, ℎ∗ (10), and maximum dose equivalent, ℎ∗max , calculatedusing PHITS for photons, neutrons, electrons, positrons, protons, muons, pions, and helium ions. The
deﬁnitions of 𝑑𝑑 ∗ (10), ℎ∗ (10), and ℎ∗max are given in Equations (7)–(9). In addition, the tables show
the corresponding quality factor, 𝑄𝑄, at the 10-mm depth region evaluated from 𝑑𝑑 ∗ (10) and ℎ∗ (10).
Furthermore, the dose coeﬃcients for the ambient dose, ℎ∗ , central to the discussion in this report, aretaken from ICRU Report 9515) and are provided in these tables.
Figure 3 illustrates a sample set of dose equivalent distributions on a cross-section traversing the central
axis of the ICRU sphere via photon incidence at three diﬀerent energies. At 0.1 MeV, the maximum
dose equivalent occurs in a superﬁcial region of the sphere. Notably, with increasing photon energy, thismaximum value moves to deeper regions within the sphere. This suggests that 𝐻𝐻 ∗ (10), representing thedose equivalent at a depth of 10 mm in the ICRU sphere, may not be an appropriate quantity for assessing
eﬀective dose to the human body from high-energy photon irradiation.
The characteristics of the energy dependence of 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄 for each particle are describedin Section 3.2.

3.1

Validation of calculation

The calculations performed with PHITS were validated by comparing the values of ℎ∗ (10) and ℎ∗max
presented in Tables 2–10 with data published by Ferrari and Pelliccioni19, 33, 35–39) . Ferrari and Pelliccioni
computed ℎ∗ (10) and ℎ∗max for photons, neutrons, electrons, positrons, protons, muons, and pions over awide energy range using the FLUKA code33, 35–39) . The compiled dataset was subsequently published in
200019) . Despite the limited incident particle energy points, the data serve as valuable reference points forvalidating the calculations presented in this report. Note that the comparison does not include the helium
ion data presented in Table 11 as it was not part of the Ferrari and Pelliccioni study and is therefore
missing from the analysis.

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In addition, the ℎ∗ (10) values for photons, neutrons, and electrons were compared with those presented
in ICRP Publication 749) and ICRU Report 5710) . This comparison demonstrates the impact of diﬀerent
calculation methods on the dose coeﬃcient values. In particular, ICRP Publication 74 and ICRU
Report 57 used a calculation method known as the kerma approximation. This approximation assumes
that all secondary particles, especially charged particles, are in equilibrium with the primary particle atthe point of interest. However, the calculations used in this report and by Ferrari and Pelliccioni did not
use the kerma approximation and tracked secondary particles.
Sections 3.1.1 and 3.1.2 provide comparisons of ℎ∗ (10) and ℎ∗max , respectively.
3.1.1 Comparison of 𝒉𝒉∗ (10)Figures 4–12 show comparisons of ℎ∗ (10) values. Overall, the values calculated by PHITS and
FLUKA for electrons (Figure 6), positrons (Figure 7), and protons (Figure 8) correlate satisfactorily.
However, noticeable diﬀerences are observed for photons (Figure 4), neutrons (Figure 5), negativeand positive muons (Figures 9 and 10), and negative and positive pions (Figures 11 and 12). These
discrepancies are investigated below to determine possible underlying causes.
1) Photons (Figure 4)
The ℎ∗ (10) values calculated using PHITS and FLUKA for photons show good agreement up to
10 MeV. However, in the PHITS calculation, remarkable broad peaks are observed from 20 MeV to
100 MeV and from 200 MeV to 3 GeV, which are absent in the FLUKA result. These peaks in the PHITS
result are due to quality factors greater than one caused by charged particles produced by photon-induced
nuclear reactions. Further analysis of these phenomena is given in Section 3.2.
Notably, two peaks in the ℎ∗ (10) plot are not observed in the calculation of Ferrari and Pelliccioni. While their papers lack speciﬁc information regarding the treatment of photon-induced nuclear
reactions19, 33, 35) , the discrepancies between PHITS and FLUKA calculations are attributed to diﬀerent
approaches employed for simulating the photon interaction. To clarify this discrepancy, the author has
performed calculations for 𝑑𝑑 ∗ (10) and ℎ∗ (10) using the FLUKA code, version FLUKA201132) , and theresults are shown in Figure 13. In terms of the energy dependence of 𝑑𝑑 ∗ (10) and ℎ∗ (10), which activatedphoton-induced nuclear reactions, PHITS and FLUKA calculations in this study show good agreement. In
particular, the two peaks in the ℎ∗ (10) plot, which are missing in the calculations reported by Ferrari and
Pelliccioni, conﬁrm the validity of the PHITS calculations, considering all processes of photon transport
and interaction.
Figure 4 also shows the ℎ∗ (10) values obtained from ICRP Publication 74 and ICRU Report 57. Below
3 MeV, these values are very close to those calculated using PHITS and FLUKA. However, the values
reported in ICRP Publication 74/ICRU Report 57 increase substantially beyond 3 MeV. This discrepancy
is due to the kerma approximation used in ICRP Publication 74/ICRU Report 57, which deposits theenergy of the secondary particles locally, while PHITS and FLUKA follow secondary particle transports.
This simpliﬁcation in ICRP Publication 74/ICRU Report 57 leads overestimation of ℎ∗ (10) above 3 MeV.

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2) Neutrons (Figure 5)
Figure 5 compares the ℎ∗ (10) values for neutrons with those reported in ICRP Publication 74 and
ICRU Report 57, which provide ℎ∗ (10) values for up to 201 MeV. Below 200 MeV, the ℎ∗ (10) values
from PHITS calculation are in close agreement with the values obtained from the FLUKA calculation
and reported in ICRP Publication 74/ICRU Report 57. However, above 200 MeV discrepancies arise
between values obtained in the PHITS and FLUKA calculations.
The divergence above 200 MeV can be attributed to diﬀerences of types and energies of secondary
particles produced by nuclear reactions. PHITS uses the INCL4.6 model in combination with GEM
for energies between 20 MeV and 3.5 GeV, while it uses the JAM model with GEM for energies above
3.5 GeV. Meanwhile, FLUKA uses three models to describe hadronic inelastic interactions depending on
projectile energy ranges above 20 MeV38). A speciﬁc model comprising an explicit intranuclear cascadestage and a pre-equilibrium stage based on a geometry-dependent excition approach is used for nucleons
with energies in the range of approximately 20 MeV–2 GeV. Primary interactions between 2 and 5 GeV
are described using resonance production and decay, while above 5 GeV interactions are simulated bymultichain fragmentation in the framework of the Dual Parton Model. Based on the nuclear reaction
models employed, the diﬀerences in the ℎ∗ (10) values are likely due to diﬀerences in energy deposition
at 10-mm depth within the ICRU sphere and/or diﬀerences in the energy spectra of the secondary charged
particles contributing 𝑄𝑄 values.
3) Negative and positive muons (Figures 9 and 10)
The PHITS and FLUKA results generally correlate for negative and positive muons over the entire
energy range. The energy dependence of the ℎ∗ (10) values calculated using PHITS shows a peak at
15 MeV of incident muons, corresponding to the range of a 15-MeV muon, which spans approximately
10 mm in ICRU soft tissue40) . The 15-MeV muon reaches the 10-mm depth region of the ICRU sphereand deposits its energy, resulting in the peak in the energy dependence of ℎ∗ (10). Because Pelliccioni
did not perform calculations between 10 and 50 MeV39) , this peak does not appear in the FLUKA results.
4) Negative and positive pions (Figures 11 and 12)
Figures 11 and 12 highlight the comparison of ℎ∗ (10) values for negative and positive pions, respectively, showing diﬀerences between PHITS and FLUKA results above 1 GeV. These diﬀerences could
be due to variations in the 𝑑𝑑 ∗ (10) values. For example, considering negative pions at 100 GeV, the
PHITS results of this study show ℎ∗ (10) and 𝑄𝑄 values of 1.45 × 10 −9 Sv cm2 and 1.93, respectively,
as shown in Table 9. In contrast, the corresponding values for FLUKA provided by Pelliccioni39) are
7.13 × 10−10 Sv cm2 and 1.7, respectively. The signiﬁcant diﬀerence in ℎ∗ (10) compared to the discrepancy in 𝑄𝑄 suggests a probable divergence in the 𝑑𝑑 ∗ (10) values, which could be due to the calculation of the
stopping power of the pions. Unfortunately, a more in-depth analysis is hampered because Pelliccioni’s
paper does not present the 𝑑𝑑 ∗ (10) values, making a comprehensive comparison impossible.
The energy dependence of the ℎ∗ (10) values calculated using PHITS shows a peak at 15 MeV for
negative and positive pions, corresponding to the range of 15-MeV pions, which is about 10 mm within
the ICRU sphere. Because Pelliccioni did not perform calculations between 10 and 50 MeV39) , this peakdoes not exist in the FLUKA results, as in the case of muons.

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3.1.2 Comparison of 𝒉𝒉∗max
Figures 14–22 present comparisons of the ℎ∗max values. Overall, the ℎ∗max values derived from PHITS
and FLUKA show substantial agreement for neutrons (Figure 15), electrons (Figure 16), positrons(Figure 17), protons (Figure 18), positive muons (Figure 20), and positive pions (Figure 22). However,noticeable discrepancies exist for photons (Figure 14), negative muons (Figure 19), and negative pions(Figure 21). These discrepancies are further investigated below to identify possible underlying causes.
1) Photons (Figure 14)
Figure 14 illustrates a noticeable diﬀerence in ℎ∗max for photons with incident energies between 10
and 20 keV. For low-energy photon incidence, ℎ∗max tends to concentrate in the frontal region facing
the incident photon direction, considerably aﬀecting the absorbed dose sensitivity due to scoring region
geometry.
Figure 23 shows the scoring region geometries used in the PHITS and FLUKA calculations, andabsorbed dose distribution in the frontal region facing the incident direction of 10-keV photons. In thisstudy using PHITS, a cylindrical scoring region with a radius of 0.5 cm was used for calculating absorbed
doses. By contrast, a larger radius of 1.0 cm was used in the FLUKA calculations33) . Speciﬁcally, inthe spherical geometry, a scoring region closer to the cylinder side reduces the distance from the surfaceof sphere. Thus, photons are more likely to reach the scoring region within the 1.0-cm radius than the
0.5-cm radius. The higher ℎ∗max values observed in the FLUKA results are attributed to this geometricdiﬀerence.
To conﬁrm this result, Figure 24 compares ℎ∗max calculated using the 0.5-cm radius scoring region
by FLUKA in this study, along with the results from FLUKA reported by Ferrari and Pelliccioni,
and PHITS. For a 0.5-cm radius scoring region, the PHITS and FLUKA calculations show excellent
agreement. Therefore, the discrepancy in ℎ∗max below 40 keV in Figure 14 is due to the choice of thescoring region radius.
2) Negative muons (Figure 19)
A remarkable diﬀerence is observed in ℎ∗max for negative muons at 1 MeV between PHITS and FLUKA.
At this incident energy, ℎ∗max is found in the frontal region (0.1–0.3 cm depth) facing the direction of
the incident muons. This discrepancy could be due to diﬀerences in the modeling of the negative muon
behavior within the two codes. A negative muon is captured by an atom in matter just before it stops,
resulting in the formation of a muonic atom. The captured muon cascades down to the 1s orbit, emitting
characteristic X-rays, and then decays in the 1s orbit or is captured by the nucleus.
While PHITS and FLUKA consider muon capture reactions, PHITS uses models that follow negative
muon capture in more detail30) . Conversely, FLUKA’s description of the muon capture reaction is notdescribed in the paper39) . Therefore, a more detailed analysis for the diﬀerence in ℎ∗max at 1 MeV between
PHITS and FLUKA is hampered by the lack of speciﬁc information.
3) Negative pions (Figure 21)
Noticeable discrepancy in ℎ∗max is observed for negative pions at 1 MeV between PHITS and FLUKA.
This discrepancy is due to diﬀerences in the modeling of the negative pion behavior within the two codes.
When a negative pion reaches its stopping point, it is typically captured by a nucleus, producing various-8-

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secondary charged particles. PHITS and FLUKA include this process, where charged particle types andtheir energy distribution inﬂuence the determination of 𝑄𝑄 values. The diﬀerences in 𝑄𝑄 values could be
due to the observed diﬀerences in ℎ∗max at 1 MeV between the two codes. However, the lack of detailed
descriptions for the speciﬁcs of each model or their validity makes further detailed discussion diﬃcult.
Furthermore, discrepancies in the ℎ∗max values appear from approximately 10 GeV and become more
pronounced with increasing energy. This escalation is thought to be due to diﬀerences in stopping power
calculation methods, as discussed in Section 3.1.1.
Sections 3.1.1 and 3.1.2 comprehensively compared the ℎ∗ (10) and ℎ∗max values calculated using
PHITS and FLUKA, showing good overall agreement. Cases of observed diﬀerences were clearly related
to diﬀerences in the transport and nuclear reaction models employed within PHITS and FLUKA. Hence,
it is important to acknowledge that the selection of these models may involve a degree of subjectivity.
Overall, the results lead to the conclusion that PHITS performs the calculations appropriately, given
the context of the observed agreement and identiﬁed sources of discrepancies due to model variations.

3.2

Overview of 𝒅𝒅 ∗ (10), 𝒉𝒉∗ (10), and 𝑸𝑸Tables 2–11 present the numerical values for 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄 for various particles — photons,
neutrons, electrons, positrons, protons, muons, pions, and helium ions. Figures 25–34 present two graphs
each: the upper graph illustrates the energy dependence of 𝑑𝑑 ∗ (10) and ℎ∗ (10) and lower graph shows 𝑄𝑄.
A brief review of the main characteristics of the energy dependence of the 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄 values
is given here.
1) Photons (Figure 25)
The values of 𝑑𝑑 ∗ (10) and ℎ∗ (10) for photons are almost same from 10 keV to 15 MeV. Within thisenergy range, photons interact primarily through the photoelectric eﬀect, Compton scattering, and pair(and triplet) production. Energy deposition occurs in matter is due to the energy transferred to andthen lost by electrons and positrons along their paths. Electrons and positrons can produce secondary
photons as bremsstrahlung and characteristic X-rays emitted after ionization and via particle annihilationof positrons. Because the 𝑄𝑄 values determined from the LET of electrons and positrons generated fromphotons in this energy range become one, 𝑑𝑑 ∗ (10) and ℎ∗ (10) have the same values.
However, ℎ∗ (10) shows two distinct peaks in the energy ranges 20 MeV–100 MeV and 200 MeV–3 GeV.
These peaks correspond to the 𝑄𝑄 values greater than one, which result from charged particles producedby photon-induced nuclear reactions.
2) Neutrons (Figure 26)
Neutrons interact with nuclei through various interactions, including scattering (elastic and inelastic
scatterings), absorption (capture, ﬁssion), and transfer reactions (neutron emission, charged particle
ejection). The cross-sections for these interactions vary with incident neutron energy and target nucleus.
The complexity of the neutron interactions aﬀects 𝑑𝑑 ∗ (10) values and LET distributions for the produced
charged particles. Consequently, this diversity in interactions and subsequent particle production leads
to variability in the values of 𝑄𝑄 and ℎ∗ (10) associated with the neutron energy, as shown in Figure 26.
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3) Electrons and positrons (Figures 27 and 28)
For electrons and positrons, a noticeable increase in the 𝑑𝑑 ∗ (10) and ℎ∗ (10) values occurs at approximately 2 MeV because electron and positron ranges in the ICRU sphere become about 10 mm. Above
this energy, the energy dependence of the 𝑑𝑑 ∗ (10) and ℎ∗ (10) values is small for electrons and positrons.
A distinct diﬀerence between electrons and positrons appears below 2 MeV. Positrons produce photons
via annihilation with electrons, considerably increasing the energy deposition. Hence, 𝑑𝑑 ∗ (10) values for
positrons substantially exceed than those of electrons due to the photon contribution to energy deposition.
Despite these diﬀerences, the value of 𝑄𝑄 remains close to one because the primary contributors to energy
deposition are predominantly electrons and positrons in this energy range.
4) Protons (Figure 29)
The values of 𝑑𝑑 ∗ (10) and ℎ∗ (10) for protons increase rapidly around 30 MeV because the range of
protons in the ICRU sphere becomes at approximately 10 mm. Beyond 300 MeV, the energy dependenceof the 𝑑𝑑 ∗ (10) and ℎ∗ (10) values is small.
The 𝑄𝑄 value increases gradually with increasing energy, except for a transient and sharp increase at
30 MeV. This phenomenon at 30 MeV is due to the LET distribution of protons within the ICRU sphere.
Figure 35 shows the LET distributions in the 10-mm depth region for incidence with 30- and 40-MeV
protons. As deﬁned in Figure 1, the 𝑄𝑄 values remain at one until 𝐿𝐿 = 10 keV 𝜇𝜇m−1 and then increase
to 30 as 𝐿𝐿 increases. For incidence of 30-MeV protons, the LET distribution of protons ranges from 3
to 80 keV 𝜇𝜇m−1 , with a peak observed at 15 keV 𝜇𝜇m−1 , where the 𝑄𝑄 value exceeds one, as indicated in
Figure 1. Conversely, for incidence of 40-MeV protons, the peak is observed between 2 and 3 keV 𝜇𝜇m −1
in the LET distribution of protons, where the 𝑄𝑄 value remains at one. The LET distribution shows thathigher LET protons also contribute to the energy deposition, but in a smaller proportion. A 30-MeV
proton shows elevated LET values for protons at 10-mm depth within the ICRU sphere, corresponding to
the position where it almost stops. As a result, this provokes a notable increase in the 𝑄𝑄 value, as shownin Figure 29.
5) Negative and positive muons (Figures 30 and 31)
The energy dependence of the 𝑑𝑑 ∗ (10) and ℎ∗ (10) values shows similarity with negative and positive
muons, with a peak at 15 MeV for incident muons. The range of the 15-MeV muon is approximately
10 mm in the ICRU soft tissue40) , and the 15-MeV muon deposits energy in the 10-mm depth region of
the ICRU sphere, resulting in a peak in the energy dependence of ℎ∗ (10). Regardless of muon energy,
the 𝑄𝑄 values remain consistently close to one, except for the low-energy negative muons where negative
muon capture occurs.
6) Negative and positive pions (Figures 32 and 33)
The energy dependence of 𝑑𝑑 ∗ (10) and ℎ∗ (10) shows a peak at 15 MeV for negative and positive pions.
This peak corresponds to the range of 15-MeV pions, which is approximately 10 mm within the ICRU
sphere. Above this energy, the energy dependence of 𝑑𝑑 ∗ (10) and ℎ∗ (10) is similar for negative andpositive pions.
Meanwhile, notable diﬀerences are observed in the energy dependence of the ℎ∗ (10) and 𝑄𝑄 values
below 15 MeV between negative and positive pions. These diﬀerences are due to the peculiar behaviorof negative pions. Upon reaching a rest state, negative pions are often captured by a nucleus, producing
charged particles that increase the 𝑄𝑄 and ℎ∗ (10) values.
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7) Helium ions (Figure 34)
The values of 𝑑𝑑 ∗ (10) and ℎ∗ (10) for helium ions show a rapid increase at energies above 30 MeV n−1 ,coinciding with a range of about 10 mm within the ICRU sphere. Beyond this energy, the energy
dependence of 𝑑𝑑 ∗ (10) and ℎ∗ (10) becomes relatively small.
The value of 𝑄𝑄 reaches a maximum at about 10 MeV n−1 and remains at about 1.5–2 for higher energy
ranges. This increase in 𝑄𝑄, peaking at 10 MeV n−1 , is attributed to the LET distribution of helium ions,contributing substantially to energy deposition.

3.3

Comparison of 𝑯𝑯 ∗ (10) and 𝑬𝑬 max

A comparison is made between 𝐻𝐻 ∗ (10), deﬁned in ICRU Reports 394) and 517) for area monitoring andused worldwide, and 𝐸𝐸 max , which represents the maximum value of eﬀective dose for diﬀerent directionsof incident particle on the anthropomorphic phantoms, as published in ICRP Publication 11614) . The
operational quantities are intended to provide a reasonable, generally conservative, estimate of theprotection quantity values associated with an exposure or a potential exposure of persons under various
irradiation conditions3) . The comparison in this section aims to analyze whether 𝐻𝐻 ∗ (10), the operational
quantity, meets the requirements for estimating 𝐸𝐸 max , the protection quantity for external exposures.
The comparison is performed using the dose coeﬃcients ℎ∗ (10) and 𝑒𝑒 max , normalized to the particle
ﬂuence deﬁned in Equations (8) and (5), respectively. The ℎ∗ (10) values were obtained from Tables 2–
11, while the 𝑒𝑒 max values were evaluated from the dataset of ICRP Publication 116. Note that, asdeﬁned in Equation (5), the 𝑒𝑒 max values are numerically equal to the ℎ∗ values tabulated in Tables 2–11.
Figures 36–45 graphically show the energy dependence of ℎ∗ (10) and 𝑒𝑒 max (upper graph) and their ratio,ℎ∗ (10)/𝑒𝑒 max (lower graph).
In the graph of ℎ∗ (10)/𝑒𝑒 max , a horizontal line is drawn at the point where the vertical axis equals
one. ℎ∗ (10) exceeds 𝑒𝑒 max for data points plotted above this line, indicating that the operational quantity
overestimates the protection quantity, consistent with the objectives of the operational quantity. However,extremely large values of ℎ∗ (10)/𝑒𝑒 max suggest an undesirable level of overestimation. Conversely, ℎ∗ (10)is less than 𝑒𝑒 max for data points below the line. In such cases, the operational quantity underestimates theprotection quantity, which is undesirable from a radiation monitoring perspective.
Detailed comparisons of ℎ∗ (10) and 𝑒𝑒 max for each particle are shown below.
1) Photons (Figure 36)
The values of ℎ∗ (10)/𝑒𝑒 max for photons are ≥ 1 in the energy range from 10 keV to 3 MeV. In particular,
at 15–50 keV, ℎ∗ (10)/𝑒𝑒 max is remarkably high, reaching a maximum of 5.3 at 15 keV. However, once theenergy exceeds 3 MeV, the ratios fall below one and decrease with increasing energy, dropping below 0.1
beyond 500 MeV. This suggests that 𝐻𝐻 ∗ (10) is unsuitable for evaluating 𝐸𝐸 max for energies above 3 MeV.
2) Neutrons (Figure 37)
The values of ℎ∗ (10)/𝑒𝑒 max for neutrons undergo complex variations depending on the neutron energy.
In the energy range from 1 × 10−9 to 2 MeV, the ratio is almost always greater than one, indicating that
𝐻𝐻 ∗ (10) conservatively estimates 𝐸𝐸 max . However, in the high-energy region beyond 50 MeV, the ratios
fall below one, indicating that 𝐻𝐻 ∗ (10) underestimates 𝐸𝐸 max .
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3) Electrons and positrons (Figures 38 and 39)
For electrons in the energy range from 100 keV to 1.5 MeV, the 𝑒𝑒 max values are considerably higher thanthose of ℎ∗ (10), resulting in ℎ∗ (10)/𝑒𝑒 max values becoming substantially lower than one. The increased
values of 𝑒𝑒 max for low-energy electrons are primarily due to the skin dose. This results from the direct
exposure of the skin region in the computational phantoms to the incident electrons14) , in contrast to thedepth of 10 mm in the ICRU sphere below 2 MeV. The values of ℎ∗ (10) increase sharply around 2 MeV,
because electrons reach the 10-mm depth in the ICRU sphere. Above 10 MeV, ℎ∗ (10) remains nearly
constant regardless of the incident electron energy, while 𝑒𝑒 max increases as electrons reach organs locateddeep inside the body. Hence, ℎ∗ (10)/𝑒𝑒 max for electrons is less than one from 100 keV to 2 MeV, exceeds
one from 3 to 30 MeV, and falls below one again beyond 40 MeV. Thus, 𝐻𝐻 ∗ (10) conservatively evaluates
𝐸𝐸 max only in the energy range from 3 MeV to 30 MeV.
For positrons, because photons produced by positron annihilation with electrons contribute to energy
deposition, the ℎ∗ (10) values exceed those of electrons below 2 MeV. The values of ℎ∗ (10)/𝑒𝑒 max remainslightly larger than one in the 100–600 keV range, in contrast to those of electrons. Above approximately
2 MeV, ℎ∗ (10) trend for positrons is similar to that of electrons.
4) Protons (Figure 40)
In the energy range from 10 to 30 MeV, the 𝑒𝑒 max values are much higher than those of ℎ∗ (10), resulting
in ℎ∗ (10)/𝑒𝑒 max values becoming remarkably lower than one. From 40 to 60 MeV, ℎ∗ (10)/𝑒𝑒 max exceeds
one, falling below one again above 80 MeV. Similar to electrons, the use of 𝐻𝐻 ∗ (10) for protons is limitedin the 40–60 MeV range for the conservative estimation of 𝐸𝐸 max .
5) Negative and positive muons (Figures 41 and 42)
The energy dependence of ℎ∗ (10) shows a peak at around 15 MeV for negative and positive muons,corresponding to the 10-mm range in the ICRU sphere. At other energies, energy dependence for negativeand positive muons is small. The values of ℎ∗ (10)/𝑒𝑒 max fall below one in the 40–150 MeV range and areclose to or greater than one at other energies for negative and positive muons.
6) Negative and positive pions (Figures 43 and 44)
Negative and positive pions show a peak at approximately 15 MeV in ℎ∗ (10), corresponding to the
10-mm range in the ICRU sphere. Above 15 MeV, the energy dependence of ℎ∗ (10) is similar for negativeand positive pions.
However, below 15 MeV, negative pions show higher ℎ∗ (10) values than positive pions due to the behavior of negative pions described in Section 3.1.2. Figures 43 and 44 reveal that 𝐻𝐻 ∗ (10) underestimates
𝐸𝐸 max in several energy regions for negative and positive pions.
7) Helium ions (Figure 45)
The ℎ∗ (10) values increase sharply between 30 and 50 MeV n−1 , corresponding to the 10-mm range ofhelium ions in the ICRU sphere. At the lower energies, ℎ∗ (10) is considerably smaller than 𝑒𝑒 max . Even
above 50 MeV n −1 , ℎ∗ (10) remains an order of magnitude smaller than 𝑒𝑒 max , indicating that 𝐻𝐻 ∗ (10) is
not suitable for evaluating 𝐸𝐸 max for helium ions.

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The main points of the comparison between 𝐻𝐻 ∗ (10) and 𝐸𝐸 max for all particles discussed in this section
are as follows. The energy dependence of ℎ∗ (10) and 𝑒𝑒 max is determined by the interaction propertiesof each particle in matter. Hence, the ℎ∗ (10)/𝑒𝑒 max values demonstrate a complex and diﬀerent energy
dependence for each particle. While 𝐻𝐻 ∗ (10) conservatively estimates 𝐸𝐸 max to a reasonable extent in certain
energy regions, it greatly overestimates or underestimates 𝐸𝐸 max in many other energy regions. Basedon the requirement that the operational quantities provide a reasonable estimate, generally conservative,of the protection quantity values under most irradiance conditions, it can be concluded that 𝐻𝐻 ∗ (10) has
limitations for assessing 𝐸𝐸 max for all irradiance types and energy ranges provided in ICRP Publication 116.

∗
3.4 Comparison of 𝑯𝑯max
and 𝑬𝑬 max

In Section 3.3, limitations were identiﬁed regarding 𝐻𝐻 ∗ (10) for evaluating 𝐸𝐸 max . This section explores∗
can serve as an alternative operational quantity for evaluating 𝐸𝐸 max by analyzing the energy
whether 𝐻𝐻max
dependence of their dose coeﬃcients ℎ∗max and 𝑒𝑒 max and their ratio ℎ∗max /𝑒𝑒 max for each particle.
The ℎ∗max values were obtained from Tables 2–11, while the 𝑒𝑒 max values were evaluated from thedataset of ICRP Publication 11614) . Figures 46–55 illustrate the energy dependence of ℎ∗max and 𝑒𝑒 max(upper graph) and ℎ∗max /𝑒𝑒 max (lower graph). A horizontal line in the ℎ∗max /𝑒𝑒 max graph represents the point
where the vertical axis equals one. ℎ∗max exceeds 𝑒𝑒 max for data points above this line, representing an
overestimation of the protection quantity by the operational quantity. Conversely, data points below theline indicate an underestimation, which is undesirable for radiation monitoring.
1) Photons (Figure 46)∗
conservatively estimates 𝐸𝐸 max over all energy ranges. However, a
The ℎ∗max /𝑒𝑒 max plot shows that 𝐻𝐻max
signiﬁcant overestimation occurs for energies below 50 keV, especially at 10 keV by a factor of 46.

2) Neutrons (Figure 47)
Although the values of ℎ∗max /𝑒𝑒 max mostly exceed one, they fall below one for a limited energy range.
∗
𝐻𝐻max increasingly overestimates 𝐸𝐸 max as the neutron energy decreases towards 1 × 10−9 MeV.
3) Electrons and positrons (Figures 48 and 49)
For electrons, the ℎ∗max values are considerably smaller than those of 𝑒𝑒 max below 30 keV, but they aresubstantially higher by up to two orders of magnitude from 40 keV to 10 MeV.
∗
generally overestimates 𝐸𝐸 max and a subFor positrons, the ℎ∗max /𝑒𝑒 max graph demonstrates that 𝐻𝐻max
stantial overestimation occurs in the 500 keV–3 MeV energy range.
4) Protons (Figure 50)
The ℎ∗max /𝑒𝑒 max values fall slightly below one for a limited energy range; however, their values mostly
exceed one excessively below 50 MeV.

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5) Negative and positive muons (Figures 51 and 52)
Negative and positive muons have ℎ∗max /𝑒𝑒 max values below one for a limited range; however, theirvalues are generally above one, with excessive highs between 4 and 15 MeV.
6) Negative and positive pions (Figures 53 and 54)
The ℎ∗max /𝑒𝑒 max values exceed one for negative and positive pions over a wide energy range, and thevalues are especially high below 100 MeV for negative pions.
7) Helium ions (Figure 55)
For helium ions, the ℎ∗max /𝑒𝑒 max values are mostly below one except for the 10–50 MeV n−1 energy∗
underestimates 𝐸𝐸 max . The degree of underestimation varies with the incident
range, indicating that 𝐻𝐻max
energy of helium ions.
∗and 𝐸𝐸 max for all particles discussed in this section are
The main points of the comparison between 𝐻𝐻max∗
as follows. The use of 𝐻𝐻max , which is the maximum dose equivalent along the central axis of the ICRU
sphere, reduces the underestimation of 𝐸𝐸 max over a wide energy range compared to 𝐻𝐻 ∗ (10). However,∗∗generally tends to overestimate 𝐸𝐸 max . Moreover, for certain energy ranges and particles, 𝐻𝐻max
shows
𝐻𝐻max
extreme overestimation of 𝐸𝐸 max , especially in the low-energy region of incident particles, reaching two∗
is notor three orders of magnitude, leading to excessive radiation protection measures. Therefore, 𝐻𝐻max
suitable for evaluating 𝐸𝐸 max for all particles presented in ICRP Publication 116.

3.5 Comparison of 𝑯𝑯 ∗ and 𝑬𝑬
ICRU Report 9515) introduced the concept of ambient dose, 𝐻𝐻 ∗ , as an operational quantity for area
monitoring to address the limitations associated with 𝐻𝐻 ∗ (10). 𝐻𝐻 ∗ is deﬁned as the maximum eﬀective
dose, 𝐸𝐸 max , calculated for various directions of particle incidence in radiation protection contexts; hence
𝐻𝐻 ∗ = 𝐸𝐸 max . This concept is considerably diﬀerent from ICRU Reports 394) and 517) , where the numericalvalues of the operational quantity are based on the dose equivalent at a ﬁxed depth in the ICRU 4-element
sphere. 𝐻𝐻 ∗ is directly related to the eﬀective dose values and will therefore provide a better estimate of
the protection quantity. 𝐻𝐻 ∗ usage simpliﬁes systems of protection and operational quantities and helps
users to understand the radiological protection quantities.
Here, a comparison is made between 𝐻𝐻 ∗ and 𝐸𝐸 for two representative irradiation geometries, antero–posterior (AP) and isotropic (ISO), using their dose coeﬃcients, ℎ∗ , 𝑒𝑒 AP , and 𝑒𝑒 ISO , respectively. AP
irradiation represents a state where a worker is facing a radiation source, while ISO irradiation represents
a situation where a worker is exposed in a highly scattered radiation ﬁeld and/or facing various directions.
Each of Figures 56–65 presents two graphs: the upper graph shows the dose coeﬃcients for eﬀective
dose, 𝑒𝑒, obtained from ICRP Publication 11614) for diﬀerent irradiation geometries, including theirmaximum values, 𝑒𝑒 max , and lower graph shows the ratios, ℎ∗ /𝑒𝑒 AP and ℎ∗ /𝑒𝑒 ISO . Additionally, as deﬁned
in Equation (5), the 𝑒𝑒 max values are numerically equal to the ℎ∗ values provided in Tables 2–11.
In the graphs of ℎ∗ /𝑒𝑒, a horizontal line at the value of one indicates that ℎ∗ is equal to 𝑒𝑒 AP and 𝑒𝑒 ISO .
Data points above this line correspond to ℎ∗ higher than 𝑒𝑒 AP and 𝑒𝑒 ISO , implying that the protection
quantity 𝐸𝐸 is overestimated by the operational quantity 𝐻𝐻 ∗ . Conversely, data points below one imply that- 14 -

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𝐻𝐻 ∗ underestimates 𝐸𝐸, although it is theoretically impossible for ℎ∗ /𝑒𝑒 AP and ℎ∗ /𝑒𝑒 ISO to fall below one asℎ∗ is deﬁned based on 𝑒𝑒 max .
1) Photons (Figure 56)ℎ∗ /𝑒𝑒 AP and ℎ∗ /𝑒𝑒 ISO intersect at approximately 10 MeV. Below 10 MeV, the eﬀective dose for AP
irradiation is maximized among all geometries, leading to the coincidence of ℎ∗ and 𝑒𝑒 AP . Conversely, theℎ∗ values exceed those of 𝑒𝑒 ISO . As the energy exceeds 10 MeV, photons penetrate deeply into the human
body, causing the eﬀective dose for ISO irradiation to exceed that for AP irradiation. Consequently,ℎ∗ /𝑒𝑒 ISO approaches one, while the ratios of ℎ∗ /𝑒𝑒 AP exceed one.
Over the entire energy range, the operational quantity 𝐻𝐻 ∗ consistently overestimates eﬀective dose 𝐸𝐸,with the magnitude of the overestimation reaching a maximum of 3.4 times for ℎ∗ /𝑒𝑒 AP at 10 GeV.
2) Neutrons (Figure 57)
The 𝑒𝑒 values for neutrons (upper graph) are dependent on the incident direction and energy, ranging
from 1 × 10 −9 to 100 MeV. However, beyond 100 MeV, these values show a reduced dependence on theincident direction and energy of neutrons.
The lower graph shows that ℎ∗ /𝑒𝑒 AP and ℎ∗ /𝑒𝑒 ISO intersect at about 100 MeV. Similar to photons, theeﬀective dose for AP irradiation is maximized among all geometries up to about 100 MeV. Beyond thisenergy, the eﬀective dose for ISO irradiation exceeds that for AP irradiation.
Over the entire energy range, 𝐻𝐻 ∗ consistently overestimates 𝐸𝐸. This overestimation reaches a maximumof 2.4 times for ℎ∗ /𝑒𝑒 AP at 1 × 10−9 MeV.
3) Electrons and positrons (Figures 58 and 59)
For electrons and positrons, the 𝑒𝑒 values for AP irradiation are maximized in the energy range from
10 keV to 100 MeV, making the ℎ∗ /𝑒𝑒 AP values are equal to one. Above 100 MeV, the 𝑒𝑒 ISO values become
higher than those of 𝑒𝑒 AP .
While the ℎ∗ /𝑒𝑒 values vary with the incident energy of electrons and positrons, their peak values reach
3.1 for ℎ∗ /𝑒𝑒 ISO at 2 MeV for electrons and 3.0 for ℎ∗ /𝑒𝑒 ISO at 2 MeV for positrons.
4) Protons (Figure 60)
The 𝑒𝑒 values for protons are dependent on the incident direction and energy between 1 and 200 MeV.
However, the values show less dependence on the incident direction and energy of protons beyond
200 MeV. The range of 200-MeV protons in the human body is approximately 26 cm and passes throughthe trunk, resulting in reduced directional dependence.
While the values of ℎ∗ /𝑒𝑒 AP and ℎ∗ /𝑒𝑒 ISO vary with the energy of the incident protons, the maximum
value reaches 3.1 for ℎ∗ /𝑒𝑒 ISO at 20 MeV.
5) Negative and positive muons (Figures 61 and 62)
The energy dependence of 𝑒𝑒 for negative and positive muons is quite similar, as shown in Figures 61
and 62, respectively. Up to 60 MeV, the 𝑒𝑒 values depend on the incident direction and energy of muons.
However, beyond this energy, the values of 𝑒𝑒 become less dependent on the incident direction and energyof muons, as they penetrate through the trunk.
For negative and positive muons, the peak value reaches 2.6 for ℎ∗ /𝑒𝑒 ISO at 10 MeV and the ℎ∗ /𝑒𝑒 AP andℎ∗ /𝑒𝑒 ISO values are nearly one above 100 MeV.
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JAEA-Research 2024-002

6) Negative and positive pions (Figures 63 and 64)
The 𝑒𝑒 values for negative and positive pions depend on the incident direction and energy of pions. The
maximum value of ℎ∗ /𝑒𝑒 reaches 3.0 for ℎ∗ /𝑒𝑒 ISO at 8 MeV for negative pions, while that of positive pions
reaches 2.8 for ℎ∗ /𝑒𝑒 ISO at 10 MeV.
7) Helium ions (Figure 65)
The 𝑒𝑒 values for helium ions are dependent on the incident direction of the helium ion between 15 and150 MeV n−1 . However, as the energy reaches 200 MeV n −1 , the range of helium ions extends across thetrunk, leading to a reduced directional dependence of the 𝑒𝑒 values.
The observed peak of ℎ∗ /𝑒𝑒 for helium ions reaches 3.2 for ℎ∗ /𝑒𝑒 ISO at 20 MeV n −1 .
The main points of the comparison between 𝐻𝐻 ∗ and 𝐸𝐸 for all particles discussed in this section are as
follows. Because 𝐻𝐻 ∗ is deﬁned as the maximum eﬀective dose, 𝐸𝐸 max , calculated for various directions ofparticle incidence, it does not underestimate 𝐸𝐸. 𝐻𝐻 ∗ reasonably estimates 𝐸𝐸 for the AP and ISO incident
conditions, which are typical workplace irradiation geometries. Although occasional overestimation of
𝐸𝐸 by 𝐻𝐻 ∗ may occur, such instances are limited to a factor of 3 or less. This would be acceptable than∗often overestimates 𝐸𝐸 by two or three orders of magnitude.
situations where 𝐻𝐻 ∗ (10) or 𝐻𝐻max

3.6 Discussion on appropriate quantity for use in area monitoring for assessment ofeﬀective dose from external radiation
Sections 3.3–3.5 compared the relationship between three quantities used for area monitoring —∗ , and ambient dose 𝐻𝐻 ∗ — and eﬀective
ambient dose equivalent 𝐻𝐻 ∗ (10), maximum dose equivalent 𝐻𝐻max
dose 𝐸𝐸 for external irradiation from various particles, including photons, neutrons, electrons, positrons,
protons, muons, pions, and helium ions.
The ambient dose equivalent 𝐻𝐻 ∗ (10) is deﬁned as the dose equivalent at a ﬁxed depth of 10 mm in
the ICRU sphere irradiated in the expanded and aligned ﬁeld. The eﬀective dose 𝐸𝐸 is deﬁned as theweighted sum of absorbed doses for all speciﬁed organs and tissues in the human body irradiated from
diﬀerent directions. Comparison of the dose coeﬃcients for 𝐻𝐻 ∗ (10) and 𝐸𝐸, ℎ∗ (10) and 𝑒𝑒, respectively,
shows that the ℎ∗ (10) and 𝑒𝑒 values have diﬀerent energy dependencies for each particle. Hence, 𝐻𝐻 ∗ (10)underestimates or overestimates 𝐸𝐸 under many conditions of the type and energy of incident particles.
∗ , deﬁned as the maximum value of theCompared with 𝐻𝐻 ∗ (10), the maximum dose equivalent 𝐻𝐻max
dose equivalent along the central axis of the ICRU sphere, reduces the underestimation of 𝐸𝐸. However,∗tends to extremely overestimate 𝐸𝐸, especially for the incidence of low-energy particles.
𝐻𝐻max
The comparative analysis across all particles highlights the consistent and conservative nature of 𝐻𝐻 ∗in the evaluation of 𝐸𝐸 for various incident directions and particle energies provided in ICRP Publication 11614) . While 𝐻𝐻 ∗ overestimates 𝐸𝐸 occasionally, such instances are limited to a factor of 3 or less.
∗ , which exhibit signiﬁcant underestimation or overestimation of 𝐸𝐸 by two or three
Unlike 𝐻𝐻 ∗ (10) and 𝐻𝐻max
orders of magnitude, overestimation by 𝐻𝐻 ∗ is more controlled. The potential for extreme overestimation∗
can lead to unwarranted and excessive radiation protection measures. Therefore,
in 𝐻𝐻 ∗ (10) and 𝐻𝐻max∗
𝐻𝐻 is aligned with the criteria of the operational quantity, aiming to provide a reasonable, generally
conservative, estimate of the protection quantity values for various exposure scenarios3) .
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JAEA-Research 2024-002

Consequently, 𝐻𝐻 ∗ emerges as a suitable candidate for evaluating 𝐸𝐸 over all radiation types and energy
ranges presented in ICRP Publication 116. This conﬁrms the decision of the ICRU Report Committee 26
to adopt 𝐻𝐻 ∗ for area monitoring.

4 Conclusion

4 Conclusion

The present study analyzed the relationship between three quantities used for area monitoring —∗ , and ambient dose 𝐻𝐻 ∗ — and eﬀective
ambient dose equivalent 𝐻𝐻 ∗ (10), maximum dose equivalent 𝐻𝐻max
dose 𝐸𝐸 for external irradiation from various particles, including photons, neutrons, electrons, positrons,∗ , andprotons, muons, pions, and helium ions. The analysis reveals limitations of 𝐻𝐻 ∗ (10) and 𝐻𝐻max
highlights the superiority of 𝐻𝐻 ∗ for estimating 𝐸𝐸 over various particle types and energy ranges covered
in ICRP Publication 116. The results support the use of 𝐻𝐻 ∗ for area monitoring due to its tendency to∗ . Radiation
provide a controlled margin of overestimation in estimating 𝐸𝐸 compared to 𝐻𝐻 ∗ (10) and 𝐻𝐻max∗
can result in substantial underestimation or overestimation of 𝐸𝐸, while
monitoring using 𝐻𝐻 ∗ (10) and 𝐻𝐻max∗
𝐻𝐻 provides a more consistent estimate that is more in line with protection quantities. The conclusionof this study supports the decision of the Report Committee 26 of ICRU to recommend 𝐻𝐻 ∗ for theestimation of 𝐸𝐸 for various exposure scenarios. This recommendation provides reasonable estimates of
𝐸𝐸 in radiation monitoring, particularly in situations where various types of radiation are encountered,such as the use of radiation in the medical and academic ﬁelds and exposure in aviation. The proposed
adoption of 𝐻𝐻 ∗ increases the reliability of practical radiation monitoring and ensures more eﬀective andappropriate radiation protection measures.

Acknowledgements
The author is grateful to the members, consultants, and sponsors of the ICRU Report Committee 26
for their support and fruitful discussions. The calculations described in this report were performed on
the HPE SGI8600 supercomputer at the Center for Computational Science & e-Systems, Japan Atomic
Energy Agency.

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JAEA-Research 2024-002

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Table 1 Particles and energy ranges for calculation of dose coeﬃcients.
Particle type

Lower energy (MeV)

Upper energy (MeV)

Photon1.0E-02

1.0E+04

Neutron

1.0E-09

1.0E+04

Electron

1.0E-01

1.0E+04

Positron

1.0E-01

1.0E+04

Proton1.0E+01

1.0E+04

Negative muon

1.0E+00

1.0E+04

Positive muon

1.0E+00

1.0E+04

Negative pion

1.0E+00

2.0E+05

Positive pion

1.0E+00

2.0E+05

Helium ion‡

2.0E+00

1.0E+05‡ The unit of energy for helium ion is MeV n −1 (MeV per nucleon).

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JAEA-Research 2024-002

Table 2 Photons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV
1.0E-02
1.5E-022.0E-02
3.0E-02
4.0E-02
5.0E-02
6.0E-02
7.0E-028.0E-02
1.0E-01
1.5E-01
2.0E-01
3.0E-01
4.0E-01
5.0E-01
6.0E-01
8.0E-01
1.0E+00
1.5E+00
2.0E+00
3.0E+00
4.0E+00
5.0E+00
6.0E+00
8.0E+00
1.0E+01
1.5E+01
2.0E+01
3.0E+01
4.0E+01
5.0E+01
6.0E+01
8.0E+01
1.0E+02
1.5E+02
2.0E+02
3.0E+02
4.0E+02
5.0E+02
6.0E+02
8.0E+02𝑑𝑑 ∗ (10) / Gy cm2

6.90E-14
8.25E-13
1.01E-12
8.22E-13
6.30E-13
5.15E-13
5.14E-13
5.30E-13
5.49E-13
6.22E-13
8.98E-13
1.21E-12
1.76E-12
2.39E-12
2.90E-12
3.31E-12
4.23E-12
5.26E-12
7.12E-12
8.50E-12
1.03E-11
1.09E-11
1.04E-11
1.02E-11
9.48E-12
8.74E-12
8.44E-12
8.48E-12
8.88E-12
9.10E-12
9.23E-12
9.43E-12
9.98E-12
9.93E-12
1.00E-11
1.05E-11
1.28E-11
1.35E-11
1.29E-11
1.29E-11
1.29E-11ℎ∗ (10) / Sv cm2

6.90E-14
8.25E-13
1.01E-12
8.22E-13
6.30E-13
5.15E-13
5.14E-13
5.30E-13
5.49E-13
6.22E-13
8.98E-13
1.21E-12
1.76E-12
2.39E-12
2.90E-12
3.31E-12
4.23E-12
5.26E-12
7.12E-12
8.50E-12
1.03E-11
1.09E-11
1.04E-11
1.02E-11
9.48E-12
8.74E-12
8.44E-12
9.20E-12
1.36E-11
1.49E-11
1.13E-11
9.73E-12
1.11E-11
1.03E-11
1.01E-11
1.07E-11
1.90E-11
2.15E-11
1.73E-11
1.76E-11
1.62E-11‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 22 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.09
1.53
1.63
1.22
1.03
1.11
1.04
1.01
1.02
1.49
1.59
1.34
1.37
1.26

3.12E-12
2.51E-12
1.67E-12
9.23E-13
6.72E-13
5.59E-13
5.27E-13
5.34E-13
5.53E-13
6.29E-13
9.07E-13
1.23E-12
1.88E-12
2.46E-12
3.03E-12
3.53E-12
4.70E-12
5.44E-12
7.12E-12
8.60E-12
1.09E-11
1.34E-11
1.49E-11
1.71E-11
2.12E-11
2.44E-11
3.34E-11
4.15E-11
6.13E-11
7.71E-11
8.94E-11
1.04E-10
1.28E-10
1.50E-10
1.95E-10
2.23E-10
2.65E-10
2.93E-10
3.11E-10
3.26E-10
3.48E-10

6.85E-14
1.56E-13
2.25E-13
3.12E-13
3.50E-13
3.69E-13
3.89E-13
4.11E-13
4.43E-13
5.18E-13
7.47E-13
1.00E-12
1.51E-12
2.00E-12
2.47E-12
2.91E-12
3.73E-12
4.49E-12
6.12E-12
7.48E-12
9.75E-12
1.17E-11
1.34E-11
1.50E-11
1.86E-11
2.21E-11
3.04E-11
3.82E-11
5.13E-11
6.18E-11
7.23E-11
8.21E-11
9.81E-11
1.10E-10
1.30E-10
1.44E-10
1.61E-10
1.73E-10
1.81E-10
1.87E-10
1.96E-10

JAEA-Research 2024-002

Table 2 (Continued).
𝐸𝐸 p / MeV
1.0E+03
1.5E+03
2.0E+03
3.0E+03
4.0E+03
5.0E+03
6.0E+03
8.0E+03
1.0E+04𝑑𝑑 ∗ (10) / Gy cm2

1.30E-11
1.30E-11
1.31E-11
1.32E-11
1.32E-11
1.32E-11
1.32E-11
1.32E-11
1.33E-11ℎ∗ (10) / Sv cm2

1.64E-11
1.62E-11
1.59E-11
1.61E-11
1.57E-11
1.53E-11
1.54E-11
1.49E-11
1.54E-11‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 23 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.27
1.24
1.22
1.22
1.19
1.16
1.17
1.13
1.16

3.66E-10
3.97E-10
4.18E-10
4.48E-10
4.70E-10
4.87E-10
5.01E-10
5.22E-10
5.39E-10

2.06E-10
2.13E-10
2.36E-10
2.53E-10
2.67E-10
2.77E-10
2.85E-10
2.99E-10
3.07E-10

JAEA-Research 2024-002

Table 3 Neutrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV
1.0E-09
1.0E-08
2.5E-08
1.0E-072.0E-07
5.0E-07
1.0E-06
2.0E-06
5.0E-06
1.0E-05
2.0E-05
5.0E-05
1.0E-04
2.0E-04
5.0E-04
1.0E-032.0E-035.0E-03
1.0E-022.0E-02
3.0E-02
5.0E-02
7.0E-02
1.0E-01
1.5E-01
2.0E-01
3.0E-01
5.0E-01
7.0E-01
9.0E-01
1.0E+00
1.2E+00
1.5E+00
2.0E+00
3.0E+00
4.0E+00
5.0E+00
6.0E+00
7.0E+00
8.0E+00
9.0E+00

𝑑𝑑 ∗ (10) / Gy cm2

1.67E-12
2.13E-12
2.39E-12
2.91E-12
3.01E-12
3.07E-12
3.21E-12
3.20E-12
3.13E-12
3.01E-12
2.86E-12
2.77E-12
2.66E-12
2.64E-12
2.46E-12
2.47E-12
2.42E-12
2.45E-12
2.69E-12
3.10E-12
3.70E-12
4.59E-12
5.41E-12
6.72E-12
8.62E-12
1.06E-11
1.33E-11
1.80E-11
2.20E-11
2.57E-11
2.82E-11
2.80E-11
3.03E-11
3.58E-11
4.21E-11
4.94E-11
4.84E-11
4.78E-11
5.14E-11
5.48E-11
5.91E-11ℎ∗ (10) / Sv cm2

6.42E-12
9.08E-12
1.09E-11
1.28E-11
1.31E-11
1.26E-11
1.35E-11
1.24E-11
1.14E-11
1.07E-11
1.01E-11
9.71E-12
9.31E-12
9.07E-12
7.83E-12
7.89E-12
8.02E-12
7.73E-12
9.59E-12
1.45E-11
2.06E-11
3.56E-11
5.16E-11
7.68E-11
1.19E-10
1.58E-10
2.23E-10
3.04E-10
3.55E-10
4.05E-10
4.46E-10
4.13E-10
4.18E-10
4.37E-10
4.30E-10
4.51E-10
3.86E-10
3.43E-10
3.44E-10
3.61E-10
4.30E-10‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 24 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

3.84
4.26
4.57
4.42
4.37
4.12
4.21
3.89
3.64
3.57
3.52
3.51
3.51
3.44
3.18
3.20
3.31
3.16
3.56
4.68
5.58
7.75
9.54
11.42
13.84
14.93
16.83
16.89
16.16
15.76
15.81
14.76
13.79
12.22
10.21
9.11
7.98
7.18
6.69
6.59
7.28

1.73E-11
1.50E-11
1.24E-11
1.28E-11
1.37E-11
1.41E-11
1.49E-11
1.47E-11
1.45E-11
1.45E-11
1.44E-11
1.41E-11
1.35E-11
1.34E-11
1.30E-11
1.26E-11
1.25E-11
1.20E-11
1.22E-11
1.77E-11
2.84E-11
5.08E-11
7.39E-11
1.05E-10
1.58E-10
2.01E-10
2.69E-10
3.28E-10
3.76E-10
4.22E-10
5.11E-10
4.47E-10
4.49E-10
4.44E-10
4.38E-10
4.72E-10
4.14E-10
3.97E-10
3.86E-10
3.89E-10
4.44E-10

3.09E-12
3.55E-12
4.00E-12
5.20E-12
5.87E-12
6.59E-12
7.03E-12
7.39E-12
7.71E-12
7.82E-12
7.84E-12
7.82E-12
7.79E-12
7.73E-12
7.54E-12
7.54E-12
7.61E-12
7.97E-12
9.11E-12
1.22E-11
1.57E-11
2.30E-11
3.06E-11
4.19E-11
6.06E-11
7.88E-11
1.14E-10
1.77E-10
2.32E-10
2.79E-10
3.01E-10
3.30E-10
3.65E-10
4.07E-10
4.58E-10
4.83E-10
4.94E-10
4.98E-10
4.99E-10
4.99E-10
5.00E-10

JAEA-Research 2024-002

Table 3 (Continued).
𝐸𝐸 p / MeV
1.0E+01
1.2E+01
1.4E+01
1.5E+01
2.1E+01
3.0E+01
5.0E+01
7.5E+01
1.0E+02
1.3E+02
1.5E+02
1.8E+02
2.0E+02
3.0E+02
4.0E+02
5.0E+02
6.0E+02
7.0E+02
8.0E+02
9.0E+02
1.0E+03
2.0E+03
5.0E+03
1.0E+04𝑑𝑑 ∗ (10) / Gy cm2

6.55E-11
6.83E-11
7.28E-11
7.28E-11
6.90E-11
7.26E-11
6.46E-11
5.50E-11
5.10E-11
4.88E-11
4.84E-11
4.93E-11
5.01E-11
5.54E-11
6.17E-11
7.19E-11
7.99E-11
8.70E-11
9.23E-11
9.44E-11
9.85E-11
1.08E-10
1.33E-10
1.44E-10ℎ∗ (10) / Sv cm2

4.94E-10
4.84E-10
5.49E-10
5.39E-10
4.78E-10
4.65E-10
3.69E-10
3.25E-10
3.21E-10
3.15E-10
3.20E-10
3.29E-10
3.41E-10
3.73E-10
4.24E-10
4.65E-10
5.01E-10
5.38E-10
5.51E-10
5.53E-10
5.56E-10
5.81E-10
6.77E-10
7.00E-10‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 25 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

7.55
7.09
7.55
7.41
6.93
6.41
5.72
5.91
6.29
6.44
6.61
6.67
6.80
6.73
6.87
6.46
6.27
6.18
5.96
5.86
5.65
5.36
5.08
4.86

5.12E-10
4.99E-10
5.49E-10
5.63E-10
5.14E-10
4.92E-10
4.28E-10
3.91E-10
3.95E-10
4.09E-10
4.17E-10
4.33E-10
4.41E-10
4.89E-10
5.52E-10
6.32E-10
6.91E-10
7.46E-10
7.73E-10
7.89E-10
8.13E-10
8.99E-10
1.30E-09
1.71E-09

5.00E-10
4.99E-10
4.95E-10
4.93E-10
4.74E-10
4.53E-10
4.33E-10
4.39E-10
4.44E-10
4.46E-10
4.46E-10
4.47E-10
4.48E-10
4.73E-10
5.15E-10
5.33E-10
5.69E-10
6.25E-10
6.38E-10
6.45E-10
6.63E-10
7.69E-10
1.04E-09
1.39E-09

JAEA-Research 2024-002

Table 4 Electrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV
1.0E-01
1.5E-01
2.0E-01
3.0E-01
4.0E-01
5.0E-01
6.0E-01
8.0E-01
1.0E+00
1.5E+00
2.0E+00
3.0E+00
4.0E+00
5.0E+00
6.0E+00
8.0E+00
1.0E+01
1.5E+01
2.0E+01
3.0E+01
4.0E+01
5.0E+01
6.0E+01
8.0E+01
1.0E+02
1.5E+02
2.0E+02
3.0E+02
4.0E+02
5.0E+02
6.0E+02
8.0E+02
1.0E+03
1.5E+03
2.0E+03
3.0E+03
4.0E+03
5.0E+03
6.0E+03
8.0E+03
1.0E+04𝑑𝑑 ∗ (10) / Gy cm2

7.28E-16
1.41E-15
2.17E-15
4.38E-15
6.97E-15
1.04E-14
1.49E-14
2.50E-14
3.78E-14
8.38E-14
7.35E-12
3.26E-10
4.47E-10
4.27E-10
3.85E-10
3.53E-10
3.27E-10
3.19E-10
3.16E-10
3.11E-10
3.11E-10
3.11E-10
3.13E-10
3.12E-10
3.09E-10
3.14E-10
3.07E-10
3.14E-10
3.12E-10
3.11E-10
3.16E-10
3.10E-10
3.12E-10
3.11E-10
3.11E-10
3.11E-10
3.16E-10
3.06E-10
3.11E-10
3.11E-10
3.21E-10ℎ∗ (10) / Sv cm2

7.27E-16
1.41E-15
2.17E-15
4.38E-15
6.97E-15
1.04E-14
1.49E-14
2.50E-14
3.78E-14
8.38E-14
7.35E-12
3.26E-10
4.47E-10
4.27E-10
3.85E-10
3.53E-10
3.27E-10
3.19E-10
3.16E-10
3.11E-10
3.11E-10
3.11E-10
3.13E-10
3.12E-10
3.09E-10
3.14E-10
3.07E-10
3.18E-10
3.12E-10
3.11E-10
3.16E-10
3.10E-10
3.12E-10
3.11E-10
3.11E-10
3.11E-10
3.16E-10
3.06E-10
3.11E-10
3.11E-10
3.21E-10‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 26 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.01
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00

3.05E-15
5.57E-15
8.24E-15
1.58E-14
1.82E-11
1.00E-10
2.02E-10
4.00E-10
5.07E-10
4.90E-10
4.98E-10
4.66E-10
4.47E-10
4.36E-10
4.30E-10
4.14E-10
3.80E-10
3.69E-10
3.52E-10
3.46E-10
3.48E-10
3.51E-10
3.53E-10
3.59E-10
3.63E-10
3.99E-10
4.36E-10
4.86E-10
5.30E-10
5.75E-10
6.00E-10
6.38E-10
6.76E-10
7.70E-10
8.11E-10
8.78E-10
9.52E-10
9.72E-10
1.08E-09
1.09E-09
1.17E-09

2.75E-13
4.18E-13
5.69E-13
8.89E-13
1.24E-12
1.63E-12
2.05E-12
4.04E-12
7.10E-12
1.50E-11
2.24E-11
3.61E-11
4.82E-11
5.93E-11
7.06E-11
9.79E-11
1.25E-10
1.88E-10
2.36E-10
3.02E-10
3.29E-10
3.37E-10
3.44E-10
3.58E-10
3.66E-10
3.79E-10
3.88E-10
4.11E-10
4.35E-10
4.49E-10
4.64E-10
4.88E-10
5.08E-10
5.25E-10
5.68E-10
6.08E-10
6.38E-10
6.61E-10
6.83E-10
7.16E-10
7.42E-10

JAEA-Research 2024-002

Table 5 Positrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV
1.0E-01
1.5E-01
2.0E-01
3.0E-01
4.0E-01
5.0E-01
6.0E-01
8.0E-01
1.0E+00
1.5E+00
2.0E+00
3.0E+00
4.0E+00
5.0E+00
6.0E+00
8.0E+00
1.0E+01
1.5E+01
2.0E+01
3.0E+01
4.0E+01
5.0E+01
6.0E+01
8.0E+01
1.0E+02
1.5E+02
2.0E+02
3.0E+02
4.0E+02
5.0E+02
6.0E+02
8.0E+02
1.0E+03
1.5E+03
2.0E+03
3.0E+03
4.0E+03
5.0E+03
6.0E+03
8.0E+03
1.0E+04𝑑𝑑 ∗ (10) / Gy cm2

5.76E-12
5.68E-12
5.81E-12
5.69E-12
5.92E-12
6.40E-12
6.18E-12
6.33E-12
6.46E-12
7.31E-12
1.73E-11
3.42E-10
4.22E-10
3.97E-10
3.57E-10
3.32E-10
3.19E-10
3.11E-10
3.14E-10
3.07E-10
3.12E-10
3.07E-10
3.10E-10
3.15E-10
3.13E-10
3.10E-10
3.13E-10
3.11E-10
3.18E-10
3.18E-10
3.20E-10
3.18E-10
3.12E-10
3.14E-10
3.11E-10
3.15E-10
3.17E-10
3.20E-10
3.15E-10
3.12E-10
3.12E-10ℎ∗ (10) / Sv cm2

5.76E-12
5.68E-12
5.80E-12
5.69E-12
5.92E-12
6.40E-12
6.18E-12
6.33E-12
6.46E-12
7.31E-12
1.73E-11
3.42E-10
4.22E-10
3.97E-10
3.57E-10
3.32E-10
3.19E-10
3.11E-10
3.14E-10
3.07E-10
3.12E-10
3.07E-10
3.10E-10
3.15E-10
3.13E-10
3.10E-10
3.13E-10
3.11E-10
3.18E-10
3.18E-10
3.20E-10
3.18E-10
3.12E-10
3.14E-10
3.11E-10
3.15E-10
3.17E-10
3.24E-10
3.15E-10
3.12E-10
3.12E-10‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 27 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.01
1.00
1.00
1.00

9.66E-12
1.00E-11
9.60E-12
1.06E-11
2.93E-11
1.15E-10
2.18E-10
4.12E-10
5.11E-10
4.82E-10
4.85E-10
4.54E-10
4.22E-10
4.30E-10
4.03E-10
3.73E-10
3.64E-10
3.39E-10
3.34E-10
3.30E-10
3.24E-10
3.32E-10
3.40E-10
3.45E-10
3.52E-10
4.21E-10
4.43E-10
4.87E-10
5.29E-10
5.45E-10
5.77E-10
6.49E-10
6.75E-10
7.52E-10
8.09E-10
8.75E-10
9.58E-10
9.92E-10
1.02E-09
1.10E-09
1.09E-09

3.53E-12
3.67E-12
3.84E-12
4.16E-12
4.52E-12
4.90E-12
5.36E-12
7.41E-12
1.05E-11
1.83E-11
2.57E-11
3.91E-11
5.10E-11
6.17E-11
7.29E-11
9.90E-11
1.26E-10
1.84E-10
2.29E-10
2.94E-10
3.20E-10
3.27E-10
3.34E-10
3.49E-10
3.57E-10
3.71E-10
3.83E-10
4.12E-10
4.35E-10
4.49E-10
4.62E-10
4.85E-10
5.05E-10
5.22E-10
5.66E-10
6.04E-10
6.33E-10
6.59E-10
6.83E-10
7.16E-10
7.46E-10

JAEA-Research 2024-002

Table 6 Protons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV
1.0E+01
1.5E+01
2.0E+01
3.0E+01
4.0E+01
5.0E+01
6.0E+01
8.0E+01
1.0E+02
1.5E+02
2.0E+02
3.0E+02
4.0E+02
5.0E+02
6.0E+02
8.0E+02
1.0E+03
1.5E+03
2.0E+03
3.0E+03
4.0E+03
5.0E+03
6.0E+03
8.0E+03
1.0E+04𝑑𝑑 ∗ (10) / Gy cm2

7.78E-15
3.57E-14
7.82E-14
2.24E-13
3.91E-09
2.63E-09
2.09E-09
1.55E-09
1.28E-09
9.42E-10
7.84E-10
6.29E-10
5.55E-10
5.21E-10
4.96E-10
4.72E-10
4.59E-10
4.44E-10
4.37E-10
4.45E-10
4.69E-10
4.80E-10
4.87E-10
4.99E-10
5.09E-10ℎ∗ (10) / Sv cm2

7.95E-15
3.97E-14
9.34E-14
5.33E-13
4.42E-09
3.08E-09
2.42E-09
1.81E-09
1.52E-09
1.18E-09
1.07E-09
9.32E-10
8.88E-10
9.14E-10
9.08E-10
8.97E-10
8.94E-10
9.07E-10
8.73E-10
9.18E-10
1.03E-09
1.03E-09
1.07E-09
1.05E-09
1.07E-09‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 28 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.02
1.11
1.19
2.38
1.13
1.17
1.16
1.16
1.18
1.25
1.36
1.48
1.60
1.76
1.83
1.90
1.95
2.04
2.00
2.06
2.21
2.15
2.20
2.11
2.09

1.57E-08
2.16E-08
2.07E-08
2.24E-08
2.19E-08
4.71E-09
4.28E-09
3.70E-09
5.30E-09
3.85E-09
3.11E-09
1.03E-09
1.01E-09
1.01E-09
1.04E-09
1.09E-09
1.11E-09
1.16E-09
1.17E-09
1.21E-09
1.50E-09
1.60E-09
1.69E-09
1.90E-09
2.03E-09

5.49E-11
1.89E-10
4.28E-10
7.50E-10
1.02E-09
1.18E-09
1.48E-09
2.16E-09
2.51E-09
2.82E-09
2.18E-09
1.45E-09
1.30E-09
1.24E-09
1.23E-09
1.23E-09
1.23E-09
1.25E-09
1.28E-09
1.35E-09
1.48E-09
1.46E-09
1.71E-09
1.88E-09
1.93E-09

JAEA-Research 2024-002

Table 7 Negative muons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV
1.0E+00
1.5E+00
2.0E+00
3.0E+00
4.0E+00
5.0E+00
6.0E+00
8.0E+00
1.0E+01
1.5E+01
2.0E+01
3.0E+01
4.0E+01
5.0E+01
6.0E+01
8.0E+01
1.0E+02
1.5E+02
2.0E+02
3.0E+02
4.0E+02
5.0E+02
6.0E+02
8.0E+02
1.0E+03
1.5E+03
2.0E+03
3.0E+03
4.0E+03
5.0E+03
6.0E+03
8.0E+03
1.0E+04𝑑𝑑 ∗ (10) / Gy cm2

3.83E-10
3.83E-10
3.86E-10
3.95E-10
4.01E-10
4.14E-10
4.29E-10
4.60E-10
5.39E-10
1.90E-09
1.22E-09
7.73E-10
5.99E-10
5.02E-10
4.39E-10
3.77E-10
3.54E-10
3.28E-10
3.19E-10
3.15E-10
3.14E-10
3.15E-10
3.17E-10
3.20E-10
3.24E-10
3.33E-10
3.40E-10
3.50E-10
3.57E-10
3.63E-10
3.77E-10
3.74E-10
3.79E-10ℎ∗ (10) / Sv cm2

4.12E-10
4.09E-10
4.14E-10
4.33E-10
4.41E-10
4.41E-10
4.57E-10
4.88E-10
5.76E-10
1.92E-09
1.24E-09
7.76E-10
6.03E-10
5.02E-10
4.39E-10
3.78E-10
3.54E-10
3.28E-10
3.19E-10
3.15E-10
3.14E-10
3.15E-10
3.17E-10
3.20E-10
3.24E-10
3.33E-10
3.40E-10
3.50E-10
3.57E-10
3.63E-10
3.77E-10
3.74E-10
3.79E-10‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 29 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.08
1.07
1.07
1.10
1.10
1.07
1.07
1.06
1.07
1.01
1.02
1.00
1.01
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00

6.28E-10
6.38E-10
6.54E-10
7.35E-10
4.98E-09
6.16E-09
7.18E-09
6.97E-09
5.49E-09
6.13E-09
2.00E-09
2.04E-09
1.72E-09
1.35E-09
1.01E-09
9.59E-10
3.54E-10
3.29E-10
3.20E-10
3.16E-10
3.15E-10
3.18E-10
3.22E-10
3.29E-10
3.35E-10
3.49E-10
3.58E-10
3.75E-10
3.86E-10
3.90E-10
4.35E-10
4.16E-10
4.08E-10

1.80E-10
1.80E-10
1.84E-10
1.88E-10
1.93E-10
2.05E-10
2.42E-10
2.93E-10
3.32E-10
4.14E-10
4.65E-10
6.57E-10
7.35E-10
7.55E-10
7.75E-10
5.05E-10
4.35E-10
3.55E-10
3.33E-10
3.22E-10
3.22E-10
3.24E-10
3.28E-10
3.33E-10
3.42E-10
3.38E-10
3.41E-10
3.44E-10
3.47E-10
3.48E-10
3.47E-10
3.49E-10
3.49E-10

JAEA-Research 2024-002

Table 8 Positive muons: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV
1.0E+00
1.5E+00
2.0E+00
3.0E+00
4.0E+00
5.0E+00
6.0E+00
8.0E+00
1.0E+01
1.5E+01
2.0E+01
3.0E+01
4.0E+01
5.0E+01
6.0E+01
8.0E+01
1.0E+02
1.5E+02
2.0E+02
3.0E+02
4.0E+02
5.0E+02
6.0E+02
8.0E+02
1.0E+03
1.5E+03
2.0E+03
3.0E+03
4.0E+03
5.0E+03
6.0E+03
8.0E+03
1.0E+04𝑑𝑑 ∗ (10) / Gy cm2

3.81E-10
3.93E-10
3.98E-10
4.02E-10
4.26E-10
4.35E-10
4.34E-10
4.67E-10
5.55E-10
1.99E-09
1.25E-09
7.88E-10
5.99E-10
5.06E-10
4.40E-10
3.78E-10
3.54E-10
3.28E-10
3.19E-10
3.15E-10
3.14E-10
3.15E-10
3.17E-10
3.20E-10
3.24E-10
3.33E-10
3.40E-10
3.50E-10
3.57E-10
3.63E-10
3.77E-10
3.74E-10
3.79E-10ℎ∗ (10) / Sv cm2

3.81E-10
3.93E-10
3.98E-10
4.02E-10
4.26E-10
4.35E-10
4.34E-10
4.67E-10
5.55E-10
1.99E-09
1.25E-09
7.88E-10
5.99E-10
5.06E-10
4.40E-10
3.78E-10
3.54E-10
3.28E-10
3.19E-10
3.15E-10
3.14E-10
3.15E-10
3.17E-10
3.20E-10
3.24E-10
3.33E-10
3.40E-10
3.50E-10
3.57E-10
3.63E-10
3.77E-10
3.74E-10
3.79E-10‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 30 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00

6.18E-10
6.34E-10
6.52E-10
6.99E-10
3.67E-09
4.83E-09
5.76E-09
5.58E-09
4.78E-09
4.93E-09
1.81E-09
1.98E-09
1.52E-09
1.29E-09
9.23E-10
8.39E-10
3.54E-10
3.28E-10
3.20E-10
3.16E-10
3.15E-10
3.18E-10
3.22E-10
3.29E-10
3.35E-10
3.49E-10
3.58E-10
3.75E-10
3.86E-10
3.90E-10
4.35E-10
4.16E-10
4.08E-10

1.94E-10
1.96E-10
1.98E-10
2.02E-10
2.07E-10
2.16E-10
2.51E-10
3.00E-10
3.40E-10
4.25E-10
4.81E-10
6.74E-10
7.51E-10
7.68E-10
7.87E-10
5.10E-10
4.37E-10
3.54E-10
3.33E-10
3.20E-10
3.21E-10
3.23E-10
3.25E-10
3.30E-10
3.34E-10
3.39E-10
3.41E-10
3.44E-10
3.47E-10
3.48E-10
3.47E-10
3.49E-10
3.49E-10

JAEA-Research 2024-002

Table 9 Negative pions: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV
1.0E+00
1.5E+00
2.0E+00
3.0E+00
4.0E+00
5.0E+00
6.0E+00
8.0E+00
1.0E+01
1.5E+01
2.0E+01
3.0E+01
4.0E+01
5.0E+01
6.0E+01
8.0E+01
1.0E+02
1.5E+02
2.0E+02
3.0E+02
4.0E+02
5.0E+02
6.0E+02
8.0E+02
1.0E+03
1.5E+03
2.0E+03
3.0E+03
4.0E+03
5.0E+03
6.0E+03
8.0E+03𝑑𝑑 ∗ (10) / Gy cm2

1.82E-10
1.85E-10
1.85E-10
1.90E-10
2.03E-10
2.12E-10
2.30E-10
3.01E-10
5.04E-10
5.67E-09
1.43E-09
9.15E-10
7.33E-10
6.51E-10
5.89E-10
5.36E-10
5.20E-10
5.06E-10
4.82E-10
4.43E-10
4.27E-10
4.24E-10
4.30E-10
4.43E-10
4.55E-10
4.64E-10
4.82E-10
4.94E-10
5.87E-10
6.05E-10
6.04E-10
6.24E-10ℎ∗ (10) / Sv cm2

1.15E-09
1.15E-09
1.17E-09
1.12E-09
1.21E-09
1.23E-09
1.32E-09
1.54E-09
2.22E-09
1.53E-08
2.75E-09
1.79E-09
1.41E-09
1.31E-09
1.24E-09
1.22E-09
1.31E-09
1.37E-09
1.31E-09
1.07E-09
9.74E-10
9.18E-10
9.07E-10
9.20E-10
9.60E-10
9.03E-10
9.59E-10
9.40E-10
1.23E-09
1.24E-09
1.17E-09
1.21E-09‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 31 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

6.31
6.25
6.32
5.91
5.97
5.80
5.76
5.12
4.41
2.70
1.92
1.95
1.92
2.02
2.10
2.28
2.51
2.71
2.72
2.41
2.28
2.16
2.11
2.08
2.11
1.95
1.99
1.90
2.10
2.05
1.93
1.95

9.21E-09
1.03E-08
1.22E-08
2.39E-08
2.25E-07
3.08E-07
3.10E-07
3.09E-07
3.04E-07
2.96E-07
1.93E-07
5.43E-08
4.32E-08
3.20E-08
2.35E-08
1.30E-08
1.38E-08
1.47E-09
1.36E-09
1.14E-09
1.02E-09
9.63E-10
9.70E-10
1.01E-09
1.06E-09
1.12E-09
1.12E-09
1.17E-09
1.65E-09
1.78E-09
1.91E-09
2.11E-09

4.06E-10
4.22E-10
4.33E-10
4.58E-10
4.91E-10
5.28E-10
6.73E-10
9.65E-10
1.09E-09
1.25E-09
1.28E-09
1.77E-09
1.92E-09
1.93E-09
1.99E-09
1.31E-09
1.03E-09
9.27E-10
9.02E-10
8.48E-10
8.50E-10
8.80E-10
9.17E-10
9.76E-10
1.02E-09
1.08E-09
1.12E-09
1.13E-09
1.17E-09
1.23E-09
1.26E-09
1.39E-09

JAEA-Research 2024-002

Table 9 (Continued).
𝐸𝐸 p / MeV
1.0E+04
1.5E+04
2.0E+04
3.0E+04
4.0E+04
5.0E+04
6.0E+048.0E+04
1.0E+05
1.5E+05
2.0E+05𝑑𝑑 ∗ (10) / Gy cm2

6.39E-10
6.59E-10
6.75E-10
6.91E-10
7.08E-10
7.13E-10
7.23E-10
7.42E-10
7.52E-10
7.78E-10
8.06E-10ℎ∗ (10) / Sv cm2

1.22E-09
1.20E-09
1.31E-09
1.27E-09
1.32E-09
1.34E-09
1.38E-09
1.45E-09
1.45E-09
1.47E-09
1.66E-09‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 32 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.91
1.81
1.93
1.83
1.86
1.88
1.91
1.96
1.93
1.89
2.06

2.31E-09
2.71E-09
3.09E-09
3.68E-09
4.00E-09
4.50E-09
4.73E-09
5.35E-09
5.79E-09
6.73E-09
7.55E-09

1.46E-09
1.60E-09
1.70E-09
1.86E-09
1.99E-09
2.11E-09
2.21E-09
2.42E-09
2.60E-09
2.98E-09
3.14E-09

JAEA-Research 2024-002

Table 10 Positive pions: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV
1.0E+00
1.5E+00
2.0E+00
3.0E+00
4.0E+00
5.0E+00
6.0E+00
8.0E+00
1.0E+01
1.5E+01
2.0E+01
3.0E+01
4.0E+01
5.0E+01
6.0E+01
8.0E+01
1.0E+02
1.5E+02
2.0E+02
3.0E+02
4.0E+02
5.0E+02
6.0E+02
8.0E+02
1.0E+03
1.5E+03
2.0E+03
3.0E+03
4.0E+03
5.0E+03
6.0E+03
8.0E+03𝑑𝑑 ∗ (10) / Gy cm2

2.21E-10
2.34E-10
2.52E-10
2.88E-10
3.40E-10
4.01E-10
4.20E-10
4.58E-10
5.11E-10
3.83E-09
1.64E-09
1.03E-09
7.97E-10
6.77E-10
6.16E-10
5.70E-10
5.72E-10
6.10E-10
5.96E-10
5.06E-10
4.58E-10
4.46E-10
4.47E-10
4.68E-10
4.77E-10
4.98E-10
5.08E-10
5.16E-10
5.96E-10
6.07E-10
6.19E-10
6.34E-10ℎ∗ (10) / Sv cm2

2.21E-10
2.34E-10
2.52E-10
2.88E-10
3.40E-10
4.02E-10
4.22E-10
4.60E-10
5.13E-10
4.55E-09
2.16E-09
1.57E-09
1.27E-09
1.13E-09
1.09E-09
1.15E-09
1.22E-09
1.41E-09
1.40E-09
1.13E-09
9.38E-10
8.58E-10
8.81E-10
9.67E-10
9.58E-10
9.76E-10
9.72E-10
9.78E-10
1.13E-09
1.20E-09
1.17E-09
1.20E-09‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 33 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.01
1.00
1.19
1.32
1.52
1.60
1.67
1.77
2.01
2.13
2.31
2.36
2.24
2.05
1.92
1.97
2.07
2.01
1.96
1.91
1.89
1.89
1.97
1.89
1.89

9.20E-10
1.06E-09
1.25E-09
1.87E-09
6.00E-09
8.61E-09
9.93E-09
9.11E-09
8.59E-09
8.19E-09
7.32E-09
3.59E-09
2.27E-09
1.59E-09
1.43E-09
1.15E-09
1.25E-09
1.49E-09
1.52E-09
1.20E-09
1.05E-09
9.83E-10
9.87E-10
1.05E-09
1.08E-09
1.14E-09
1.18E-09
1.23E-09
1.68E-09
1.85E-09
1.95E-09
2.12E-09

3.14E-10
3.24E-10
3.40E-10
3.79E-10
4.29E-10
4.89E-10
5.40E-10
7.17E-10
8.19E-10
1.00E-09
1.10E-09
1.52E-09
1.75E-09
1.83E-09
1.82E-09
1.38E-09
1.13E-09
1.22E-09
1.25E-09
1.10E-09
9.98E-10
9.70E-10
9.80E-10
1.04E-09
1.09E-09
1.16E-09
1.19E-09
1.18E-09
1.21E-09
1.27E-09
1.29E-09
1.39E-09

JAEA-Research 2024-002

Table 10 (Continued).
𝐸𝐸 p / MeV
1.0E+04
1.5E+04
2.0E+04
3.0E+04
4.0E+04
5.0E+04
6.0E+048.0E+04
1.0E+05
1.5E+05
2.0E+05𝑑𝑑 ∗ (10) / Gy cm2

6.49E-10
6.65E-10
6.78E-10
6.98E-10
7.14E-10
7.20E-10
7.28E-10
7.43E-10
7.42E-10
7.76E-10
7.92E-10ℎ∗ (10) / Sv cm2

1.26E-09
1.27E-09
1.26E-09
1.34E-09
1.35E-09
1.31E-09
1.32E-09
1.39E-09
1.27E-09
1.50E-09
1.52E-09‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 34 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.94
1.91
1.86
1.92
1.90
1.82
1.82
1.87
1.71
1.94
1.92

2.31E-09
2.74E-09
3.04E-09
3.62E-09
4.03E-09
4.40E-09
4.74E-09
5.41E-09
5.80E-09
6.72E-09
7.55E-09

1.46E-09
1.60E-09
1.69E-09
1.86E-09
1.97E-09
2.09E-09
2.20E-09
2.38E-09
2.53E-09
2.90E-09
3.24E-09

JAEA-Research 2024-002

Table 11 Helium ions: 𝑑𝑑 ∗ (10), ℎ∗ (10), 𝑄𝑄, ℎ∗max , and ℎ∗ values.
𝐸𝐸 p / MeV n −1
2.0E+00
3.0E+00
5.0E+00
1.0E+01
1.4E+01
2.0E+01
3.0E+01
5.0E+01
7.5E+01
1.0E+02
1.5E+02
2.0E+02
3.0E+02
5.0E+02
7.0E+02
1.0E+03
2.0E+03
3.0E+03
5.0E+03
1.0E+04
2.0E+04
5.0E+04
1.0E+05𝑑𝑑 ∗ (10) / Gy cm2

4.68E-16
2.44E-15
1.48E-14
1.09E-13
9.40E-13
9.23E-12
5.62E-11
1.04E-08
6.56E-09
5.05E-09
3.68E-09
3.04E-09
2.43E-09
1.99E-09
1.83E-09
1.72E-09
1.66E-09
1.67E-09
1.80E-09
1.97E-09
2.22E-09
2.64E-09
2.89E-09ℎ∗ (10) / Sv cm2

5.24E-16
3.00E-15
2.87E-14
6.00E-13
3.54E-12
2.14E-11
1.15E-10
1.19E-08
7.61E-09
6.24E-09
4.42E-09
3.92E-09
3.36E-09
3.29E-09
3.23E-09
2.94E-09
2.92E-09
3.11E-09
3.32E-09
3.61E-09
3.80E-09
4.34E-09
4.92E-09‡ 𝑄𝑄 value at 10-mm depth§ ℎ∗ cited from ICRU Report 9515)- 35 -

𝑄𝑄 ‡ℎ∗max / Sv cm2ℎ∗ / Sv cm2 §

1.12
1.23
1.94
5.50
3.77
2.31
2.05
1.15
1.16
1.24
1.20
1.29
1.38
1.65
1.77
1.71
1.76
1.86
1.84
1.83
1.72
1.64
1.70

7.35E-16
4.01E-15
1.44E-13
2.34E-07
3.55E-07
3.55E-07
3.76E-07
7.35E-08
7.67E-08
7.05E-08
5.40E-08
2.10E-08
3.50E-09
3.31E-09
3.65E-09
3.87E-09
4.20E-09
4.34E-09
5.58E-09
7.51E-09
1.06E-08
1.60E-08
2.23E-08

4.38E-10
6.57E-10
1.09E-09
2.19E-09
4.61E-09
1.72E-08
3.01E-08
4.75E-08
8.05E-08
1.01E-07
1.10E-07
7.29E-08
5.33E-08
4.49E-08
4.60E-08
4.47E-08
4.80E-08
5.01E-08
5.17E-08
6.26E-08
7.10E-08
9.67E-08
1.24E-07

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Figure 1 Quality factor, 𝑄𝑄, as a function of linear energy transfer, 𝐿𝐿.

Figure 2 Model used for calculation of 𝐷𝐷 ∗ (𝑑𝑑) and 𝐻𝐻 ∗ (𝑑𝑑).

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Figure 3 Distributions of dose equivalent in the ICRU sphere irradiated by photons.

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Figure 4 Comparison of ℎ∗ (10) for photons.

Figure 5 Comparison of ℎ∗ (10) for neutrons.

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Figure 6 Comparison of ℎ∗ (10) for electrons.

Figure 7 Comparison of ℎ∗ (10) for positrons.

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Figure 8 Comparison of ℎ∗ (10) for protons.

Figure 9 Comparison of ℎ∗ (10) for negative muons.

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Figure 10 Comparison of ℎ∗ (10) for positive muons.

Figure 11 Comparison of ℎ∗ (10) for negative pions.

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Figure 12 Comparison of ℎ∗ (10) for positive pions.

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Figure 13 Comparison of 𝑑𝑑 ∗ (10) and ℎ∗ (10) for photons calculated by FLUKA and PHITS.

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Figure 14 Comparison of ℎ∗max for photons.

Figure 15 Comparison of ℎ∗max for neutrons.

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Figure 16 Comparison of ℎ∗max for electrons.

Figure 17 Comparison of ℎ∗max for positrons.

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Figure 18 Comparison of ℎ∗max for protons.

Figure 19 Comparison of ℎ∗max for negative muons.

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Figure 20 Comparison of ℎ∗max for positive muons.

Figure 21 Comparison of ℎ∗max for negative pions.

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Figure 22 Comparison of ℎ∗max for positive pions.

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Figure 23 Absorbed dose distribution in the frontal region of the ICRU sphere.

Figure 24 Eﬀect of radius of the scoring region on ℎ∗max .

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Figure 25 Photons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 26 Neutrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 27 Electrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 28 Positrons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 29 Protons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 30 Negative muons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 31 Positive muons: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 32 Negative pions: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 33 Positive pions: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 34 Helium ions: 𝑑𝑑 ∗ (10), ℎ∗ (10), and 𝑄𝑄.

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Figure 35 LET distributions of charged particles in the ICRU sphere irradiated by protons.

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Figure 36 Photons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 37 Neutrons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 38 Electrons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 39 Positrons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 40 Protons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 41 Negative muons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 42 Positive muons: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 43 Negative pions: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 44 Positive pions: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 45 Helium ions: ℎ∗ (10), 𝑒𝑒 max , and ℎ∗ (10)/𝑒𝑒 max .

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Figure 46 Photons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 47 Neutrons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 48 Electrons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 49 Positrons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 50 Protons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 51 Negative muons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 52 Positive muons: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 53 Negative pions: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 54 Positive pions: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 55 Helium ions: ℎ∗max , 𝑒𝑒 max , and ℎ∗max /𝑒𝑒 max .

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Figure 56 Photons: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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Figure 57 Neutrons: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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Figure 58 Electrons: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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Figure 59 Positrons: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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Figure 60 Protons: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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Figure 61 Negative muons: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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Figure 62 Positive muons: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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Figure 63 Negative pions: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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Figure 64 Positive pions: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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Figure 65 Helium ions: 𝑒𝑒 and ℎ∗ /𝑒𝑒.

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