# Transfer functions for QA/QB international regulatory limits for the safe transport of radioactive materials

Thomas Frosio, Samuel Thomas, Janis Endres, Holger Eberhardt, Baptiste Louis, Tiberio Cabianca, Iain Brown, Matthew Foster, Nabil Menaa, Philippe Bertreix

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Thomas Frosio, Samuel Thomas, Janis Endres, Holger Eberhardt, Baptiste Louis, et al.. Transfer functions for QA/QB international regulatory limits for the safe transport of radioactive materials. Journal of Radiological Protection, 2024, 44 (3), pp.031504. 10.1088/1361-6498/ad6453. irsn-04877710

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# Transfer functions for Q<sub>A</sub>/Q<sub>B</sub> international regulatory limits for the safe transport of radioactive materials

To cite this article: Thomas Frosio et al 2024 J. Radiol. Prot. 44 031504

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PAPER

Transfer functions for Q_A/Q_B international regulatory limits for the
safe transport of radioactive materials

Thomas Frosio¹,* ID, Samuel Thomas³, Janis Endres³ ID, Holger Eberhardt³, Baptiste Louis² ID,
Tiberio Cabianca⁴ ID, Iain Brown⁴, Matthew Foster⁴ ID, Nabil Menaa⁵ ID and Philippe Bertreix⁵

¹ SLAC National Accelerator Laboratory, Menlo Park, CA 94025-7015, United States of America

² Institut de Radioprotection et de Sûreté Nucléaire, 92260 Fontenay-aux-Roses, France

³ Gesellschaft für Anlagen- und Reaktorsicherheit gGmbH, 50667 Cologne, Germany

⁴ UK Health Security Agency, Chilton Didcot, Oxfordshire, United Kingdom

⁵ Radiation Protection Group, European Organization for Nuclear Research, 1211 Geneva 23, Switzerland

* Author to whom any correspondence should be addressed.

E-mail: thomas.frosio@gmail.com

Keywords: A₁/A₂ values, Monte-Carlo simulations, transport of radioactive materials, international regulation

Abstract

This paper presents a proposed revision of the International Atomic Energy Agency transport regulations, related to the A₁ and A₂ limit values used to determine the radioactive transport classification. Based on the 'Q system', a novel methodology was introduced to derive Qₐ and Qₐ values related to scenarios involving external exposure from a distant source. These values are key parameters that respectively represent the total effective dose and total equivalent dose to the skin, from all primary and secondary particles contributing to radiation exposure. The International Working Group (WG A₁/A₂) is established and associated with the TRANSSC Technical Expert Group on Radiation Protection. A review of the A₁ and A₂ values is performed in response to identified limitations within the existing Q system. The followed approach is based on Monte Carlo simulations that enabled the development of transfer functions aimed at reducing computational time and increasing the flexibility of dose evaluations for any radionuclide with known particle emission spectra. This method allows updating the Qₐ and Qₐ values to account for future data evolutions (decay data, fluence-to-dose conversion coefficients) and standardizing the calculation of regulation limits across all referenced radionuclides and scenarios related to external exposure. The transfer functions are established using three Monte Carlo simulation codes—FLUKA, Geant4, and MCNP—and address the previous limitations of the 'Q system', reflecting the latest International Commission for Radiation Protection recommendations and improvements in calculation techniques. The results of the WG show consistent agreement across the codes, with minor discrepancies observed at low primary energies due to statistical uncertainties and different handling of stopping power for electrons/positrons in the codes. This revised approach aligns with current standards and recommendations, ensuring that the radiological consequences of transport accidents are acceptable for the new A₁ and A₂ limits from a radiological protection perspective.

**1. Introduction**

The International Atomic Energy Agency transport regulations outlined in SSR-6 [1] establish the A₁ and A₂ values, which are “used to determine the activity limits for the requirements of these Regulations” (para. 201 of SSR-6 [1]). They essentially determine the maximum permissible activity within a package to ensure that, in the event of an accident and subsequent loss of the package’s safety features, *the radiological consequences [...] are deemed to be acceptable, within the principles of radiological protection*” (para. 402.1 of SSG-26 [2]).

Derived from the ‘Q system’ radiological model presented in the advisory material SSG-26 [2], the A₁ and A₂ values are based on five distinct exposure scenarios. The latter utilize reference dose values established to prevent significant health detriment in the event of an accident. These reference doses are based on the
annual dose limits defined by the International Commission for Radiation Protection (ICRP) when the ‘Q system’ was first defined in 1980: 50 mSv for the effective dose, 500 mSv for the skin equivalent dose, and 150 mSv for the lens of the eye equivalent dose [3, 4]. From the exposure scenarios, five activity limits, $Q_A$, $Q_B$, $Q_C$, $Q_D$ and $Q_E$ are derived to evaluate the $A_1$ and $A_2$ values<fnref n="6" />. Notably, $A_1$ and $A_2$ values serve to express the same level of radiological consequences for any radionuclide, playing a crucial role in defining the package standard performances required under various transport conditions stipulated in SSR-6.

Initially introduced in 1985 [5], the current ‘Q system’ superseded the earlier radiotoxicity classification system defined in the 60 s and incorporated the latest ICRP recommendations (ICRP 26 [4]) at the time to refine the ‘$A_1/A_2$ system’ defined in the 70 s [5]. $A_1$ and $A_2$ values were further updated in 1996 to incorporate the new ICRP 60 recommendations [4]. However, the system has remained unchanged since then because the values were perceived as stable and acceptable to both regulators and operators alike.

Several limitations have been identified within the current ‘Q system’:

* Outdated data: the existing Q and A values rely on data that predates current ICRP recommendations. $Q_C$ has been updated to include the last ICRP updates, ICRP 130–151 [6–11]. $Q_D$ has been updated and split into two values $Q_{D,skin}$ and $Q_{D,ing}$ that rely respectively on skin dose due to contamination [12] and ingestion dose taken from ICRP 130–151. $Q_E$ has been updated to comply with ICRP 144 [13].

* Limited traceability: documentation is missing, and certain dose coefficients appear to be reversely ‘calculated’ from already established Q values, hindering accurate value reproduction. This leads to uncertainties in the calculation of additional $A_1/A_2$ values for specific radionuclides.

* Inconsistent treatment of progenies: the approach to handling radioactive progenies varies inconsistently across Q-value pathways.

* Insufficient justification: certain assumptions, such as the low ingestion dose and the arbitrary replacement of $Q_A$ by $10^4$, $Q_C$ for alpha emitters if this value is more restrictive than $Q_A$, lack proper justification.

* Physics approximations: approximations applied in energy deposition calculations are not necessarily accurate [14, 15] and current improvements in high performance computing efficiency allows for fully standardized Monte-Carlo simulations of particle transport.

In response to these identified challenges and limitations, the International Working Group on the review of $A_1$ and $A_2$ Values (WG $A_1/A_2$) was established to review and update the ‘Q system’, drawing upon advancements in recently available data and calculation methods.

This paper focuses on the dose ‘transfer functions’ that are derived to evaluate $Q_A$, $Q_{B,skin}$ and $Q_{B,eye}$, which respectively represent the total effective dose, total equivalent dose to the skin and total equivalent dose to the lens of the eye, for all types of primary and secondary particles contributing to the dose. Other quantities evaluated by the Working Group ($Q_C$, $Q_{D,skin}$, $Q_{D,ing}$, $Q_E$) for the derivation of the $A_1/A_2$ values have already been published [16].

## 2. Simulation models

The WG developed a geometry model to simulate the potential radiation exposure during a potential transport accident. The geometry model for the MC calculations, see figure 1, relies on a 1 m radius sphere with a point source at its center, surrounded by a 0.5 mm residual shield made of stainless steel 316 [17] but with a density of $7.8 \text{ g cm}^{-3}$. The WG opted to consider this shielding thickness for both $Q_A$ and $Q_B$ calculations, considering its practicality and consistency with previous practices. The inner part of the sphere is filled with air. Particle fluences are calculated at the surface of the sphere. Considering that backscattering was incorporated in deriving the ICRP 116 dose coefficients, the surface of the sphere was chosen as the boundary of the calculation universe.

Instead of performing individual Monte Carlo simulations for each radionuclide to calculate the dose at 1 m, the WG opted for a more efficient approach: generating ‘transfer functions’ that convert emitted particle intensities into dose rates. These functions, when combined (convolved) with the particle emission spectrum of any radionuclide, can directly determine the dose for that specific scenario and radionuclide. This approach offers several benefits:

<footnote n="6">⁶ In the Q system, the general accident scenario considers that a person will be in the vicinity of a severely damaged package during 30 min. $Q_A$ and $Q_B$ represent the external effective and skin/eye lens equivalent dose calculated at 1 m from a point source; $Q_C$ represents the dose due to inhalation; $Q_D$ represents either the skin equivalent dose due to contamination or the effective dose due to subsequent ingestion; $Q_E$ represents either the effective or skin equivalent dose due to submersion in a noble gas. $A_1$ is derived as the minimum between $Q_A$ and $Q_B$ (external dose), while $A_2$ is the minimum between all Q values (all pathways).</footnote>
<figure><img src="image_6.png" /></figure>

* Reduced computational cost: only a single set of calculations, dependent on the energy and type of primary particle, needs to be performed, significantly reducing the number of redundant computationally expensive Monte Carlo simulations compared to individual simulations for each radionuclide.

* Enhanced flexibility: the generated fluence database can be reused for future calculations. Whenever new decay data becomes available for additional radionuclides, their $Q_A$ and $Q_B$ values can be readily computed using the existing database, eliminating the need for further simulations.

The approach of calculating surface fluence through a detector positioned 1 m from the point source folded with nuclide spectrum to assess the dose rate in the specific scenarios was confirmed through comparisons with dedicated Monte Carlo simulations conducted for particular radionuclides [18]. This comparison has been used to validate the usage of the transfer function instead of dedicated Monte-Carlo simulations for each nuclide. The generated fluence values were then processed using agreed-upon fluence-to-dose coefficients, specifically considering the fully isotropic (ISO) field, acknowledging the potential conservativeness of the ROT field [19–21]. These coefficients are designed to estimate effects of radiations on the whole body. ICRP 116 relies on detailed Monte Carlo simulations with reference human phantoms representing average human anatomy. These internationally recognized coefficients provide reliable and standardized estimates for radiation protection. Furthermore, this method represents a conservative yet reasonable approach covering geometrical uncertainties of the model.

Fluences were calculated for photons, electrons, and positrons for discrete energy values ranging from 1 keV to 12 MeV. For neutrons, individual energy bins of the source were derived from spectra used in ICRP publication 107 [22], and fluences were evaluated similarly in the corresponding energy groups from 0.4 eV to 15 MeV.

The transfer functions provide the dose rate per primary emitted particle in [Sv per primary] or [Sv h⁻¹ per primary/s]. These functions play a crucial role in determining the dose rate per Becquerel and subsequently the $Q_A$, $Q_B$, and $Q_E$ values for each radionuclide. Table 1 lists the fluence-to-dose conversion coefficients used to derive the transfer functions. These coefficients are used to convert the calculated fluence into the different dose flavors required for each Q-value. The transfer functions are expressed as follows (all interpolations are of log-log type):

$$TF_{p,Q_x}(E) = \sum_t \left( \sum_{E_{gp}} \phi_{p,E}(E_{gp}, t) \cdot CFD_{Q_x}(\hat{E}_{gp}, t) \right)$$

where:

* $TF_{p,Q_x}(E)$: dose transfer function [Sv per primary] converted to [Sv h⁻¹ per primary/s] of the $Q_x$ scenario for the energy $E$ of the primary particle $p$;

* $\phi_{p,E}(E_{gp}, t)$: fluence [cm⁻² per primary] of the particle type $t$ at 1 m from the source in the energy group $E_{gp}$, for the energy $E$ of the primary particle $p$;

* $CFD_{Q_x}(E_{gp}, t)$: fluence-to-dose conversion coefficient [Sv·cm²] of the $Q_x$ scenario for the primary particle of type $t$. Those values are log-log interpolated at the average value $\hat{E}_{gp}$ of $E_{gp}$.
<table><caption>**Table 1.** Fluence-to-dose conversion coefficients used to the derivation of the transfer functions.</caption><thead><tr><th></th><th>Electrons</th><th>Photons</th><th>Positrons</th><th>Neutrons</th></tr></thead><tbody><tr><td>Q<sub>A</sub></td><td colspan="4">ICRP116 ISO effective dose (sex averaged) [23]</td></tr><tr><td>Q<sub>B,skin</sub></td><td>Local skin dose<br>ICRP 116 Annex G<br>table G.1 [23]</td><td>Local skin dose<br>generated by the<br>WG [24]</td><td>Local skin dose<br>from Bourgois<br><i>et al</i> [25]</td><td>Local skin dose<br>generated by the<br>WG [16]</td></tr><tr><td>Q<sub>B,eye</sub></td><td colspan="4">ICRP 116 ISO MALE eye lens dose [23]</td></tr></tbody></table>

The dose per activity unit $D_{Q_x}$ (RN) for the radionuclide RN (in [Sv/h per Bq]) in the $Q_x$ scenario is calculated as:

$$D_{Q_x}(\text{RN}) = \sum_{E} \text{TF}_{p,Q_x}(E) \cdot \theta(E,p,\text{RN})$$

where:

* $\theta(E, p, \text{RN})$: continuous or discrete emission spectrum at energy E for particle p and radionuclide RN provided in ICRP107 in [#particles per nuclear transformation]. For the following radionuclides, JEFF3.3 [26] decay data have been used to differentiate between beta plus and beta minus emissions: Ag-106, Ag-108, As-74, Br-78, Br-80, Cl-36, Cs-130, Cs-132, Cu-64, Eu-150 m, Eu-152, Eu-152 m, I-126, I-128, In-112, In-114, K-40, Mn-54, Rb-84, Sb-122, Tm-168. For Rh-102, ENDF/BVIII.0 [27] decay data have been used for the $\beta+|\beta-|$ spectrum.

This new method enables the dose evaluation of any radionuclide, as long as its corresponding emission decay spectrum is known. Additionally, it facilitates the incorporation of evolving standards on spectra with less effort compared to recalculating values for each radionuclide. This method can be considered a standardization approach, applicable to all radionuclides referenced in the literature, theoretically allowing the evaluation of dose rates and, consequently, $Q_A$ and $Q_B$ values, for example, for all ENDF/B-VIII.0 radionuclides (over 1700).

The WG decided to abandon the principle of using only one type of radiation to determine either the effective dose or the equivalent dose to an organ, allowing the inclusion of all relevant particle types. This change reflects the availability of ICRP recommendations for most incident radiations and advancements in calculation techniques (large-scale MC methods) that enable precise evaluation of the associated total exposure.

With the new approach, all contributing particles (photons, electrons, positrons, neutrons) are considered for $Q_A$ and $Q_B$, and not limited to photons for $Q_A$ and electrons for $Q_B$. Because of new considerations about the effects of radiations to the lens of the eye mentioned in ICRP 118 [28], the WG also evaluated the total equivalent dose to the lens of the eye ($Q_{B,eye}$) using the same approach as $Q_{B,skin}$. While the eye lens dose is mentioned in the current 'Q system', it was not evaluated, since it was considered at that time that 'the dose to the skin is always limiting for maximum beta energies up to approximately 4 MeV'.

Three Monte Carlo simulation codes are used for the evaluation of the transfer functions. The final function considered by the WG for the derivation of the $Q_A$ and $Q_B$ values, provided in tables 2 and 3 of appendix 1 of this paper, represent the arithmetic average of the transfer function values produced with FLUKA [29–31], Geant4 [32–34] and MCNP6 [35, 36].

The $Q_A$ and $Q_B$ values are then computed with the same assumption as for the current 'Q system', for a person standing at 1 m from the source during a 30 min exposure, namely:

* The $Q_A$ value is the activity of a given radionuclide in the material contained in a Type A package damaged in such an accident that leads to an effective dose of 50 mSv from external exposure. The calculation considers the effective dose rate per unit activity from a point source at one meter, and the exposure duration.

* The $Q_{B,skin}$ (or $Q_{B,eye}$) value is the activity of a given radionuclide in a source contained in a Type A package damaged in an accident that leads to an equivalent dose to the skin of 500 mSv (or to the eye lens of 150 mSv).

The Q-value is calculated as follows:

$$Q_x(\text{RN}) = \frac{\text{DL}}{D_{Q_x}(\text{RN}) \cdot t}$$
With:

* $D_{Q_x}$ (RN): dose of the radionuclide RN for the $Q_x$. exposure pathway in [Sv h⁻¹ per Bq].

* DL. is the dose criterion limit of the $Q_x$ exposure pathway (50 mSv for $Q_A$, 500 mSv for $Q_{B,skin}$, 150 mSv for $Q_{B,eye}$).

* *t* is the exposure time of 0.5 h.

* $Q_x$ (RN) is the $Q_x$ value in [Bq] for the radionuclide RN.

Specific transfer functions were also evaluated for $(\alpha, n\gamma)$ [37] reactions; they are included in the dose evaluation $D_{Q_x}$ (RN) of alpha emitters.

## 2.1. FLUKA simulations

FLUKA [29, 30] is a general purpose Monte Carlo code for the interaction and transport of hadrons, leptons, and photons from keV (with the exception of neutrons, tracked down to thermal energies) to cosmic ray energies in any material. FLUKA has a wide range of applications, spanning accelerator design and shielding, radiation protection, particle physics, dosimetry, detector simulation, and hadron therapy. It has pre-defined physics models that provide accurate simulations for complex geometries and materials. However, standard users cannot modify these core models, but can adjust certain parameters for precision, such as energy thresholds and activating or deactivating specific physical processes such as photonuclear interactions etc.

In this study, FLUKA2011.3 is used to simulate the transport and interactions of various primary particles: photons, electrons, positrons, alphas, and neutrons. It also tracks all secondary particles generated during the process. Notably, for photons, electrons, and positrons, the minimum energy threshold for transport and production is set to 1 keV. Additionally, FLUKA employs different stopping power and bremsstrahlung data for electrons and positrons, and accurately models both continuous and discrete energy loss depending on particle energy. For photons, pair production, Compton scattering, and photoelectric effects are all simulated.

For neutron energies below 20 MeV, we use a multigroup approach with 260 energy groups. Cross-section data are derived from established libraries like ENDF/B-VII [38], ENDF/B-VI [39], and JEFF-3.1 [40]. The results are then re-binned to match the energy binning used in the International Commission on Radiological Protection (ICRP) publication 107.

## 2.2. GEANT4 simulations

GEANT4 [32, 33] is a versatile Monte Carlo toolkit developed by CERN for simulating particle interactions and transport. In this work, it is used to simulate the same primary particles as FLUKA (photons, electrons, positrons, alphas, and neutrons) and also tracks all secondary particles generated during the simulation.

GEANT4.10 offers various pre-defined physics lists tailored to specific research needs. For this study, the QGSP_BIC HP physics list was chosen. This list prioritizes high-precision electromagnetic physics (option 4), making it suitable for the goals of this work, even though it may be slower than the standard electromagnetic package offered by GEANT4. Importantly, stopping powers for electrons and positrons are treated differently within this list.

For neutron simulations, the QGSP_BIC HP list utilizes the high-precision (HP) neutron package, which accurately describes neutron interactions from thermal energies to 20 MeV. Additionally, the G4NDL4.6 nuclear database is employed, allowing for point-wise cross sections. Simulations are initially performed using the same energy binning as FLUKA for comparison purposes, but are then re-binned to match the ICRP 107 binning. Some simulations for photons, electrons and positrons were even performed using a 1 keV binning.

## 2.3. MCNP simulations

Developed by Los Alamos National Laboratory, MCNP6.2 [35, 36] is another general-purpose Monte Carlo code used to track various particles. Similar to FLUKA and GEANT4, this study employs MCNP to simulate the transport of the same primary particles (photons, electrons, positrons, alphas, and neutrons) and accounts for all secondary particles generated during the process.

This work utilizes MCNP version 6.2 and relies on established nuclear libraries for simulations: ENDF/B-VII [41] for neutrons and protons, and ENDF/B-VI.8 for photons. Electron transport algorithms and libraries come from the ITS code version 3. While electron and positron physics share similarities in MCNP6, positrons are treated differently regarding tracking directions in magnetic fields and the inclusion of positron annihilation. Notably, unlike electrons that are terminated below a certain energy cutoff, positrons produce annihilation photons when falling below the cutoff. For all particles except neutrons, MCNP employs a low transport energy threshold of 1 keV and the F2 tally is used to record particle fluences.
<figure><img src="image_7.png" /><figcaption>**Figure 2.** Transfer functions for $Q_A$ for each primary particle.</figcaption></figure>

### 3. Results

In this section, results are provided for $Q_A$ only. $Q_{B,skin}$ and $Q_{B,eye}$ curves are presented in appendix 2, respectively in figure 4 and figure 5. The uncertainties are quite similar for $Q_B$ due to the use of the same fluences since only the fluence-to-dose conversion coefficients are different.

Figure 2 shows the transfer functions obtained from the three Monte Carlo simulation codes (FLUKA, Geant4, and MCNP) for each primary particle type (photon, electron, positron, and neutron) used in the $Q_A$ calculations. This figure also includes a curve representing the average transfer function across all three codes. The small crosses on the graph represent the relative difference between each individual code output and the average output.

For photons and electrons (top two graphs in figure 2), there are larger discrepancies at lower energies, because lower-energy particles have a lower probability of reaching the scoring volume where the dose is scored. These discrepancies can reach up to 2% for photons and 18% for electrons below 50 keV compared to the average curve. This phenomenon is not observed for positrons because they undergo annihilation, creating 511 keV photons with enough energy to reach the scoring volume. The relative difference between the individual code outputs and the average output for photons is comparable to the statistical uncertainty, which is less than 1% at one standard deviation ($1\sigma$). This indicates that the results from the different codes are generally consistent within 1% for photons.

For electrons and positrons, neither particle has enough energy to reach the scoring volume for source particles below 1 MeV. This explains the different behavior of the curves observed at 1 MeV, where the dose starts to increase rapidly for both particles as they begin to enter the scoring volume, while, below 1 MeV, the dose evaluated in the scoring area is mostly due to secondary photons. The statistical uncertainty for these particles is around 2% at $1\sigma$ (except for low-energy electrons below 50 keV), which is similar to the relative difference observed with the average curve, except around 1 MeV.

The differences observed between the three codes around 1 MeV are likely due to how each code calculates stopping powers using the Bethe theory. The analytical formulation of Bethe theory is not entirely accurate at the energy range of interest in this study. Therefore, at lower energies, all three codes (FLUKA, MCNP, and Geant4) apply corrections to their respective physics models to improve accuracy. These unique correction methods used by each code can lead to slight variations in the transport results for electrons and positrons [12, 42].

As for neutrons (bottom right curve of figure 2), the transfer function exhibits stability from 0.4 eV to 10 keV. In this energy range, capture reactions dominate, primarily involving oxygen-16 ($^{16}$O) and nitrogen-14 ($^{14}$N), resulting in the production of photons and electrons. Between 10 keV and 1 MeV, the dominant interaction type transitions to elastic scattering. During this process, the neutrons collide with air nuclei, bouncing off and losing some energy. Above 1 MeV, inelastic scattering becomes increasingly
<figure><img src="image_8.png" /><figcaption>**Figure 3.** Example of fluences scored at 1 m from the source for different primary neutron energies (left plot) and transfer function for each secondary particles (right plot) after application of fluence-to-dose conversion coefficients for QA, Neutron fluences calculated with GEANT4.</figcaption></figure>

prevalent. Here, the neutrons excite the target nuclei, transferring more energy, potentially causing the emission of various secondary particles, as illustrated in figure 3.

Differences in the neutron transfer functions between the three codes are lower than 10%, likely due to the different nuclear evaluation databases used.

Figure 3 provides further insights. The left graph displays the neutron fluence at 1 m from the source for different primary neutron energies. Particularly, fluences become more spread out above 10 keV due to the increased prevalence of elastic scattering, while they appear more compact below 10 keV due to capture reactions. The right graph focuses on the transfer function for each type of secondary particle after applying the ICRP 116 fluence-to-dose conversion coefficients used for the QA exposure pathway. It highlights that for low-energy primary neutrons, secondary photons significantly contribute to the transfer function. However, other secondary particles like protons, electrons, positrons, and heavy ions have negligible impact on the transfer function.

For the sake of completeness, transfer functions for primary alpha particles have been evaluated for energies between 5 MeV to 12 MeV. The transfer function for this energy range varies between $1 \times 10^{-20}$ and $5 \times 10^{-15}$ Sv h$^{-1}$ per primary/s, being at least a factor of $1 \times 10^4$ lower than the transfer functions for positrons, electrons, neutrons and photons. For this reason, alpha particles are neglected in the derivation of the QA and QB values.

## 4. Conclusions

This study addresses the limitations identified within the existing Q system, particularly those related to the derivation of QA and QB values. These values represent, in the current Q system, the total effective dose due to photons and the total equivalent dose to the skin due to electrons, respectively. They were examined within the context of a transport accident scenario involving exposure to a source located 1 m away for a period of 30 min.

A new method for deriving QA and QB values was developed, using pre-calculated transfer functions which include fluence-to-dose conversion coefficients. This approach allows for the evaluation of the dose resulting from the exposure to any radionuclide for the QA and QB exposure pathways, as long as the emission spectrum is known, facilitating future evolutions of the regulations.

The current approach of using only one type of radiation to determine the dose for those pathways was abandoned, reflecting the availability of recent ICRP recommendations and the advancements in computation techniques. The new QA, QB,skin and QB,eye values represent the total effective dose, the total equivalent dose to the skin and the total equivalent dose to the lens of the eye, incorporating all relevant primary and secondary particles (photons, electrons, positrons, neutrons).

Three Monte Carlo simulation codes (FLUKA, GEANT4, and MCNP) were employed to evaluate the transfer functions. The final transfer function used to derive the Q values is the arithmetic average of the outputs of these Monte-Carlo codes.

The derived transfer functions show good agreement between the different codes for most energy ranges. Discrepancies, which are of minor importance are explained and understood.
Alpha particles exhibit significantly lower transfer functions compared to other particle types and are therefore neglected in the derivation of $Q_A$, $Q_{B,skin}$ and $Q_{B,eye}$.

Overall, this work provides a revised and updated approach for deriving $Q_A$ and $Q_B$ values, which addresses limitations of the current $Q$ system and incorporates advancements in data and calculation methods. This offers improved accuracy, flexibility, and efficiency for evaluating the radiological consequences of accidents involving transport of radioactive materials.

**Data availability statement**

All data that support the findings of this study are included within the article (and any supplementary files).

**Acknowledgments**

The work of GRS is funded by the Federal Ministry for the Environment, Nature Conservation, Nuclear Safety and Consumer Protection, support code 4723E03210.
Appendix 1. Tables of transfer functions

<table><caption>Table 2. Transfer functions used for Q-values calculations in the the A₁/A₂ WG for primary photons and positrons from 1 keV to 12 MeV.</caption><thead><tr><th rowspan="2">Energy (MeV)</th><th colspan="3">Transfer functions for primary photons</th><th colspan="3">Transfer functions for primary positrons</th></tr><tr><th>Q<sub>A</sub> Sv h<sup>-1</sup> per primary/s</th><th>Q<sub>B</sub> Sv/h per primary/s</th><th>Q<sub>B,eye</sub> Sv h<sup>-1</sup> per primary/s</th><th>Energy (MeV)</th><th>Q<sub>A</sub> Sv h<sup>-1</sup> per primary/s</th><th>Q<sub>B,skin</sub> Sv h<sup>-1</sup> per primary/s</th><th>Q<sub>B,eye</sub> Sv h<sup>-1</sup> per primary/s</th></tr></thead><tbody><tr><td><b>0.015</b></td><td>0.00 × 10<sup>0</sup></td><td>8.14 × 10<sup>-23</sup></td><td>0.00 × 10<sup>0</sup></td><td><b>0.001</b></td><td>9.38 × 10<sup>-14</sup></td><td>2.11 × 10<sup>-13</sup></td><td>1.17 × 10<sup>-13</sup></td></tr><tr><td><b>0.02</b></td><td>7.97 × 10<sup>-20</sup></td><td>1.79 × 10<sup>-18</sup></td><td>3.98 × 10<sup>-19</sup></td><td><b>0.01</b></td><td>9.43 × 10<sup>-14</sup></td><td>2.18 × 10<sup>-13</sup></td><td>1.18 × 10<sup>-13</sup></td></tr><tr><td><b>0.025</b></td><td>1.24 × 10<sup>-17</sup></td><td>1.48 × 10<sup>-16</sup></td><td>4.44 × 10<sup>-17</sup></td><td><b>0.1</b></td><td>9.43 × 10<sup>-14</sup></td><td>2.20 × 10<sup>-13</sup></td><td>1.18 × 10<sup>-13</sup></td></tr><tr><td><b>0.03</b></td><td>1.44 × 10<sup>-16</sup></td><td>1.01 × 10<sup>-15</sup></td><td>3.86 × 10<sup>-16</sup></td><td><b>0.5</b></td><td>9.49 × 10<sup>-14</sup></td><td>2.20 × 10<sup>-13</sup></td><td>1.19 × 10<sup>-13</sup></td></tr><tr><td><b>0.035</b></td><td>5.20 × 10<sup>-16</sup></td><td>2.64 × 10<sup>-15</sup></td><td>1.14 × 10<sup>-15</sup></td><td><b>0.6</b></td><td>9.52 × 10<sup>-14</sup></td><td>2.19 × 10<sup>-13</sup></td><td>1.19 × 10<sup>-13</sup></td></tr><tr><td><b>0.04</b></td><td>1.13 × 10<sup>-15</sup></td><td>4.17 × 10<sup>-15</sup></td><td>2.03 × 10<sup>-15</sup></td><td><b>0.65</b></td><td>9.53 × 10<sup>-14</sup></td><td>2.21 × 10<sup>-13</sup></td><td>1.19 × 10<sup>-13</sup></td></tr><tr><td><b>0.05</b></td><td>2.53 × 10<sup>-15</sup></td><td>6.40 × 10<sup>-15</sup></td><td>3.51 × 10<sup>-15</sup></td><td><b>0.7</b></td><td>9.55 × 10<sup>-14</sup></td><td>2.21 × 10<sup>-13</sup></td><td>1.19 × 10<sup>-13</sup></td></tr><tr><td><b>0.06</b></td><td>3.77 × 10<sup>-15</sup></td><td>7.74 × 10<sup>-15</sup></td><td>4.64 × 10<sup>-15</sup></td><td><b>0.75</b></td><td>9.57 × 10<sup>-14</sup></td><td>2.23 × 10<sup>-13</sup></td><td>1.20 × 10<sup>-13</sup></td></tr><tr><td><b>0.07</b></td><td>4.81 × 10<sup>-15</sup></td><td>8.97 × 10<sup>-15</sup></td><td>5.57 × 10<sup>-15</sup></td><td><b>0.8</b></td><td>9.59 × 10<sup>-14</sup></td><td>2.21 × 10<sup>-13</sup></td><td>1.20 × 10<sup>-13</sup></td></tr><tr><td><b>0.08</b></td><td>5.75 × 10<sup>-15</sup></td><td>1.03 × 10<sup>-14</sup></td><td>6.41 × 10<sup>-15</sup></td><td><b>0.85</b></td><td>9.64 × 10<sup>-14</sup></td><td>2.30 × 10<sup>-13</sup></td><td>1.20 × 10<sup>-13</sup></td></tr><tr><td><b>0.09</b></td><td>6.66 × 10<sup>-15</sup></td><td>1.19 × 10<sup>-14</sup></td><td>7.34 × 10<sup>-15</sup></td><td><b>0.9</b></td><td>9.70 × 10<sup>-14</sup></td><td>2.81 × 10<sup>-13</sup></td><td>1.21 × 10<sup>-13</sup></td></tr><tr><td><b>0.1</b></td><td>7.51 × 10<sup>-15</sup></td><td>1.33 × 10<sup>-14</sup></td><td>8.21 × 10<sup>-15</sup></td><td><b>1.0</b></td><td>1.00 × 10<sup>-13</sup></td><td>1.73 × 10<sup>-12</sup></td><td>1.29 × 10<sup>-13</sup></td></tr><tr><td><b>0.12</b></td><td>9.32 × 10<sup>-15</sup></td><td>1.66 × 10<sup>-14</sup></td><td>1.03 × 10<sup>-14</sup></td><td><b>1.1</b></td><td>1.02 × 10<sup>-13</sup></td><td>4.71 × 10<sup>-12</sup></td><td>1.53 × 10<sup>-13</sup></td></tr><tr><td><b>0.15</b></td><td>1.19 × 10<sup>-14</sup></td><td>2.12 × 10<sup>-14</sup></td><td>1.34 × 10<sup>-14</sup></td><td><b>1.2</b></td><td>1.03 × 10<sup>-13</sup></td><td>8.19 × 10<sup>-12</sup></td><td>1.87 × 10<sup>-13</sup></td></tr><tr><td><b>0.18</b></td><td>1.47 × 10<sup>-14</sup></td><td>2.59 × 10<sup>-14</sup></td><td>1.69 × 10<sup>-14</sup></td><td><b>1.3</b></td><td>1.04 × 10<sup>-13</sup></td><td>9.54 × 10<sup>-12</sup></td><td>2.33 × 10<sup>-13</sup></td></tr><tr><td><b>0.2</b></td><td>1.65 × 10<sup>-14</sup></td><td>2.97 × 10<sup>-14</sup></td><td>1.92 × 10<sup>-14</sup></td><td><b>1.4</b></td><td>1.06 × 10<sup>-13</sup></td><td>1.02 × 10<sup>-11</sup></td><td>2.89 × 10<sup>-13</sup></td></tr><tr><td><b>0.25</b></td><td>2.14 × 10<sup>-14</sup></td><td>4.01 × 10<sup>-14</sup></td><td>2.55 × 10<sup>-14</sup></td><td><b>1.5</b></td><td>1.09 × 10<sup>-13</sup></td><td>1.06 × 10<sup>-11</sup></td><td>3.60 × 10<sup>-13</sup></td></tr><tr><td><b>0.3</b></td><td>2.63 × 10<sup>-14</sup></td><td>5.50 × 10<sup>-14</sup></td><td>3.18 × 10<sup>-14</sup></td><td><b>1.6</b></td><td>1.17 × 10<sup>-13</sup></td><td>1.05 × 10<sup>-11</sup></td><td>4.62 × 10<sup>-13</sup></td></tr><tr><td><b>0.35</b></td><td>3.12 × 10<sup>-14</sup></td><td>6.85 × 10<sup>-14</sup></td><td>3.83 × 10<sup>-14</sup></td><td><b>1.8</b></td><td>1.35 × 10<sup>-13</sup></td><td>1.02 × 10<sup>-11</sup></td><td>7.26 × 10<sup>-13</sup></td></tr><tr><td><b>0.4</b></td><td>3.62 × 10<sup>-14</sup></td><td>8.15 × 10<sup>-14</sup></td><td>4.49 × 10<sup>-14</sup></td><td><b>2</b></td><td>1.59 × 10<sup>-13</sup></td><td>9.91 × 10<sup>-12</sup></td><td>1.02 × 10<sup>-12</sup></td></tr><tr><td><b>0.5</b></td><td>4.61 × 10<sup>-14</sup></td><td>1.05 × 10<sup>-13</sup></td><td>5.76 × 10<sup>-14</sup></td><td><b>2.2</b></td><td>1.84 × 10<sup>-13</sup></td><td>9.66 × 10<sup>-12</sup></td><td>1.30 × 10<sup>-12</sup></td></tr><tr><td><b>0.6</b></td><td>5.57 × 10<sup>-14</sup></td><td>1.27 × 10<sup>-13</sup></td><td>6.94 × 10<sup>-14</sup></td><td><b>2.4</b></td><td>2.10 × 10<sup>-13</sup></td><td>9.48 × 10<sup>-12</sup></td><td>1.57 × 10<sup>-12</sup></td></tr><tr><td><b>0.7</b></td><td>6.49 × 10<sup>-14</sup></td><td>1.47 × 10<sup>-13</sup></td><td>8.04 × 10<sup>-14</sup></td><td><b>2.6</b></td><td>2.36 × 10<sup>-13</sup></td><td>9.35 × 10<sup>-12</sup></td><td>1.82 × 10<sup>-12</sup></td></tr><tr><td><b>0.8</b></td><td>7.42 × 10<sup>-14</sup></td><td>1.59 × 10<sup>-13</sup></td><td>9.13 × 10<sup>-14</sup></td><td><b>2.8</b></td><td>2.62 × 10<sup>-13</sup></td><td>9.27 × 10<sup>-12</sup></td><td>2.02 × 10<sup>-12</sup></td></tr><tr><td><b>0.9</b></td><td>8.32 × 10<sup>-14</sup></td><td>1.66 × 10<sup>-13</sup></td><td>1.01 × 10<sup>-13</sup></td><td><b>3</b></td><td>2.88 × 10<sup>-13</sup></td><td>9.19 × 10<sup>-12</sup></td><td>2.20 × 10<sup>-12</sup></td></tr><tr><td><b>1</b></td><td>9.22 × 10<sup>-14</sup></td><td>1.71 × 10<sup>-13</sup></td><td>1.11 × 10<sup>-13</sup></td><td><b>3.2</b></td><td>3.14 × 10<sup>-13</sup></td><td>9.14 × 10<sup>-12</sup></td><td>2.34 × 10<sup>-12</sup></td></tr><tr><td><b>1.2</b></td><td>1.09 × 10<sup>-13</sup></td><td>1.80 × 10<sup>-13</sup></td><td>1.28 × 10<sup>-13</sup></td><td><b>3.6</b></td><td>3.66 × 10<sup>-13</sup></td><td>9.07 × 10<sup>-12</sup></td><td>2.60 × 10<sup>-12</sup></td></tr><tr><td><b>1.5</b></td><td>1.33 × 10<sup>-13</sup></td><td>1.90 × 10<sup>-13</sup></td><td>1.52 × 10<sup>-13</sup></td><td><b>4</b></td><td>4.19 × 10<sup>-13</sup></td><td>9.04 × 10<sup>-12</sup></td><td>2.82 × 10<sup>-12</sup></td></tr><tr><td><b>1.8</b></td><td>1.54 × 10<sup>-13</sup></td><td>1.88 × 10<sup>-13</sup></td><td>1.74 × 10<sup>-13</sup></td><td><b>4.5</b></td><td>4.84 × 10<sup>-13</sup></td><td>9.02 × 10<sup>-12</sup></td><td>3.03 × 10<sup>-12</sup></td></tr><tr><td><b>2</b></td><td>1.69 × 10<sup>-13</sup></td><td>1.85 × 10<sup>-13</sup></td><td>1.89 × 10<sup>-13</sup></td><td><b>5</b></td><td>5.49 × 10<sup>-13</sup></td><td>9.00 × 10<sup>-12</sup></td><td>3.19 × 10<sup>-12</sup></td></tr><tr><td><b>2.5</b></td><td>2.01 × 10<sup>-13</sup></td><td>1.78 × 10<sup>-13</sup></td><td>2.21 × 10<sup>-13</sup></td><td><b>5.5</b></td><td>6.11 × 10<sup>-13</sup></td><td>9.00 × 10<sup>-12</sup></td><td>3.31 × 10<sup>-12</sup></td></tr><tr><td><b>3</b></td><td>2.32 × 10<sup>-13</sup></td><td>1.73 × 10<sup>-13</sup></td><td>2.50 × 10<sup>-13</sup></td><td><b>6</b></td><td>6.73 × 10<sup>-13</sup></td><td>8.98 × 10<sup>-12</sup></td><td>3.42 × 10<sup>-12</sup></td></tr><tr><td><b>4</b></td><td>2.87 × 10<sup>-13</sup></td><td>1.67 × 10<sup>-13</sup></td><td>3.03 × 10<sup>-13</sup></td><td><b>6.5</b></td><td>7.37 × 10<sup>-13</sup></td><td>8.96 × 10<sup>-12</sup></td><td>3.53 × 10<sup>-12</sup></td></tr><tr><td><b>5</b></td><td>3.40 × 10<sup>-13</sup></td><td>1.66 × 10<sup>-13</sup></td><td>3.41 × 10<sup>-13</sup></td><td><b>7</b></td><td>8.02 × 10<sup>-13</sup></td><td>8.95 × 10<sup>-12</sup></td><td>3.63 × 10<sup>-12</sup></td></tr><tr><td><b>6</b></td><td>3.89 × 10<sup>-13</sup></td><td>1.68 × 10<sup>-13</sup></td><td>3.78 × 10<sup>-13</sup></td><td><b>7.5</b></td><td>8.70 × 10<sup>-13</sup></td><td>8.95 × 10<sup>-12</sup></td><td>3.72 × 10<sup>-12</sup></td></tr><tr><td><b>7</b></td><td>4.35 × 10<sup>-13</sup></td><td>1.71 × 10<sup>-13</sup></td><td>4.13 × 10<sup>-13</sup></td><td><b>8</b></td><td>9.39 × 10<sup>-13</sup></td><td>8.96 × 10<sup>-12</sup></td><td>3.82 × 10<sup>-12</sup></td></tr><tr><td><b>8</b></td><td>4.80 × 10<sup>-13</sup></td><td>1.75 × 10<sup>-13</sup></td><td>4.47 × 10<sup>-13</sup></td><td><b>8.5</b></td><td>1.01 × 10<sup>-12</sup></td><td>8.98 × 10<sup>-12</sup></td><td>3.91 × 10<sup>-12</sup></td></tr><tr><td><b>9</b></td><td>5.25 × 10<sup>-13</sup></td><td>1.78 × 10<sup>-13</sup></td><td>4.79 × 10<sup>-13</sup></td><td><b>9</b></td><td>1.08 × 10<sup>-12</sup></td><td>8.99 × 10<sup>-12</sup></td><td>4.00 × 10<sup>-12</sup></td></tr><tr><td><b>10</b></td><td>5.68 × 10<sup>-13</sup></td><td>1.84 × 10<sup>-13</sup></td><td>5.10 × 10<sup>-13</sup></td><td><b>10</b></td><td>1.23 × 10<sup>-12</sup></td><td>8.98 × 10<sup>-12</sup></td><td>4.20 × 10<sup>-12</sup></td></tr><tr><td><b>12</b></td><td>6.54 × 10<sup>-13</sup></td><td>1.91 × 10<sup>-13</sup></td><td>5.70 × 10<sup>-13</sup></td><td><b>12</b></td><td>1.54 × 10<sup>-12</sup></td><td>8.95 × 10<sup>-12</sup></td><td>4.53 × 10<sup>-12</sup></td></tr></tbody></table>
<table><caption>**Table 3.** Transfer functions used for Q-values calculations in the A₁/A₂ WG for primary neutrons from 0.4 eV to 15 MeV and electrons from 1 keV to 12 MeV.</caption><thead><tr><th colspan="4">Transfer functions for primary neutrons</th><th colspan="4">Transfer functions for primary electrons</th></tr><tr><th>Energy<br>(MeV)</th><th>Q<sub>A</sub><br>Sv h<sup>-1</sup> per<br>primary/s</th><th>Q<sub>B,skin</sub><br>Sv h<sup>-1</sup> per<br>primary/s</th><th>Q<sub>B,eye</sub><br>Sv h<sup>-1</sup> per<br>primary/s</th><th>Energy<br>(MeV)</th><th>Q<sub>A</sub><br>Sv h<sup>-1</sup> per<br>primary/s</th><th>Q<sub>B,skin</sub><br>Sv h<sup>-1</sup> per<br>primary/s</th><th>Q<sub>B,eye</sub><br>Sv h<sup>-1</sup> per<br>primary/s</th></tr></thead><tbody><tr><td>4.14 × 10<sup>-7</sup></td><td>9.00 × 10<sup>-14</sup></td><td>6.96 × 10<sup>-14</sup></td><td>6.73 × 10<sup>-14</sup></td><td><strong>0.026</strong></td><td>0.00 × 10<sup>0</sup></td><td>0.00 × 10<sup>0</sup></td><td>0.00 × 10<sup>0</sup></td></tr><tr><td>1.00 × 10<sup>-6</sup></td><td>1.01 × 10<sup>-13</sup></td><td>5.24 × 10<sup>-14</sup></td><td>7.50 × 10<sup>-14</sup></td><td><strong>0.028</strong></td><td>4.86 × 10<sup>-22</sup></td><td>5.30 × 10<sup>-21</sup></td><td>1.74 × 10<sup>-21</sup></td></tr><tr><td>1.00 × 10<sup>-5</sup></td><td>1.03 × 10<sup>-13</sup></td><td>4.19 × 10<sup>-14</sup></td><td>7.93 × 10<sup>-14</sup></td><td><strong>0.03</strong></td><td>1.42 × 10<sup>-21</sup></td><td>1.34 × 10<sup>-20</sup></td><td>4.54 × 10<sup>-21</sup></td></tr><tr><td>5.00 × 10<sup>-5</sup></td><td>1.02 × 10<sup>-13</sup></td><td>3.64 × 10<sup>-14</sup></td><td>7.93 × 10<sup>-14</sup></td><td><strong>0.032</strong></td><td>7.31 × 10<sup>-21</sup></td><td>4.96 × 10<sup>-20</sup></td><td>1.89 × 10<sup>-20</sup></td></tr><tr><td>1.00 × 10<sup>-4</sup></td><td>1.02 × 10<sup>-13</sup></td><td>3.90 × 10<sup>-14</sup></td><td>7.94 × 10<sup>-14</sup></td><td><strong>0.036</strong></td><td>1.81 × 10<sup>-20</sup></td><td>1.14 × 10<sup>-19</sup></td><td>4.50 × 10<sup>-20</sup></td></tr><tr><td>2.00 × 10<sup>-4</sup></td><td>1.01 × 10<sup>-13</sup></td><td>3.47 × 10<sup>-14</sup></td><td>7.72 × 10<sup>-14</sup></td><td><strong>0.04</strong></td><td>5.10 × 10<sup>-20</sup></td><td>2.94 × 10<sup>-19</sup></td><td>1.20 × 10<sup>-19</sup></td></tr><tr><td>4.00 × 10<sup>-4</sup></td><td>1.00 × 10<sup>-13</sup></td><td>3.37 × 10<sup>-14</sup></td><td>7.53 × 10<sup>-14</sup></td><td><strong>0.045</strong></td><td>1.31 × 10<sup>-19</sup></td><td>6.44 × 10<sup>-19</sup></td><td>2.96 × 10<sup>-19</sup></td></tr><tr><td>7.00 × 10<sup>-4</sup></td><td>1.00 × 10<sup>-13</sup></td><td>3.63 × 10<sup>-14</sup></td><td>7.46 × 10<sup>-14</sup></td><td><strong>0.05</strong></td><td>2.52 × 10<sup>-19</sup></td><td>1.10 × 10<sup>-18</sup></td><td>4.95 × 10<sup>-19</sup></td></tr><tr><td>1.00 × 10<sup>-3</sup></td><td>1.02 × 10<sup>-13</sup></td><td>4.63 × 10<sup>-14</sup></td><td>7.50 × 10<sup>-14</sup></td><td><strong>0.055</strong></td><td>4.34 × 10<sup>-19</sup></td><td>1.69 × 10<sup>-18</sup></td><td>7.96 × 10<sup>-19</sup></td></tr><tr><td>3.00 × 10<sup>-3</sup></td><td>1.09 × 10<sup>-13</sup></td><td>6.80 × 10<sup>-14</sup></td><td>8.11 × 10<sup>-14</sup></td><td><strong>0.06</strong></td><td>7.05 × 10<sup>-19</sup></td><td>2.58 × 10<sup>-18</sup></td><td>1.23 × 10<sup>-18</sup></td></tr><tr><td>6.00 × 10<sup>-3</sup></td><td>1.19 × 10<sup>-13</sup></td><td>1.03 × 10<sup>-13</sup></td><td>9.36 × 10<sup>-14</sup></td><td><strong>0.065</strong></td><td>1.06 × 10<sup>-18</sup></td><td>3.57 × 10<sup>-18</sup></td><td>1.79 × 10<sup>-18</sup></td></tr><tr><td>1.00 × 10<sup>-2</sup></td><td>1.50 × 10<sup>-13</sup></td><td>1.89 × 10<sup>-13</sup></td><td>1.30 × 10<sup>-13</sup></td><td><strong>0.07</strong></td><td>1.48 × 10<sup>-18</sup></td><td>4.72 × 10<sup>-18</sup></td><td>2.36 × 10<sup>-18</sup></td></tr><tr><td>2.00 × 10<sup>-2</sup></td><td>2.24 × 10<sup>-13</sup></td><td>4.52 × 10<sup>-13</sup></td><td>2.28 × 10<sup>-13</sup></td><td><strong>0.075</strong></td><td>1.97 × 10<sup>-18</sup></td><td>5.94 × 10<sup>-18</sup></td><td>3.06 × 10<sup>-18</sup></td></tr><tr><td>4.00 × 10<sup>-2</sup></td><td>3.16 × 10<sup>-13</sup></td><td>8.71 × 10<sup>-13</sup></td><td>3.79 × 10<sup>-13</sup></td><td><strong>0.08</strong></td><td>2.55 × 10<sup>-18</sup></td><td>7.36 × 10<sup>-18</sup></td><td>3.83 × 10<sup>-18</sup></td></tr><tr><td>6.00 × 10<sup>-2</sup></td><td>4.11 × 10<sup>-13</sup></td><td>1.35 × 10<sup>-12</sup></td><td>5.49 × 10<sup>-13</sup></td><td><strong>0.085</strong></td><td>3.17 × 10<sup>-18</sup></td><td>8.86 × 10<sup>-18</sup></td><td>4.66 × 10<sup>-18</sup></td></tr><tr><td>8.00 × 10<sup>-2</sup></td><td>5.04 × 10<sup>-13</sup></td><td>1.85 × 10<sup>-12</sup></td><td>7.23 × 10<sup>-13</sup></td><td><strong>0.09</strong></td><td>3.94 × 10<sup>-18</sup></td><td>1.07 × 10<sup>-17</sup></td><td>5.69 × 10<sup>-18</sup></td></tr><tr><td>1.00 × 10<sup>-1</sup></td><td>6.87 × 10<sup>-13</sup></td><td>2.79 × 10<sup>-12</sup></td><td>1.06 × 10<sup>-12</sup></td><td><strong>0.1</strong></td><td>5.64 × 10<sup>-18</sup></td><td>1.44 × 10<sup>-17</sup></td><td>7.83 × 10<sup>-18</sup></td></tr><tr><td>1.50 × 10<sup>-1</sup></td><td>9.13 × 10<sup>-13</sup></td><td>4.04 × 10<sup>-12</sup></td><td>1.53 × 10<sup>-12</sup></td><td><strong>0.11</strong></td><td>7.50 × 10<sup>-18</sup></td><td>1.86 × 10<sup>-17</sup></td><td>1.02 × 10<sup>-17</sup></td></tr><tr><td>2.00 × 10<sup>-1</sup></td><td>1.13 × 10<sup>-12</sup></td><td>5.19 × 10<sup>-12</sup></td><td>1.99 × 10<sup>-12</sup></td><td><strong>0.12</strong></td><td>9.85 × 10<sup>-18</sup></td><td>2.37 × 10<sup>-17</sup></td><td>1.31 × 10<sup>-17</sup></td></tr><tr><td>2.50 × 10<sup>-1</sup></td><td>1.35 × 10<sup>-12</sup></td><td>6.31 × 10<sup>-12</sup></td><td>2.44 × 10<sup>-12</sup></td><td><strong>0.13</strong></td><td>1.23 × 10<sup>-17</sup></td><td>2.89 × 10<sup>-17</sup></td><td>1.62 × 10<sup>-17</sup></td></tr><tr><td>3.00 × 10<sup>-1</sup></td><td>1.55 × 10<sup>-12</sup></td><td>7.24 × 10<sup>-12</sup></td><td>2.87 × 10<sup>-12</sup></td><td><strong>0.14</strong></td><td>1.50 × 10<sup>-17</sup></td><td>3.47 × 10<sup>-17</sup></td><td>1.95 × 10<sup>-17</sup></td></tr><tr><td>3.50 × 10<sup>-1</sup></td><td>1.75 × 10<sup>-12</sup></td><td>8.16 × 10<sup>-12</sup></td><td>3.27 × 10<sup>-12</sup></td><td><strong>0.15</strong></td><td>1.82 × 10<sup>-17</sup></td><td>4.15 × 10<sup>-17</sup></td><td>2.33 × 10<sup>-17</sup></td></tr><tr><td>4.00 × 10<sup>-1</sup></td><td>1.95 × 10<sup>-12</sup></td><td>9.18 × 10<sup>-12</sup></td><td>3.67 × 10<sup>-12</sup></td><td><strong>0.16</strong></td><td>2.13 × 10<sup>-17</sup></td><td>4.74 × 10<sup>-17</sup></td><td>2.70 × 10<sup>-17</sup></td></tr><tr><td>4.50 × 10<sup>-1</sup></td><td>2.15 × 10<sup>-12</sup></td><td>9.51 × 10<sup>-12</sup></td><td>4.07 × 10<sup>-12</sup></td><td><strong>0.18</strong></td><td>2.87 × 10<sup>-17</sup></td><td>6.22 × 10<sup>-17</sup></td><td>3.59 × 10<sup>-17</sup></td></tr><tr><td>5.00 × 10<sup>-1</sup></td><td>2.33 × 10<sup>-12</sup></td><td>1.01 × 10<sup>-11</sup></td><td>4.45 × 10<sup>-12</sup></td><td><strong>0.2</strong></td><td>3.73 × 10<sup>-17</sup></td><td>7.93 × 10<sup>-17</sup></td><td>4.62 × 10<sup>-17</sup></td></tr><tr><td>5.50 × 10<sup>-1</sup></td><td>2.52 × 10<sup>-12</sup></td><td>1.08 × 10<sup>-11</sup></td><td>4.79 × 10<sup>-12</sup></td><td><strong>0.22</strong></td><td>4.69 × 10<sup>-17</sup></td><td>9.80 × 10<sup>-17</sup></td><td>5.76 × 10<sup>-17</sup></td></tr><tr><td>6.00 × 10<sup>-1</sup></td><td>2.81 × 10<sup>-12</sup></td><td>1.17 × 10<sup>-11</sup></td><td>5.34 × 10<sup>-12</sup></td><td><strong>0.24</strong></td><td>5.71 × 10<sup>-17</sup></td><td>1.19 × 10<sup>-16</sup></td><td>6.99 × 10<sup>-17</sup></td></tr><tr><td>7.00 × 10<sup>-1</sup></td><td>3.16 × 10<sup>-12</sup></td><td>1.28 × 10<sup>-11</sup></td><td>5.95 × 10<sup>-12</sup></td><td><strong>0.26</strong></td><td>6.87 × 10<sup>-17</sup></td><td>1.41 × 10<sup>-16</sup></td><td>8.36 × 10<sup>-17</sup></td></tr><tr><td>8.00 × 10<sup>-1</sup></td><td>3.50 × 10<sup>-12</sup></td><td>1.39 × 10<sup>-11</sup></td><td>6.50 × 10<sup>-12</sup></td><td><strong>0.28</strong></td><td>8.15 × 10<sup>-17</sup></td><td>1.65 × 10<sup>-16</sup></td><td>9.90 × 10<sup>-17</sup></td></tr><tr><td>9.00 × 10<sup>-1</sup></td><td>3.82 × 10<sup>-12</sup></td><td>1.66 × 10<sup>-11</sup></td><td>7.06 × 10<sup>-12</sup></td><td><strong>0.3</strong></td><td>9.47 × 10<sup>-17</sup></td><td>1.91 × 10<sup>-16</sup></td><td>1.15 × 10<sup>-16</sup></td></tr><tr><td>1.00 × 10<sup>-0</sup></td><td>4.23 × 10<sup>-12</sup></td><td>1.64 × 10<sup>-11</sup></td><td>7.73 × 10<sup>-12</sup></td><td><strong>0.32</strong></td><td>1.09 × 10<sup>-16</sup></td><td>2.18 × 10<sup>-16</sup></td><td>1.31 × 10<sup>-16</sup></td></tr><tr><td>1.20 × 10<sup>-0</sup></td><td>4.66 × 10<sup>-12</sup></td><td>1.61 × 10<sup>-11</sup></td><td>8.29 × 10<sup>-12</sup></td><td><strong>0.36</strong></td><td>1.42 × 10<sup>-16</sup></td><td>2.81 × 10<sup>-16</sup></td><td>1.71 × 10<sup>-16</sup></td></tr><tr><td>1.40 × 10<sup>-0</sup></td><td>5.04 × 10<sup>-12</sup></td><td>1.60 × 10<sup>-11</sup></td><td>8.73 × 10<sup>-12</sup></td><td><strong>0.4</strong></td><td>1.77 × 10<sup>-16</sup></td><td>3.60 × 10<sup>-16</sup></td><td>2.12 × 10<sup>-16</sup></td></tr><tr><td>1.60 × 10<sup>-0</sup></td><td>5.39 × 10<sup>-12</sup></td><td>1.62 × 10<sup>-11</sup></td><td>9.15 × 10<sup>-12</sup></td><td><strong>0.45</strong></td><td>2.28 × 10<sup>-16</sup></td><td>4.55 × 10<sup>-16</sup></td><td>2.74 × 10<sup>-16</sup></td></tr><tr><td>1.80 × 10<sup>-0</sup></td><td>5.70 × 10<sup>-12</sup></td><td>1.63 × 10<sup>-11</sup></td><td>9.48 × 10<sup>-12</sup></td><td><strong>0.5</strong></td><td>2.84 × 10<sup>-16</sup></td><td>5.61 × 10<sup>-16</sup></td><td>3.41 × 10<sup>-16</sup></td></tr><tr><td>2.00 × 10<sup>-0</sup></td><td>6.07 × 10<sup>-12</sup></td><td>1.57 × 10<sup>-11</sup></td><td>9.89 × 10<sup>-12</sup></td><td><strong>0.55</strong></td><td>3.48 × 10<sup>-16</sup></td><td>6.88 × 10<sup>-16</sup></td><td>4.18 × 10<sup>-16</sup></td></tr><tr><td>2.30 × 10<sup>-0</sup></td><td>6.42 × 10<sup>-12</sup></td><td>1.49 × 10<sup>-11</sup></td><td>1.02 × 10<sup>-11</sup></td><td><strong>0.6</strong></td><td>4.16 × 10<sup>-16</sup></td><td>8.45 × 10<sup>-16</sup></td><td>5.01 × 10<sup>-16</sup></td></tr><tr><td>2.60 × 10<sup>-0</sup></td><td>6.84 × 10<sup>-12</sup></td><td>1.42 × 10<sup>-11</sup></td><td>1.06 × 10<sup>-11</sup></td><td><strong>0.65</strong></td><td>4.93 × 10<sup>-16</sup></td><td>1.00 × 10<sup>-15</sup></td><td>5.94 × 10<sup>-16</sup></td></tr><tr><td>3.00 × 10<sup>-0</sup></td><td>7.24 × 10<sup>-12</sup></td><td>1.36 × 10<sup>-11</sup></td><td>1.09 × 10<sup>-11</sup></td><td><strong>0.7</strong></td><td>5.74 × 10<sup>-16</sup></td><td>1.13 × 10<sup>-15</sup></td><td>6.93 × 10<sup>-16</sup></td></tr><tr><td>3.50 × 10<sup>-0</sup></td><td>7.62 × 10<sup>-12</sup></td><td>1.27 × 10<sup>-11</sup></td><td>1.11 × 10<sup>-11</sup></td><td><strong>0.75</strong></td><td>6.64 × 10<sup>-16</sup></td><td>1.38 × 10<sup>-15</sup></td><td>8.03 × 10<sup>-16</sup></td></tr><tr><td>4.00 × 10<sup>-0</sup></td><td>7.92 × 10<sup>-12</sup></td><td>1.13 × 10<sup>-11</sup></td><td>1.13 × 10<sup>-11</sup></td><td><strong>0.8</strong></td><td>7.57 × 10<sup>-16</sup></td><td>1.53 × 10<sup>-15</sup></td><td>9.18 × 10<sup>-16</sup></td></tr><tr><td>4.50 × 10<sup>-0</sup></td><td>8.20 × 10<sup>-12</sup></td><td>9.97 × 10<sup>-12</sup></td><td>1.14 × 10<sup>-11</sup></td><td><strong>0.85</strong></td><td>8.65 × 10<sup>-16</sup></td><td>5.01 × 10<sup>-15</sup></td><td>1.05 × 10<sup>-15</sup></td></tr><tr><td>5.00 × 10<sup>-0</sup></td><td>8.54 × 10<sup>-12</sup></td><td>8.67 × 10<sup>-12</sup></td><td>1.17 × 10<sup>-11</sup></td><td><strong>0.9</strong></td><td>9.84 × 10<sup>-16</sup></td><td>4.10 × 10<sup>-14</sup></td><td>1.19 × 10<sup>-15</sup></td></tr><tr><td>6.00 × 10<sup>-0</sup></td><td>8.85 × 10<sup>-12</sup></td><td>7.17 × 10<sup>-12</sup></td><td>1.18 × 10<sup>-11</sup></td><td><strong>1</strong></td><td>1.66 × 10<sup>-15</sup></td><td>1.06 × 10<sup>-12</sup></td><td>1.48 × 10<sup>-15</sup></td></tr><tr><td>7.00 × 10<sup>-0</sup></td><td>9.09 × 10<sup>-12</sup></td><td>6.48 × 10<sup>-12</sup></td><td>1.18 × 10<sup>-11</sup></td><td><strong>1.1</strong></td><td>4.41 × 10<sup>-15</sup></td><td>3.70 × 10<sup>-12</sup></td><td>1.82 × 10<sup>-15</sup></td></tr><tr><td>8.00 × 10<sup>-0</sup></td><td>9.28 × 10<sup>-12</sup></td><td>6.23 × 10<sup>-12</sup></td><td>1.18 × 10<sup>-11</sup></td><td><strong>1.2</strong></td><td>1.03 × 10<sup>-14</sup></td><td>7.21 × 10<sup>-12</sup></td><td>2.17 × 10<sup>-15</sup></td></tr><tr><td>9.00 × 10<sup>-0</sup></td><td>9.43 × 10<sup>-12</sup></td><td>6.40 × 10<sup>-12</sup></td><td>1.18 × 10<sup>-11</sup></td><td><strong>1.3</strong></td><td>1.79 × 10<sup>-14</sup></td><td>8.78 × 10<sup>-12</sup></td><td>5.22 × 10<sup>-15</sup></td></tr><tr><td>1.00 × 10<sup>+1</sup></td><td>9.55 × 10<sup>-12</sup></td><td>6.27 × 10<sup>-12</sup></td><td>1.18 × 10<sup>-11</sup></td><td><strong>1.4</strong></td><td>2.75 × 10<sup>-14</sup></td><td>9.66 × 10<sup>-12</sup></td><td>2.29 × 10<sup>-14</sup></td></tr><tr><td>1.10 × 10<sup>+1</sup></td><td>9.64 × 10<sup>-12</sup></td><td>6.24 × 10<sup>-12</sup></td><td>1.18 × 10<sup>-11</sup></td><td><strong>1.5</strong></td><td>3.90 × 10<sup>-14</sup></td><td>1.02 × 10<sup>-11</sup></td><td>9.54 × 10<sup>-14</sup></td></tr><tr><td>1.20 × 10<sup>+1</sup></td><td>9.75 × 10<sup>-12</sup></td><td>5.94 × 10<sup>-12</sup></td><td>1.18 × 10<sup>-11</sup></td><td><strong>1.6</strong></td><td>5.03 × 10<sup>-14</sup></td><td>1.02 × 10<sup>-11</sup></td><td>2.08 × 10<sup>-13</sup></td></tr><tr><td>1.30 × 10<sup>+1</sup></td><td>9.80 × 10<sup>-12</sup></td><td>5.67 × 10<sup>-12</sup></td><td>1.17 × 10<sup>-11</sup></td><td><strong>1.8</strong></td><td>7.65 × 10<sup>-14</sup></td><td>1.01 × 10<sup>-11</sup></td><td>5.39 × 10<sup>-13</sup></td></tr><tr><td>1.40 × 10<sup>+1</sup></td><td>9.87 × 10<sup>-12</sup></td><td>5.82 × 10<sup>-12</sup></td><td>1.17 × 10<sup>-11</sup></td><td><strong>2</strong></td><td>1.04 × 10<sup>-13</sup></td><td>9.86 × 10<sup>-12</sup></td><td>8.57 × 10<sup>-13</sup></td></tr><tr><td></td><td></td><td></td><td></td><td><strong>2.2</strong></td><td>1.31 × 10<sup>-13</sup></td><td>9.64 × 10<sup>-12</sup></td><td>1.16 × 10<sup>-12</sup></td></tr><tr><td></td><td></td><td></td><td></td><td><strong>2.4</strong></td><td>1.59 × 10<sup>-13</sup></td><td>9.48 × 10<sup>-12</sup></td><td>1.46 × 10<sup>-12</sup></td></tr></tbody></table>

(Continued.)
<table><caption>**Table 3.** (Continued.)</caption><thead><tr><th colspan="4">Transfer functions for primary neutrons</th><th colspan="4">Transfer functions for primary electrons</th></tr><tr><th>Energy (MeV)</th><th>Q<sub>A</sub> Sv h<sup>-1</sup> per primary/s</th><th>Q<sub>B,skin</sub> Sv h<sup>-1</sup> per primary/s</th><th>Q<sub>B,eye</sub> Sv h<sup>-1</sup> per primary/s</th><th>Energy (MeV)</th><th>Q<sub>A</sub> Sv h<sup>-1</sup> per primary/s</th><th>Q<sub>B,skin</sub> Sv h<sup>-1</sup> per primary/s</th><th>Q<sub>B,eye</sub> Sv h<sup>-1</sup> per primary/s</th></tr></thead><tbody><tr><td><b>2.6</b></td><td>1.87 × 10<sup>-13</sup></td><td></td><td></td><td><b>2.6</b></td><td>1.87 × 10<sup>-13</sup></td><td>9.36 × 10<sup>-12</sup></td><td>1.75 × 10<sup>-12</sup></td></tr><tr><td><b>2.8</b></td><td>2.13 × 10<sup>-13</sup></td><td></td><td></td><td><b>2.8</b></td><td>2.13 × 10<sup>-13</sup></td><td>9.26 × 10<sup>-12</sup></td><td>1.98 × 10<sup>-12</sup></td></tr><tr><td><b>3</b></td><td>2.40 × 10<sup>-13</sup></td><td></td><td></td><td><b>3</b></td><td>2.40 × 10<sup>-13</sup></td><td>9.16 × 10<sup>-12</sup></td><td>2.19 × 10<sup>-12</sup></td></tr><tr><td><b>3.2</b></td><td>2.66 × 10<sup>-13</sup></td><td></td><td></td><td><b>3.2</b></td><td>2.66 × 10<sup>-13</sup></td><td>9.06 × 10<sup>-12</sup></td><td>2.36 × 10<sup>-12</sup></td></tr><tr><td><b>3.6</b></td><td>3.20 × 10<sup>-13</sup></td><td></td><td></td><td><b>3.6</b></td><td>3.20 × 10<sup>-13</sup></td><td>8.89 × 10<sup>-12</sup></td><td>2.68 × 10<sup>-12</sup></td></tr><tr><td><b>4</b></td><td>3.73 × 10<sup>-13</sup></td><td></td><td></td><td><b>4</b></td><td>3.73 × 10<sup>-13</sup></td><td>8.77 × 10<sup>-12</sup></td><td>2.94 × 10<sup>-12</sup></td></tr><tr><td><b>4.5</b></td><td>4.37 × 10<sup>-13</sup></td><td></td><td></td><td><b>4.5</b></td><td>4.37 × 10<sup>-13</sup></td><td>8.70 × 10<sup>-12</sup></td><td>3.16 × 10<sup>-12</sup></td></tr><tr><td><b>5</b></td><td>5.01 × 10<sup>-13</sup></td><td></td><td></td><td><b>5</b></td><td>5.01 × 10<sup>-13</sup></td><td>8.65 × 10<sup>-12</sup></td><td>3.34 × 10<sup>-12</sup></td></tr><tr><td><b>5.5</b></td><td>5.66 × 10<sup>-13</sup></td><td></td><td></td><td><b>5.5</b></td><td>5.66 × 10<sup>-13</sup></td><td>8.64 × 10<sup>-12</sup></td><td>3.46 × 10<sup>-12</sup></td></tr><tr><td><b>6</b></td><td>6.30 × 10<sup>-13</sup></td><td></td><td></td><td><b>6</b></td><td>6.30 × 10<sup>-13</sup></td><td>8.63 × 10<sup>-12</sup></td><td>3.56 × 10<sup>-12</sup></td></tr><tr><td><b>6.5</b></td><td>6.94 × 10<sup>-13</sup></td><td></td><td></td><td><b>6.5</b></td><td>6.94 × 10<sup>-13</sup></td><td>8.64 × 10<sup>-12</sup></td><td>3.65 × 10<sup>-12</sup></td></tr><tr><td><b>7</b></td><td>7.60 × 10<sup>-13</sup></td><td></td><td></td><td><b>7</b></td><td>7.60 × 10<sup>-13</sup></td><td>8.66 × 10<sup>-12</sup></td><td>3.73 × 10<sup>-12</sup></td></tr><tr><td><b>7.5</b></td><td>8.29 × 10<sup>-13</sup></td><td></td><td></td><td><b>7.5</b></td><td>8.29 × 10<sup>-13</sup></td><td>8.71 × 10<sup>-12</sup></td><td>3.83 × 10<sup>-12</sup></td></tr><tr><td><b>8</b></td><td>9.00 × 10<sup>-13</sup></td><td></td><td></td><td><b>8</b></td><td>9.00 × 10<sup>-13</sup></td><td>8.76 × 10<sup>-12</sup></td><td>3.93 × 10<sup>-12</sup></td></tr><tr><td><b>8.5</b></td><td>9.71 × 10<sup>-13</sup></td><td></td><td></td><td><b>8.5</b></td><td>9.71 × 10<sup>-13</sup></td><td>8.81 × 10<sup>-12</sup></td><td>4.03 × 10<sup>-12</sup></td></tr><tr><td><b>9</b></td><td>1.04 × 10<sup>-12</sup></td><td></td><td></td><td><b>9</b></td><td>1.04 × 10<sup>-12</sup></td><td>8.82 × 10<sup>-12</sup></td><td>4.14 × 10<sup>-12</sup></td></tr><tr><td><b>10</b></td><td>1.20 × 10<sup>-12</sup></td><td></td><td></td><td><b>10</b></td><td>1.20 × 10<sup>-12</sup></td><td>8.76 × 10<sup>-12</sup></td><td>4.39 × 10<sup>-12</sup></td></tr><tr><td><b>12</b></td><td>1.53 × 10<sup>-12</sup></td><td></td><td></td><td><b>12</b></td><td>1.53 × 10<sup>-12</sup></td><td>8.75 × 10<sup>-12</sup></td><td>4.76 × 10<sup>-12</sup></td></tr></tbody></table>

## Appendix 2. Transfer function curves for Q<sub>B</sub> scenarios

<figure><img src="image_9.png" /><figcaption>**Figure 4.** Transfer functions for Q<sub>B,skin</sub> for each primary particle.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure 5. Transfer functions for Q<sub>B,eye</sub> for each primary particle.</figcaption></figure>

ORCID iDs

Thomas Frosio https://orcid.org/0000-0002-3430-2811

Janis Endres https://orcid.org/0000-0002-9804-4225

Baptiste Louis https://orcid.org/0000-0002-8651-3362

Tiberio Cabianca https://orcid.org/0000-0001-6328-677X

Matthew Foster https://orcid.org/0009-0002-7243-6762

Nabil Menaa https://orcid.org/0000-0002-8509-9665

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