# Hydrated electron and hydroxyl radical end-of-track yields under proton beam in water

Julien Audouin, Laurent Desorgher, Petter Hofverberg, Gérard Baldacchino

► To cite this version:

Julien Audouin, Laurent Desorgher, Petter Hofverberg, Gérard Baldacchino. Hydrated electron and hydroxyl radical end-of-track yields under proton beam in water. Radiation Physics and Chemistry, 2025, 237, pp.112995. 10.1016/j.radphyschem.2025.112995. hal-05118361

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# Hydrated electron and hydroxyl radical end-of-track yields under proton beam in water

Julien Audouin<sup>a,e</sup>, Laurent Desorgher<sup>c</sup>, Petter Hofverberg<sup>d</sup>, Gérard Baldacchino<sup>a,b,*</sup>

## ARTICLE INFO

Handling Editor: Dr. Jay Laverne

### Keywords:

- Water radiolysis

- High LET

- Track-segment yield

- Bragg peak

- Proton track

- Hydrated electron

- Hydroxyl radical

- Real time spectroscopy

- Distal part

- Absorption

- Fluorescence

## ABSTRACT

This article reports on the local variations of the average yields of hydrated electron and *OH induced by 62-MeV proton beams within the final 10 mm of their propagation in liquid water. The dose rate was at least 30 Gy/s in the Bragg peak. The yields were determined by conducting in-situ and real-time acquisitions along the beam track using scavengers in solution, which produce either a fluorescence light or a UV-visible light absorbance. We used Resazurin and AmplexRed as scavengers, that respectively react with the hydrated electron and *OH to form the fluorescent Resorufin. We also performed absorption measurements with the ferro/ferricyanide system to study the combined yields involving these two radicals. Proton irradiations revealed a minimum value of 2.2 × 10⁻⁷ mol/J for *OH yields measured with the ferrocyanide system in the Bragg peak. Yields of the hydrated electron and *OH obtained by fluorescence were significantly lower, probably due to both the dose rate effect that degrades the Resorufin fluorescence and the time resolution limit of the detection. For both absorbance and fluorescence measurements, the yields partially recovered in the distal part of the Bragg peak. The origin of this behavior is difficult to explain. We suggest that it might be related to the longitudinal straggling of the beam associated with the complex track structures found in and after the Bragg peak.

## 1. Introduction

Whether to better control the effects of ionizing radiations on living matter in radioprotection or radiotherapy, or to control water radiolysis under high Linear Energy Transfer (LET) radiation in nuclear installations, it is necessary to know properly the yields of radiation induced species along the path of the particles with the best spatial resolution, in particular in the region where every particles are expected to stop, namely in the Bragg peak (BP) region(Yamashita et al., 2011). In the context of proton therapy, effectively targeting and inducing damage with energetic protons is crucial for eliminating localized tumor cells (Mohan and Grosshans, 2017). To reach this objective a precise understanding and control of the chemical processes occurring in the BP are essential. Nevertheless, some biological (cell and DNA damage) and clinical (radio-induced cancer) observations attributed to high LET effect found their origin in the area of the BP situated after the peak of the dose named distal part(Britten et al., 2013; Heemskerk et al., 2025;

Horendeck et al., 2021). Thus, the production of reactive oxygen species (ROS: *OH, H₂O₂, O₂⁻), of hydrated electrons (e⁻aq) and H* formed in the ion track(Maurizot-Spotheim et al., 2008) and especially in the distal part of BP must be carefully determined. This was mentioned in a recent roadmap dedicated to the multiscale approaches across various fields of particle-matter interactions(Solov'yov et al., 2024). Moreover in the context of the proton FLASH radiotherapy, high dose rates are expected to be applied in the BP region(Rødland et al., 2024). To support experimental research work, simulations going beyond the effects of the energy deposition structures of a single particle are also actively being developed(Chappuis et al., 2024; Masilela and Prezado, 2023; Shin et al., 2024; Tran et al., 2024).

The differential radiolysis yields in water along the proton track have been studied by several authors and are now well understood (Baldacchino, 2008; Baldacchino et al., 2000; Baldacchino and Katsumura, 2010; Blain et al., 2022; Kusumoto et al., 2024; LaVerne, 2000; LaVerne and Schuler, 1994; Pimblott and LaVerne, 2002; Smith et al.,

<footnote><sup>a</sup> Université Paris-Saclay, CEA, LIDYL, F-91191, Gif-sur-Yvette, France</footnote>

<footnote><sup>b</sup> CY Cergy Paris Université, CEA, LIDYL, 91191, Gif-sur-Yvette, France</footnote>

<footnote><sup>c</sup> Institute of Radiation Physics (IRA), Lausanne University Hospital and University of Lausanne, CH-1007, Lausanne, Switzerland</footnote>

<footnote><sup>d</sup> Centre Antoine Lacassagne, F-06100, Nice, France</footnote>

<footnote><sup>e</sup> Centre de Protonthérapie d'Orsay, Institut Curie, F-91450, Orsay, France</footnote>

<footnote>* Corresponding author. Université Paris-Saclay, CEA, LIDYL, F-91191, Gif-sur-Yvette, France.</footnote>

<footnote>E-mail address: gerard.baldacchino@cea.fr (G. Baldacchino).</footnote>
2021; Taguchi et al., 2001; Yamashita et al., 2008, 2011). In a mono-energetic proton beam, within the plateau region of the beam, experimental yields can be directly assimilated to differential yield values since the individual LET values are low, show limited variation, and the proton energy spectrum remains narrow. However, in the BP, this is not feasible because the individual LET values of protons change rapidly along the track are higher, and the proton energy spectrum is broader. This makes measuring yields in the BP essential. However, due to the narrow spatial width of the BP in proton beams (1–2 mm), studying yields in low-energy proton beams is challenging, and few measurements exist in this region. Moreover, these measurements generally have a low spatial resolution (about a millimeter at best). Fortunately, advances in fiber optics manufacturing have enabled the development of fiber bundles with diameters ranging from a few tens to hundreds of microns per fiber. Such bundles have allowed the conception of a spectrometer with a spatial resolution of 280 µm, which is sufficient to measure multiple local track-averaged yields within the BP of proton beams in a single acquisition(Audouin, 2023; Audouin et al., 2023).

This present article focuses on determining the local track-averaged yields of $e_{\bar{a}q}$ and $^{\bullet}$OH, in the track end of a 62-MeV proton beam. To carry out this study, we used scavengers to determine the primary yields at several positions along the track end. We used the optical setup that was developed recently with the aim to measure the Fricke dosimeter yield in the tracks of continuous energetic proton and carbon beams especially in the BP and the distal part(Audouin et al., 2023). In this previous study, the authors observed that the yields of the Fricke system reach a minimum value at the BP maximum, followed by a recovery in the distal edge of the BP(Audouin et al., 2023). Since the Fricke chemical system provides a global yield representing the sum of the individual yields of the water radiolysis species(Jayson et al., 1975), this paved the way to new investigations concerning the measurement of the local track-averaged yield of these individual radiolytic species in the BP of proton tracks. In this article, we present the results that we obtained for the most reducing and the most oxidizing species, $e_{\bar{a}q}$ and $^{\bullet}$OH, respectively.

The direct measurement of $e_{\bar{a}q}$ and $^{\bullet}$OH yields with absorbance spectroscopy is indeed not feasible under continuous irradiation. Their ultrashort lifetimes, in pure water, require using an intense and ultrashort-pulsed proton beam. Therefore, for both species ($e_{\bar{a}q}$ and $^{\bullet}$OH), we chose to use scavengers to detect them using absorbance or fluorescence spectroscopy (Pimbblott et al., 1996). We are then going to determine primary yields in small segments inside the proton beam-end using the inline spectrometer described in our previous article(Audouin et al., 2023).

## 2. Materials and methods

### 2.1. Space-resolved yields determination

The determination of radiolytic yields and their calculation using our experimental method have been extensively described in previous articles(Audouin et al., 2023; Yamashita et al., 2010). The general expression for the track-segment yield concerning a specific fiber within the bundle is defined by equation (1).

$$G(S)_n = \frac{\left(\frac{dC}{dt}\right)_{n,t0}}{\left(\frac{dD}{dt}\right)_n} \frac{1}{\rho} \qquad (1)$$

Where $G(S)_n$ is the primary yield at 1 µs after the ionization event of the species S at the fiber n. ($dC/dt$)$_{n,t0}$ is the variation of concentration of S at the fiber n and time t0 (the moment when the irradiation begins). ($dD/dt$)$_n$ is the dose rate at fiber n and $\rho$ is the density of the solution (1 kg dm$^{-3}$ in the case of aqueous solution).

When concentration is assessed via absorbance measurements, this expression can be reformulated utilizing the Beer-Lambert law, leading to expression 2:

$$G(S)_n = \frac{\left(\frac{dA}{dt}\right)_{n,t0}}{\left(\frac{dD}{dt}\right)_n} \frac{1}{\rho \times \epsilon \times l} \qquad (2)$$

Where ($dA/dt$)$_{n,t0}$ in Equation (2) is the variation of absorbance at fiber n and time t0 in the case where the variation of concentration is measured by absorbance. $\epsilon$ is the absorbance coefficient of S and $l$ is the optical length of the cuvette used for the absorbance measurement.

Alternatively, when concentration variations are monitored through fluorescence, we can explicitly describe the concentration changes as a function of the variations in light intensity over time, incorporating a calibration factor (See SI-1,2,3). The resulting expression of the radiolytic yields is given by expression 3.

$$G(S)_n = \frac{\left(\frac{dI}{dt}\right)_{n,t0}}{\left(\frac{dD}{dt}\right)_n} \frac{1}{\rho \times \alpha} \qquad (3)$$

Where ($dI/dt$)$_{n,t0}$ is the variation of fluorescence light intensity at fiber n and t0 in the case where the variation of concentration is monitored by fluorescence. $\alpha$ represents a calibration coefficient needed to evaluate the concentration from an intensity value of the collected fluorescence light.

### 2.2. Chemical systems

1. We performed absorption measurements with the ferro/ferricyanide system to study the combined yields of $e_{\bar{a}q}$ and $^{\bullet}$OH. The ferrocyanide/ferricyanide is a system of scavengers that has been extensively used for radical yield studies. The characteristic absorption spectrum of ferricyanide enables real-time monitoring of its formation during irradiation using absorption spectroscopy(Adams and Willson, 1969; Barker and Fowles, 1970; Khlyustova et al., 2016; Le Caër et al., 2006; Stark et al., 1999). This system is based on the oxidation of Fe (CN)$_6^{4-}$ into Fe(CN)$_6^{3-}$ by the oxidizing radicals generated within ion tracks. Usually, the wavelength used for the monitoring via absorption spectroscopy is set at 420 nm since at this wavelength the absorption coefficient of Fe(CN)$_6^{3-}$ is conveniently equal to 1000 M$^{-1}$ cm$^{-1}$ and is unaffected by a change in pH from 1 to 11 while the absorption of Fe(CN)$_6^{4-}$ is negligible(Rabani and Stein, 1962). Fe (CN)$_6^{4-}$ is known to be a good scavenger of $^{\bullet}$OH and reacts with it according to the following reactions(Rabani and Matheson, 1966; Zehavi and Rabani, 1972).

$$^{\bullet}OH + Fe(CN)_6^{4-} \rightarrow OH^{-} + Fe(CN)_6^{3-} \quad k \approx 1 \times 10^{10} \text{ M}^{-1}\text{s}^{-1} \qquad (4)$$

$$H_2O_2 + Fe(CN)_6^{4-} \rightarrow OH^{-} + ^{\bullet}OH + Fe(CN)_6^{3-} \quad k < 1 \times 10^9 \text{ M}^{-1}\text{s}^{-1} \qquad (5)$$

The rate constant $k$ of reaction (5) is at least one order of magnitude lower than that of reaction (4). The contribution of $H_2O_2$ to the yield of Fe(CN)$_6^{3-}$ can therefore be neglected in case of a low concentration of $H_2O_2$ for example in low LET conditions. At high LET, $H_2O_2$ can be produced very early in the radiolysis processes by recombination of $^{\bullet}$OH in the track core. Then primary yield of $H_2O_2$ can rise to close to $10^{-7}$ mol/J (see for example at 30 keV/µm with 1 GeV Carbon ion (Wasselin-Trupin et al., 2002)). In this condition, reactions (4) and (5) compete themselves and with the whole water radiolysis mechanism. That is then difficult to conclude easily especially in the BP domain where LET and dose rate change a lot. Simulation can help to decide. Nevertheless, in case of early over production of $^{\bullet}$OH provided by
another reaction (see infra, by adding N₂O for instance), reaction (5) should be really neglected.

Reduction reactions of Fe(CN)₆³⁻ can occur with the reductive species produced in the tracks and in particular with e⁻_aq and H⁺. The implied reactions are described with equations (6) and (7)(Adams et al., 1965; Gordon et al., 1963; Le Caër et al., 2007; Rabani and Meyerstein, 1968; Rabani and Stein, 1962).

$$e_{aq}^{-} + Fe(CN)_{6}^{3-} \rightarrow Fe(CN)_{6}^{4-} \quad k = 4 \times 10^{9} M^{-1}s^{-1} \qquad (6)$$

$$H + Fe(CN)_{6}^{3-} \rightarrow Fe(CN)_{6}^{4-} + H^{+} \quad k \approx 6.5 \times 10^{9} M^{-1}s^{-1} \quad (pH = 2-3) \qquad (7)$$

The rate constant of the reaction between Fe(CN)₆³⁻ and H⁺ depends on pH but remains very high (k > 10⁷ M⁻¹s⁻¹) over a pH range from 1 to 11. It competes with the following reaction.

$$H + H^{+} \rightarrow H_{2} \quad k = 7.8 \times 10^{9} M^{-1}s^{-1} \qquad (8)$$

Where H⁺ recombines with itself, leading to the formation of H₂. However, H⁺ is produced in much smaller quantities than Fe(CN)₆³⁻, so reaction (7) is predominantly responsible for the disappearance of H⁺. The reaction (6) can be prevented by working under saturated atmosphere of N₂O. Under these conditions e⁻_aq is converted into *OH with the following reaction.

$$e_{aq}^{-} + N_{2}O \rightarrow N_{2} + OH^{-} + OH^{+} \quad k = 8.7 \times 10^{9} M^{-1}s^{-1} \qquad (9)$$

Another advantage of working with N₂O is that it prevents the reactions that occur with the reactive oxygen species (ROS) produced under aerobic conditions(Adams et al., 1965; Le Caër et al., 2006; Zehavi and Rabani, 1972).

Aqueous solution of Fe(CN)₆⁴⁻ (potassium hexacyanoferrate(II) hydrate, Merck) were prepared with a concentration of 6.9 × 10⁻⁵ M, which corresponds to a scavenging time for *OH a little bit higher than 1 µs. The solvent was ultrapure water provided by a Millipore Milli-Q system (18.2 MΩ cm, total organic carbon of 3 ppb). The solutions were placed under N₂O (electronic grade, Air product) atmosphere at least 15 min prior to the irradiation and during the irradiation.

2 We used the Resazurin system to measure the yield of e⁻_aq under fluorescence spectroscopy. Resazurin or 7-hydroxy-3H-phenoxazin-3-one-10-oxide (RNO) is a slightly fluorescent blue dye that is sensitive to water radiolysis products. In particular, it can be irreversibly reduced by the aqueous electron into resorufin, or 7-Hydroxy-3H-phenoxazin-3-one (RN), a pink and highly fluorescent molecule, with a fluorescence quantum yield of approximately 0.7, making it readily detectable in situ using fluorescence spectroscopy(Ibáñez et al., 2020; Knapp et al., 2018). This compound has a good sensitivity at low dose and has already been employed in several in situ studies of radicals generated by ionizing beams. Kim et al. have demonstrated that it is possible to determine the dose distribution of a proton beam inside cells by detecting and locating the production of fluorescent RN(Kim et al., 2007). The mechanism of RNO reduction to RN has been extensively studied and is well understood. Prütz et al. demonstrated that this reduction occur through several processes, including a reaction with e⁻_aq. This reduction pathway of RNO has also been studied by Balcerzyk et al. and the reactions involved are described with equations (11) and (12)(Balcerzyk and Baldacchino, 2014; Prütz et al., 1996).

$$RNO + e_{aq}^{-} \rightarrow RN \cdot O^{-} \quad k = 4.3 \times 10^{10} M^{-1}s^{-1} \qquad (10)$$

$$2RN \cdot O^{-} + 2H^{+} \rightarrow RN + RNO + H_{2}O \quad 2k = 5.0 \times 10^{7} M^{-1}s^{-1} \qquad (11)$$

It is worth noting that the rate constant of reaction (11) found by Balcerzyk et al. is almost two times higher than the one determined by Prütz et al. (2.3 × 10¹⁰ M⁻¹s⁻¹). This discrepancy was assumed to be the

result of the much higher sensitivity of the measurement system used by Balcerzyk et al. Since reaction (12) needs the production of two RNO radicals by reaction (11), the yield of e⁻_aq can be written as a function of the produced RN yield.

$$G(RN)_{RNO} = \frac{1}{2} G(e_{aq}^{-}) \qquad (12)$$

3 The 10-acetyl-3,7-dihydroxyphenoxazine, better known with its commercial names of ADHP or AmplifluRed™ or AmplexRed (AR), is a non-fluorescent and non-absorbing molecule in UV-visible range. It exhibits similar properties to RNO, including high reactivity with water radiolysis products and strong sensitivity at low doses. It has been employed in various fields, such as investigating changes in *OH yields in the presence of gold nanoparticles and detecting and characterizing hydrogen peroxide in the extracellular environment of living cells (Baldacchino et al., 2019; Debski et al., 2016; Okazaki et al., 2024). Furthermore, the fact that the oxidation product of AR is RN makes it very interesting to use in tandem with RNO for water radiolysis study. Debski et al. have studied the mechanism of AR oxidation to RN. They showed that this mechanism is a single-electron oxidation mechanism(Debski et al., 2016). By saturating an AR solution with N₂O, hydrated electrons generated during irradiation are converted into *OH through reaction (9), which allows us to express the yield of RN with this scavenging system as follows:

$$G(RN)_{AR} = G(e_{aq}^{-}) + G(OH) \qquad (13)$$

By combining the expression (12) and (13) we are able to obtain the individual yield of OH⁺ with equation (14).

$$G(RN)_{AR} - G(RN)_{RNO} = G(OH) \qquad (14)$$

The fluorescence properties of RN are strongly influenced by the pH (Ryder et al., 2003). It is therefore necessary to use a buffer as solvent when manipulating with RN. In our case, we used a phosphate buffer, which offers several advantages. The phosphate ions react poorly with the product of water radiolysis and this type of buffer can be used in a large range of pH. For this study, the phosphate buffer was made with anhydrous monobasic sodium phosphate (NaH₂PO₄, purity ≥99.0 %; Sigma-Aldrich) and anhydrous dibasic sodium phosphate (Na₂HPO₄, purity ≥99.0 %; Sigma-Aldrich). The concentration of both component was 1 mM and the pH was 6.8. The water used for the buffer was also ultrapure water provided by a Millipore Alpha-Q device. The solution of RNO were prepared with sodium salts of resazurin (Sigma-Aldrich) with a concentration of 2 × 10⁻⁵ M. 10⁻² M of ethanol (spectroscopic quality, Merck) was also added to protect RNO from OH⁺ attacks. The solution samples of RNO were also bubbled with argon gas during 1 min just before the irradiation to remove molecular oxygen. The solutions of AR had a concentration of 2 × 10⁻⁴ M and were prepared with pre-weighed sample of 5 mg of AmplifluRed™ (purity ≥98.0 %, Sigma-Aldrich). The solutions were magnetically stirred for 1 h to ensure the full dissolution of AR. Then, the AR samples were bubbled with N₂O during 1 min just before the irradiation. Some solutions of RN have also been prepared to carry out the fluorescence intensity calibration. They were prepared with sodium salts of resorufin (Sigma-Aldrich) and their concentration range was from 10⁻⁷ to 10⁻⁵ M. Phosphate buffer to maintain pH at 6.8 was also used.

## 2.3. Ion beam parameters

Proton irradiations were conducted using the R&D beam-line at the MEDICYC cyclotron located at the Centre Antoine Lacassagne in Nice, France. The characteristics of this installation have been extensively detailed in a previous article(Audouin et al., 2023). The proton beams used in this study was collimated to a diameter of 8 mm, with a flattop
profile, and had a single energy of 64 MeV at the exit of the vacuum chamber with an energy spread of 0.3 MeV. Average fluence rates of 3.10 × 10⁹, 6.21 × 10⁹, 1.24 × 10¹⁰ and 2.48 × 10¹⁰ proton. s⁻¹. cm⁻² were applied, corresponding to beam currents of 0.25, 0.5, 1 and 2 nA, respectively, for an 8 mm diameter beam in the samples.

## 2.4. In line absorption and fluorescence detection

We designed a spectrometer providing two optical configurations. The first configuration was designed to performed absorbance measurements and has already been described elsewhere (Audouin et al., 2023). The second one was used for fluorescence measurement with the RNO and AR systems and is illustrated in Fig. 1. Compared to the absorption configuration, the fluorescence configuration includes a second optical filter placed between sample and the light collection system, which selects the fluorescence light generated by the fluorescent molecules. At the excitation port (yellow optical beam with the arrow on the right side of Fig. 1), a white light provided by a fibre coupled to a Xe-arc lamp (LDLS, Energetiq) is first collimated with a light collimator (CVH100-COL, Thorlabs). A bandpass filter centered at 514.5 nm with a spectral bandwidth of 10 nm (FL514.5–10, Thorlabs) is inserted at the exit of the collimator to select the excitation wavelength. The filter placed at the sample holder outlet and filtering the fluorescence light was a high-pass filter with a cut-off wavelength at 570 nm (type OG570 Schott: FGL570, Thorlabs). As mentioned in previous description (Audouin et al., 2023), the fiber bundle - 20 m in length and consisting of 20 optical fibers, each with a diameter of 250 µm - brings the collected emitted fluorescence to a monochromator (Zolix). It was set at a wavelength of 585 nm using a grating blazed at 500 nm. We used disposable PMMA cuvette as sample holder for all the measurements in fluorescence. The dimensions of these cuvettes were 10 × 10 × 50 mm³ (inside) with wall thickness of 1 mm (Kartell, Fisher Scientific). Each irradiation was made with a new cuvette and they were charged and discharged from the holder with a robotic arm between each irradiation.

As already mentioned, the measurements with the Fe(CN)₆⁻ system were performed using the absorption configuration. In this case, the optical filter placed at the exit of the light collimator (Namely the “Excitation light filter” in Fig. 1) was a high-pass filter with a cut-off wavelength of 395 nm (FSR-GG395, Newport). The monochromator was then set at 420 nm using a grating blazed at 300 nm. We kept the same model of cuvette than for the fluorescence configuration as it suits perfectly for absorption spectroscopy.

We must notice that the use of disposable PMMA cuvette had the significant drawback to modify the position of the Bragg peak from one cuvette to another due to the fact that each cuvette has a PMMA window with a thickness varying up to 10 %. We therefore performed

experiments using a single cuvette in quartz for all irradiation concerning the Fe(CN)₆⁻ samples by renewing the solution with a remotely controlled pump. We used a Suprasil Quartz cuvette (model 175-15-10-40, Hellma Analytics) with a dimension of 12.5 × 12.5 × 45 mm³ (outside). In the beam direction the dimension were 3 mm of quartz, 6.5 mm of water and 3 mm of quartz. In the light direction (perpendicular to the beam direction) the dimension were 1.25 mm of quartz, 10 mm of water and 1.25 mm of quartz.

A sCMOS camera (Orca-Flash4.0, Hamamatsu) performed the detection of the light at the output port of the monochromator. The acquisition parameters for all irradiations were mono-channel, having a resolution of 1024 × 1024 pixels and an integration time of 100 ms. The image processing was described in a previous article (Audouin et al., 2023). The variation of absorbance of Fe(CN)₆⁻ over time was obtained for each fiber through a linear regression over 25 points with the first point roughly corresponding to the beginning of the irradiation. For the fluorescence measurements using RNO, the method was the same with a linear regression over up to 160 points. For the measurement with AR, the increase of fluorescence during time was not linear but rather exponential. We correlated the expression (15) with our data and deduced from it the expression (16) of the variation of the fluorescence intensity over time.

$$I_n = C + A_n \exp(R_n t) \quad (15)$$

$$\frac{dI}{dt_{n,t0}} = A_n R_n \exp(R_n t_0) \quad (16)$$

With $I_n(t)$ the fluorescence intensity for a given time t and fiber n; $A_n$, $R_n$ and C some fitted coefficients, $t_0$ the moment where the irradiation starts and $(dI/dt)_{n,t0}$ the variation of the fluorescence intensity for the fiber n and at the time $t_0$.

## 2.5. Dose rate determination along the track

The dose rate for a fiber n and for a proton beam is given by equation (17).

$$\left(\frac{dD}{dt}\right)_n = \text{ELF}_n \times \frac{I}{1.6 \times 10^{-19}} \quad (17)$$

I is the beam current in ampere (A). $ELF_n$ is the mean value calculated on the fiber n of the Energy Loss Function (Gy.ion⁻¹). The ELF was calculated for each configuration with the Monte-Carlo open-source code GEANT4 (Version11.0) and the calculation method we used to obtain $ELF_n$ from the ELF has already been explained somewhere else (Agostinelli et al., 2003; Allison et al., 2006, 2016; Audouin et al., 2023).

The complete trajectory of the proton beam between the exit of the accelerator vacuum chamber and the sample was simulated with

<figure><img src="image_3.png" /><figcaption>Fig. 1. Optical setup to detect in line under radiation the fluorescence intensity in a cuvette containing the scavenger aqueous solution.</figcaption></figure>
GEANT4. The proton beam at the exit of the vacuum chamber was modelled as a normal incident circular beam with diameter of 8 mm, a homogeneous profile and a Gaussian energy spectrum with a mean energy of 64.0 MeV and a variance of 0.3 MeV. For all configurations, the detailed interactions of the beam with the exit window, the PMMA degrader, the collimator and the sample were considered. This allows taking into account the degradation of the beam reaching a 25 MeV mean energy in front the water sample as well as the energy straggling along the beam line. The parameters of the crossed material used in the simulation are detailed in the SI-4 for each configuration. The ELF was computed as the absorbed dose in the water sample with 50 µm resolution along the beam line and averaged over a circular lateral section of 8 mm diameter. Fig. 2 presents the calculated dose rate in the water sample along with LET value (both are normalized over the total incident protons) and the total proton fluence. Detailed dose rate values as function of beam intensity are gathered in tables in SI-5. To give typical values, for 1 nA, dose rate at maximum is 128.5 Gy/s in BP whereas at the entrance of the sample, it is 24.3 Gy/s.

## 3. Results

### 3.1. Ferro/ferricyanide system

Fig. 3-A shows the absorbance measured for an irradiation of ferro-cyanide solutions with a proton beam whose energy was degraded to 25 MeV at the cuvette entrance, and a current of 1 nA. In total, eight solutions were irradiated for 30 s, and the absorbance was recorded over 40 s. The absorbance increase follows the same pattern for all solutions. There is no absorbance before irradiation. Upon the start of irradiation, the absorbance begins to increase immediately, reaching a maximum value before plateauing at approximately 0.06, even with continued irradiation for several additional dozens of seconds. This indicates that the system reaches chemical equilibrium in less than 5 s and that the ferricyanide produced by proton irradiation is stable in the presence of ongoing proton exposure. The absorption signal exhibits significant noise due to the very low absorbance values recorded during our measurements. Fig. 3-B shows the mean yield calculated over 8 yields deduced from the measured absorbances using equation (2). The change in absorbance was determined through a linear regression on 25 data points following the start of irradiation. The behavior of the yields is consistent across different solutions. Initially, the yields hover around 3 molecules/100eV at the beginning of the track (1 mm into the solution). This value decreases until it reaches a minimum of approximately

<figure><img src="image_4.png" /><figcaption>Fig. 2. Normalized dose rate (ELF), average LET and fluence in liquid water sample, in a fused silica cuvette, obtained by calculation using GEANT4 for protons of 64 MeV at the nozzle exit.</figcaption></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. A- Absorbance in the central part of the beam propagation axis in the sample (about 3 mm in the track) obtained for a 30s-irradiation. The proton beam has an energy of 25 MeV and a current of 1 nA at the entrance window of the sample. B- Formation yield of ferricyanide at every position along the track (mean value over 8 yields).</figcaption></figure>

2.3–2.4 molecules/100eV in the region where the dose rate is maximal. Subsequently, the yields increase in the final few millimeters of the proton track, where the dose rate is decreasing and LET is increasing (Fig. 2). Despite the error bar generated by the low value of dose rate in this distal part, Fig. 3B show clearly the yield rise tendency is significant.

### 3.2. RNO-AR-RN systems

Fig. 4 shows the variation of fluorescence intensity recorded during the irradiation of RNO and AR solutions with a 25 MeV proton beam with different beam intensities at fiber 11, located at 4.86 mm along the track from the start of the sample. For the RNO solution, the fluorescence initially increases linearly, then accelerates after some time during irradiation (after 2 s for a current of 2 nA, 4 s for 1 nA, 10 s for 0.5 nA, and more than 15 s for 0.25 nA), until it reaches a maximum between 250 and 300 a. u. After removing the light intensity background, this corresponds to a value between 120 and 170 a. u. After that, the fluorescence decreases.

For the AR solutions, the fluorescence growth is exponential, reaching a maximum between 160 and 180 a. u. (representing after background extraction a value between 55 and 75 a. u.) before decreasing. For both solutions, the fluorescence growth is directly related to the beam current/dose rate: the higher the beam current or dose rate, the greater the fluorescence growth and the sooner the
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Variation of fluorescence intensity in the middle of the cuvette (the central fiber is taken into account which corresponds to about 3 mm length of proton track) during the proton irradiation at different beam currents (from 0.25 to 2 nA) of RNO (top) and AR (bottom) solutions with protons.</figcaption></figure>

maximum fluorescence intensity is reached. The decrease of the fluorescence after reaching a maximum indicates that other chemical phenomena occur in the tracks of the RNO and AR solutions. This point will be discussed in the next section.

Figs. 5 and 6 present the radiolytic yields deduced from measurements taken with 25 MeV and 62 MeV proton beams (no degrader) for RNO and AR solutions with beam intensities ranging from 0.25 nA to 2 nA. The variation in fluorescence intensity was determined using the method described in the 2.4 section, and the yields were deduced using equation (3). The yields displayed on the left side of the graph's breakpoint were measured with the 62 MeV proton beam, while those on the right side were measured with the 25 MeV proton beam. Thus, these graphs provide an overview of the yields under proton beams with an initial energy of 62 MeV until the end of their track. It should be noted that for the yields obtained with RNO solutions (Fig. 5), the yield of RN multiplied by 2 is displayed on the y-axis. This presentation choice was made because the yield of $e_{aq}$ is equal to 2 times that of RN with this sensor system. Therefore, the displayed yield for RNO solutions also represents the yield of the hydrated electron.

The yields measured with the 25 MeV proton beam range from 0.05

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Formation yield of RN from RNO solution, under 62-MeV proton irradiation for the interval 1.8–7.5 mm and for the interval 28–33 mm by using 25-MeV protons. Here we consider the full bundle of fiber. We skipped the fiber signals when the signal is roughly zero and noisy. The black plot is the calculated dose rate along the track.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Formation yield of RN from AR solution, under 62-MeV proton irradiation for the interval 1.8–7.5 mm and for the interval 28–33 mm by using 25-MeV protons. Here we consider the full bundle of fiber. We skipped the fiber signals when the signal is roughly zero and noisy. The black plot is the normalized calculated dose rate along the track.</figcaption></figure>

to 0.21 molecules/100eV for RNO solutions and from 0.08 to 0.30 molecules/100eV for AR solutions. Most of the yield curves are characterized by a decrease in value along the track until reaching a minimum around 31.0–31.4 mm, where the dose rate is maximal. From this point, the yields increase again. Some of the yields presented in the figure do not show this increase after the breakpoint. However, since this is not the predominant behavior observed and other results using a different chemical system have also shown an increase in yields after the BP (ref: SF article), we can conclude that the increase in yields is genuine and not a measurement artifact.

The yields measured with 62 MeV proton beams range from 0.12 to 0.32 molecules/100eV for RNO solutions and from 0.11 to 0.30 molecules/100eV for AR solutions. The overall behavior of the yields in this part of the track is similar for both solutions, showing a slow decrease along the track that follows the slow increase in dose rate along the track. However, for the RNO solutions, we observed an increase in yields
starting 5 mm into the track. A technical issue in this series of measurements likely caused this increase, as there is no supporting evidence in the literature or theory to justify an increase in a proton track region where many measurements have already been conducted and where the LET is nearly constant.

## 4. Discussion

Figs. 3–6 show that, with three different chemical systems, proton beam irradiation exhibits the same radiolytic yield behavior along the track. Initially, yields decrease slowly in the high-energy, low-LET region of the track. This decay accelerates sharply to a minimum value when the dose rate reaches a maximum value (BP). After the BP, yields increase in the region where the dose rate drops since more protons are stopped in the medium by delivering their remained kinetic energy. This overall pattern of radiolytic yields in proton tracks has also been observed by using the Fricke dosimeter (Audouin et al., 2023). The post-peak yield increase is a novel observation for individual species, $e_{\alpha q}$ and $\cdot OH$, enabled by the new experimental fluorescence technique described in this article, which was also used in the article presenting the Fricke dosimeter results with an absorption spectrophotometry version. An explanation provided in that article suggested that longitudinal straggling is the main factor for the increase of the yields after BP. It was stated the straggling is maximal at the dose peak, which leads to a maximal energy dispersion of the remaining protons in the beam. Therefore, after the peak, we observe a highly dispersed energy distribution of protons (Garcia-Molina et al., 2011) and a sparse distribution of individual entities, as most protons come to stop near the dose peak (see Fig. 2). Our conclusion was that the combination of a large energetic dispersion of the protons with a low density of radiolytic species would result in higher macroscopic yields after the BP than inside. This would be due to a higher proportion of protons with intermediate LET in this region of the track compared to the dose peak. However, this explanation has a major weakness: it does not consider the average LET values along the track, which contradict the hypothesis of a maximal LET value at the peak followed by a decrease to intermediate values. Fig. 2 shows that the track segment LET steadily increases along the track, being higher and higher after BP than at the peak itself. Coupled with the proton fluence, this indicates that after the dose peak, there is a highly dispersed proton distribution with low particle density, but with an average LET significantly higher than at the dose peak. Moreover this was already identified elsewhere (Rodland et al., 2024). This discrepancy does not justify higher radical yields in this area since elevated LET generally provokes low radical yields (LaVerne, 2000; Yamashita et al., 2011).

We then considered another explanation based on the change of track structure happening along the track end, especially when LET reaches high value. Indeed, we can distinguish two track structures depending on the energy (and therefore the LET) of the protons (Chatterjee and Magee, 1980). The first one is composed of ionization events widely dispersed along the track and is characteristic of high-energy proton (energy higher than 2 MeV, which can be considered as low LET proton). The spurs consequently are widely spaced and do not overlap allowing radicals to escape without recombining, which leads to rather high radical yields. This "dispersed" track structure predominates at the initial segments of our yield curves (from 1 to 2 mm in Fig. 3B, from 2 to 29 mm in Figs. 5 and 6) because, at these points, the vast majority of protons possesses high energy (at least several MeV) and consequently relatively low LET value. This observation is corroborated by Fig. 2, which illustrates that in this region, the proton flux is very high while the average LET remains low. At these locations, the slight decrease of the radical yields primarily stems from changes in the energy spectrum of the secondary electrons (de Vera et al., 2019; De Vera et al., 2018; Vera et al., 2018).

The second track structures is characterized by the ionization events closely packed together and is associated with low energy proton (with

relatively high LET). Here, the spurs overlap due to the extremely high ionization density, forming a cylindrical structure with a core surrounded by a penumbra (Kusumoto et al., 2024; Mozumder, 1989; Ogawa et al., 2021; Pimblott and LaVerne, 2002). In the core, the density of ionization events caused by the primary particle is extreme. The penumbra consists in a dense distribution of tracks from secondary electrons generated by the primary particle's passage. This structural arrangement favors radical recombination and is associated with low radical yields. It is prevalent in the track-end of energetic ions where their energy is low and their LET is high.

In a proton beam, the intrinsic energy distribution of the beam and the stochastic nature of the energy loss along the path of each proton causes a longitudinal dispersion that broadens the initial energy spectrum, leading to a change of track structure at different depths along the trajectory depending on the individual proton history. This means that within the track, there is a transition segment where the proton population gradually shifts from a dispersed track structure to a core-penumbra structure as described theoretically in the 80's (Chatterjee and Magee, 1980). This segment in the track is likely located where the proton fluence drops (Fig. 2), which also corresponds to the area where the yield values shown in Figs. 4–6 are at their minimum. It could then be conceivable that the drop in yields followed by their increase is caused by a local dose-rate effect. Indeed, in this region, the transition in track structure is associated with a still relatively high fluence, which could allow inter-track interactions. These inter-track interactions would promote radical recombination, resulting in an even greater decrease in radical yields. However, these inter-track interactions would be much localized along the beam trajectory, as the beam fluence drops rapidly after the peak corresponding to the maximum dose. Beyond a certain depth in the track, these interactions can no longer occur. Although the track structure remains of the core-penumbra type, the proton population would be too low for the probability of inter-track interactions to be significant. This would result in a localized increase in yields, albeit limited by the fact that the average LET in this region remains high, leading to inherently lower associated yields. Thompson et al. recently conducted simulations to investigate inter-track interactions in proton beams (Thompson et al., 2023). These simulations seem to confirm that such interactions can indeed occur in proton beams near the Bragg peak in significant proportions. However, the dose rate conditions under which these simulations were performed are far higher than the dose rate conditions in our experimental setup. This invalidates this explanation in our case and does not correspond to previous observations by LaVerne et al. (LaVerne, 2000).

Regarding the yield values measured after the dose peak in the Fricke dosimeter, they surpass the differential yields determined by Pimblott and LaVerne, primarily because our experimental measurements cover a 280 µm segment in the trajectory (Pimblott and LaVerne, 2002). These yields we determined are thus average yields, and considering the non-linear variation of LET along the proton trajectory associated with the larger energy spectrum of the proton beam in this region, it tends to accentuate higher yield values in such calculations.

The yields recovery in distal part of BP should evoke the fragmentation phenomenon when using high energy ions (Maeyama et al., 2011). Protons of sufficient energy, generally higher than 80 MeV, could provide neutrons and fragments of water oxygen atoms as it is mentioned in literature (Embriaco et al., 2020; Paganetti, 2002). Fragments have generally a high LET and deposit their energy close to where they were generated (Embriaco et al., 2020; Kodaira et al., 2013). So they could only contribute to mitigate radiolytic yields, which is not the trend we observed in distal BP.

In Figs. 5 and 6, the yield values in the left part of the graphs—corresponding to high-energy protons (low LET)—decrease with increasing dose rate. This indicates the presence of a dose rate effect at low LET for the RNO and AR systems. The dose rate at 0.25 nA, 0.5 nA, 1 nA and 2 nA in this region of the track are respectively around 6.0, 12.0, 24.0 and 48.0 Gy/s (see SI-5). A similar observation was reported by
Kusumoto et al. (2020) using a different scavenger system: coumarin-3-carboxylic acid (C3CA). Kusumoto et al. irradiated C3CA solutions with 27.5 MeV proton pulses (average LET of 2.9 keV/µm), using dose rates ranging from 0.05 to 160 Gy/s and total delivered doses between 30 and 80 Gy, and they evaluated the yields of 7-hydroxy-coumarin-3-carboxylic acid (7OH-C3CA) formed by water radiolysis (Kusumoto et al., 2020). They observed decreasing 7OH-C3CA yields with increasing dose rates and attributed this effect to oxygen depletion. More recently, Precek et al. (2022) reported 7OH-C3CA yield measurements using pulsed radiolysis with 4.5 MeV electron pulses and dose rates in the range of $10^{11}-10^{12}$ Gy/s (Precek et al., 2022). They observed a 60% decrease in 7OH-C3CA yield, similar to that observed by Kusumoto et al. However, they did not attribute this effect to oxygen depletion, as the dose threshold for such depletion is estimated to be around 500 Gy. Instead, they suggested that the observed dose rate effect may result from radical recombination processes occurring during the homogeneous chemistry stage. In our case, oxygen depletion can be ruled out as the cause of the observed decrease in RN yields with increasing dose rate at low LET. It is therefore plausible that this effect arises from a mechanism similar to the one described by Precek et al. (2022).

It is challenging to compare the yields we determined with the ferrocyanide sensor system because there are no measured yields for proton beams in the literature using this method. This system has primarily been used in association with pulsed electron beams, with some yield values presented in Table 1. Our yield values are about twice as low as those of Adams et al. and are equivalent to those of Le Caër et al. for a total electron-deposited dose of 1400 Gy. It should be noted that the yield value depends on the total deposited dose. This is because reaction 4 sees its participation increase as more dose is deposited due to the production of H•. Our values seem consistent with the literature since the LET of protons is at least 10 times higher than that of electrons. Thus, a decrease in the radical yields in proton tracks and a decrease of G (Fe(CN)₆³⁻) is expected. It should also be kept in mind that the scavenging capacity in our experiments is more than 100 times lower than those in the literature, which mechanically mitigates the values obtained in this work.

The yields for $e_{aq}$ presented in Table 2 for RNO system are taken from the literature and range from 0.72 (for an average LET of 61 keV/µm) to 1.48 molecules/100 eV (for an average LET of 12.3 keV/µm). The yields in Fig. 5 clearly show that the yields measured by fluorescence with RNO are at least 10 times lower than those reported in the literature for

<caption>**Table 1**</caption>

Comparison of ferricyanide formation yields given in literature as function of the type of particle, the LET and the scavenging capacity. The deposited dose is also specified for the references.

<table><caption>**Table 2**</caption><thead><tr><th>References</th><th>Particle</th><th>LET range (Deposited dose)<br>keV/µm</th><th>Scavenging capacity<br>1/s</th><th>G(Fe(CN)₆³⁻)<br>molecules/100eV</th></tr></thead><tbody><tr><td>This work</td><td>p+ (15.7 MeV - 1.14 mm in track)<br>p+ (4.5 MeV - 3.67 mm in track)</td><td>~3.2<br>~8.8-84</td><td>6.9 × 10<sup>5</sup></td><td>3.04<br>2.25</td></tr><tr><td>Adams et al. (1965)</td><td>pulsed electrons<br>1.8 MeV - 10 Gy/pulse</td><td>0.2-11 (10 Gy)<br>0.2-11 (40 Gy)</td><td>1.0 × 10<sup>8</sup></td><td>6.08<br>5.55</td></tr><tr><td>Le Caër et al. (2007)</td><td>pulsed electrons<br>10 MeV - 7 Gy/pulse</td><td>0.2-11 (1400 Gy)<br>0.2-11 (4200 Gy)</td><td>1.0 × 10<sup>8</sup></td><td>3.40<br>1.70</td></tr></tbody></table>

Comparison of hydrated electron yields given in literature as function of LET and scavenging capacity, for the RNO and AR molecules used as molecular probe.

<table><thead><tr><th>References</th><th>LET range<br>keV/µm</th><th>Scavenging capacity<br>1/s</th><th>Yield<br>molecules/100eV</th></tr></thead><tbody><tr><td><strong>Hydrated electron yield</strong><br>This work using RNO</td><td>1.1<br>4.0<br>8.8-84</td><td>8.60 × 10<sup>5</sup></td><td>0.21<br>0.12<br>0.09</td></tr><tr><td>Appleby and Schwarz (1969)</td><td>12.3<br>61.0</td><td>1.0 × 10<sup>6</sup></td><td>1.48<br>0.72</td></tr><tr><td>LaVerne et al. (2005)</td><td>16.6-100</td><td>3.0 × 10<sup>5</sup><br>3.0 × 10<sup>6</sup></td><td>0.70<br>0.90</td></tr><tr><td><strong>Hydroxyl radical yield</strong><br>This work using AR</td><td>1.1<br>4.0<br>8.8-84</td><td>8.6 × 10<sup>5</sup></td><td>0.19<br>0.17<br>0.12</td></tr><tr><td>Appleby and Schwarz (1969)</td><td>12.3<br>61.0</td><td>1.0 × 10<sup>6</sup></td><td>1.78<br>0.91</td></tr><tr><td>Smith et al. (2021)</td><td>8-100<br>3.3-100</td><td>1.3 × 10<sup>6</sup></td><td>1.60<br>2.30</td></tr><tr><td>Anderson and Hart (1961)</td><td>4.7-100</td><td>1.3 × 10<sup>7</sup></td><td>1.92</td></tr><tr><td>Burns and Sims (1981)</td><td>4.7-100</td><td>1.3 × 10<sup>6</sup><br>1.3 × 10<sup>7</sup></td><td>1.30<br>1.90</td></tr></tbody></table>

equivalent scavenging capacities (around $10^6$ s⁻¹). Table 2 for AR system presents •OH yields taken in the literature, which also range from 0.91 to 1.78 molecules/100 eV. However, similarly to RNO, the yields measured with AR in this work, which are the sum of the yields of $e_{aq}$ and •OH, are 8–11 times lower than the literature values for the highest LETs. At lower LETs (1.1 and 4.0 keV/µm), the yields measured in this work are slightly higher than those obtained at higher LET (particularly in the Bragg peak). This is expected, though they do not reach the values seen with gamma-ray LET or several MeV electrons, whose well-known yields reach 2.7 molecules/100 eV for a LET around 0.24 keV/µm.

The combination of the RNO/RN and AR/RN scavenging systems to simultaneously study the yields of $e_{aq}$ and •OH provides yields significantly lower than those reported in the literature. Even though the conditions and methods differ and there are only few determinations available in the literature, there is still a significant discrepancy, often by at least an order of magnitude. Several possible explanations for these discrepancies can be explored.

The first explanation is that RN reacts in the ionization tracks with other radiolysis products, resulting in non-fluorescent or non-absorbing species at the wavelengths studied. Actually, several authors have noted that RN can be reversibly reduced to dihydrorhodamine, a non-fluorescent molecule (Ibáñez et al., 2020). Given that a large quantity of reducing species (starting with $e_{aq}$) is produced within the ionization tracks, it is likely that some of the produced RN is reduced to dihydrorhodamine during our irradiations, thus diminishing the RN yields. This remark can be associated to the fact that the acquisition of fluorescence intensity is performed every 100 ms by the camera. This time interval combined to a relatively high dose rate is enough to provide a local strong degradation of the formed Resorufin, which mitigates the measure of the initial slope. The current measured yield is not then a primary yield but an observed yield at the ms-s range. A faster acquisition is clearly needed for future investigations if these chemical systems are used.

Another possible explanation involves the phenomenon of "quenching" or fluorescence attenuation within the ionization tracks. The fluorescence properties of a molecule depend indeed greatly on its chemical environment. Thus, the high ionization density, high local concentration of radical species and ions, and the acidity of the tracks observed in some
articles could likely impact the quantum yield of RN fluorescence(Islam et al., 2018).

The use of AR as a scavenger has also some limitations because its mechanism of conversion to RN is not yet well understood. Debski et al. has shown that this mechanism is a one-electron oxidation(Debski et al., 2013, 2016). The second step of forming RN from the intermediate radical requires further attention. Debski et al. postulated that it dis- mutes (similar to the mechanism with RNO), while results from continuous gamma radiolysis conducted by our team show equality between G(RN) and G(OH). A dismutation, like the reduction mecha- nism of RNO, would require two oxidations of AR to form 1 mol of RN. The transformation step of the AR oxide radical into RN is of another type. This step is not yet adequately characterized (type, rate constant, assistance from another species, such as O₂, etc.). The intermediate species and reactions in a multi-step mechanism can be sensitive to the radical environment in ionization tracks, which are dense for high LET.

## 5. Conclusions

We used a spectrometer developed in-house, as presented in a pre- vious article, to measure yields in the BP of proton beams with different scavenger systems. The yield curves along the track determined with the ferrocyanide/ferricyanide, RNO/RN, and AR/RN systems all exhibit the same pattern. The yield curves show a decrease at the beginning of the track, where the average LET values are low (<2 keV/µm) and increase slowly. The yields decrease until they reach a minimum approximately localized at the maximum of the dose rate, which also corresponds to the region of the track where the proton beam fluence collapses. A rise in yield values is then observed in the distal region of the BP, where the average LET values are high (>4 keV/µm) and the proton beam fluence becomes extremely low. The origin of this behavior is difficult to explain. We suggest that it might be related to the longitudinal strag- gling of the beam associated with the complex track structures found in and after the BP. The absolute yield values obtained with the ferrocya- nide/ferricyanide system are consistent with the yield values reported in the literature for electron beam, although additional measurements with this system in proton beams are necessary for definitive validation. Finally, the absolute values of $e_{aq}^-$ and •OH yields recorded respectively for the RNO/RN and AR/RN systems are significantly lower than those reported in the literature. A combination of several factors explains these abnormally low values: the reduction of RN into di-hydro- rhodamine and the quenching of fluorescence in the extreme chemical environment of ionization tracks are the main reasons. A dose rate effect caused by radical recombination during the homogeneous chemical phase may contribute as well. For the AR/RN system, the incomplete understanding of the mechanism converting AR into RN must also be considered, as it may be sensitive to the specific chemical conditions of ionization tracks.

These experimental results give more details on the physico- chemical origin of phenomena depicted in the distal part of proton BP in biological and clinical systems(Horendeck et al., 2021). They also underline the difficulties to obtain absolute values of primary yields by using organic molecules as scavenger (here RNO and AR), as already described in the past(LaVerne, 2000). The ferrocyanide solution seems more relevant but its complex chemistry prevents from deducing a unique radical species in the BP similarly to the Fricke system. The ideal scavengers for yield determination with absorbance/fluorescence spec- troscopy under continuous mono-energetic irradiation are not yet identified. Detection at earliest times after the beginning of irradiation is certainly the best way to investigate yields in the future to avoid considering any scavenger degradation. Monte Carlo simulations are also paving the way of the understanding of the early dose rate effect in realistic proton beam(Chappuis et al., 2024; Jay-Gerin, 2020; Tran et al., 2021). Comparisons will then be possible.

## CRediT authorship contribution statement

**Julien Audouin:** Writing – review & editing, Writing – original draft, Software, Methodology, Investigation, Formal analysis. **Laurent Desorgher:** Writing – review & editing, Software. **Petter Hofverberg:** Writing – review & editing, Resources, Methodology. **Gérard Baldac-chino:** Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Investigation, Funding acquisi-tion, Conceptualization.

## Declaration of generative AI in scientific writing

During the preparation of this work, the authors used ChatGPT/ OpenAI and LeChat/Mistral AI in order to correct and improve the language level of the manuscript. After using these services, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

Experiments were carried out using the therapeutic proton beamline Medicyc in CAL, Nice (France). The authors would like to thank the staff of the CAL for assistance and support in using Medicyc beamline. The authors also acknowledge R. Trimaud, J. Hérault, J.-M. Bergerot and J. Provost for facilitating the planning and the access to CAL and Medicyc experimental cave. We also thank S. Incerti and G. Montarou for their significant help in the discussions for the access to CAL beamline and their critical view in the Biorad3 project.

The authors acknowledge CEA through the FOCUSDEM Program 2020, ESA through the Biorad3 project and Plan Cancer through the Bitmap project (PC201604) for their financial contributions. This study was also carried out in the frame of iNanoTheRad program of the Uni- versity Paris-Saclay.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.radphyschem.2025.112995.

## Data availability

Data will be made available on request.

## References

Adams, G.E., Boag, J.W., Michael, B.D., 1965. Spectroscopic studies of reactions of the OH radical in aqueous solutions: reaction of OH with the ferrocyanide ion. Trans. Faraday Soc. 61, 492–505. https://doi.org/10.1039/tf9656100492.

Adams, G.E., Willson, R.L., 1969. Pulse radiolysis studies on the oxidation of organic radicals in aqueous solution. Trans. Faraday Soc. 65, 2981–2987. https://doi.org/10.1039/TF9696502981.

Agostinelli, S., Allison, J., Amako, K., Apostolakis, J., Araujo, H., Arce, P., Asai, M., Axen, D., Banerjee, S., Barrand, G., Behner, F., Bellagamba, L., Boudreau, J., Broglia, L., Brunengo, A., Burkhardt, H., Chauvie, S., Chuma, J., Chytracek, R., Cooperman, G., Cosmo, G., Degtyarenko, P., Dell'Acqua, A., Depaola, G., Dietrich, D., Enami, R., Feliciello, A., Ferguson, C., Fesefeldt, H., Folger, G., Foppiano, F., Forti, A., Garelli, S., Giani, S., Giannitrapani, R., Gibin, D., Gomez Cadenas, J.J., Gonzalez, I., Gracia Abril, G., Greeniaus, G., Greiner, W., Grichine, V., Grossheim, A., Guatelli, S., Gumplinger, P., Hamatsu, R., Hashimoto, K., Hasui, H., Heikkinen, A., Howard, A., Ivanchenko, V., Johnson, A., Jones, F.W., Kallenbach, J., Kanaya, N., Kawabata, M., Kawabata, Y., Kawaguti, M., Kelner, S., Kent, P., Kimura, A., Kodama, T., Kokoulin, R., Kossov, M., Kurashige, H., Lamanna, E., Lampen, T., Lara, V., Lefebure, V., Lei, F., Liendl, M., Lockman, W., Longo, F., Magni, S., Maire, M., Medernach, E., Minamimoto, K., Mora de Freitas, P., Morita, Y.,
Murakami, K., Nagamatu, M., Nartallo, R., Nieminen, P., Nishimura, T., Ohtsubo, K., Okamura, M., O'Neale, S., Oohata, Y., Paech, K., Perl, J., Pfeiffer, A., Pia, M.G., Ranjard, F., Rubin, A., Sadilov, S., di Salvo, E., Santin, G., Sasaki, T., Savvas, N., Sawada, Y., Scherer, S., Sei, S., Sirotenko, V., Smith, D., Starkov, N., Stoecker, H., Sukimo, J., Takahata, M., Tanaka, S., Tcherniaev, E., Safai Tehrani, E., Tropeano, M., Truscott, P., Uno, H., Urban, L., Urban, P., Verderi, M., Walkden, A., Wander, W., Weber, H., Wellisch, J.P., Wenaas, T., Williams, D.C., Wright, D., Yamada, T., Yoshida, H., Zschiesche, D., 2003. GEANT4 - a simulation toolkit. Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip. 506, 250-303. https://doi.org/10.1016/S0168-9002(03)01368-0.

Allison, J., Amako, K., Apostolakis, J., Araujo, H., Dubois, P.A., Asai, M., Barrand, G., Capra, R., Chauvie, S., Chytracek, R., Cirrone, G.A.P., Cooperman, G., Cosmo, G., Cuttone, G., Daquino, G.G., Donszelmann, M., Dressel, M., Folger, G., Foppiano, F., Generowicz, J., Grichine, V., Guatelli, S., Gumplinger, P., Heikkinnen, A., Hrivacova, I., Howard, A., Incerti, S., Ivanchenko, V., Johnson, T., Jones, F., Koi, T., Kokoulin, R., Kossov, M., Kurashige, H., Lara, V., Larsson, S., Lei, F., Longo, F., Maire, M., Mantero, A., Mascialino, B., McLaren, I., Lorenzo, P.M., Minamimoto, K., Murakami, K., Nieminen, P., Pandola, L., Parlati, S., Peralta, L., Perl, J., Pfeiffer, A., Pia, M.G., Ribon, A., Rodrigues, P., Russo, G., Sadilov, S., Santin, G., Sasaki, T., Smith, D., Starkov, N., Tanaka, S., Tcherniaev, E., Tomé, B., Trindade, A., Truscott, P., Urban, L., Verderi, M., Walkden, A., Wellisch, J.P., Williams, D.C., Wright, D., Yoshida, H., Peirgidenti, M., 2006. Geant4 developments and applications. IEEE Trans. Nucl. Sci. 53, 270-278. https://doi.org/10.1109/TNS.2006.869826.

Allison, J., Amako, K., Apostolakis, J., Arce, P., Asai, M., Aso, T., Bagli, E., Bagulya, A., Banerjee, S., Barrand, G., Beck, B.R., Bogdanov, A.G., Brandt, D., Brown, J.M.C., Burkhardt, H., Canal, P., Cano-Ott, D., Chauvie, S., Cho, K., Cirrone, G.A.P., Cooperman, G., Cortés-Giraldo, M.A., Cosmo, G., Cuttone, G., Depaola, G., Desorgher, L., Dong, X., Dotti, A., Elvira, V.D., Folger, G., Francis, Z., Galoyan, A., Garnier, L., Gayer, M., Genser, K.L., Grichine, V.M., Guatelli, S., Guéye, P., Gumplinger, P., Howard, A.S., Hriváncová, I., Hwang, S., Incerti, S., Ivanchenko, A., Ivanchenko, V.N., Jones, F.W., Jun, Y.S., Kaitaniemi, P., Strakatsanis, N., Karamitrosi, M., Kelsey, M., Kimura, A., Koi, T., Kurashige, H., Lechner, A., Lee, S.B., Longo, F., Maire, M., Mancusi, D., Mantero, A., Mendoza, E., Morgan, B., Murakami, K., Nikitina, T., Pandola, L., Paprocki, P., Perl, J., Petrović, I., Pia, M.G., Pokorski, W., Quesada, J.M., Raine, M., Reis, M.A., Ribon, A., Ristić Fira, A., Romano, F., Russo, G., Santin, G., Sasaki, T., Sawkey, D., Shin, J.I., Strakovsky, I.I., Taborda, A., Tanaka, S., Tomé, B., Toshito, T., Tran, H.N., Truscott, P.R., Urban, L., Uzhinsky, V., Verbeke, J.M., Verderi, M., Wendt, B.L., Wenzel, H., Wright, D.H., Wright, D.M., Yamashita, T., Yarba, J., Yoshida, H., 2016. Recent developments in GEANT4. Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 835, 186-225. https://doi.org/10.1016/j.nima.2016.06.125.

Anderson, A.R., Hart, E.J., 1961. Molecular product and free radical yields in the decomposition of water by protons, deuterons, and helium ions. Radiat. Res. 14, 689-704. https://doi.org/10.2307/3571010.

Appleby, A., Schwarz, H.A., 1969. Radical and molecular yields in water irradiated by γ rays and heavy ions. J. Phys. Chem. 73, 1937-1941. https://doi.org/10.1021/jl00726a048.

Audouin, J., 2023. Analyse des processus physico-chimiques dans le pic de Bragg de faisceaux d'ions continus dans l'eau.

Audouin, J., Hofverberg, P., Ngono-Ravache, Y., Desorgher, H., Baldacchino, G., 2023. Intermediate LET-like effect in distal part of proton Bragg peak revealed by track-ends imaging during super-Fricke radiolysis. Sci. Rep. 13, 15460. https://doi.org/10.1038/s41598-023-42639-4.

Balcerzyk, A., Baldacchino, G., 2014. Implementation of laser induced fluorescence in a pulse radiolysis experiment - a new way to analyze resazurin-like reduction mechanisms. Analyst 139, 1707-1712. https://doi.org/10.1016/j.cmarc02000b.

Baldacchino, G., 2008. Pulse radiolysis in water with heavy-ion beams. A short review. Radiat. Phys. Chem. 77, 1218-1223. https://doi.org/10.1016/j.radphyschem.2008.05.033.

Baldacchino, G., Brun, E., Denden, I., Bouhadoun, S., Roux, H., Khodja, H., Sicard-Roselli, C., 2019. Importance of radiolytic reactions during high-LET irradiation modalities: LET effect, role of O2 and radiosensitization by nanoparticles. Cancer Nanotechnol 10, 1-12. https://doi.org/10.1186/s12645-019-0047-y.

Baldacchino, G., Katsumura, Y., 2010. Chemical processes in heavy ion tracks. In: Recent Trends in Radiation Chemistry. World Scientific Publishing Co. Pte. Ltd., pp. 231-253. https://doi.org/10.1142/9789814282093_0008

Baldacchino, G., Trupin, V., Bouffard, S., Balanzat, E., Gardes-Albert, M., Abedinzadeh, Z., Jore, D., Deycard, S., Hickel, B., 2000. Heavy-ion pulse radiolysis studies: direct measurement of superoxide free radicals. In: Radiation Research, vol. 2. Congress Proceedings.

Barker, G.C., Fowles, P., 1970. Pulse radiolytic induced transient electrical conductance in liquid solutions. Trans. Faraday Soc. 66, 1661-1669. https://doi.org/10.1039/TF9706601661.

Blain, G., Vandenborre, J., Villoing, D., Fiegel, V., Fois, G.R., Haddad, F., Koumeir, C., Maigne, L., Métivier, V., Poirier, F., Potiron, V., Supiot, S., Servagent, N., Delpon, G., Chiavassa, S., 2022. Proton irradiations at ultra-high dose rate vs. Conventional dose rate: strong impact on hydrogen peroxide yield. Radiat. Res. 198, 318-324. https://doi.org/10.1667/RADE-22-00021.1.

Britten, R.A., Nazaryan, V., Davis, L.K., Klein, S.B., Nichiporov, D., Mendonca, M.S., Wolanski, M., Nie, X., George, J., Keppel, C., 2013. Variations in the RBE for cell killing along the depth-dose profile of a modulated proton therapy beam. Radiat. Res. 179 (1), 21-28. https://doi.org/10.1667/RR2737.

Burns, W.G., Sims, H.E., 1981. Effect of radiation type in water radiolysis. J. Chem. Soc. Faraday Trans. 1 Phys. Chem. Condens. Phases 77, 2803-2813. https://doi.org/10.1039/F19817702803.

Chappuis, F., Tran, H.N., Jorge, P.G., Zein, S.A., Kyriakou, I., Emfietzoglou, D., Bailat, C., Bochud, F., Incerti, S., Desorgher, L., 2024. Investigating ultra-high dose rate water radiolysis using the Geant4-DNA toolkit and a Geant4 model of the Oriatron eRT6 electron linac. Sci. Rep. 14, 26707. https://doi.org/10.1038/s41598-024-76769-0.

Chatterjee, J.A., Mawake, J.L., 1980. Radiation chemistry. J. Phys. Chem. 84, 3537-3543. https://doi.org/10.1021/j100463a009.

De Vera, P., Abril, I., Garcia-Molina, R., 2018. Energy spectra of protons and generated secondary electrons around the Bragg peak in materials of interest in proton therapy. Radiat. Res. 190, 282-297. https://doi.org/10.1667/RR14988.1.

De Vera, P., Garcia-Molina, R., Abril, I., 2019. Simulation of the energy spectra of swift light ion beams after traversing cylindrical targets: a consistent interpretation of experimental data relevant for hadron therapy. Eur. Phys. J. D 73. https://doi.org/10.1140/epjd/e2019-100083-4.

Debski, D., Michałowski, B., Adamus, J., Wojciechowski, J., Zielonka, J., Kalyanaraman, B., Sikora, A., 2013. Direct characterization of transient species formed upon one-electron oxidation of amplex red. Free Radic. Biol. Med. 65, S88-S89. https://doi.org/10.1016/j.freeradiomed.2013.10.607.

Debski, D., Smulik, R., Zielonka, J., Michałowski, B., Jakubowska, M., Debowska, K., Adamus, J., Marcinek, A., Kalyanaraman, B., Sikora, A., 2016. Mechanism of oxidative conversion of Amplex® Red to resorufin: pulse radiolysis and enzymatic studies. Free Radic. Biol. Med. 95, 323-332. https://doi.org/10.1016/j.freeradiomed.2016.03.027.

Embriaco, A., Attili, A., Bellinzona, E.V., Dong, Y., Grzanka, L., Mattei, I., Muraro, S., Scifoni, E., Tommasino, F., Valle, S.M., Battistoni, G., 2020. FLUKA simulation of target fragmentation in proton therapy. Phys. Med. 80, 342-346. https://doi.org/10.1016/j.ejmp.2020.09.018.

Garcia-Molina, R., Abril, I., Heredia-Avalos, S., Kyriakou, I., Emfietzoglou, D., 2011. A combined molecular dynamics and Monte Carlo simulation of the spatial distribution of energy deposition by proton beams in liquid water. Phys. Med. Biol. 56, 6475-6493. https://doi.org/10.1088/0031-9155/56/19/019.

Gordon, S., Hart, E.J., Matheson, M.S., Rabani, J., Thomas, J.K., 1963. Reactions of the hydrated water. Discuss. Faraday Soc. 36, 193-205. https://doi.org/10.1039/DF9633600193.

Heemskerk, T., Groenendijk, C., Rovituso, M., van der Wal, E., van Burik, W., Chatzipapas, K., Lathouwers, D., Kanaar, R., Brown, J.M.C., Essers, J., 2025. Position in proton Bragg curve influences DNA damage complexity and survival in head and neck cancer cells. Clin. Transl. Radiat. Oncol. 51, 100908. https://doi.org/10.1016/j.ctro.2024.100908.

Horendeck, D., Walsh, K.D., Hirakawa, H., Fujimori, A., Kitamura, H., Kato, T.A., 2021. High LET-like radiation tracks at the distal side of accelerated proton Bragg peak. Front. Oncol. 11, 690042. https://doi.org/10.3389/fonc.2021.690042.

Ibáñez, D., Izquierdo-Bote, D., Pérez-Junquera, A., González-García, M.B., Hernández-Santos, D., Fanjul-Bolado, P., 2020. Raman and fluorescence spectroelectrochemical monitoring of resazurin-resorufin fluorogenic system. Dyes Pigments 172. https://doi.org/10.1016/j.dyeipig.2019.107848.

Islam, M.M., Kanike, V., Meesungnoen, J., Lertnaisa, P., Katsumura, Y., Jay-Gerin, J.P., 2018. In situ generation of ultrafast transient "acid spikes" in the 10B(n,α)7Li radiolysis of water. Chem. Phys. Lett. 693. https://doi.org/10.1016/j.cplett.2017.12.037.

Jay-Gerin, J.-P., 2020. Ultra-high dose-rate (FLASH) radiotherapy: generation of early, transient, strongly acidic spikes in the irradiated tumor environment. Cancer Radiother. 24, 332-334. https://doi.org/10.1016/j.cmarc.2019.11.004.

Jayson, G.G., Parsons, B.J., Swallow, A.J., 1975. The mechanism of the fricke dosimeter. Int. J. Radiat. Phys. Chem. 7, 363-370. https://doi.org/10.1016/0020-7055(75)90075-3.

Khylustova, A., Khomyakova, N., Sirotkin, N., Marfin, Y., 2016. The effect of pH on OH radical generation in aqueous solutions by atmospheric pressure glow discharge. Plasma Chem. Plasma Process. 36, 1229-1238. https://doi.org/10.1007/s11090-016-9732-3.

Kim, M.J., Pal, S., Tak, Y.K., Lee, K.H., Yang, T.K., Lee, S.J., Song, J.M., 2007. Determination of the dose-depth distribution of proton beam using resazurin assay in vitro and diode laser-induced fluorescence detection. Anal. Chim. Acta 593, 214-223. https://doi.org/10.1016/j.aca.2007.05.009.

Knapp, J.L.A., González-Pinzón, R., Haggerty, R., 2018. The resazurin-resorufin system: insights from a decade of "smart" tracer development for hydrologic applications. Water Resour. Res. 54, 6877-6889. https://doi.org/10.1029/2018WR023103.

Kodaira, S., Yasuda, N., Konishi, T., Kitamura, H., Kurano, M., Kawashima, H., Uchihori, Y., Ogura, K., Benton, E.R., 2013. Calibration of CR-39 with atomic force microscope for the measurement of short range tracks from proton-induced target fragmentation reactions. Radiat. Meas. 50, 232-236. https://doi.org/10.1016/j.radmeas.2012.10.001.

Kusumoto, T., Danvin, A., Mamiya, T., Arnone, A., Chefson, S., Galindo, C., Peapardin, P., Raffy, Q., Kamiguchi, N., Amano, D., Sasaki, K., Konishi, T., Kodaira, S., 2024. Dose rate effects on hydrated electrons, hydrogen peroxide, and a OH radical molecular probe under clinical energy protons. Radiat. Res. 201, 287-293. https://doi.org/10.1667/RADE-23-00244.1.

Kusumoto, T., Kitamura, H., Hojo, S., Konishi, T., Kodaira, S., 2020. Significant changes in yields of 7-hydroxy-coumarin-3-carboxylic acid produced under FLASH radiotherapy conditions. RSC Adv. 10, 38709-38714. https://doi.org/10.1039/d0ra07999e.

LaVerne, J.A., 2000. Track effects of heavy ions in liquid water. Radiat. Res. 153, 487-496.

LaVerne, J.A., Schuler, R.H., 1994. Track effects in water radiolysis: yields of the Fricke dosimeter for carbon ions with energies up to 1700 MeV. J. Phys. Chem. 98, 4043-4049. https://doi.org/10.1021/j100066a023.
LaVerne, J.A., Stefanić, I., Pimblott, S.M., 2005. Hydrated electron yields in the heavy ion radiolysis of water. J. Phys. Chem. A 109, 9393-9401. https://doi.org/10.1021/jp0530303.

Le Caër, S., Vigneron, G., Renault, J.P., Pommeret, S., 2007. Radiolysis of ferrocyanide solutions studied by infrared spectroscopy. Radiat. Phys. Chem. 76, 1280-1284. https://doi.org/10.1016/j.radphyschem.2007.02.019.

Le Caër, S., Vigneron, G., Renault, J.P., Pommeret, S., 2006. First coupling between a LINAC and FT-IR spectroscopy: the aqueous ferrocyanide system. Chem. Phys. Lett. 426, 71-76. https://doi.org/10.1016/j.cplett.2006.05.076.

Maeyama, T., Yamashita, S., Taguchi, M., Baldacchino, G., Sihver, L., Murakami, T., Katsumura, Y., 2011. Production of a fluorescence probe in ion-beam radiolysis of aqueous coumarin-3-carboxylic acid solution-2: effects of nuclear fragmentation and its simulation with PHITS. Radiat. Phys. Chem. 80, 1352-1357. https://doi.org/10.1016/j.radphyschem.2011.07.004.

Masilela, M.T., Prezado, Y., 2023. A Monte Carlo study of the free radical production in minibeam radiation therapy. Phys. Med. 104, S156. https://doi.org/10.1016/s1120-1797(22)02492-9.

Maurizot-Spotheim, M., Mostafavi, M., Douki, T., Belloni, J., 2008. Radiation Chemistry: From Basics to Applocations in Material and Life Sciences. Editions EDP Sciences, France.

Mohan, R., Grosshans, D., 2017. Proton therapy – present and future. Adv. Drug Deliv. Rev. https://doi.org/10.1016/j address.2016.11.006.

Mozumder, A., 1989. Early events in radiation chemistry: an introduction. Int. J. Radiat. Appl. Instrumentation. Part 34, 1-3. https://doi.org/10.1016/1359-0197(89)90004-0.

Ogawa, T., Hirata, Y., Matsuya, Y., Kai, T., 2021. Development and validation of proton track-structure model applicable to arbitrary materials. Sci. Rep. 11, 1-10. https://doi.org/10.1038/s41598-021-01822-1.

Okazaki, Y., Kusumoto, T., Roux, S., Hirayama, R., Fromm, M., Bazzi, R., Kodaira, S., Kataoka, J., 2024. Increase of OH radical yields due to the decomposition of hydrogen peroxide by gold nanoparticles under X-ray irradiation. RSC Adv. 14, 9509-9513. https://doi.org/10.1039/d4ra00208c.

Paganetti, H., 2002. Nuclear interactions in proton therapy: dose and relative biological effect distributions originating from the primary and secondary particles. Phys. Med. Biol. 47, 747-764. https://doi.org/10.1088/0031-9155/47/5/305.

Pimblott, S.M., LaVerne, J.A., 2002. Effects of track structure on the ion radiolysis of the fricke dosimeter. J. Phys. Chem. A 106, 9420-9427. https://doi.org/10.1021/jp020830u.

Pimblott, S.M., Laverne, J.A., Bartels, D.M., Jonah, C.D., 1996. Reconciliation of transient absorption and chemically scavenged yields of the hydrated electron in radiolysis. J. Phys. Chem. 100, 9412-9415. https://doi.org/10.1021/jp960816f.

Precek, M., Kubelik, P., Vysin, L., Schmidhammer, U., Larbre, J.P., Demarque, A., Jeunesse, P., Mostafavi, M., Juha, L., 2022. Dose rate effects in fluorescence chemical dosimeters exposed to picosecond electron pulses: an accurate measurement of low doses at high dose rates. Radiat. Res. 197, 131-148. https://doi.org/10.1667/RADE-20-00292.1.

Prütz, W.A., Butler, J., Land, E.J., 1996. Photocatalytic and free radical interactions of the heterocyclic N-oxide resazurin with NADH, GSH, and Dopa. Arch. Biochem. Biophys. 327, 239-248. https://doi.org/10.1006/abbi.1996.0116.

Rabani, J., Matheson, M.S., 1966. The pulse radiolysis of aqueous solutions of potassium ferrocyanide. J. Phys. Chem. 70, 761-769. https://doi.org/10.1021/j100875a025.

Rabani, J., Meyerstein, D., 1968. Pulse radiolytic studies of the competition H + H and H + ferricyanide. The absolute rate constants. J. Phys. Chem. 72, 1599-1603. https://doi.org/10.1021/j100851a035.

Rabani, J., Stein, G., 1962. The reactivity of OH radicals with ferro-ferricyanide, formate, ethanol and amino acids in irradiated solutions. J. Chem. Educ. 638-640. https://doi.org/10.1021/ed030p638.

Rødland, G.E., Temelie, M., Eek Mariampillai, A., Hauge, S., Gilbert, A., Chevalier, F., Savu, D.I., Syljušen, R.G., 2024. Potential benefits of combining proton or carbon ion therapy with DNA damage repair inhibitors. Cells. https://doi.org/10.3390/cells13121058.

Ryder, A.G., Power, S., Glynn, T.J., 2003. Fluorescence lifetime based pH sensing using Resorufin. Proc. SPIE 4876, Opto-irel. 2002 Opt. Photonics Technol. Appl. 4876, 827-835.

Shin, W.G., D-Kondo, J.N., Ramos-Méndez, J., LaVerne, J.A., Rothwell, B., Bertolet, A., McNamara, A., Faddegon, B., Paganetti, H., Schuemann, J., 2024. Investigation of hydrogen peroxide yields and oxygen consumption in high dose rate irradiation: a TOPAS-nBio Monte Carlo study. Phys. Med. Biol. 70. https://doi.org/10.1088/1361-6560/ad9ce2.

Smith, M., Pimblott, S.M., LaVerne, J.A., 2021. Hydroxyl radical yields in the heavy ion radiolysis of water. Radiat. Phys. Chem. 188, 109629. https://doi.org/10.1016/j.radphyschem.2021.109629.

Solov'yov, A.V., Verkhovtsev, A.V., Mason, N.J., Amos, R.A., Bald, I., Baldacchino, G., Dromey, B., Falk, M., Fedor, J., Gerhards, L., Hausmann, M., Hildenbrand, G., Hrabovský, M., Kadlec, S., Kočísek, J., Lépine, F., Ming, S., Nisbet, A., Ricketts, K., Sala, L., Schlathölter, T., Wheatley, A., Solov'yov, I.A., 2024. Condensed matter systems exposed to radiation: multiscale theory, simulations, and experiment. Chem. Rev. 124, 8014-8129. https://doi.org/10.1021/ACS.CHEMREV.3C00902.

Stark, J., Woehrle, D., Rabani, J., 1999. Pulse radiolysis studies of a perylene derivative in aqueous solution. Radiat. Phys. Chem. 56, 457-466. https://doi.org/10.1016/S0969-806X(99)00329-1.

Taguchi, M., Hayano, K., Xu, Y., Moriyama, M., Kobayashi, Y., Hiratsuka, H., Ohno, S.I., 2001. Yields of tyrosines in the radiolysis of aqueous phenylalanine solutions by energetic heavy ions. In: Radiation Physics and Chemistry, pp. 263-268. https://doi.org/10.1016/S0969-806X(00)00359-5.

Thompson, S.J., Prise, K.M., McMahon, S.J., 2023. Investigating the potential contribution of inter-track interactions within ultra-high dose-rate proton therapy. Phys. Med. Biol. 68, 055006. https://doi.org/10.1088/1361-6560/acb88a.

Tran, H.N., Archer, J., Baldacchino, G., Brown, J.M.C., Chappuis, F., Cirrone, G.A.P., Desorgher, L., Dominguez, N., Fattori, S., Guatelli, S., Ivantchenko, V., Méndez, J.R., Nieminen, P., Perrot, Y., Sakata, D., Santin, G., Shin, W.G., Villagrasa, C., Zein, S., Incerti, S., 2024. Review of chemical models and applications in geant4-DNA: report from the ESA BioRad III project. Med. Phys. 1-17. https://doi.org/10.1002/ mp.17256.

Tran, H.N., Chappuis, F., Incerti, S., Bochud, F., Desorgher, L., 2021. Geant4-dna modeling of water radiolysis beyond the microsecond: an on-lattice stochastic approach. Int. J. Mol. Sci. 22, 6023-6036. https://doi.org/10.3390/ijsms22116023.

Vera, P. de, Abril, I., Garcia-Molina, R., 2018. Energy spectra of protons and generated secondary electrons around the Bragg peak in materials of interest in proton therapy. Radiat. Res. 190, 282-297. https://doi.org/10.1667/RR14988.1.

Wasselin-Trupin, V., Baldacchino, G., Bouffard, S., Hickel, B., 2002. Hydrogen peroxide yields in water radiolysis by high-energy ion beams at constant LET. Radiat. Phys. Chem. 65, 53-61. https://doi.org/10.1016/S0969-806X(01)00682-X.

Yamashita, S., Katsumura, Y., Lin, M., Muroya, Y., Miyazakia, T., Murakami, T., 2008. Water radiolysis with heavy ions of energies up to 28 GeV. 1. Measurements of primary g values as track segment yields. Radiat. Phys. Chem. 77, 439-446. https://doi.org/10.1016/j.radphyschem.2007.07.005.

Yamashita, S., Taguchi, M., Baldacchino, G., Katsumura, Y., 2011. Radiation chemistry of liquid water with heavy ions: steady-states and pulse radiolysis studies. In: Hatano, Y., Katsumura, Y., Mozumder, A. (Eds.), Charged Particle and Photon Interactions with Matter. Recent Advances, Applications, and Interfaces. CRC Press, Taylor and Francis Group, Boca Raton, pp. 325-354. https://doi.org/10.1201/b10389.

Yamashita, S., Taguchi, M., Baldacchino, G., Katsumura, Y., 2010. Radiation chemistry of liquid water with heavy ions: steady-state and pulse radiolysis studies. In: Charged Particle and Photon Interactions with Matter: Recent Advances, Applications, and Interfaces. https://doi.org/10.1201/b10389.

Zehavi, D., Rabani, J., 1972. Pulse radiolysis of the aqueous ferro-ferricyanide system. I. The reactions of OH, HO2, and O2- radicals. J. Phys. Chem. 76, 3703-3709. https://doi.org/10.1021/j100669a006.