# The production rate of cosmogenic deuterium at the Moon's surface

Evelyn Füri, Etienne Deloule, Reto Trappitsch

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Evelyn Füri, Etienne Deloule, Reto Trappitsch. The production rate of cosmogenic deuterium at the Moon's surface. Earth and Planetary Science Letters, 2017, 474, pp.76-82. 10.1016/j.epsl.2017.05.042. hal-02123069

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# The production rate of cosmogenic deuterium at the Moon's surface

E. Fueri, E. Deloule, R. Trappitsch

May 16, 2017

Earth and Planetary Science Letters
This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.
# The production rate of cosmogenic deuterium at the Moon's surface

Evelyn Füri<sup>a,*</sup>, Etienne Deloule<sup>a</sup>, Reto Trappitsch<sup>b</sup>

<sup>a</sup> Centre de Recherches Pétrographiques et Géochimiques, CNRS-UL, 15 rue Notre-Dame des Pauvres, BP20, 54501 Vandoeuvre-lès-Nancy Cedex, France

<sup>b</sup> The University of Chicago, Department of Geophysical Sciences and Chicago Center for Cosmochemistry, 5734 South Ellis Avenue, Chicago, IL 60637, USA

Now at: Lawrence Livermore National Laboratory, Nuclear and Chemical Sciences Division, 7000 East Ave, L-231, Livermore, CA 94550, USA

* Corresponding author e-mail address: efueri@crpg.cnrs-nancy.fr

Figures: 5

Tables: 1

Supplementary material: Tables S1-S4

## ABSTRACT

The hydrogen (D/H) isotope ratio is a key tracer for the source of planetary water. However, secondary processes such as solar wind implantation and cosmic ray induced spallation reactions have modified the primordial D/H signature of 'water' in all rocks and soils recovered on the Moon. Here, we re-evaluate the production rate of cosmogenic D at the Moon's surface through ion microprobe analyses of hydrogen isotopes in olivines from eight Apollo 12 and 15 mare basalts. These in situ measurements are complemented by CO₂ laser extraction-static mass spectrometry analyses of cosmogenic noble gas nuclides (³He, ²¹Ne, ³⁸Ar). Cosmic ray exposure (CRE) ages of the mare basalts, derived from their cosmogenic ²¹Ne content, range from 60 to 422 Ma. These CRE ages are 35% higher, on average, than the published values for the same samples. The amount of D detected in the olivines increases linearly with increasing CRE ages, consistent with a production rate of (2.17 ± 0.11) × 10⁻¹² mol(g rock)⁻¹Ma⁻¹. This value is more than twice as high as previous estimates for the production of D by galactic cosmic rays, indicating that for water-poor lunar samples, i.e., samples with water concentrations ≤50 ppm, corrected D/H ratios have been severely overestimated.

**Keywords:** Deuterium; noble gases; water, cosmic rays; olivine; mare basalts; Moon

## 1. Introduction

The discovery of indigenous H-bearing species (H₂, OH, H₂O, in the following referred

to as 'water') in lunar volcanic glasses (Saal et al., 2008), olivine-hosted melt inclusions (Hauri et
al., 2011), apatite (McCubbin et al., 2010), and highland plagioclase (Hui et al., 2013) – together with the detection of water ice in permanently shadowed polar regions of the Moon (Feldman et al., 1998) – has led to a paradigm shift in our knowledge and understanding of the water inventory of Earth's sole natural satellite. These findings have stimulated new investigations of the origin of volatiles within the Earth-Moon system, as well as of the physical and chemical conditions that prevailed in the post-impact protolunar disk (Barnes et al., 2016; Hauri et al., 2015; Pahlevan et al., 2016). A major caveat is that the primordial isotopic signature of water and other volatile elements in samples returned by the Apollo and Luna missions has been modified because the Moon's surface lacks full atmospheric shielding and magnetic field protection against the solar wind (SW) as well as against high-energy galactic (GCR) and solar cosmic rays (SCR). Hence, SW-derived gases are implanted into the top few tens of nanometers of any regolith grain or rock exposed to the lunar surface environment (e.g., Hashizume et al., 2000), and cosmic-ray induced spallation reactions – triggered by GCR and SCR particles that can penetrate lunar matter to depths of several meters and a few centimeters, respectively – are important sources of cosmogenic nuclides, such as deuterium ($^2$H or D) and noble gases (e.g., $^3$He, $^{21}$Ne, $^{38}$Ar) in lunar samples with long cosmic ray exposure (CRE) ages (Rao et al., 1994; Reedy, 2015, 1981). Given the recently emerged interest in the origin of water on the Moon – both at the surface (Liu et al., 2012; Stephant and Robert, 2014) and in the mantle (e.g., Barnes et al., 2016; Füri et al., 2014; Saal et al., 2013) –, accurate knowledge of the cosmogenic D production rate ($P_D$) is critical for correcting measured D/H ratios for the cosmogenic contribution, and, ultimately, for comparing lunar hydrogen isotope signatures with those of potential Solar System sources (i.e., solar, terrestrial, chondritic, cometary).

Merlivat et al. (1976) estimated the GCR-induced production of cosmogenic deuterium to be $0.92 \times 10^{-12} \text{ mol(g rock)}^{-1}\text{Ma}^{-1}$, based on the abundances of water, hydrogen, and deuterium in eight sub-samples from different depths of basalt 70215. This $P_D$ value entirely relies on the assumption that the measured deuterium is a mixture between D generated by the reduction of terrestrial water during the experimental process (with a D/H ratio of 138 ppm or $\delta D = -115 \text{ ‰}$, where $\delta D = [(D/H)_{\text{sample}}/(D/H)_{\text{SMOW}} - 1] \times 1000$, with $(D/H)_{\text{SMOW}} = 155.76 \times 10^{-6}$) and cosmogenic D, which has been produced *in situ* by spallation reactions during space exposure over a period of $10^8$ years. Importantly, Merlivat et al. (1976) concluded that the uniform distribution of cosmogenic D within basalt 70215 can be explained by continuous erosion of the uppermost rock surface (at a rate of $\ge 0.5 \text{ mm/Ma}$) which prevented the accumulation of cosmogenic D produced by SCRs. From theoretical calculations, Reedy (1981) derived a similar value (i.e., $\sim 1200 \text{ atoms/min/kg}$ or $1 \times 10^{-12} \text{ mol(g rock)}^{-1}\text{Ma}^{-1}$) for the GCR production of D in
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lunar rocks from the target elements O, Mg, Al, Si, and Fe for the top 40 g/cm² of shielding.

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However, the additional D production by SCRs (for a rigidity $R_0$ = 100 MV and $2\pi$ exposure) would result in a higher $P_D$ value of up to $2 \times 10^{-12} \text{ mol(g rock)}^{-1}\text{Ma}^{-1}$ at the uppermost surface of mare basalts without any surface erosion.

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To this date, a $P_D$ value of $0.92 \times 10^{-12} \text{ mol(g rock)}^{-1}\text{Ma}^{-1}$ has been used in all studies of lunar samples (e.g., volcanic glasses, apatites) to correct the measured D/H ratios for the cosmogenic contribution and to determine the isotopic signature of the indigenous water component. However, the production of a given nuclide depends on the abundance of multiple target elements and the irradiation conditions. Consequently, it is of key importance to note here that the $P_D$ value determined by Merlivat et al. (1976) cannot be used to correct the D/H ratio of apatite because the chemical composition of the sample must be taken into account. Based on Reedy's model, the production rate of D would be ~35% lower in apatite than in a mare basalt; all previous studies of water in extraterrestrial (lunar, eucrite) apatite have failed to address this issue.

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Bulk lunar basalt samples may contain hydrous phases (such as OH-rich apatite) as well as surface-sited SW-derived hydrogen; thus, they are not well-suited for the quantification of cosmogenic deuterium abundances. In contrast, “dry”, nominally anhydrous minerals (such as olivine) in the interior of lunar basalts are expected to be dominated by deuterium produced *in situ* during cosmic ray irradiation. Therefore, in this study, we re-evaluate the production rate of cosmogenic deuterium at the Moon's surface by determining the deuterium content of olivine from eight Apollo 12 and 15 mare basalts (12004, 12009, 12018, 12020, 12075, 12076, 15016, 15535), which cover a wide range of previously published CRE ages, from ~30 to 335 Ma (Table 1). In parallel to the hydrogen isotope analyses by secondary ionization mass spectrometry, we determined the noble gas characteristics of bulk rock fragments and olivine separates of the same basalts by CO₂ laser extraction-static mass spectrometry in order to quantify the abundances of cosmogenic noble gas nuclides (³He, ²¹Ne, ³⁸Ar) and to verify previously published CRE ages. In this way, we can compare the abundance of deuterium with the duration of cosmic ray irradiation to obtain the average production rate of cosmogenic deuterium for the past few hundreds of million years.

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## 2. Samples and analytical techniques

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The mare basalts studied here (12004, 12009, 12018, 12020, 12075, 12076, 15016, 15535) are all of the low-Ti variety (Neal and Taylor, 1992) and contain between 11 and 15 wt.% MgO (Supplementary Table S1). Up to four olivine grains of each basalt sample were mounted in

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indium together with four standards with known H₂O contents: StHs6/80-G andesitic glass (250 ± 7 ppm and δD = -95 ± 2 ‰; Jochum et al., 2006), MON9 pyrope (56 ± 6 ppm; Bell et al., 1995), synthetic forsterite (4.5 ± 1 ppm; Wetzel et al., 2015), and a synthetic Suprasil 3002 quartz glass (≤1.3 ppm; Wetzel et al., 2015). The major element composition of the olivine grains was determined using the Cameca SX100 at the Université de Lorraine (Service Commun de Microscopies Electroniques et de Microanalyses X) with a primary beam current of 12 nA and an acceleration voltage of 15 kV. Counting times on peaks and background were 10 s for all elements. Results are reported in Supplementary Table S2 and show that the targeted olivines display a significant range in Fo contents (between Fo57 and Fo77).

The CAMECA 1280 HR2 ion microprobe at CRPG, Nancy, was used for the hydrogen isotope analysis of the olivines. The Au-coated sample mount was left in the airlock of the instrument at ~5 × 10⁻⁹ Torr for 48 hours in order to ensure thorough removal of any terrestrial adsorbed water before introduction into the sample chamber. In addition, a liquid nitrogen cold trap was used to reduce the hydrogen background and maintain a pressure of ≤1.5 × 10⁻⁹ Torr during analyses. Spot analyses of hydrogen and deuterium were carried out using a 10 keV Cs⁺ primary ion beam with a current of 10 nA and a normal-incidence electron gun (emission = 0.21 mA) for charge compensation. Standards and olivines were pre-sputtered for 180 s over an area of 30 × 30 µm prior to signal acquisition. For analysis, the ~30 µm beam was rastered over an area of 20 × 20 µm, and a dynamical transfer operating system was used to compensate the primary rastering and to refocus the beam in the secondary part of the ion probe. To eliminate any hydrogen contamination from the crater edges, a 1800 µm field aperture limiting the analyses to ions from the central ~10 µm of the beam and an electronic gate of 80 % were used. The H⁻ and D⁻ ion intensities were determined for 4 and 20 s, respectively, for 30 cycles. Measurements were carried out in mono-collection mode on an electron multiplier at a mass resolving power (M/ΔM) of ~1250. Under these analytical conditions, typical count rates on StHs6/80-G were ~118,000 cps for H⁻ and 16 cps for D⁻, whereas count rates on the 'driest' standard averaged 1747 ± 662 cps for H⁻ and 0.22 ± 0.16 cps for D⁻ (Supplementary Table S3).

Noble gas (He-Ne-Ar) abundances and isotope ratios were determined by CO₂ laser-extraction static-mass spectrometry (Hashizume and Marty, 2004; Humbert et al., 2000). Small bulk rock fragments and three olivine separates, between 1.0 and 3.5 mg in mass (Supplementary Table S4), were loaded into different pits of the laser chamber connected to the purification line of the Micromass© VG5400 mass spectrometer at the CRPG noble gas analytical facility. The sample chamber was pumped to ultra high vacuum and kept at a temperature of 120°C for 60
hours. After leaving the samples under high vacuum ($P \le 10^{-8}$ Torr) for 10 days prior to analysis, they were heated individually with a continuous-mode infrared $CO_2$ laser ($\lambda = 10.6$ µm). A low-temperature step was aimed at removing surface-sited (solar and/or atmospheric) gases. Fusion was achieved in the second heating step, and all sub-samples were reheated after being melted (heating steps 3 to 5) to ensure complete gas extraction. The extracted noble gases were purified using Ti sponge getters and two hot and cold SAESTM Ti-Al getters. Argon was separated from helium and neon by absorption onto a charcoal finger at 77 K, and noble gas abundances and isotope ratios were then determined sequentially on the VG5400 mass spectrometer. Neon was exposed to a charcoal finger at 77 K and a SAESTM AP-10 getter during analysis to minimize the contribution of doubly charged $^{40}$Ar and $CO_2$ to the $^{20}$Ne and $^{22}$Ne signals, respectively. The $^{40}$Ar$^{++}$ contribution to $^{20}$Ne was carefully monitored and was found to be negligible (i.e., $\le 5$ cps). The $CO_2^{++}$ signal of all samples was comparable to the mass-spectrometer background, and the contribution of $CO_2^{++}$ was corrected as part of the blank. With the laser off, blanks averaged $2.6 \times 10^{-16}$ mol $^{4}$He, $1.2 \times 10^{-16}$ mol $^{20}$Ne, and $3.3 \times 10^{-17}$ mol $^{36}$Ar. Procedural blanks (laser on) may be higher due to the release of noble gases from the container walls during sample heating; however, several gas fractions extracted at maximum laser power are comparable to the measured blanks, arguing against a significant underestimation of the true blank values. Heating steps for which the blank contribution to the measured noble gas abundances represents $\ge 50$ % are not considered for discussion and are omitted in Figure 2.

## 3. Results

Measured hydrogen and deuterium count rates, as well as estimated deuterium concentrations, for lunar olivine grains are reported in Supplementary Table S3. Blank-corrected noble gas (He, Ne, Ar) abundances and isotope ratios of bulk rock fragments and three olivine separates are given in Supplementary Table S4, together with results from previous single-step heating analyses of basalts 12004, 12009, 12018, 12020, 12075, and 12076 for comparison (Bogard et al., 1971; Hintenberger et al., 1971).

### 3.1. Hydrogen and deuterium content of olivines

There is no clear evidence for the presence of indigenous lunar water (hydrogen) in the olivine grains, as the majority ($n = 22$ out of 40) of the H-measurements fall within the range observed for the 'dry' Suprasil 3002 quartz glass ($\le 1.3$ ppm $H_2O$; Wetzel et al., 2015) (Fig. 1). While several olivines show higher H$^+$ count rates than the quartz, comparable to those of the synthetic forsterite standard ($4.5 \pm 1$ ppm $H_2O$; Wetzel et al., 2015), a minor contribution from
terrestrial adsorbed water to the measured H⁻ signal cannot be ruled out. SW-derived hydrogen is not expected to contribute to the signal because the measurements were carried out near the center of the crystals, away from the outermost rim. Furthermore, there is no increase of the hydrogen abundances with increasing exposure ages. The D⁻ ion intensities measured on the olivines vary between 0.91 and 4.78 cps (Fig. 1), and are significantly higher than those of the quartz glass (0.22 ± 0.16 cps) and forsterite (0.32 ± 0.14 cps) standards. These D⁻ signals correspond to D concentrations between 0.2 and 1.2 × 10⁻⁹ mol/g (Supplementary Table S3), based on the known D content (3.9 × 10⁻⁹ mol/g) and the measured D⁻ count rate (16.0 ± 2.2 cps), normalized to the primary ion beam intensity (~10 nA), of standard StHs6/80-G. Importantly, the D content shows a clear correlation with the previously published CRE ages of the mare basalts (Fig. 1). This is interpreted as evidence for the *in situ* production of cosmogenic D in the olivines by cosmic ray-induced spallation reactions during exposure at the Moon's surface.

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<figure><img src="image_3.png" /></figure>

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**Figure 1:** Measured hydrogen and deuterium ion count rates (in counts per second, cps) for olivines from eight Apollo 12 and 15 mare basalts in comparison with the signals observed for the two driest standards, i.e., Suprasil 3002 quartz glass (≤1.3 ppm H₂O; Wetzel et al., 2015) and synthetic forsterite (4.5 ± 1 ppm H₂O; Wetzel et al., 2015). Results are shown in order of increasing cosmic ray exposure ages of the mare basalts (T~CRE~; Table 1).
## 3.2. Noble gas characteristics of bulk rock fragments and olivine separates

The neon and argon isotope data indicate that the whole rock fragments of basalts 12004, 12075, 12076, and 15535 studied here, as well as olivine separates of basalts 12075 and 15535, contain a small fraction of trapped solar noble gases. The $^{20}$Ne/$^{22}$Ne ratios of these samples range from 6.35 ± 0.13 to 12.91 ± 0.08 during the first heating step, and in a three-isotope plot of neon (Fig. 2a), the isotope signatures fall onto a mixing line between cosmogenic and SW-like neon. All of these samples also record elevated $^{36}$Ar/$^{38}$Ar ratios in the first heating step (i.e., between 2.47 and 5.02), significantly higher than the value for cosmogenic argon ($^{36}$Ar/$^{38}$Ar$_{cosm}$ ≈ 0.65). Similarly, SW-derived noble gases were previously found in sub-samples of basalts 12004, 12009, 12018, 12020, 12075, and 12076 during single-step heating analyses (Bogard et al., 1971; Hintenberger et al., 1971), as indicated by high $^{20}$Ne/$^{22}$Ne and $^{36}$Ar/$^{38}$Ar ratios of up to 8.4 and 3.5, respectively (Fig. 2a and Supplementary Table S3). Hence, these fragments are inferred to be derived from the outermost rim of rocks recovered on the Moon – unless the sub-samples were contaminated by SW-loaded dust during cutting (Füri et al., 2015).

<figure><img src="image_4.png" /><figcaption>**Figure 2:** Three-isotope plots of neon for Apollo 12 and 15 whole rock (wr) samples and olivine (ol) separates. a) Neon extracted during the first heating step together with results from single-step heating analyses of splits from the same samples (Bogard et al., 1971; Hintenberger et al., 1971). b) Neon extracted by melting. The neon isotope composition of modern solar wind (SW; Heber et al., 2009), Earth's atmosphere (Air; Ozima and Podosek, 2002), and neon produced by galactic cosmic rays (GCR; Leya et al., 2001) or solar cosmic rays (SCR; Reedy, 1992; Trappitsch and Leya, 2014) is shown for comparison. Measurements for which the blank contribution represents ≥50 % are omitted. Error bars for the samples from this study represent 1σ uncertainties and are, in some cases, smaller than symbol sizes.</figcaption></figure>

Noble gases released upon melting of the mare basalt fragments and olivine separates are purely cosmogenic in most cases; only fragments of 12004 and 12076 still release some trapped
SW gases at the second heating step. Importantly, Figure 2b shows that the isotopic composition of neon extracted at the highest temperatures is consistent with the theoretical signature of GCR-produced neon, which can be calculated using the $2\pi$ exposure model from Leya et al. (2001) for low shielding (0 to 20 g/cm²), together with the mare basalt and olivine compositions given in Supplementary tables S2 and S3. The slight $^{20}$Ne excess of the measured values compared to the modeled endmembers likely results from uncertainties in the target cross sections for the production of $^{20}$Ne and/or from small-scale chemical/mineralogical heterogeneities in the samples. Neon produced by SCRs, derived using the models of Reedy (1992) and Trappitsch and Leya (2014) for a rigidity $R_0 = 100$ MV and an incident particle flux $J_0 = 100$ protons/s/cm², has a distinctly higher $^{20}$Ne/$^{22}$Ne and lower $^{21}$Ne/$^{22}$Ne ratio. Given that the neon isotope production rates by SCRs are significantly higher than those by GCRs at the uppermost rock surface (e.g., by a factor ~10 for $^{20}$Ne; Reedy, 1992; Trappitsch and Leya, 2014), any contribution of SCR-derived neon is expected to result in a noticeable shift of the isotopic signature of the cosmogenic neon component. Such a (small) shift is only observed for sample 12004, whereas all other measurements agree, within error, with the $^{21}$Ne/$^{22}$Ne ratio of the modeled GCR endmember. Hence, even though several whole rock fragments have been exposed to solar wind irradiation at the uppermost rock surface – as indicated by the presence of SW-derived noble gases –, there is no evidence for SCR-induced spallation effects on the neon isotope signature of the majority of the mare basalts studied here. In contrast, Rao et al. (1993, 1994) observed $^{21}$Ne/$^{22}$Ne ratios ≤0.7 (for $^{20}$Ne/$^{22}$Ne$_{cosm}$ = 0.9) in fragments derived from the top 4 cm of Apollo samples 61016 and 68815, clearly indicating the presence of a SCR-derived neon component at the surface of these rocks.

## 4. Discussion

The abundance of cosmogenic D in lunar olivines depends on the duration of cosmic ray irradiation and the D production rate, which itself is a function of the chemical composition (i.e., the abundance of the target elements O, Mg, Si, and Fe; Reedy, 1981) and the shielding depth (i.e., the depth of irradiation below the lunar surface). The olivines studied here show a wide range in Fo contents (between Fo57 and Fo77; Supplementary Table S2); nonetheless, the model of Reedy (1981) indicates that 75 to 78% of the cosmogenic D in olivine is produced from the target elements oxygen and silicon, and the observed variations in the MgO-FeO content have a negligible effect on the $P_D$ value. The location of the studied sub-samples within their host rocks is unknown, and the orientation of the rocks might have varied over the course of their exposure histories at the lunar surface (Merlivat et al., 1976); hence, the shielding conditions for individual
olivine crystals cannot precisely be constrained. However, given that the mare basalt rocks selected for this study were originally between ~4 and 10 cm in size, variations of the GCR-induced production of cosmogenic D between the surface and bottom of the rocks are inferred to be insignificant. Consequently, an accurate estimate of the production rate of cosmogenic deuterium at the Moon's surface can be obtained by comparing the measured deuterium concentrations in olivines with the CRE ages of their host rocks.

## 4.1. Cosmogenic noble gases and cosmic ray exposure (CRE) ages

The CRE age can be determined by quantifying the concentrations of cosmogenic noble gas nuclides (e.g., ³He, ²¹Ne, ³⁸Ar) in a given sample, and by comparing them with published noble gas production rates (e.g., Hohenberg et al., 1978; Leya et al., 2001; Reedy, 1981). The concentrations of cosmogenic ³He, ²¹Ne, and ³⁸Ar in the mare basalts and olivine separates studied here are given in Table 1, together with the (recalculated) values from previous single-step analyses for comparison (Bogard et al., 1971; Hintenberger et al., 1971). For the samples that contain a mixture of SW-derived and cosmogenic noble gases, the amount of ²¹Ne cosm and ³⁸Ar cosm can be derived numerically, based on the isotope composition of the two endmembers (see Füri et al. (2014, 2012) for details on the component deconvolution). The measured ³He is assumed to be entirely of cosmogenic origin. Although it may seem straightforward to convert these cosmogenic noble gas abundances into CRE ages, a number of caveats exist: i) published GCR production rates for ³He, ²¹Ne, and ³⁸Ar, either estimated empirically (e.g., Bogard et al., 1971; Turner et al., 1971) or calculated based on nuclear systematics (e.g., Hohenberg et al., 1978; Leya et al., 2001; Reedy, 1981), are highly variable (see Supplementary Table S1); ii) given the small sample amounts analyzed here (≤3.5 mg), any small-scale chemical/mineralogical heterogeneities could significantly affect the concentration of target elements and their cosmogenic products at the sample scale; iii) the shielding conditions of the studied samples are not well constrained; iv) the surface erosion rate is unknown, and v) the constancy of the GCR flux in the past remains a matter of debate (Reedy, 2015; Wieler et al., 2013). Notably, the P₃₈ value is more sensitive to variations in rock chemistry/mineralogy than P₃ and P₂₁, because the major target element for the production of ³⁸Ar cosm in lunar samples is Ca, whereas ³He cosm and ²¹Ne cosm are predominantly produced from O and Mg-Si, respectively. Furthermore, empirically-derived P₃₈ values (Bogard et al., 1971; Turner et al., 1971) are significantly higher than the modeled production rate from Hohenberg et al. (1978), possibly because the cross sections for the Ar production from Ca were unknown (Leya et al., 2001). Due to these uncertainties, CRE ages based on ³⁸Ar cosm abundances are not reported here. In contrast, the isotope signature of the cosmogenic neon component
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observed in the Apollo 12 and 15 whole rock fragments and olivines is in good agreement with the GCR endmember derived from the model of Leya et al. (2001), and these authors argued that their modeled noble gas data are consistent with radionuclide results; therefore, we consider their physical model to be the most robust.

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Based on the model of Leya et al. (2001), the average GCR production rate of cosmogenic <sup>21</sup>Ne within the top 20 g/cm<sup>2</sup> is on the order of 5.2 to 6.0 × 10<sup>-14</sup> mol(g rock)<sup>-1</sup>Ma<sup>-1</sup> for the mare basalts studied here, and 8 to 10 × 10<sup>-14</sup> mol(g rock)<sup>-1</sup>Ma<sup>-1</sup> for olivine. We attribute an uncertainty of ±15% to these values, assuming that the shielding depth for the samples studied here was in the range of 0 to 20 g/cm<sup>2</sup>. The resulting CRE ages (given in Table 1) vary from 60 ± 11 to 422 ± 73 Ma, and they are 35% higher on average than the values given in the literature (Fig. 3). Significantly lower CRE ages would be obtained based on the observed <sup>3</sup>He<sub>cosm</sub> concentrations, for example, when the P<sub>3</sub> value from the model of Reedy (1981) is applied (T<sub>3</sub>; Table 1). This could either indicate that the samples have lost a fraction of their <sup>3</sup>He<sub>cosm</sub> content by diffusion, or, alternatively, that the modeled <sup>3</sup>He production rate is too high. This example illustrates that the different production rates for cosmogenic noble gas nuclides reported in the literature (Supplementary Table S1) can result in a considerable range of exposure ages for a given sample, and published CRE ages of lunar samples cannot always be taken at face value.

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

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<caption>**Figure 3:** Exposure ages (T<sub>21</sub>) of eight Apollo 12 and 15 mare basalts, derived from the measured <sup>21</sup>Ne<sub>cosm</sub> concentrations and the <sup>21</sup>Ne production rate from Leya et al. (2001), compared to the previously published cosmic ray exposure ages (T<sub>CRE</sub>; Table 1).</caption>

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**4.2. Production rate of cosmogenic deuterium**

The deuterium content of the olivines can now be compared to the duration of cosmic ray
irradiation in order to obtain the average production rate of cosmogenic D at the Moon's surface over the past ~400 Ma. For previously published CRE ages, a production rate of $3 \times 10^{-12}$ mol(g rock)$^{-1}$Ma$^{-1}$ would be derived (Füri and Deloule, 2016). However, Figure 4 shows that the linear relationship between the D concentrations and the new CRE ages determined from the $^{21}$Ne$_{cosm}$ content ($T_{21}$) is consistent with a $P_{D}$ value of $(2.171 \pm 0.111) \times 10^{-12}$ mol(g rock)$^{-1}$Ma$^{-1}$. Notably, our data define a linear array with surprisingly low scatter (mean square weighted deviation (MSWD) = 1.7), considering that the different Apollo 12 and 15 whole rock fragments and olivines analyzed here may have experienced various and/or variable irradiation conditions at the lunar surface.

The production rate of cosmogenic D derived here is more than twice as high as the previous estimates for the GCR production of D in lunar basalts ($0.92 \times 10^{-12}$ mol(g rock)$^{-1}$Ma$^{-1}$; Merlivat et al., 1976; Reedy, 1981). The new $P_{D}$ value would be in agreement with Reedy's model if both the GCR and SCR productions of D were considered (Füri and Deloule, 2016); yet, we re-emphasize here that there is no evidence for the presence of neon produced by SCRs in the basalt fragments, implying a substantial surface erosion rate. Thus, even though at least four of the sub-samples are derived from the outermost rim of basalts recovered on the Moon (as indicated by the presence of implanted SW-derived neon and argon), the olivines are not expected to contain SCR-derived D. Consequently, our new coupled D-$^{21}$Ne$_{cosm}$ data imply that Merlivat et al. (1976) and Reedy (1981) significantly underestimated the production of cosmogenic D by GCRs.

<figure><img src="image_6.png" /><figcaption>**Figure 4:** Deuterium abundances in olivines (in nmol/g) as a function of the cosmic ray exposure ages calculated from the $^{21}$Ne$_{cosm}$ concentrations in the mare basalts ($T_{21}$; Table 1). The solid line indicates the D production rate of $(2.171 \pm 0.111) \times 10^{-12}$ mol(g rock)$^{-1}$Ma$^{-1}$ derived here, whereas</figcaption></figure>
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the dashed line represents the value of ~1 × 10⁻¹² mol(g rock)⁻¹Ma⁻¹ for the GCR production of D from Merlivat et al. (1976) and Reedy (1981). We used the linear regression from Mahon (1996) to determine the slope and intercept (± 1σ) of the best-fit line through our data. This regression is the same as that from York (1969); however, as pointed out by Mahon (1996), the uncertainty determination of York (1969) is incorrect and thus underestimates the uncertainties for the slope and intercept.

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**4.3. Implications for studies of lunar water**

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Our findings have major implications for studies of water in lunar and other extraterrestrial samples, given that only corrected D/H ratios can be used to assess the importance of secondary processes that can modify the hydrogen isotope characteristics (e.g., equilibrium or kinetic degassing) as well as to determine the source of planetary water (i.e., solar, terrestrial, chondritic, cometary). For water-poor lunar samples, such as lunar volcanic glasses (LVGs; Füri et al., 2014; Saal et al., 2013), corrected D/H ratios have been severely overestimated. When the new $P_D$ value is applied, together with the CRE ages of individual glass beads (~28 Ma), the hydrogen isotope signatures of 74002 LVGs no longer reflect a H₂-degassing process (Füri et al., 2014). Instead, the Apollo 17 high-Ti ('orange') LVGs and olivine-hosted melt inclusions fall onto a mixing line between solar hydrogen ($D/H$ = (25 ± 5) ×10⁻⁶; Robert, 2006) and isotopically heavier lunar 'water' ($D/H$ ≈ (1.98 ± 0.06) × 10⁻⁴ or $δD$ ≈ 274 ± 42‰) (Fig. 5). The hydrogen inventory of the 'driest' or most-degassed glasses is dominated by the solar component, possibly due to rapid inward diffusion of hydrogen implanted by the SW (Zhang and Arbor, 2011), or, alternatively, assimilation of SW-derived hydrogen from the lunar regolith or exosphere (Farrell et al., 2015) by the erupting melt. Notably, the uncertainties for the spallation-corrected D/H ratios of the 74220 LVGs are very large because the exposure ages of individual glass beads have not been determined, and a CRE age of 30 ± 10 Ma is assumed here, as in Saal et al. (2013). Since the CRE ages of the 'green' and 'yellow' 15426 and 15427 glasses are even more uncertain (284 ± 51 Ma; Saal et al., 2013), applying the new $P_D$ value for the spallation correction would not yield scientifically meaningful results.

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For the water-rich olivine-hosted melt inclusions (Saal et al., 2013) – as well as for the many mare basalt apatites with water concentrations ≥1000 ppm (McCubbin et al., 2015) – the new $P_D$ value has virtually no effect on the corrected hydrogen isotope ratios. Thus, the most primitive Apollo 17 high-Ti melts point to a $δD$ value of 274 ± 42‰ for lunar water, provided that they retain the original pre-eruptive isotope ratio; this value is consistent with a carbonaceous chondrite heritage (Alexander et al., 2012; Barnes et al., 2016; Saal et al., 2013). Alternatively, the hydrogen isotope signature of water in the mare basalt source may have been fractionated from an originally Earth-like composition ($δD_{Earth}$ ≈ -43‰; Lecuyer et al., 1998) as a result of
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volatile loss during formation and differentiation of the Moon (Kato et al., 2015). This example demonstrates that published production rates of deuterium (and noble gases), as well as published exposure ages, must be taken with care if the D/H ratio is to be used as a reliable source tracer of planetary water.

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<figure><img src="image_7.png" /></figure>

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**Figure 5:** Hydrogen isotope ratios – corrected for the cosmogenic D contribution using a $P_D$ value of (2.171 ± 0.111) × 10⁻¹² mol(g rock)⁻¹Ma⁻¹ – as a function of the inverse of the hydrogen concentrations in Apollo 17 high-Ti ('orange') volcanic glass beads (74220: Saal et al., 2013, 74002: Füri et al., 2014) and olivine-hosted melt inclusions (Saal et al., 2013). The data define a mixing line between solar hydrogen (D/H = (25 ± 5) × 10⁻⁶; Robert, 2006) and lunar 'water' (D/H ≈ (1.98 ± 0.06) × 10⁻⁴ or δD ≈ 274 ± 42‰).

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**5. Conclusions**

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A new value of (2.171 ± 0.111) × 10⁻¹² mol(g rock)⁻¹Ma⁻¹ has been obtained for the production rate of cosmogenic deuterium at the Moon's surface, based on coupled deuterium-noble gas analyses of subsamples from Apollo 12 and 15 mare basalts with cosmic ray exposure ages of tens to hundreds of million years. This $P_D$ value is twice as high as the estimates given in the literature, indicating that previous studies have severely underestimated the production of cosmogenic deuterium by galactic cosmic rays. The new $P_D$ value can be used to correct the D/H ratio of 'water' trapped within MgO-FeO-rich silicates such as olivine and basaltic rocks that have been exposed to cosmic ray irradiation within the upper ~10 cm of planetary surfaces lacking atmospheric shielding and magnetic field protection. It is not appropriate for deriving the proportion of cosmogenic deuterium in apatite because the chemical composition of the sample

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must be taken into account. The results obtained here demonstrate that in light of future sample return missions that will collect extraterrestrial material from the surface of asteroids (e.g., OSIRIS-REX, Hayabusa 2), space exposure effects will have to be carefully evaluated if the D/H ratio is to be used as an indicator for the source(s) of water.

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Table 1: Abundances of cosmogenic noble gas nuclides (in $10^{-12}$ mol/g) and cosmic ray exposure (CRE) ages (in Ma) calculated using the production rate for $^3$He and $^{21}$Ne from Reedy (1981) and Leya et al. (2001), respectively. Previously published CRE ages are given for comparison.

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<table><thead><tr><th>Sample ID</th><th><sup>3</sup>He<sub>cosm</sub></th><th><sup>21</sup>Ne<sub>cosm</sub></th><th><sup>38</sup>Ar<sub>cosm</sub></th><th>T<sub>3</sub><br>Ma</th><th>T<sub>21</sub><br>Ma</th><th>T<sub>CRE</sub><sup>c</sup><br>Ma</th></tr></thead><tbody><tr><td>12004</td><td>21.46</td><td>3.32</td><td>2.99</td><td>42</td><td>60 ± 11</td><td>30-85</td></tr><tr><td>12004<sup>a</sup></td><td>32.12</td><td>3.75</td><td>1.55</td><td>63</td><td>68 ± 12</td><td></td></tr><tr><td>12004<sup>b</sup></td><td>28.20</td><td>3.84</td><td>2.71</td><td>53</td><td>70 ± 12</td><td></td></tr><tr><td>12009</td><td>52.56</td><td>13.02</td><td>10.68</td><td>103</td><td>241 ± 42</td><td>112-160</td></tr><tr><td>12009<sup>a</sup></td><td>51.31</td><td>9.69</td><td>6.45</td><td>101</td><td>179 ± 31</td><td></td></tr><tr><td>12018</td><td>63.78</td><td>14.05</td><td>10.27</td><td>125</td><td>242 ± 42</td><td>152-221</td></tr><tr><td>12018 ol</td><td>84.12</td><td>36.75</td><td>0.84</td><td>165</td><td>371 ± 75</td><td></td></tr><tr><td>12018<sup>a</sup></td><td>83.88</td><td>14.34</td><td>6.33</td><td>160</td><td>247 ± 42</td><td></td></tr><tr><td>12018<sup>b</sup></td><td>81.86</td><td>15.91</td><td>9.56</td><td>165</td><td>274 ± 47</td><td></td></tr><tr><td>12020</td><td>18.38</td><td>4.36</td><td>3.79</td><td>36</td><td>73 ± 13</td><td>56-100</td></tr><tr><td>12020</td><td>26.12</td><td>6.46</td><td>4.08</td><td>51</td><td>111 ± 19</td><td></td></tr><tr><td>12020<sup>a</sup></td><td>45.95</td><td>5.28</td><td>2.91</td><td>90</td><td>91 ± 15</td><td></td></tr><tr><td>12020<sup>b</sup></td><td>34.88</td><td>5.29</td><td>2.64</td><td>67</td><td>91 ± 15</td><td></td></tr><tr><td>12075</td><td>85.02</td><td>17.08</td><td>14.83</td><td>170</td><td>305 ± 54</td><td>240-300</td></tr><tr><td>12075 ol</td><td>86.31</td><td>30.36</td><td>1.24</td><td>173</td><td>319 ± 63</td><td></td></tr><tr><td>12075<sup>a</sup></td><td>133.84</td><td>18.94</td><td>11.57</td><td>268</td><td>338 ± 60</td><td></td></tr><tr><td>12076</td><td>102.62</td><td>24.03</td><td>9.92</td><td>201</td><td>429 ± 76</td><td>240-270</td></tr><tr><td>12076<sup>a</sup></td><td>102.61</td><td>17.68</td><td>11.88</td><td>201</td><td>316 ± 56</td><td></td></tr><tr><td>15016</td><td>167.77</td><td>19.66</td><td>11.84</td><td>336</td><td>378 ± 66</td><td>285-335</td></tr><tr><td>15016</td><td>162.27</td><td>21.93</td><td>14.68</td><td>325</td><td>422 ± 73</td><td></td></tr><tr><td>15535</td><td>56.01</td><td>12.38</td><td>2.65</td><td>112</td><td>238 ± 43</td><td>110</td></tr><tr><td>15535 ol</td><td>61.23</td><td>11.89</td><td>1.36</td><td>122</td><td>159 ± 31</td><td></td></tr></tbody></table>

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<sup>a</sup> Noble gas data from Bogard et al. (1971), recalculated.

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<sup>b</sup> Noble gas data from Hintenberger et al. (1971), recalculated.

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<sup>c</sup> Previously published cosmic ray exposure ages (Alexander et al., 1973; Bogard et al., 1971; Hintenberger et al., 1971; Husain, 1974; Kirsten et al., 1973; Marti and Lugmair, 1971; Stettler et al., 1973).

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Acknowledgements

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We thank NASA CAPTEM for allocation of the Apollo samples. L. Zimmermann is

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thanked for assistance and support during noble gas analyses, and we gratefully acknowledge

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D.V. Bekaert for noble gas measurements of Apollo sample 15016. We also thank D.V. Bekaert,

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G. Avice, and B. Marty for fruitful discussions, and Erik Hauri for constructive review of this

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manuscript. This work was supported by the Programme National de Planétologie (PNP-INSU)

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and the Conseil Régional de la région Lorraine (E.F.), as well as by the NASA Cosmochemistry
387 Program (R.T.; grant NNX09AG39G to A.M. Davis). This is CRPG-CNRS contribution XXXX.

388 LLNL-JRNL-731359

389

390

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