On 9 October 2009, the Lunar Crater Observation and Sensing Satellite (LCROSS) mission impacted a spent Centaur rocket into the permanently shadowed region (PSR) within Cabeus crater and detected water vapor and ice, as well as other volatiles, in the ejecta plume. The Lyman Alpha Mapping Project (LAMP), a far ultraviolet (FUV) imaging spectrograph on board the Lunar Reconnaissance Orbiter (LRO), observed this plume as FUV emissions from the fluorescence of sunlight by molecular hydrogen (H2) and other constituents. Energetic charged particles, such as galactic cosmic rays (GCRs) and solar energetic particles (SEPs), can dissociate the molecules in water ice to form H2. We examine how much H2can be formed by these types of particle radiation interacting with water ice sequestered in the regolith within PSRs, and we assess whether it can account for the H2 observed by LAMP. To estimate H2formation, we use the GCR and SEP radiation dose rates measured by the LRO Cosmic Ray Telescope for the Effects of Radiation (CRaTER). The exposure time of the ice is calculated by considering meteoritic gardening and the penetration depth of the energetic particles. We find that GCRs and SEPs could convert at least 1–7% of the original water molecules into H2. Therefore, given the amount of water detected by LCROSS, such particle radiation‒induced dissociation of water ice could likely account for a significant percentage (10–100%) of the H2measured by LAMP.
 Energetic charged particles such as galactic cosmic rays (GCRs) and solar energetic particles (SEPs), meteoritic impacts, and the solar wind all cause space weathering by changing the physical and chemical composition of the lunar regolith, including any water ice there [Hapke, 2001]. These processes have affected the Moon's surface for its entire history and have also been important on airless bodies throughout the solar system.
 On 9 October 2009, a Centaur rocket impacted within Cabeus crater, a permanently shadowed crater near the Moon's south pole [Colaprete et al., 2010]. The impact created a cloud of ejecta containing, among other things, water and molecular hydrogen. The former was detected by the Lunar Crater Observation and Sensing Satellite (LCROSS), and the latter by the Lyman Alpha Mapping Project (LAMP), an ultraviolet spectrograph on board the Lunar Reconnaissance Orbiter (LRO) [Gladstone et al., 2010]. The amount of water by mass in the impact region is estimated to be 5.6±2.9%.
Gladstone et al.  estimate the amount of H2by mass to be 1.4% by assuming that the impact plume had an average mass of 10,000 kg. Using the LCROSS measurements, however, Colaprete et al.  estimate the plume had a mass of 3150 kg. Hurley et al. [2012a] argue that the more volatile H2 was almost certainly released from a larger amount of regolith than contained in the plume. They use hydrogen estimates based on LRO/LEND (Lunar Exploration Neutron Detector) observations [Mitrofanov et al., 2010] to determine that the H2originated from about 250,000 kg of regolith, which is still less than the mass excavated by the expected impact crater [Schultz et al., 2010; Korycansky et al., 2009]. The revised estimate for the observed amount of H2 is 0.047±0.006% by mass.
Gladstone et al.  point out that H2forming from H2O by photolysis as the vapor plume entered sunlight was insufficient to explain the LAMP observations. Therefore, it must have been either trapped as H2within the regolith or formed by the impact. Possible mechanisms for creating H2 had been suggested before the LCROSS impact. Solar wind protons implanted in the lunar surface may form H2, which then migrates into permanently shadowed regions, or PSRs [Crider and Vondrak, 2000, 2002]. These works did not specify the mechanisms that could create a source of H2, but just assumed they existed. Hurley et al. [2012a] suggest that a mechanism proposed by Duley and Williams  could create H2gas in Cabeus using OH as a catalyst. As Hurley et al. [2012a] note, however, this mechanism occurs at 10 K, which is colder than the 40 K in Cabeus [Paige et al., 2010].
 In this paper, we consider another mechanism to create H2 from lunar ice, as first suggested by Schwadron et al. . While PSRs receive no direct sunlight [Mazarico et al., 2011] and very little solar wind [Zimmerman et al., 2011, 2012], GCRs and SEPs can almost fully access them, since their fluxes tend to be more isotropic. They are also energetic enough to be essentially unperturbed by local electric or magnetic fields (cf. Stubbs et al., Dependence of lunar surface charging on solar wind plasma conditions and solar irradiation, submitted to Planet. Space Sci., 2013). Furthermore, they can be energetic enough to penetrate below the lunar surface, enabling them to dissociate any subsurface water and create molecular hydrogen at depth.
 Therefore, using data from the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) [Spence et al., 2010], on board LRO, we estimate how much H2 can be created by GCRs and SEPs impacting ice in PSRs. We also consider how loss by thermal diffusion and meteoritic impacts affect these estimates. This study furthers our understanding of how energetic particles affect water ice, not only on the Moon but also on airless bodies throughout the solar system.
2 Space Radiation Environment
 GCRs are relativistic ions and electrons that fill interplanetary space, with a solar minimum flux of about 4 particles·cm−2·s−1 and a solar maximum flux of ∼2 particles·cm−2·s−1 [Smart and Shea, 1985]. The majority of cosmic rays have likely received their high energies in supernova shocks. Over 80% of these particles are protons, and the rest are heavier ions and electrons. In this paper, we focus on GCRs at the low end of the energy spectrum (∼200 MeV), where the flux is greatest.
 We can estimate the long‒term GCR dose rate using measurements by the CRaTER instrument. According to Schwadron et al. , the GCR dose rate is about 0.022 eV/(molecule·Myr) in the first meter or so of regolith. Previous GCR studies show that this dose rate varied little in the past. Analysis of iron meteorites indicates that variations in cosmic ray fluxes over the past 1 Gyr have not exceeded a factor of 2 [Arnold et al., 1961]. Bhandari and Padia  also show, by analyzing meteorites and lunar samples, that GCR composition has remained nearly constant up to 100 Myr in the past. In addition, McCracken and Beer  show that in the approximately 550 years prior to the Space Age, the GCR flux was higher than that measured by CRaTER. From this, we conclude that the CRaTER dose rate is a reasonable estimate for historical rates and that we are, if anything, underestimating the rate.
 Unlike GCRs, SEPs are intermittent and have a lower characteristic energy. SEPs receive their energy in shocks associated with solar flares or coronal mass ejections. These events are thus sporadic, occurring mainly during elevated solar activity. Major events can still occur, however, near solar minimum. SEP electrons may also play an important role (cf. work by Cooper et al.  on how Jupiter's radiation belt electrons affect the icy Galilean satellites), but we consider only the protons and heavier ions, as these can be detected at the Moon by CRaTER. While SEP protons rarely have energies greater than ∼1 GeV, their fluxes can exceed that of GCRs by many orders of magnitude. The hardness of the energy spectrum varies by event. The flux of SEP protons is also highly variable and peaks at low energies.
 To estimate the SEP contribution to dose, we use 3 years of CRaTER dose rate data. The calculation of CRaTER dose rates is described by Schwadron et al. . Protons must have energies of at least 15 MeV to penetrate the instrument's endcaps and reach the detectors. Figure 1 shows the accumulated dose from 18 September 2009 to 18 September 2012. The steps in the plot occur at SEP events, with the largest occurring in January 2012. The total accumulated dose over the period shown is about 380 centigray (1 gray corresponds to 1 joule of radiation deposited in 1 kg of material), corresponding to an average dose rate of 0.24 eV/(molecule·Myr).
 Because CRaTER has collected data during a period of low solar activity, we might expect this SEP dose rate to be lower than the dose rate averaged over many solar cycles. To estimate the rate of SEP events, we use the OMNI data set, which covers most of the Space Age, for the flux of >10 MeV protons from 1 January 1964 through the end of 17 September 2012 [King and Papitashvili, 2005]. The advantage of this data set is that it is relatively uncontaminated by energetic magnetospheric particles, which is not the case for the data set of protons with energies >1 MeV. We define a SEP event as occurring whenever the daily average flux of 10 MeV protons is ≥1 proton·cm−2·sr−1·s−1(see Feynman et al. ). Consecutive days meeting that criterion are considered to be a single event, although this method likely combines some multiple events. Throughout this period, there are 334 events, corresponding to about 7 events/year. Twenty of these events occurred during the 3 years shown in Figure 1—also about 7 events/year (note that most events contribute little to the accumulated dose). Thus, the rate of SEP events measured by CRaTER appears typical for the period covered by the OMNI data set. Furthermore, studies by Russ and Emerson  and Reedy suggest that SEP fluxes over the last 10 Myr have remained similar to modern fluxes. We conclude that the CRaTER SEP dose rate is also a reasonable estimate for historical rates.
3 Space Radiation Exposure Time of the Regolith
 Because the peak fluxes of GCRs and SEPs occur at different energies, their dose rates apply to different depths in the regolith. In this section, we estimate the range of depths to which each dose rate applies. This will enable us to characterize how energetic particles interact with and modify water ice in the regolith.
 To find how deeply energetic protons penetrate the regolith, we use the National Institute of Standards' Stopping‒Power and Range Tables for Protons (PSTAR). These tables estimate the penetration range—in units of mass column density—of protons within various materials by calculating the effects of electronic and nuclear collisions [ICRU, 1993; Berger et al., 2005]. The stopping‒powers and ranges are given for a variety of materials.
 The regolith is composed mostly of silicate minerals, which consist mainly of silicon and oxygen [Papike et al., 1991]. Therefore, we use the PSTAR values for silicon dioxide as our chosen proxy for lunar regolith. PSTAR's range of protons (σ) within silicon dioxide is in terms of a mass column density (g/cm2). To convert the column density to a depth within the regolith, we assume a soil density of ρ=1.6 g/cm3, which is within the range of best estimates for the regolith's mean density from 0–30 cm [Carrier et al., 1991]. The penetration distance is thus σ/ρ. Figure 2 shows the distance as a function of energy that a particle travels in the regolith along its incident path. That distance is only the same as the depth reached for particles at normal incidence. The depth z below the surface at which the particle stops depends on its angle of incidence:
where θ is the angle of incidence with respect to the normal. (Note that, at the energies considered, the chemical composition of the soil only slightly affects the penetration depth of the protons. For example, a pure aluminum regolith would increase the penetration depth by less than 10%.)
 Normally incident, mono‒energetic particles penetrate to a depth σ/ρ. Grazing incidence particles (θ=90°) penetrate to z=0. Therefore, the flux of particles through a layer at depth z is
where J is the omnidirectional flux (particles·cm−2·s−1·sr−1). The factor of 2πlimits the flux to what is incident over half the sky, since the Moon blocks the other half. (Note that the exact location of the LCROSS impact site may not be exposed to half the sky because of local topography. On the other hand, the diameter of Cabeus crater (98 km) is great enough and its average depth (4 km) shallow enough that, ignoring finer‒scale topography, the surrounding crater walls insignificantly (on the order of a few percent) affect the exposure of the crater's floor to half the sky [Kozlova and Lazarev, 2010]. Therefore, it is reasonable to assume this half‒sky estimate applies to the LCROSS impact site.) According to the equation, all the particle flux passes through z=0. Because z=σ/ρ is the depth at which normally incident particles stop, there is no flux at or below that depth.
 Now, we need to consider the range of depths over which these GCR and SEP dose rates apply. Because the particles lose energy while interacting with the regolith along their path, we assume the dose rate to be constant down to the depth below which the flux of energetic particles is much less than the incident flux (2πJ). This nominally occurs at the depth where the flux is an order of magnitude less than that at the surface (z=0.9σ/ρ).
 The bulk of the GCR flux is at energies below about 300 MeV [Smart and Shea, 1985]. According to Figure 2, the depth to which protons with this energy can penetrate is ∼40 cm. Therefore, using z=0.9σ/ρ, we estimate that the GCR dose rate of 0.022 eV/(molecule·Myr) applies down to 36 cm. This agrees with the conclusion that GCRs penetrate centimeters to meters into the regolith, as mentioned in reviews describing cosmic ray tracks and radioisotope production within the regolith [Walker, 1980; Reedy et al., 1983]. Also, this is similar to results from experiments done by Miller et al. , in which most of the normally incident ions deposit their energy within the first 50 cm of regolith. Note, though, that they use ions more massive than protons and therefore less penetrative. On the other hand, the particles are normally incident, whereas we assume an isotropic particle flux that, on average, results in particles penetrating to shallower depths (e.g., see equation ((1))).
 The depth to which the SEP dose rate applies depends on CRaTER's energy threshold. CRaTER detects protons with energies greater than ∼15 MeV. Normally incident protons at that energy threshold penetrate about 0.2 cm into the regolith. Because the average energy spectrum of SEP events peaks at energies lower than this threshold, the SEP dose rates of 0.24 eV/(molecule·Myr), discussed in section 2, likely do not apply much deeper than 0.18 cm. (Incorporating SEPs below the energies CRaTER can measure would increase the dose rate. These particles, however, have even shallower penetration depths and are thus insignificant.) Again, this is consistent with previous findings that SEPs penetrate millimeters to centimeters into the regolith.
 These GCR and SEP penetration depths are important because they affect the amount of time a given layer of the regolith can be exposed to the incident particles. Meteoritic impacts overturn the regolith, thus limiting the time a layer spends near the surface. Arnold  shows that the regolith has been reworked, or gardened, down to a depth depending on time. Because an impactor's ejecta blanket is much larger than the area excavated by that impact, on average, a given location on the Moon tends to be buried rather than excavated. This means that impacts mix the regolith horizontally, with a median distance on the order of 10 m [Arnold, 1975]. Because large impacts are less frequent than smaller ones, lower depths are gardened on much longer timescales. Arnold  shows that the relation between the average gardened depth, zr(in cm), and the time, t (in Myr), is
Morris  and McKay et al.  show that this relation fits the analyses of reworking depths from Apollo core samples.
 This model allows us to estimate the length of time that a thin layer of water ice will be irradiated by energetic particles. The length of time that each layer is irradiated is the length of time it spends at a depth ≤zEP, where zEPis the maximum penetration of the energetic particles. The gardening zone (the vertical extent of mixed regolith) is thoroughly reworked, with the regolith's maturity being almost constant throughout the zone [McKay et al., 1991; Crider and Vondrak, 2003]. In other words, “thoroughly mixed” means that, on average, a given layer contains grains that have spent time at any depth within the gardening zone. Thus, all reworked layers have the same average maturity. It is therefore reasonable to approximate each layer of regolith in the reworked zone as having spent an equal length of time at all depths down to the bottom of the zone. The ratio of the exposure time to the gardening time is thus equal to the ratio of zEP to zr. The exposure time is thus
 Note that t is the total amount of time that has passed, while τis the exposure time, that is, the time spent at depths less than zEP. For zr>zEP, only a fraction zEP/zr of the regolith at the top of the gardening zone is exposed to radiation at any given time. The thorough vertical mixing of all the regolith down to depth zr, however, causes all regolith in the gardening zone to spend, on average, a fraction zEP/zr of its time exposed to particle radiation from space.
 We can write the exposure time (for zr>zEP) in terms of reworking time (see equation ((3))):
In terms of the reworked depth, the exposure time (again for zr>zEP) is
The results of equation ((6)), assuming that zEPfor GCRs is 36 cm and for SEPs is 0.18 cm, are shown in Figure 3. The plots show how the regolith's exposure time to GCRs and SEPs increases as the gardening depth increases. For the GCRs, the exposure time is at first equal to the length of time passed (note that time is not linear with respect to the gardening depth). Once zr>zGCR, however, the exposure time no longer increases as rapidly. The transition is not discernible in the SEP plot because zr>zSEPby the second time‒step (each time‒step is 10 Myr).
 To estimate the exposure times, we must estimate the gardening depths in the ice‒laden regolith within Cabeus crater. The age of the ice deposit gives the gardening depth through equation ((3)). Modeling by Hurley et al. [2012b] suggests that the deposit has been there for more than 1000 Myr, which corresponds to ∼80 cm of gardening. Thus, the gardening depth is deeper than the penetration depth of even the GCRs. The actual age could, however, be older. As we will show, as long as the age of the ice is on the order of 1000 Myr, an even older age for the deposition of water ice has little effect.
 The GCR exposure time is therefore found by substituting this ice age into equation ((5)), giving 460 Myr. This applies to all material within the reworked zone. (Note that we assume the ice to be evenly distributed, on average, throughout the top meter or so of the regolith. This is reasonable, since most of the ejecta in the LCROSS impact was from the top meter of regolith [Korycansky et al., 2009], and that top meter has been reworked, as we have described). The total GCR dose received by any water ice within the top 80 cm of regolith is thus this exposure time multiplied by the GCR dose rate: 9.2 eV/molecule. For SEPs, the exposure time is 2.3 Myr, giving a total SEP dose of 0.55 eV/molecule. While the dose ratefor SEPs is much higher than for GCRs, a given layer of water ice will be exposed to SEPs for much less time than to GCRs. Therefore, the total SEP dose is lower than that due to GCRs.
 The above estimates apply only statistically. Any given location on the Moon has a unique history of burials and impacts that affect the exposure time. Yet because GCRs and SEPs essentially blanket the Moon uniformly, these statistical results are a good estimate of average conditions in PSRs.
4 Space Radiation and Water Ice
 Energetic particles can dissociate water molecules and create secondary products (for a detailed review, see Johnson ). As described in Johnson , each radiation product has an associated G value, which is the number of chemical reactions resulting in that product per 100 eV deposited per molecule (reactions/[100 eV/molecule]). For fast light ions, such as GCR and SEP protons, the products depend on the number of ionizations created by each incident ion. The G value is roughly equal to the number of ionizations multiplied by the yield of H2 per ionization event divided by the original energy of the incident ion. In other words, G is the yield of H2per ionization event divided by the average energy the incident particle loses per ionization event. According to Johnson , that average energy for the reaction from H2O to H2 is ∼27 eV. The yield, in turn, depends on the temperature of the ice and the energy spectrum and fluence of incident particles. The fraction of H2 molecules produced with respect to the irradiated original H2O molecules is thus
where D is the radiation dose rate per molecule, τ is the exposure time and G is the G value (note that G must be divided by 100 eV) [Johnson, 1989]. As we discuss in the following section, this equation does not consider the fraction of original molecules that are destroyed by radiolysis.
 To our knowledge, there are no laboratory measurements of the yield of H2due to protons with GCR and SEP energies; therefore, we must estimate this by other means. According to Hart and Platzman , the G value for H2 being produced from H2O at 77 K is 0.1, 0.3, and 0.7, for gamma, beta, and alpha radiation, respectively. Although PSRs can be tens of kelvin colder [Paige et al., 2010], these are the only experimental data available. Gerakines et al.[2000, 2001] show that various compounds have similar G values whether created by ultraviolet photons (∼10 eV per photon) or created by 0.8 MeV protons. This indicates that the G value in which we are interested is likely to be at least the same as that for gamma rays; so G≥0.1. The presence of heavier GCR and SEP ions may make the G value more similar to that for alpha radiation, since heavier ions can create a high density of ionization events [Johnson, 2011]. Modeling by Jia and Lin  of the radiation dose due to GCR protons indicates that they account for only about half the total GCR dose. Alphas contribute about one fifth and heavier ions about one third of the total GCR dose. Therefore, although we show results below using G values for H2 of 0.1 and 0.7, the actual value is likely closer to 0.7.
 The most likely loss mechanisms for H2are thermal diffusion from the regolith and vaporization via impacts. (We discuss a third in the next section.) As Arnold  points out, impacts are more effective at burying volatiles than vaporizing them; that is, impacts tend to be protective. Also, because we limit our study to PSRs, the thermal diffusion timescale is at least the age of the Moon and thus much longer than the other timescales relevant to our study [Starukhina and Shkuratov, 2000; Feldman et al., 2001]. Therefore, we do not include any thermal diffusion loss term in our calculations.
 As mentioned above, the amount of water by mass in the LCROSS impact was 5.6±2.9%. The amount of H2 was 0.047±0.006% by mass. The observed fraction of H2to H2O molecules is
where Nxis the number of molecules of species x as a fraction of total molecules (i.e., the total number of H2 and H2O molecules), Mxis the mass of all the molecules of species x as a fraction of total regolith mass, and Mx is the mass of a single molecule of species x. Therefore, , and . H2O has an atomic mass of about 18 and H2 of about 2; thus, we use amu and amu. The observed ratio of H2to H2O molecules () is 0.08, (the uncertainties give a lower value of 0.04 and an upper value of 0.18).
5 Creation of H2
 Using the above values, we can estimate the fraction of water molecules that can result in H2. From equation ((7)), the total fraction of H2 molecules with respect to the original number of H2O molecules is
where DGCR and DSEP are the dose rates due to GCRs and SEPs, and τGCRand τSEP are the amounts of time the water ice is exposed to the energetic particles. This fraction applies down to the reworking depth or the penetration depth of the radiation, whichever is deeper. The quantities DGCRτGCR and DSEPτSEP are the total doses estimated above: 9.2 and 0.55 eV/molecule, respectively. Therefore, SEPs have only a minimal effect on the total fraction.
 Figure 4 shows the percentage of H2molecules created by GCRs with respect to the original number of H2O molecules, as a function of GCR penetration depth. (Note that this percentage is not with respect to the remaining number of water molecules. As we discuss below, the number of water molecules destroyed could be greater than the number of H2molecules created.) We plot this calculation as a function of penetration depth, because that depth determines the regolith's exposure time. Also, the plot shows how our depth estimate, and thus exposure time estimate, affects the calculation. Both lines on the plot assume a gardening time of 1000 Myr. The dashed line shows the percentage if G=0.1 (gamma radiation), and the solid line if G=0.7 (alpha radiation). According to section 3, the most likely penetration depth is 36 cm. Therefore, GCRs convert between 1 and 7% of the original ice into H2. These values vary little, even if the penetration depth varies over a range of 12 cm. Figure 5 similarly shows the percentage due to SEPs; their much shallower penetration (∼0.18 cm) keeps them from being as effective as GCRs in creating H2. They convert at least 0.05–0.4% of the original water ice into H2. The accuracy of the depth estimate is more important for SEPs than for GCRs, since SEP‒created H2increases by an order of magnitude if the penetration depth is increased just a few millimeters. This sensitivity, however, is unimportant, since SEPs are much less effective than GCRs at creating H2. Therefore, precisely estimating the penetration depth of the SEP dose is not critical for this study.
 Figure 6 shows the combined effect of GCRs and SEPs on the ice as a function of time, with the associated gardening depth on the upper x axis. In it, we have assumed the GCR dose to be applicable to 36 cm deep and the SEP dose to 0.18 cm. Again, the transition from zr≤zGCR to zr>zGCR is clear. As the plot shows, the more time available for gardening, the longer the exposure times become (see equation ((4))). If the ice deposit in Cabeus were 1000 Myr old, then between ∼1 and ∼7% of the original water molecules could have been dissociated, resulting in H2. As described in section 4, the important contribution of heavy ions to the total GCR dose makes the upper value of 7% more likely.
 After 1000 Myr, the gardening depth is nearly 1 m. Modeling by Korycansky et al.  shows that most of the ejecta in the LCROSS impact came from within 1 m of the surface. Therefore, most of the H2 and H2O must have come from the top meter of regolith [Hurley et al., 2012a]. This gives us confidence that the H2 we are modeling is in the same location as the H2excavated by the LCROSS impact.
 Note that, as mentioned above, the percentage of H2 shown in Figure 6 is not equivalent to the ratio of H2 to remaining H2O molecules from the LCROSS and LAMP observations (, as shown in section 4). To compare our results with the LCROSS and LAMP observations, it is necessary to estimate the destruction of H2O molecules by other processes.
 Two limits to the destruction of H2O molecules exist. The first limit occurs if every dissociated water molecule results in H2, leaving a single oxygen atom. In this case, the percentage of water molecules destroyed is equal to the percentage of H2 molecules created. Therefore, if 7% of the original water molecules have been dissociated, resulting in an equal number of H2 molecules, then the percentage of H2 to the remaining number of H2O molecules is 7% (H2) divided by 93% (remaining H2O). This final value is closer to 8%.
 The second limit occurs if more than one water molecule is needed to form H2. This could occur if the incident radiation were to dissociate two water molecules, forming two hydroxyls and two free H atoms to combine into H2. This pathway is more likely than the previous one, since the photolysis of water in its gas or solid phase is much more likely to create OH and H [McNesby et al., 1962; Slanger and Black, 1982; Huebner et al.1992; Watanabe et al., 2000]. In this case, two water molecules are destroyed to make a single H2molecule. Therefore, using the percentages above, the percentage of H2 to remaining H2O would be 7% divided by 86%, or 8%. In both limits, only a slight change from the percentage shown in Figure 6 occurs. Thus, the exact chemical pathway would appear to have little effect on the result.
 Another loss mechanism is due the energetic particles destroying H2. This, however, is factored into the experimental determination of the G value for H2. Furthermore, the second chemical pathway, in which two free H atoms form H2, is the more likely. This means that dissociated H2may still recombine into H2.
 Within the uncertainties, then, it appears possible that radiolysis by GCRs and SEPs could account for all of the H2observed by LAMP. The value could be, however, as low as ∼10%. This range of possibilities is due to the uncertainty in the G values for GCRs and SEPs.
 Our goal has been to quantify the amount of H2that could be created by GCRs and SEPs impinging on water ice in the lunar regolith. We find that over 1000 Myr, these energetic particles could convert at least 1–7% of the original water molecules in the lunar regolith into H2(up to ∼8% after 2000 Myr). Because of the important contribution of heavy GCR ions to the total dose, the upper value of 7% is more likely. Based on our analysis, radiolysis could account for between about 10 to 100% of the ratio of H2 to H2O found by combining the LCROSS and LAMP observations of the Centaur's impact plume (the observed ratio of H2 to H2O molecules was ).
 Our estimates of H2creation depend on the associated G value. While water ice radiolysis is an area of active research, particularly in relation to icy satellites, G values for relativistic particles have not been adequately characterized. Therefore, we suggest that particle accelerator experiments on water ice would improve our understanding of how important GCRs and SEPs are to H2 creation and to the radiolysis of ice in general. Pilling et al.  have done some work in this regard, although they did not focus on detecting H2. These experiments could also determine how many water molecules are destroyed for each H2molecule created, enabling a better comparison with the LCROSS and LAMP observations. Furthermore, such experiments would improve our understanding of how energetic particles modify ices throughout the solar system.
 This work was supported by NASA grant NNG11PA03C. The authors wish to thank Alex Crew and Alex Boyd for helpful discussions. The authors also wish to thank the two reviewers for their valuable suggestions for improving this paper. The OMNI data were obtained from the GSFC/SPDF OMNIWeb interface at http://omniweb.gsfc.nasa.gov.