Thermal neutron capture effects in radioactive and stable nuclide systems

Authors


Corresponding author. E-mail: ingo.leya@space.unibe.ch

Abstract

Neutron capture effects in meteorites and lunar surface samples have been successfully used in the past to study exposure histories and shielding conditions. In recent years, however, it turned out that neutron capture effects produce a nuisance for some of the short-lived radionuclide systems. The most prominent example is the 182Hf-182W system in iron meteorites, for which neutron capture effects lower the 182W/184W ratio, thereby producing too old apparent ages. Here, we present a thorough study of neutron capture effects in iron meteorites, ordinary chondrites, and carbonaceous chondrites, whereas the focus is on iron meteorites. We study in detail the effects responsible for neutron production, neutron transport, and neutron slowing down and find that neutron capture in all studied meteorite types is not, as usually expected, exclusively via thermal neutrons. In contrast, most of the neutron capture in iron meteorites is in the epithermal energy range and there is a significant contribution from epithermal neutron capture even in stony meteorites. Using sophisticated particle spectra and evaluated cross section data files for neutron capture reactions we calculate the neutron capture effects for Sm, Gd, Cd, Pd, Pt, and Os isotopes, which all can serve as neutron-dose proxies, either in stony or in iron meteorites. In addition, we model neutron capture effects in W and Ag isotopes. For W isotopes, the GCR-induced shifts perfectly correlate with Os and Pt isotope shifts, which therefore can be used as neutron-dose proxies and permit a reliable correction. We also found that GCR-induced effects for the 107Pd-107Ag system can be significant and need to be corrected, a result that is in contrast to earlier studies.

Introduction

The nuclear products that arise from the interactions of cosmic rays with meteorites or planetary surfaces are extensively used to characterize the exposure history of the objects studied (e.g., Wieler 2002; Ammon et al. 2009; Leya and Masarik 2009). Over the years the focus was mainly on cosmogenic nuclides that are produced by relatively high energetic projectiles, i.e., by protons and/or neutrons with energies above a few MeV. However, considering the spectra of primary and secondary particles in meteoroids, highest flux densities are reached for neutrons in the energy range below approximately 1 MeV, i.e., in a region called epithermal (neutron energies in the range 1–10 keV) and thermal (neutron energy in the range 0.025 eV). As some of the REE elements have relatively large cross sections for such neutrons, they can produce measurable isotopic shifts. For a few decades such isotopic shifts have been used to study the exposure and gardening history of the lunar regolith (e.g., Eugster et al. 1970a; Russ et al. 1971; Hidaka et al. 2000a; Sands et al. 2001; Hidaka and Yoneda 2007), aubrites and their parent body (Hidaka et al. 1999, 2006), Martian meteorites (Hidaka et al. 2009), various types of chondrites (e.g., Eugster et al. 1970b; Bogard et al. 1995; Hidaka et al. 2000b, 2011), mesosiderites and an iron meteorite (Hidaka and Yoneda 2011), and even to search for effects caused by an early active sun (Hidaka and Yoneda 2009).

In addition, neutron capture effects sometimes produce a nuisance for stable and radioactive nuclide studies, the effects on the Hf-W dating system being most likely the most prominent ones (e.g., Kleine et al. 2005a, 2005b; Markowski et al. 2006; Scherstén et al. 2006; Qin et al. 2008). For the Hf-W dating system, neutron capture effects lower the 182W/184W ratio and the too low ratios are then interpreted as too old core formation ages. In addition, the neutron capture effects produce a large scatter in the database for a given group of iron meteorites. The effects produced by thermal and epithermal neutron capture reactions have already been modeled for some dating systems (e.g., Masarik 1997; Leya et al. 2000a, 2003). However, a detailed discussion of neutron capture effects in various types of meteorites and a consistent modeling of neutron capture effects for a variety of radioactive and stable nuclide systems is still missing.

Here, we present a detailed description of neutron capture effects in carbonaceous chondrites, ordinary chondrites, and iron meteorites with the main focus on iron meteorites. After discussing neutron production and the slowing down of neutrons (moderation), we present neutron capture effects on various stable, i.e., Cd, Sm, Gd, Pd, Pt, Os, and radioactive, i.e., Hf-W, Pd-Ag, nuclide systems.

Neutron Production, Transport, and Capture

Below we summarize some important aspects concerning neutron production, neutron transport, and neutron capture cross sections.

Neutron Production

Since galactic cosmic-rays (GCR) consist mainly of protons and alpha-particles (heavier elements comprise less than approximately 1%), all neutrons in meteorites are secondary neutrons, i.e., they have been ejected in various nuclear reactions. Due to the zero charge of neutrons, their emission in a nuclear reaction is not hindered by the Coulomb barrier. While protons have to tunnel through the Coulomb barrier to leave the nucleus, which reduces their flux densities especially at low energies, neutrons can easily leave the nucleus even at very low energies. Consequently, the flux densities of secondary neutrons are often much larger than the flux densities of secondary protons. The flux densities of primary and secondary particles not only depend on the radius of the meteorite and the shielding depth of the studied sample but also on the chemical composition of the irradiated object, which is the so-called matrix effect (cf. Begemann and Schultz 1988; Masarik and Reedy 1994). For a recent discussion of the matrix effect for cosmogenic nuclides see Leya and Masarik (2009). The matrix effect arises for several reasons. First, the production of secondary particles in a nuclear reaction depends on the mass number of the target atom. For a fixed projectile energy the number of emitted particles is roughly proportional to the mass number of the target (e.g., Carpenter 1987; Pearlstein 1987). Consequently, the production of secondary particles in iron meteorites is more than two times higher than in, e.g., chondrites. Second, the energy spectrum of the emitted particles in a nuclear reaction depends on the mass number of the target atom. The reason is as follows: after the absorption of the projectile the number of interactions within the target nucleus is roughly proportional to A0.31, with A the mass number (Feshbach 1992). Consequently, there are on average 50% more interactions in an iron nucleus (A0.31 = 3.48) than in an oxygen nucleus (A0.31 = 2.36). For a fixed projectile energy, the larger number of intranuclear collisions directly translates into a larger number of low-energy ejectiles relative to high-energy ejectiles. Consequently, there are more secondary particles in an iron meteorite but they have (on average) lower energies than the fewer secondary particles in stony meteorites. The third reason for the matrix effect is that stopping of primary and secondary protons as well as neutron moderation also depends on the mass number of the irradiated object. As this article deals mostly with secondary neutrons, their moderation and capture is discussed in detail below.

Neutron Transport

In the following we give a brief summary of some relevant aspects for neutron transport calculations, which might help to better understand the dependence of neutron capture rates on the size of the meteoroid, the shielding depth of the sample, and especially on the chemical composition of the meteoroid. For more details, the reader is referred to, e.g., Morrison and Feld (1953) and Stacey (2007).

Considering elastic scattering of neutrons, the relationship between the incident energy E [eV] and the final energy E′ [eV] of a neutron in the laboratory system and the scattering angle in the center-of-mass system, Θc, is given by:

display math(1)

with A the atomic mass number. The maximum energy loss occurs for Θc = π, i.e., for backward scattering (e.g., Stacey 2007), in which case:

display math(2)

For hydrogen, = 1, the entire neutron energy can be lost in one single collision. For heavier nuclides, only a small fraction (4A/(+ 1)2 ∝ 1/A) of the energy can be lost in a single collision. For heavy nuclides this fraction becomes very small.

Instead of considering one individual scattering event, we now discuss the slowing down of neutrons by multiple scattering. If the energy loss in each individual collision is small, the slowing down of neutrons is a multistep process and the fractional energy loss is independent of the initial neutron energy. Thus, if one plots the successive energies of a scattered neutron on a logarithmic energy scale, the intervals between the points will, on average, be equal. It is therefore convenient to adopt the logarithm of the energy, as the energy variable for the slowing down of neutrons by elastic scattering. In almost all meteorite types many collisions are needed to reduce the neutron energy from its initial value in the MeV range to, e.g., thermal or epithermal energies. Under this assumption it is safe to assume that the effects of all elastic collisions are the same, i.e., that the energy loss per collision is given by its average value. Using the logarithmic energy scale we can define the (unit-less) logarithmic energy decrement ξ via:

display math(3)

with A the mass number of the scatter target. By way of example, to reduce a neutron energy from 1 MeV to E = 1/40 = 0.025 eV (thermal) by scattering in hydrogen (ξ = 1) requires on average 17.5 collisions. In contrast, reducing the neutron energy from 1 MeV to 0.025 eV by scattering in a carbon target (ξ = 0.1578) requires on average 17.5/0.1578 = 111 collisions. For an ordinary chondrite (A ≈ 23, ξ ≈ 0.0845) we need about 200 collisions, and for an iron meteorite (A ≈ 56, ξ ≈ 0.0353) we need about 500 collisions. These rough calculations already demonstrate that it is relatively difficult to produce large amounts of thermal neutrons in iron meteorites. Note that this discussion is only valid for targets where a large number of collisions are needed for the slowing-down process. While this approximation holds for most stony, stony-iron, and iron meteorites, it might not be satisfied for some carbonaceous chondrites because of their large amount of water and therefore hydrogen. The effect of hydrogen on the slowing-down process is twofold: first there is a higher energy loss per scattering event (see above), so that fewer collisions are required for the same energy loss and second, the scattering cross section of hydrogen decreases rapidly with increasing neutron energy. Therefore, especially at high neutron energies, the travel distance between two successive scattering events might be relatively large. There are various methods to take such effects into account (e.g., Marshak 1947). As the analytical approaches by Eberhardt et al. (1963) and Lingenfelter et al. (1972) are both based on the Fermi age theory, i.e., on the assumption that the slowing down is via multiple scattering events, they are both not strictly valid for carbonaceous chondrites.

In nature, describing the slowing down of neutrons only with such a simple multistep process is not a sufficient approximation. For targets made of heavier elements one has to take the absorption of neutrons during the slowing-down process into account. This is usually done using the (unit-less) resonance escape probability, which is given by:

display math(4)

with E0 as the starting energy of the neutron and E its final energy (both in [eV]). The probability of a capture per collision is given by (σa/σ), with σa as the absorption cross section [cm2] and σ the total cross section (absorption + scattering) [cm2].

Besides the logarithmic energy decrement ξ and the resonance escape probability p is the mean-squared distance that a neutron travels from its production until its capture as a thermal neutron, <r>2 in units [cm2], an important quantity for understanding neutron fluxes and neutron capture reactions.

display math(5)

with A as the atomic number of the target, λsc the scattering mean-free path [cm], and E and E0 the start energy and final energy of the neutron, respectively. The equation gives the mean distance that a neutron with a start energy E travels before it reaches the energy E0. As the scattering mean-free path is not well-known for neutrons in meteorites or the lunar surface we can only make some rough estimates. If we consider only A > 26 the denominator in the second term can be approximated by one. If we assume further that λsc varies only minor with the mass number of the scattering element, <r>2 is, for the same energy interval, essentially proportional to the inverse of the logarithmic energy decrement. Going back to the example above, one can see that <r>2 in an iron meteorite is about five times larger than in a carbon matrix. For carbon, we find a tabulated value for <r>2 approximately 15,000 cm2 (Morrison and Feld 1953), giving a distance for neutrons in an iron meteorite of approximately 280 cm. This calculation is most likely off by a factor of a few due to our approximation of a constant scattering mean-free path. The calculation nevertheless demonstrates that the neutrons travel large distances before they are thermalized. Since the mean-squared distance is within the range of typical meteorite dimensions (or even larger) it is easy to understand that (at least in iron meteorites) very few neutrons really reach thermal energies but that most of the neutrons leak out of the meteorite before being thermalized.

Neutron Capture Cross Sections

Considering the neutron capture cross sections, two regions have to be distinguished. For very low energies the cross sections follow a 1/ν dependence with v as the neutron velocity. At higher energies and especially for higher mass numbers, there are capture resonances, i.e., depending on the nuclear shell structure the capture of neutrons in a certain, small energy range can be enhanced by orders of magnitude. With increasing neutron energy the number of resonances per energy interval increases, resulting in overlapping resonances and an enhanced continuum. This is shown in Fig. 1 (upper two panels) for the neutron capture on 35Cl (left panel) and 59Co (right panel). For the production of 36Cl from 35Cl, the cross section follows a 1/ν dependence for energies below approximately 10 keV. At higher energies, there are narrow resonances that start to overlap at neutron energies of approximately 1 MeV. For the neutron capture on 59Co to produce 60Co, the database is different; again the low-energy cross sections follow a 1/ν behavior but there is a large capture resonance already at approximately 10 keV, which dominates neutron capture (see below). For most of the major elements in meteorites the capture cross sections follow a 1/ν dependence with no or only very low resonances; one important exception is Fe, which has a major neutron capture resonance at 1.16 keV (e.g., Wells et al. 1978). Here, it is worth emphasizing that in meteorites most of the elements relevant for the stopping down of neutrons have 1/ν dependent cross sections (the only exception is Fe) but that most of the (heavy) elements we are interested in have large capture resonances.

Figure 1.

Neutron capture cross sections for 35Cl and 59Co. The data clearly indicate that the thermal neutron capture cross sections follow a 1/ν behavior at low energies superimposed by resonances at higher energies. At high energies the number of resonances per energy increases and they start overlapping (upper panels). Capture rate for the production of 36Cl from 35Cl and 60Co from 59Co as a function of energy (lower panels).

Assuming an efficient stopping down of neutrons and a low resonance escape probability, i.e., enabling enough neutrons to reach really low energies before being captured, the spectral distribution of thermal neutrons is given by the Maxwell-Boltzmann (MB) distribution. Some examples for T = 298 K (room temperature), 373 K, and 673 K are plotted in Fig. 2 (left panel). Note that the thermal neutron capture cross sections given in cross section databases and used in compilations are calculated by averaging a 1/ν dependent neutron cross section with the MB distribution at 298 K. Consequently, the thermal neutron capture cross section is a reliable proxy for neutron capture effects only if (1) the neutron spectra follow a MB distribution and (2) the cross sections follow a 1/ν behavior, i.e., most of the capture is in the thermal range and not in resonances. Considering low-energy neutrons in meteorites especially the first point is often (always) not fulfilled. The right panel of Fig. 2 depicts the neutron spectra (in units neutron per MeV) as a function of neutron energy in the centers of an iron meteorite, a L-chondrite, and a C-chondrite, all having a radius of 120 cm. Also shown are spectra for perfectly thermalized neutrons with temperatures of 298, 373, and 673 K. The latter have been calculated by dividing the MB distributions (left panel) by the energy at each bin. It can be seen that none of the neutron spectra in meteorites follow a (renormalized) MB distribution, i.e., the neutrons in meteorites are not perfectly thermal. This becomes especially obvious for iron meteorites, where thermal neutrons are almost entirely missing. The situation is slightly better for L- and C-chondrites but also for them there is a lack of thermal neutrons compared with a MB distribution. Consequently, one always has to check whether the thermal neutron capture cross sections are, even in the absence of large capture resonances, reliable proxies for neutron capture effects.

Figure 2.

Maxwell-Boltzmann distribution for neutrons at three different temperatures (T = 298, 373, 673 K). All curves are normalized to one particle (left panel). Number of particles per energy as a function of energy for perfect Maxwell-Boltzmann distributions (T = 298, 373, 673 K) and in the centers of an iron meteorite, a L-chondrite, and a C-chondrites all having 120 cm radius. All curves are normalized to a total of one particle (right panel).

We discussed above that neutron capture for heavy elements are usually dominated by resonances. Consequently, thermal neutron capture cross sections are by no means good proxies for neutron capture effects. Assuming a spectral shape proportional to 1/E the resonance integral, which considers neutron capture by resonances for a 1/E spectral shape, is a much better approximation.

Response Integral as a Function of Energy

As described in detail in previous publications (e.g., Michel et al. 1991; Leya et al. 2000b; Ammon et al. 2009; Leya and Masarik 2009), the production rate Pj [atoms/(g × s)] of a cosmogenic nuclide j is calculated via:

display math(6)

where NA is Avogadro's number [1/mol], Ai is the mass number of the target element i [g mol−1], ci is the abundance of i [g × g−1], and k is an index for the reaction particle type (protons and neutrons). The excitation function for the production of nuclide j from target element i by reactions induced by particle type k is σj,i,k [cm2] and Jk [1/(cm2 × s × MeV)] is the differential flux density of particles of type k. The radius of the meteoroid, which is assumed to be spherical, is R and d is the shielding depth of the sample, E and M are the energy of the reacting particles and the solar modulation parameter, respectively. The solar modulation parameter M [MeV] is the energy lost by a GCR particle when it enters the solar system and approaches a given distance from the sun.

On the right hand side of Equation (6), we have introduced the so-called response integral Resp(E), which is the cross section multiplied with the differential flux density. Consequently, the integral of the response integral is, besides a few scaling factors, the total production rate. The response integral enables one to check which energy interval is most important for the production rate. This is exemplarily shown in Fig. 1 (lower two panels), where the response integrals for the neutron capture on 35Cl (left panel) and 59Co (right panel) are shown.

We first consider neutron capture on 35Cl. Despite the fact that the neutron spectra in meteorites are not really thermal (see above), most of the neutron capture is at 0.01, 0.1, and 10 eV for C-chondrites, L-chondrites, and iron meteorites, respectively. This indicates that most of the production is in the range below the resonances, i.e., in the range where the cross sections follow a 1/ν behavior. The situation is slightly different for the neutron capture on 59Co. While in C-chondrites most of the production is at thermal energies, approximately 0.02 eV, in iron meteorites 60Co is dominantly produced via the large resonance at approximately 10 keV. For L-chondrites, there is significant 60Co production at thermal energies and via the resonance, which makes the 60Co production rates in L-chondrites higher than in C-chondrites despite the fact that the latter have higher fluences of thermal neutrons (see also below).

The response integral is of special importance if we discuss neutron capture effects in iron meteorites. Since iron has a large neutron capture resonance at 1.16 keV, the shape of the neutron spectra and especially the flux density might change at this special energy. If true, we expect that the model predictions for isotope ratios are more accurate if the capture effects for the studied isotopes are both either above or below the iron resonance. In this case, the capture rates mostly depend on the cross sections and not so much on our knowledge of the neutron spectra. This is especially true considering that for most of the studied nuclides neutron capture is dominated by some resonances and is therefore in a very limited energy range only. The shape of the neutron spectra should not change much over this (small) energy range, a likely exception is the energy region around the iron resonance. Consequently, no matter how reliable the neutron spectra are, the model should be able to reliably predict capture rates if capture is for both isotopes either below or above the iron resonance.

Figure 3 depicts the energy-dependent response integrals for neutron capture on 54Fe (black line), 56Fe (red line), 57Fe (green line), and 58Fe (blue line) in ordinary chondrites (upper panel), carbonaceous chondrites (middle panel), and iron meteorites (lower panel). The response integrals are scaled with the isotopic abundance of the respective isotope, i.e., the total neutron capture response integral for natFe is simply given by the sum of the four response integrals. The data are for central regions in meteoroids having 80 cm radius. Various points are important. First, it can be seen that for all three meteorite types neutron capture on 56Fe dominates the total neutron capture, mostly because 56Fe is by far the most abundant isotope. Second, for all meteorite types considered here, neutron capture is almost entirely in the energy range at the major resonance (1.16 keV) or above. Third, the total neutron capture rates in ordinary chondrites are factors of 2 and 50 higher than the total neutron capture rates in carbonaceous chondrites and iron meteorites, respectively.

Figure 3.

Response integral as a function of neutron energy for 54Fe (black line), 56Fe (red line), 57Fe (green line), and 58Fe (blue line) at the central region of an ordinary chondrite (upper panel), a carbonaceous chondrite (middle panel), and an iron meteorite (lower panel) all with a pre-atmospheric radius of about 80 cm.

For the model predictions discussed in the following, we use the same particle spectra as used by Ammon et al. (2009), Leya and Masarik (2009), and Leya (2011). For calculating neutron capture rates, we rely on cross sections compiled in the JEFF-3.0A database and we assume a primary GCR particle flux of 2.99 cm−2 s−1 (Kollàr et al. 2006). In addition to the thermal and epithermal neutron capture reactions, we also consider reactions induced by fast particles, i.e., by protons and neutrons with energies above a few MeV to fully cover all possible burnout and production effects. Because for most of the important reactions no experimental cross sections exist, we calculated the data using the TALYS code (Koning et al. 2004). Unfortunately, TALYS is limited to projectile energies below 240 MeV. To cover the full energy range, the TALYS predictions were extrapolated toward higher energies by fully considering the individual reaction mechanism. Note that the TALYS predictions are relatively uncertain (by a factor of two, approximately) and that the extrapolation procedure is relatively crude. Since most of the neutron capture effects discussed below are dominated by thermal and epithermal neutrons, any uncertainties resulting from the ill-known cross sections and the extrapolation procedure are expected to be very minor. For the spallation reactions, we use a primary GCR spectrum of 4.47 cm−2 s−1, i.e., different from the value used for the capture reactions. At the moment, it is still unclear why two different values for the integral number of primary GCR particles are needed (Kollàr et al. 2006; Leya and Masarik 2009). However, since most of the effects discussed below are due to neutron capture and we are mostly interested in isotope ratios, any offsets and problems due to scaling the model predictions with the integral number of GCR particles should cancel out.

Comparison with Previous Modeling and Data

Radioactive Cosmogenic Nuclides

Our new model results for the production of 36Cl and 60Co in ordinary chondrites are in good agreement with earlier calculations by Eberhardt et al. (1963) and Spergel et al. (1986). Figure 4 shows the production rates of 36Cl and 60Co in the center of ordinary chondrites, carbonaceous chondrites, and iron meteorites. Also shown are the results given by Eberhardt et al. (1963) and, only for 60Co, by Spergel et al. (1986). The latter data have been renormalized to a Co concentration of 700 ppm and the radius in unit [g cm−2] has been recalculated to the unit [cm] assuming a L-chondrite density of 3.4 g cm−3 (Wilkison and Robinson 2000). The agreement is better than approximately 25% and also the dependence of the production rates on the radius is very similar for all three approaches. The thermal neutron capture rates for 60Co also agree well with measured data. By way of example, the 60Co activities in the H5 chondrite Jilin range from 53–260 dpm kg−1 with a Co concentration of 750 ppm (Heusser and Ouyang 1981; Honda et al. 1982; Spergel et al. 1986), i.e., well within the range of the modeled production rates. For Allende 60Co concentrations in the range 9–226 dpm kg−1 have been measured, but most values are between 41 and 185 dpm kg−1 (Cressy 1972; Mabuchi et al. 1975; Bourot-Denise and Pellas 1982; Evans et al. 1982), which compares relatively well to the modeled data for ordinary chondrites. As Allende has relatively little hydrogen, the thermal neutron capture rates for ordinary chondrites should apply better to Allende than the results for carbonaceous chondrites.

Figure 4.

Production of 36Cl (left panel) and 60Co (right panel) by (n,γ)-reactions in the center of spherical meteoroids as a function of the meteoroid radius. Shown are the modeling results for ordinary chondrites, carbonaceous chondrites, and iron meteorites. Also shown are the results by Eberhardt et al. (1963) and Spergel et al. (1986). The following concentrations were used: Cl: 100 ppm; Co: 700 ppm.

Stable Nuclide Systems: Sm and Gd in Stony and Stony-Iron Meteorites

Figure 5 depicts 158Gd/157Gd as a function of 150Sm/149Sm for lunar samples (Russ et al. 1971; Hidaka et al. 1999, 2000a; Sands et al. 2001; Hidaka and Yoneda 2007), aubrites (Hidaka et al. 1999, 2006), ordinary chondrites (Hidaka et al. 2000b, 2011), carbonaceous chondrites (Hidaka et al. 2000b), and mesosiderites (Hidaka and Yoneda 2011). Also shown are the correlation lines modeled for carbonaceous chondrites, ordinary chondrites, and iron meteorites. The dashed line shows the expected correlation if the isotopic shift is entirely due to thermal neutron capture reactions and the dotted line gives the correlation assuming that the nuclear shifts are entirely due to epithermal neutrons, i.e., that the production is entirely in the resonance region. We already demonstrated that the neutrons in most meteorites are not perfectly thermal and that therefore resonance capture significantly contributes. Consequently, we expect that most of the data fall in between the lines indicated by “thermal neutrons” and “Resonance capture,” as it is indeed the case.

Figure 5.

Modeled neutron capture effects on the isotope ratios 158Gd/157Gd versus 150Sm/149Sm for carbonaceous chondrites, ordinary chondrites, and iron meteorites. Also shown are the expected shifts produced by thermal neutron capture and by neutron capture in the resonance region, as well as experimental data for lunar samples, aubrites, ordinary chondrites, carbonaceous chondrites, and mesosiderites.

The model predictions indicate that the degree of neutron thermalization increases from iron meteorites, where capture is mostly in the resonance region, over ordinary chondrites, which are in between resonance capture and thermal neutron capture, to carbonaceous chondrites, where most of the captured neutrons are thermal or at least close to thermal.

Interestingly, most of the lunar samples plot close to the line modeled for ordinary chondrites, indicating that neutron capture in the resonance region significantly contributes to the overall production. The importance of epithermal neutrons to explain the data for lunar samples has already been discussed by Russ et al. (1971) and Sands et al. (2001). Here, it is interesting to note that the samples from the Apollo 15 drill core measured by Hidaka et al. (2000a) show a trend of better thermalization with increasing depth of the drill core. This can be seen because the samples deviate from the line for ordinary chondrites toward the line for carbonaceous chondrites with increasing depth. Hidaka et al. (2000a) already suggested that the neutrons are better thermalized at the lower layers of the drill core than in the upper layers. Note that we successfully modeled the correlation between ε(50Ti) versus 158Gd/157Gd and ε(50Ti) versus 150Sm/149Sm for various lunar samples using the particle spectra for ordinary chondrites (Zhang et al. 2012).

Most of the meteorite data plot in between the lines for ordinary chondrites and carbonaceous chondrites; the exceptions are aubrites that all plot on the line for carbonaceous chondrites. This indicates that the neutrons in aubrites are better thermalized than the neutrons in the other meteorite types and in the lunar surface. This is mostly due to the low iron concentration in aubrites, which increases the resonance escape probability, i.e., reduces the epithermal neutron capture on, e.g., iron, and therefore increases the chance that the neutrons reach thermal energies. The other exceptions are the mesosiderites and the IAB iron meteorite Udei station (Hidaka and Yoneda 2011) that plot, as expected, in between the lines for ordinary chondrites and iron meteorites.

Besides the meteorite data we also show the 158Gd/157Gd versus 150Sm/149Sm datum for the irradiated standard from Hidaka et al. (2006) that has been irradiated with a thermal neutron fluence of 5.94 × 1014 n cm−2. The data point plots onto the line calculated for thermal neutron capture indicating that (1) our calculations are correct and (2) that in none of the samples studied so far capture was entirely due to thermal neutrons but that resonance capture always contributes to the isotopic shifts.

Modeling Results

The Neutron-Dose Proxy Cd

Cadmium isotopes are often considered as good neutron-dose proxies because of the large thermal neutron capture cross section for 113Cd of more than 20,000 barns. We therefore modeled the neutron-induced isotope shift for the 114Cd/113Cd ratio. The result is surprising but understandable considering the neutron spectra in the different types of meteorites. The isotope shifts in ordinary and carbonaceous chondrites are large, reaching up to 0.9 ε-units per Ma of exposure. As neutrons are more efficiently thermalized in carbonaceous chondrites than in ordinary chondrites (see discussion above), the maximum effect in carbonaceous chondrites is reached at lower shielding (at the center of a 65 cm object) than in ordinary chondrites (at the center of 100 cm objects). In contrast, considering that neutron capture on 113Cd is almost entirely via thermal neutrons (resonance capture hardly contribute) but that the flux densities of thermal neutrons are low in iron meteorites, the shift in 114Cd/113Cd in iron meteorites is low, i.e., below 0.01 ε-units per Ma of exposure. Consequently, while Cd isotopes can serve as powerful neutron-dose monitors for most types of stony meteorites, the applicability to iron meteorites is limited not only due to the relatively small shift, it is essentially limited due to the low Cd concentrations, which make a precise measurement of such small shifts almost impossible (e.g., Kruijer et al. 2011).

The Neutron-Dose Proxy Pd

Humayun and Huang (2008) first proposed the use of Pd isotopes as a possible proxy for neutron capture effects in iron meteorites. They considered Pd as suitable because (1) a previous study of Pd isotopes had shown that Pd in iron meteorites is free of endemic nuclear anomalies (Chen and Papanastassiou 2005) and (2) Pd is a multi-isotopic element and therefore enables internal normalization. Unfortunately, most Pd isotopes have relatively low thermal neutron capture cross sections and resonance integrals, giving rise to only small isotopic shifts. A way out provides 103Rh, which after neutron capture produces radioactive 104Rh that decays via β-decay to the stable end-product 104Pd. Rhenium-103 has a relatively high thermal neutron capture cross section of 150 barn and a resonance integral of about 1000 barn. Thus, neutron capture effects mostly produce excess 104Pd. Note, however, that the excess 104Pd not only depends on the neutron fluence but also on the Rh/Pd elemental ratio. For modeling the Pd isotope shift due to neutron capture, we not only consider burnout and production on Pd and Rh but we also consider neutron capture on 107Ag and 109Ag, which produces after β-decay 108Pd and 110Pd, respectively. However, modeling this reaction path is not without problems because of metastable states in 108Ag and 110Ag. For example, assuming that neutron capture in 107Ag produces ground state 108Ag, about 2.85% of this 108Ag decays to 108Pd and 97.15% decays to 108Cd. In contrast, assuming that neutron capture on 107Ag feeds the metastable state in 108Ag at 109.5 keV, about 91.3% of this 108mAg decays to 108Pd and 8.7% undergoes an internal transition to the ground state, which then decays with a probability of 2.85% to 108Pd. From the nuclear level data (Blachot 1997) it can be seen that most of the de-excitations in 108Ag end in the ground state and we therefore assume that neutron capture on 107Ag produces predominantly ground state 108Ag. With the same arguments, we assume that 0.3% of the neutron capture on 109Ag ends in a net production of 110Pd.

Figure 6 depicts modeled ε(108Pd/106Pd) versus ε(105Pd/106Pd) (upper panel) and ε(104Pd/106Pd) versus ε(105Pd/106Pd) (lower panel) for iron meteoroids with radii between 10 and 120 cm and a cosmic-ray exposure age of 650 Ma. All data are normalized to 110Pd/106Pd. For both, 108Pd/106Pd and 105Pd/106Pd (upper panel) the induced shifts are low, i.e., below 0.2 ε-units for Texp = 650 Ma, which is in the range or even below present-day analytical precision (e.g., Chen and Papanastassiou 2005). In contrast, depending on the Rh/Pd elemental ratio, the isotope ratio 104Pd/106Pd can significantly be affected by neutron capture effects. By way of example, assuming a Rh/Pd elemental ratio of about 1 and an exposure age of 650 Ma, the cosmic-ray shift in 104Pd/106Pd is up to 1 ε-unit, i.e., well detectable with present-day analytical precision. Note that Chen and Papanastassiou (2005) found no anomalies in a Pd isotope study of various iron meteorites despite the fact that some of them are known to have relatively long cosmic-ray exposure ages, e.g., 300 Ma for Gibeon (Honda et al. 2009). However, the finding of a normal Pd isotope composition despite long cosmic-ray exposure ages is due to low Rh/Pd ratios. By way of example, the Rh/Pd ratio in Gibeon is 0.27 (D'Orazio and Folco 2003). Assuming now an exposure age for Gibeon of about 300 Ma (Honda et al. 2009), the maximum shift in 108Pd/104Pd and 106Pd/104Pd (normalized to 110Pd/104Pd) is −0.15 and −0.24 ε-units, respectively, i.e., hardly detectable. Consequently, Pd isotopes can only serve as neutron-dose monitors for samples with relatively high Rh/Pd ratios (Rh/Pd > 0.5).

Figure 6.

Modeled isotope shifts in 108Pd/106Pd (upper panel) and 104Pd/106Pd (lower panel) as a function of 105Pd/106Pd. Due to the neutron capture on 103Rh with subsequent β-decay to 104Pd, the 104Pd/106Pd ratio depends on the Rh/Pd elemental ratio.

Interestingly, Humayun and Huang (2008) reported isotope anomalies for ε(108Pd/106Pd) and ε(105Pd/106Pd). Their data for the iron meteorite Warburton Range deviate from the instrumental mass fraction line defined by various standards and the iron meteorite Santa Clara by more than 2 ε and 4 ε-units, respectively. Such large anomalies cannot be due to cosmogenic effects. The model predicts 108Pd/106Pd deficits of 2 ε-units only for irradiation ages larger than 6 Ga, which is obviously unrealistic. Even worse, deficits of 105Pd/106Pd in the range 4 ε units require irradiation ages in the range 15 Ga, i.e., longer than the age of the universe. In addition, in the diagram ε(108Pd/106Pd) versus ε(110Pd/106Pd) the normal meteorite data not corrected for instrumental mass fraction plot, as expected, on a line with slope approximately 0.5. The data measured by Humayun and Huang (2008) for Warburton Range have a slope of about 3/4, whereas Pd affected by cosmogenic contributions ends with a slope of about 2.9. Consequently, considering that the observed effects are much too large and that the relationship between the isotopic ratios cannot be explained by cosmogenic effects one has to conclude that the anomalies found by Humayun and Huang (2008) cannot be due to cosmogenic contributions. However, based on the limited database it is not clear if this in turn indicates that Warburton Range shows endemic Pd anomalies and further studies are needed.

The Neutron-Dose Proxy Os

Huang and Humayun (2008) were the first to detect various IVB iron meteorites' Os isotope shifts caused by cosmic-ray interactions. Later, Qin et al. (2010) found in the iron meteorite Carbo correlated shifts in 190Os/188Os and 189Os/188Os that are consistent with effects due to neutron capture. These authors also used for the first time the Os isotope variations as a neutron-dose monitor to correct cosmogenic effects on W isotopes. Recently, Wittig et al. (2013) presented cosmic-ray-induced shifts on Os isotopes for 12 of the 13 known IVB iron meteorites and used the data, together with isotope shifts on Pt isotopes (see below), as a proxy to correct the 182Hf-182W dating system for cosmogenic shifts. Here, we present first model calculations for cosmogenic effects on Os isotopes not only considering burnout and production on the Os isotopes but also considering neutron capture on 191Ir and 187Re to produce 192Os and 188Os, respectively. Note that for modeling neutron capture effects for Os we are in the comfortable situation that new experimental cross sections exist (e.g., Segawa et al. 2007).

Figure 7 shows the model predictions for ε(190Os/188Os) versus ε(189Os/188Os). For modeling, we used either Ir/Os = 0.92 and Re/Os = 0.083 (modeling for the iron meteorite Warburton Range, solid black line) or Ir/Os = 0.638 and Re/Os = 0.067 (modeling for the iron meteorite Cape of Good Hope, dashed line) (e.g., Wittig et al. 2013). Also shown are the data by Qin et al. (2010) for the iron meteorite Carbo and the recent data for 12 IVB iron meteorites by Wittig et al. (2013). For the modeled data, we assume that instrumental mass fractionation is corrected using 192Os/188Os. Two important conclusions can be drawn. First, the Os isotope shifts depend on the Ir/Os and Re/Os elemental ratios, as can be seen by the slight difference in the correlation lines modeled for Cape of Good Hope and Warburton range. Second, the model predictions describe the measured data rather well; the agreement is always within the 2σ uncertainties, which gives further confidence in the model.

Figure 7.

Modeled neutron capture effects on 190Os/188Os versus 189Os/188Os for Warburton Range (solid line, Ir/Os = 0.92, Re/Os = 0.083) and Cape of Good Hope (dashed line, Ir/Os = 0.638, Re/Os = 0.067). Also shown are the experimental data for 12 IVB iron meteorites (Wittig et al. 2013) and Carbo (Qin et al. 2010).

Note that the cosmic-ray-induced shifts can apparently be neglected for 187Re-187Os dating studies of iron meteorites, at least considering the effects for Os isotopes. By way of example, even assuming an extremely high Re/Os of about 0.2 as reached in some Re-Os dating studies (e.g., Shen et al. 1996; Sedaghatpour and Sears 2007) and an exposure age of 950 Ma results in cosmic-ray-induced shifts for ε(187Os/188Os) of less than −1.5 ε-units, i.e., small compared with the usual radiogenic shifts in the range of a few hundred ε-units. In addition, neutron capture effects can also be neglected for Os isotope studies in stony meteorites. By way of example, assuming typical Re/Os and Ir/Os ratios (e.g., Yokoyama et al. 2007) and an exposure age of 25 Ma results in cosmic-ray-induced isotope shifts of less than 0.01, 0.03, and 0.002 ε-units for 186Os/189Os, 188Os/189Os, and 190Os/189Os, respectively. Therefore, the new model calculations confirm earlier, less sophisticated model calculations (e.g., Brandon et al. 2005).

The Neutron-Dose Proxy Pt

Recently, Kruijer et al. (2013) and Wittig et al. (2013) have demonstrated that in iron meteorites Pt isotopes can serve as powerful and reliable neutron-dose proxies. Platinum-195 has a thermal neutron capture cross section of about 27 barn and even more important, a relatively large resonance integral of more than 370 barn, giving rise to measurable isotope shifts in 196Pt/195Pt (production of 196Pt due to burnout of 195Pt). In addition, 191Ir has a high capture cross section for thermal neutrons of more than 900 barn and a high resonance integral of more than 3500 barn. After 191Ir captured a neutron, 192Ir is produced, which decays via β-decay to 192Pt. Consequently, neutron capture on 191Ir can produce, depending on the Ir/Pt elemental ratio, large excesses in 192Pt. However, the excesses not only depend on shielding and exposure age but also on the Ir/Pt elemental ratio. Consequently, for applying Pt isotopes as a neutron-dose monitor one either can use 196Pt/195Pt or 192Pt/195Pt by measuring also the Ir/Pt elemental ratio of the studied sample.

Figure 8 depicts 192Pt/195Pt versus 196Pt/195Pt for all shielding depths in iron meteorites with radii between 10 and 120 cm and for Ir/Pt elemental ratios of 0.25, 0.5, 0.65, 0.75, and 1.0 (open symbols). Also shown are recent experimental data from Kruijer et al. (2013) for various iron meteorites (solid black symbols). It can be seen that (1) the cosmic-ray-induced shifts in 192Pt/195Pt depend on the Ir/Pt elemental ratio and (2) the experimental data are accurately reproduced by the model calculations. By way of example, the data for Hoba (HO, Ir/Pt = 1.01), Iquique (IQ, Ir/Pt = 1.05), and Tlatopetec (TL, Ir/Pt = 1.00) all plot within the uncertainties on the 192Pt/195Pt versus 196Pt/195Pt correlation line modeled for Ir/Pt = 1.0. In addition, the data for Carbo (Ir/Pt = 0.64) all plot perfectly on the correlation line modeled for 0.65, demonstrating the reliability of the model predictions. From the good agreement between measured and modeled data we can first conclude that Pt isotopes are reliable neutron-dose monitors in iron meteorites and second that the cosmic-ray-induced shifts can accurately be described by our model.

Figure 8.

Modeled neutron capture effects on 192Pt/195Pt versus 196Pt/195Pt in iron meteorites with Ir/Pt ratios in the range 0.25–1.0. Also shown are experimental data for various iron meteorites (Kruijer et al. 2013). HO: Hoba, SK: Skookum, SC: Santa Clara, IQ: Iquique, TL: Tlatopetec.

Tungsten Isotopes in Iron Meteorites

It is known that the interpretation of W isotope data in iron meteorites and lunar samples is hampered by cosmic-ray-induced effects (e.g., Masarik 1997; Kleine et al. 2005a, 2005b; Markowski et al. 2006; Scherstén et al. 2006; Qin et al. 2008; Leya et al. 2000a, 2003). Some previous studies used cosmogenic 3He as a proxy for neutron capture effects on W isotopes (e.g., Markowski et al. 2006; Qin et al. 2008). However, cosmogenic 3He is mainly produced by high to medium energy projectiles, while neutron capture effects are low-energy processes. Therefore, the lack of cosmogenic 3He does not necessarily imply the absence of neutron capture effects and vice versa. We therefore performed a full set of model calculations to better quantify neutron capture effects in iron meteorites. Some of the modeling results presented here have already been used to study core formation time scales using magmatic iron meteorites (Kruijer et al. 2013; Wittig et al. 2013).

In stony meteorites and lunar rocks, W isotope ratios are predominantly affected by the neutron capture reaction 181Ta(n,γ)182Ta(β)182W, resulting in elevated 182W/184W ratios (Leya et al. 2000a, 2003). This reaction is responsible for the large 182W excesses measured in some lunar rocks (e.g., Lee et al. 2002; Kleine et al. 2005b). As there is essentially no Ta in iron meteorites, the W isotope ratios are only affected by neutron capture reactions (burnout and production) on the W isotopes itself (e.g., Masarik 1997; Leya et al. 2000a, 2003). As a result, neutron capture reactions in iron meteorites induce negative shifts in 182W/184W and 186W/184W and a positive shift in 183W/184W. While the correction for instrumental mass discrimination (usually 186W/184W) largely cancels out the effect in 183W/184W, the shift in 182W/184W is magnified. Because we need one ratio to correct for instrumental mass discrimination (186W/184W) and we have one ratio with only very small effects (183W/184W), we can use only 180W/184W as an internal neutron-dose monitor. However, ratios involving 180W cannot be measured precisely enough, so we cannot correct the 182W/184W ratio using only W isotope data and we therefore have to use an external neutron-dose monitor.

Figure 9 shows modeled (small open symbols) and measured (black symbols) data in a diagram ε(182W/184W) (normalized to 186W/184W) versus ε(196Pt/195Pt) (normalized to 198Pt/195Pt). The experimental data, which are for IVB and IID iron meteorites, are from Kruijer et al. (2013) and Wittig et al. (2013). For the model calculations we assume that the pre-exposure 182W/184W ratios for the IVB and IID iron meteorites are −3.31 ± 0.05 and −3.12 ± 0.12, respectively. The value for the IVB iron meteorites is the average of the values given by Kruijer et al. (2013) and Wittig et al. 2013) and the value for the IID iron meteorites is from Kruijer et al. (2013). The solid and the dashed lines, respectively, are the best fit though the experimental data for IVB and IID iron meteorites (Kruijer et al. 2013). It can be seen that the fit for the IID data perfectly agrees with the model predictions; the slope is nearly indistinguishable. For the IVB data the situation is different, the slope of the fit is significantly shallower than the one given by the model predictions. The trend was already observed by Kruijer et al. (2013) and was interpreted as probably due to differences in the chemical composition of the meteorite matrices, which might have induced slight differences in the energy distribution of the neutrons. However, considering the trace element contents, their variability, and their resonance integrals and comparing them to the resonance integrals of the iron isotopes, we consider this explanation highly unlikely. Neutron moderation in iron meteorites is clearly dominated by moderation and absorption processes in the iron matrix and not by trace elements. Consequently, the matrix effect cannot serve as an explanation for the apparent discrepancy between model predictions and experimental data.

Figure 9.

ε(182W/184W) as a function of ε(196Pt/195Pt) for IVB and IID iron meteorites. The experimental data from Kruijer et al. (2013) and Wittig et al. (2013) are shown as solid black symbols. The solid and the dashed lines are the best fits given by Kruijer et al. (2013) for his IVB and IID data, respectively. Also shown are the model predictions (open symbols) for iron meteorites with radii between 5 and 120 cm. For further explanation see text.

Qin et al. (2008) argued that the s-process abundance of 182W might be underestimated by the models and that a better fit of the experimental r- and s-process abundance data can be achieved by reducing the thermal capture cross sections of 182W by about 20%. Indeed, reducing the capture rates on 182W by 20%, thereby assuming a 20% lower thermal neutron capture cross section and resonance integral, lowers the slope in the ε(182W/184W) versus ε(196Pt/195Pt) diagram from −1.59 to −1.39, i.e., closer to the value of about −1.05 given by Kruijer et al. (2013) for their VIB data. However, based on W isotope data in stardust SiC grains, Ávilia et al. (2012) argue that a reduction in the 182W cross section would produce a mismatch between modeled and measured SiC grain data. In addition, Burkhardt et al. (2012) also found that their W isotope data for CAIs can be better described using the standard and not the reduced cross section for 182W.

In a study of stardust SiC grains, Ávilia et al. (2012) found that the agreement between their data and s-process model predictions is best assuming an approximately 30% higher 183W neutron capture cross section. Increasing the capture rate on 183W by about 30% increases the slope from −1.58 to −1.65, i.e., it gets progressively worse. Furthermore, in an experimental study of neutron capture cross sections on 184W and 186W, Marganiec et al. (2009) suggest cross sections that are factors 1.12 and 1.25 higher, respectively, than the ones given in the JEFF database used by us. However, adapting 12% and 25% higher capture rates for 184W and 186W, respectively, increases the slope to −1.74, i.e., also much steeper than given by the experimental data. Finally, we checked whether the slope in the diagram ε(182W/184W) versus ε(196Pt/195Pt) changes if we use a different cross section database. However, using the database JEFF3.12, JENDL, ENDFB-VII, or RUSSFOND, changes the slope only very little.

Considering the discussion above, there is no safe information of whether or not to increase or reduce some of the capture rates. To be fully consistent within the model, we therefore decided not to change any of the capture rates and we consider the modeling as relatively precise, as suggested by the good agreement between model predictions and measured data for Pt and Os isotopes. Doing so, we have to conclude that the slope in the diagram ε(182W/184W) (normalized to 186W/184W) versus ε(196Pt/195Pt) (normalized to 198Pt/195Pt) is −1.58. In Fig. 10, we show all data (Kruijer et al. 2013; Wittig et al. 2013) and do not distinguish between VIB iron meteorites and IID iron meteorites. In addition, the solid line is the best fit through all the data assuming a fixed slope of −1.58, i.e., assuming that the slope is correctly given by the model calculations. It can be seen that the model predictions, although not perfect, fit the experimental data rather well, i.e., mostly within the experimental uncertainties. From this fit we can now also deduce the intersect, i.e., the 182W/184W ratio before cosmic-ray exposure. The value obtained by us is −3.06 ± 0.12 (2σ), i.e., slightly higher but in good agreement with the pre-exposure values given by Kruijer et al. (2013) and Wittig et al. (2013).

Figure 10.

ε(182W/184W) as a function of ε(196Pt/195Pt) in IVB and IID iron meteorites. The experimental data are from Kruijer et al. (2013) and Wittig et al. (2013). The solid line is the best fit through the experimental data assuming a fixed slope of −1.58 as given by the model calculations.

Silver Isotopes in Iron Meteorites

For the 107Pd-107Ag chronometer in iron meteorites, cosmogenic effects have already been calculated by Reedy (1980). Using a similar approach as we use here, he concluded that in iron meteorites cosmogenic effects on 107Ag and 109Ag by spallation reactions on Pd are negligible. For modeling, however, Reedy (1980) considered only proton- and neutron-induced reactions on Pd and he only qualitatively discussed that neutron capture rates could be a factor of 10 higher or lower than the production rate he calculated for spallation reactions. In addition, for modeling the cosmic-ray-induced shift in 107Ag he considered the full isobaric yield on mass 107, i.e., he assumed that all radioactive isobars with mass 107 have been decayed to 107Ag before the isotope measurement in the laboratory. This assumption holds if the cosmic-ray exposure age of the studied meteorite is long compared with the longest half-life in the decay chain, which is 6.5 Ma for the long-lived 107Pd. Considering that iron meteorites usually have exposure ages in the range of a few hundred million years (e.g., Voshage et al. 1983), the small amount of cosmic-ray produced 107Pd that has not yet decayed to 107Ag is small compared with the total amount of 107Ag already produced either directly or via the radioactive decay of 107Pd. Therefore, considering the full isobaric yield for 107Ag is a reasonable approximation for most (but not all) iron meteorites. In contrast, if one studies iron meteorites with short exposure ages (e.g., Kruijer et al. 2013) and/or for all stony meteorites, the assumption is no longer valid and it becomes necessary to fully consider all half-lives on the 107 decay chain. For example, for an exposure age of about 6 Ma and assuming a meteorite fall or a low terrestrial age, like, e.g., for Allende (Scherer and Schultz 2000), only about 10% of the 107Pd produced by neutron capture on 106Pd and by neutron- and proton-induced reactions on Pd, Ag, and Cd has already been decayed to 107Ag, the remaining 90% is still 107Pd and therefore do not contribute to the isotopic shift in 107Ag/109Ag measured today in the laboratory. For modeling the cosmic-ray-induced shift in 107Ag/109Ag for ordinary chondrites, carbonaceous chondrites, and iron meteorites we consider neutron- and proton-induced reactions on Pd, Ag, and Cd. In addition we consider neutron capture reactions on 106Pd, 108Pd, 107Ag, 109Ag, and 108Cd. Finally, we take into account that the isobaric yield on mass 107 depends on the cosmic-ray exposure age. Note that the calculated shifts in 107Ag/109Ag depend only very little on the Cd/Ag elemental ratio, which is in the range of 3 and 0.4 for ordinary and carbonaceous chondrites, respectively, and essentially zero for iron meteorites (e.g., Wasson and Kallemeyn 1988; Kruijer et al. 2011).

Assuming an exposure age of about 125 Ma, which is the longest exposure age ever determined for a stony meteorite, and a Pd/Ag ratio of about 40, i.e., close to the highest value given by Schönbächler et al. (2008), we calculate cosmic-ray-induced shifts in 107Ag/109Ag of −0.4 and −0.2 ε-units for ordinary and carbonaceous chondrites, respectively. Such effects would be easily measurable with present-day analytical precision. Remember, however, that due to the time dependence of the isobaric yield the shift in 107Ag/109Ag no longer linearly scales with the cosmic-ray exposure age, i.e., reducing the age by a factor of ten does not reduce the effect by the same factor of ten. For an exposure age of about 6 Ma, i.e., close to the exposure age of Allende (Scherer and Schultz 2000), and a Pd/Ag ratio of about 8, i.e., close to the value given by Schönbächler et al. (2008) for bulk Allende, we calculate a cosmic-ray-induced shift in 107Ag/109Ag of only −0.005 ε-units, which is much smaller than the current analytical precision (Carlson and Hauri 2001; Woodland et al. 2005; Schönbächler et al. 2008). Assuming an exposure age of about 7 Ma for most of the H-chondrites studied by Schönbächler et al. (2008) and Pd/Ag ratios of about 40, i.e., again close to the highest value measured by these authors for bulk H-chondrites, we calculate a cosmic-ray-induced shift in 107Ag/109Ag of −0.02 ε-units, much higher than the effect calculated for Allende but again smaller than the current analytical precision. Consequently, we can conclude that cosmic-ray-induced shifts on the 107Ag/109Ag ratio can be neglected for most of the bulk studies of ordinary and carbonaceous chondrites. The same conclusion also holds for the data obtained for Allende leach steps due to their rather limited spread in Pd/Ag ratios (e.g., Carlson and Hauri 2001; Woodland et al. 2005).

Our modeled results for iron meteorites can be compared with earlier predictions by Reedy (1980). Note, however, that he only considered production of 107Ag and 109Ag by fast proton- and neutron-induced reactions on Pd. He did not consider neutron capture reactions on Pd, Ag, and Cd leading to the production of 107Ag and 109Ag and he also ignored fast proton- and neutron-induced reactions on Ag and Cd. He calculated production rates of 670 and 270 atoms min−1 kg−1(Pd) for 107Ag and 109Ag, respectively. Limiting our model to the same type of reactions we get, depending on size and shielding depth, values in the range 60 and 890 atoms min−1 kg−1(Pd) for 107Ag and between 10 and 224 atoms min−1 kg−1(Pd) for 109Ag. If we average over all sizes and shielding depths we get approximately 500 atoms min−1 kg−1(Pd) and approximately 130 atoms min−1 kg−1(Pd) for the production of 107Ag and 109Ag, respectively, which is in reasonable agreement to the predictions by Reedy (1980). However, it needs to be emphasized that the production of 107Ag and 109Ag by fast proton- and neutron-induced reactions on Pd is only one and by far not the most important reaction pathway. By way of example, if we consider only spallation reactions on Pd, as done by Reedy (1980), the cosmic-ray-induced shift in 107Ag/109Ag is always positive, i.e., there is excess 107Ag. In contrast, if we consider all types of reactions the cosmic-ray-induced shift can either be positive or negative, depending on the size of the meteorite, the shielding depth, and the Pd/Ag ratio of the sample. Already this qualitative comparison indicates how important it is to always consider all possible reaction pathways.

How significantly the other reactions contribute, especially the neutron capture reactions on Pd, can be seen in Fig. 11 (left panel) where we plot the cosmic-ray-induced shift in 107Ag/109Ag as a function of 108Pd/109Ag. For calculating the data we averaged over all shielding depths in an iron meteorite with a preatmospheric radius of 40 cm having a cosmic-ray exposure age of 625 Ma, i.e., the data are directly applicable to the IIIB iron meteorite Grant (e.g., Ammon et al. 2009). Two things are of importance, first, the shift in 107Ag/109Ag linearly correlates with the 108Pd/109Ag ratio, the higher the 108Pd/109Ag ratio the more negative the shift in 107Ag/109Ag. Second, the cosmic-ray-induced shift is significant, reaching up to −35 ε-units for a 108Pd/109Ag ratio of about 1200, which is close to the highest ratio measured so far for a Grant sample (e.g., Chen and Wasserburg 1983). Considering the size of the cosmic-ray-induced shift, it is obvious that this effect cannot be neglected for 107Pd-107Ag dating studies of iron meteorites. An example is shown in Fig. 11 (right panel), where we plot measured 107Ag/109Ag ratios as a function of 109Pd/109Ag for Grant samples (Chen and Wasserburg 1983; Carlson and Hauri 2001; Woodland et al. 2005). The solid black symbols are the (uncorrected) literature data, the open symbols are the data corrected using the model calculations for an iron meteorite with a radius of 40 cm, an exposure age of 625 Ma, and averaging over all shielding depths. It can be seen that the corrected data are significantly higher than the uncorrected data; the effect is in most cases larger than the given uncertainties. Since correcting the data for cosmic-ray-induced effects changes them significantly, also slope and offset of the isochron change due to the correction. Using the uncorrected data, the slope of the regression line indicates an initial 107Pd/108Pd of 1.40 × 10−5. If we use instead the corrected data the slope is about 18% steeper, indicating an initial 107Pd/108Pd of 1.65 × 10−5 and therefore significantly earlier Pd-Ag fractionation. Using the solar system initial 107Pd/108Pd of (5.9 ± 2.2) × 10−5 given by Schönbächler et al. (2008) we calculate an uncorrected age for Grant (IIIB) of 13.5 Ma and a corrected age of 11.9 Ma, i.e., significantly older. Note that the offset of the isochron, i.e., the initial 107Ag/109Ag for the studied samples, changes only very little due to the cosmogenic correction, which is due to the fact that cosmic-ray-induced shifts are relatively low for samples with low Pd/Ag ratios.

Figure 11.

Modeled cosmic-ray-induced shifts ε(107Ag/109Ag) as a function of 108Pd/109Ag for an iron meteorite with an exposure age of 625 Ma and a preatmospheric radius of 40 cm. The data are averaged values for all shielding depths (left panel). ε(107Ag/109Ag) as a function of 108Pd/109Ag for the IIIB iron meteorite Grant. The solid black symbols are the experimental data from Chen and Wasserburg (C & W 1983), Carlson and Hauri (C & H 2001), and Woodland et al. (W et al. 2005). The open symbols are the experimental data corrected for cosmic-ray-induced shifts. Also given are the best fit lines through the uncorrected and uncorrected experimental data (right panel).

In earlier studies, Chen and Wasserburg (1983) and Kaiser and Wasserburg (1983) found in IVB iron meteorites (Santa Clara, Hoba, Tlatopetec, Warburton Range) and ungrouped iron meteorites (Piñon, Deep Springs) reliable isochrones but with an initial107Ag/109Ag of approximately 0, i.e., the initial Ag was essential pure 109Ag. Based on the model predictions by Reedy (1980), the authors excluded that the exotic component could be due to GCR irradiation of the meteorite and instead proposed that a large fraction of the 109Ag was produced by neutron capture on 108Pd with the high neutron fluence originating from a high-energy proton bombardment due to an extended T-Tauri phase of the early sun. Remember, however, that Reedy (1980) only considered fast particle reactions and he ignored the more important neutron capture reactions. Using our more sophisticated model, we can test whether the exotic component really cannot be explained by GCR irradiation. Assuming, for example, an Ag free iron meteorite and only production of 107Ag and 109Ag by neutron capture and fast particle reactions on Pd we obtain 107Ag/109Ag ratios in the range of 0.1 and 109Ag production rates in the range 4 × 1012–5 × 1015 atoms g−1(Pd) Ma−1, depending on size and shielding depth. Using the upper limit of the production rate and assuming a Pd concentration of approximately 10 μg g−1 and an exposure age of approximately 600 Ma results in approximately 3 × 1011 atoms 109Ag per gram of iron meteorite, which is similar in magnitude to the concentrations measured in the nickel-rich ataxites (Kaiser and Wasserburg 1983). Note that the picture does not change whether or not we consider fast particle reactions. Consequently, by irradiating Pd in an Ag poor iron meteorites we can produce 107Ag/109Ag as low as 0.1 in amounts comparable to the measured values. Therefore, the data can be explained by GCR irradiation and do not require high fluences from the sun in the early T-Tauri phase.

Conclusions

Using particle spectra for primary protons, secondary protons, and secondary neutrons together with calculated or evaluated cross sections we studied the neutron capture effects in iron meteorites, ordinary chondrites, and carbonaceous chondrites. The particle spectra were calculated using Monte-Carlo techniques and the cross sections are either determined using nuclear model codes (TALYS, Koning et al. 2004) or taken from evaluated nuclear data files (JEFF-3.0A). In this publication our focus is on iron meteorites. Studying the neutron spectra in iron meteorites, it can be seen that there are hardly any thermal neutrons. Most of the neutrons either leak out of the meteorite or are captured by the large resonance in 56Fe before reaching thermal energies. Consequently, most of the neutron capture reactions in iron meteorites are with epithermal and not with thermal neutrons. Similar results are obtained for chondrites, where epithermal neutron capture significantly contributes or even dominates total neutron capture rates.

After having demonstrated the reliability of the model calculations by comparing measured and modeled production rates for 36Cl and 60Co (Eberhardt et al. 1963; Spergel et al. 1986), we modeled neutron capture rates for Sm and Gd and compared our results to literature values (Russ et al. 1971; Hidaka et al. 1999, 2000a 2000b 2006 2011; Sands et al. 2001; Hidaka and Yoneda 2007, 2011). The agreement is in all cases good, giving further confidence in the model predictions. Also these data clearly indicate that neutron capture in stony meteorite and lunar surface samples is not exclusively via thermal neutrons, but that epithermal neutrons always significantly contribute.

We modeled neutron capture effects for the stable nuclides Cd, Pd, Os, and Pt, which might serve as neutron-dose proxies. The results obtained for Os and Pt isotopes agree well with recent iron meteorite data (Kruijer et al. 2013; Wittig et al. 2013). As expected, considering that thermal neutrons are almost missing in iron meteorites, the modeled isotopic shift in Cd is low, which limits the applicability of Cd isotopes as neutron-dose proxies. In contrast, the modeled shifts in Os, Pt, and Pd are all measurable with present-day analytical precision; enabling their use as internal neutron-dose proxies.

In the next step we modeled neutron capture effects on W isotopes as a function of the isotopic shifts in the neutron-dose monitors Pt and Os. The model seems to overpredict neutron capture effects in 182W by a factor of approximately 2 in IVB iron meteorites but describes the data within the uncertainties for IID iron meteorites. While Kruijer et al. (2013) argued that this might be due to variations in the trace element contents between IID and IVB iron meteorites, which might affect the shape of the neutron spectra, Wittig et al. (2013) argue that this might indicate a too large neutron capture cross section. In a detailed discussion we excluded that variable trace element contents can lead to effects as large as a factor of two and, doing literature research, we find no indication that the cross sections are off by a factor of two (e.g., Qin et al. 2008; Marganiec et al. 2009; Ávilia et al. 2012; Burkhardt et al. 2012). Consequently, to be consistent within the model we do not change the neutron capture cross sections and considered the modeled slope in the diagram ε(182W/184W) versus ε(196Pt/195Pt) as reliable, especially considering that the model accurately predicts all other neutron capture effects discussed in this study. Fitting the modeled slope of −1.58 to the experimental data recently determined for IVB and IID iron meteorites (Kruijer et al. 2013; Wittig et al. 2013) but not distinguishing between IVB and IID iron meteorites, we obtain a reasonable description of the experimental data, i.e., the fitted line is for almost all samples within their uncertainties. The thus obtained offset, i.e., the ε(182W/184W) for ε(196Pt/195Pt) = 0, which can be interpreted as the pre-exposure 182W/184W, is −3.06 ± 0.12 (2σ), i.e., slightly higher but in good agreement with the pre-exposure values given by Kruijer et al. (2013) and Wittig et al. (2013).

Finally, we modeled GCR-induced effects for the 107Pd-107Ag dating system, considering all relevant reactions. This is in contrast to an earlier study by Reedy (1980) who considered only fast particle reactions. The result is surprising; we found for the iron meteorite Grant, e.g., significant effects, the cosmic-ray-induced shifts in ε(107Ag/109Ag) can be as large as −35 ε-units. Since the effects depend not only on shielding depth and meteorite size but also scale linearly with the Pd/Ag elemental ratio, the cosmic-ray-induced shifts can significantly change the slope of the isochrons and can therefore have a significant effect on the inferred ages. For stony meteorites, however, the effect is in most cases negligible, mostly because of the low exposure ages and the thereby connected fact that most of the cosmic-ray-produced 107Pd has not yet decayed to 107Ag. Assuming an almost Ag-free iron meteorite and considering neutron capture and fast particle reactions on Pd, GCR interactions can produce Ag with a 107Ag/109Ag ratio as low as 0.1 and a production rate of up to 5 × 1015 atoms g−1(Pd) Ma−1, which can explain the exotic Ag composition found by Chen and Wasserburg (1983) and Kaiser and Wasserburg (1983) in some types of iron meteorites.

Acknowledgments

This study was supported by the Swiss National Science Foundation (SNF). We thank M. Humayun, T. Kleine, and T. Kruijer for their feedback on the model predictions and for pushing us to finish the publication. We also thank R. C. Reedy and H. Hidaka for their reviews and the AE for his comments and suggestions that helped improving the paper.

Editorial Handling

Dr. A. J. Timothy Jull

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