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Cosmogenic-nuclide production rates: Reaction cross section update
Nuclear Instruments and Methods in Physics Research B 294 (2013) 470–474
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Cosmogenic-nuclide production rates: Reaction cross section update R.C. Reedy ⇑ Planetary Science Institute, 1700 E Fort Lowell, Suite 106, Tucson, AZ 85719-2395, USA
a r t i c l e
i n f o
Article history: Available online 21 September 2011 Keywords: Cosmogenic nuclides Cross sections Neutron reactions Production rates
a b s t r a c t Interpretations of cosmic-ray-produced nuclide measurements are dependent on the accuracy of the production-rate estimates. Most production rates are determined using particles fluxes and cross sections for the relevant reactions. The reaction cross sections used for the production of cosmogenic nuclides are discussed. Recently, many experimental cross sections for making cosmogenic nuclides by protons have been compiled, evaluated, and used to study cosmogenic nuclides made by solar energetic protons in lunar samples. Neutrons make most galactic-cosmic-ray-produced nuclides. There are only a few measurements of cross sections for neutrons making cosmogenic nuclides because it is hard to get good fluxes of energetic neutrons, especially with energies >50 MeV. Most neutron cross sections to date have been estimated by using measured proton cross sections, occasionally adjusting them for nuclear systematics or to fit measurements of cosmogenic nuclides in documented samples. The status of spallation cross sections for the main reactions making the six main cosmogenic nuclides (3He, 10Be, 14C, 21Ne, 26Al, and 36Cl) from their major target elements is presented. Some comparisons of production rates calculated with these cross sections with measured rates are presented. The need for additional work to improve these important cross sections is discussed. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Cosmic-ray-induced (cosmogenic) nuclides, such as 10Be, 26Al, and 3He, are important because of their broad applications to many extraterrestrial and terrestrial studies, such as dating exposure ages of solar-system matter [1] and of surface features on the earth’s surface [2]. Production profiles for cosmogenic nuclides are known to vary with depth in the moon [3] and meteorites [4]. In the earth’s atmosphere and in its top surface, production rates also vary with location [5,6]. These variations can be different depending on the nuclide because of different nuclear reactions. Much work has been and is being done on modeling production systematics for these nuclides. The basic expression for calculating the production rate of a nuclide at one location depends on the composition of the sample, the fluxes of the particles (mainly neutrons and protons) to which that sample is exposed, and the excitation functions (cross sections as a function of energy) for all important reactions. The target chemistry is usually well determined. In most cases, only one or two target elements dominate the production of a cosmogenic nuclide. Usually the dominant particle making nuclides is the neutron, with protons making fewer nuclides. (Production by muons in the earth’s surface is ignored here.) The particle intensities vary much ⇑ Address: 152 Monte Rey Dr., Los Alamos, NM 87544, USA. Tel.: +1 505 6729519. E-mail address: [email protected] 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.08.034
with location (such as depth). The spectral shape of these particles also changes inside an irradiated object [3,4]. Some general discussions have been done on the excitation functions used for such production-rate calculations e.g., [7,8] and of tests of their consistencies with measurements e.g., [4,5,9–11]. This work reviews existing work on cross sections used for six important cosmogenic nuclides, 3He, 10Be, 14C, 21Ne, 26Al, and 36Cl. 2. Fluxes of cosmic-ray particles The particle flux as a function of energy to which a sample is exposed depends on when the sample was irradiated (as the fluxes of cosmic-ray particles, mainly protons, can vary over time) and the location of the sample. GCR particles penetrate up to several meters of the surface of a solid object and produce numerous secondary particles via spallation processes [3]. For the earth, the flux of cosmic rays hitting the top of the atmosphere varies with geomagnetic location, with no particles scattering into space at the earth’s poles and most particles deflected into space by the strong magnetic fields near the equator [12]. For extraterrestrial matter, the size and geometry of the irradiated object and the location of a sample inside that object strongly affect the production and transport of particles. For terrestrial matter, fluxes vary with depth in the atmosphere and, for in situ nuclides, with depth in the surface [5,6]. The flux in a sample depends on the medium around the sample and can be affected by being
R.C. Reedy / Nuclear Instruments and Methods in Physics Research B 294 (2013) 470–474
near a boundary between two very different media (such as solid, water or ice, and the atmosphere) [13]. The spectral shapes of these particles often vary significantly, with higher-energy particles being less important away from an object’s surface [4,6]. In most cases, neutrons are the dominant particles because many neutrons are made per cosmic-ray interactions and charged particles are quickly slowed down and stopped by ionization energy losses. Particle fluxes (especially for protons and neutrons) are usually calculated using codes that model the production and transport of nuclear particles, such as the Monte Carlo N Particle eXtended (MCNPX) code [4,6,11], which is well documented and tested. Much early work was done with a semi-empirical GCR model [3]. Other particle production and transport codes used include the LAHET Code System e.g., [5], the HERMES code e.g., [14], the GEANT code [15], and PHITS [16]. These calculated particle fluxes are used with excitation functions for the nuclear reactions of interest. These cross sections usually control how well calculated production rates compare to measurements for all of these GCR models. 3. Cross sections The cross sections for the nuclear reactions that make cosmogenic nuclides in matter vary much. Some nuclides are made by the capture of low-energy (E 0.01–10 eV) neutrons, and those capture cross sections are usually well determined [17]. Most nuclides are made by spallation reactions induced by particles having energies above about 1 MeV, and cross sections are needed for energies from threshold to several GeV. Protons dominate production of almost all cosmogenic nuclides by solar energetic particles [18]. For nuclides made by galactic-cosmic-ray (GCR) particles, production is mainly by neutrons with a small portion (5%) made by protons. Protons can be important for a few reactions near the surface of an irradiated object for nuclides made mainly by higher-energy particles (such as 3He). Cross sections reported here are cumulative ones and include nuclides made by the decay of other radionuclides to the nuclide of interest, such as 3H decaying to 3He, often called 3THe. Here, 3He is the cumulative of direct production and the decay of 3H. 3.1. Sources of cross sections The best cross sections are those that are well measured by at least 2 groups for a range of energies. This is usually the case for proton-induced reactions because it is easy to accelerate protons to a wide range of energies. With the use of AMS or noble-gas mass spectroscopy, cosmogenic nuclides made by protons, cross sections have been well measured. Prior to AMS, very few cross sections for cosmogenic nuclides were measured, especially the longer-lived ones (e.g., 0.7-Myr 26Al [3]) and those that do not emit a gamma ray in their decay (such as 10Be [19]). The international cross-section compilation called Cross Section Information Storage and Retrieval System (CSISRS) at the National Nuclear Data Center of the Brookhaven National Laboratory was queried to get as many measured cross sections as possible. Some cross sections have been determined using inverse reactions, like high-energy 16O on a proton-rich target with the energetic products determined by a set of detectors down beam instead of energetic protons on a 16O target [20]. Some mirror reactions have been used, such as O(p,x)7Be cross sections used for O(n,x)10Be or (p,x) cross sections used for (n,x) reactions (where x is one or more emitted particles). Good fluxes of energetic neutrons are hard to produce. Bombarding a target containing tritium (3H) with energetic deutrons (2H) can make nearly mono-energetic neutrons with energies up to 20 MeV. Higher-energy neutrons can be made by irradiating certain targets (such as 7Li or 9Be) with intense beams of
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mono-energetic protons. Many neutrons are directly emitted with energies slightly below that of the protons, but some lower-energy neutrons are also emitted. This spectrum is called quasi-monoenergetic. Corrections for these lower-energy neutrons usually are needed [21], especially for nuclides that have their largest cross sections at relatively low energies. Bombarding a thick target of a heavy element like W with energetic protons produces a high flux of neutrons with a continuum of energies up to near that of the incident protons [22]. Such a spectrum of neutrons is called white because of the continuum of energies. Although the measured cross section is an average, those for white neutrons can serve as a check of a set of cross sections for that energy range. For neutrons making many nuclides, cross sections for protoninduced reactions are often used for neutron-induced reactions. This assumption of similar neutron and proton cross sections is fairly good for product nuclides like 26Al that are between two stable nuclides or that are similar in binding energy per nucleon to an adjacent stable nuclide. Occasionally, a particle-specific reaction such as 24Mg(n,a)21Ne, 39K(n,a)36Cl, or 56Fe(p,a)53Mn, needs to be added or deleted. The assumption of approximately equal proton and neutron cross sections fails for products far from the region of the stable isotopes, such as neutron-rich 14C and 10Be [3,19]. Cross sections for analogous reactions of the same reaction type can be used to estimate cross sections, such as those for 58 Ni(n,2n)57Ni and 59Co(n,2n)58Co reactions used for the 42 Ca(n,2n)41Ca reaction. Some adjustments, such as for the threshold energies of the reactions, often are needed. There are many formulae and codes that have been for calculating cross sections. For high-energy spallation reactions (above 100 MeV), several fairly-simple formulae were developed many decades ago. Several codes have been developed to calculate cross sections. However, most formula and codes give cross sections for an individual nuclide that typically differ from measured ones by factors of 2 [23], and the use of such codes for getting good cross sections is limited. Many early estimates for neutron cross sections were adjusted using measured concentrations of cosmogenic nuclides e.g., [14,19]. Such adjustments give a set consistent with the assumptions in the modeling of the particle fluxes for the object of interest and the code used. Much work has been done recently using the MCNPX code [4,11]. There are several good sets of documented samples that can be used to test excitation functions for making cosmogenic nuclides, especially the Apollo 15 deep drill core e.g., [4], the Knyahinya L-chondrite e.g., [4,11,24], and rates determined from terrestrial in situ cosmogenic nuclides e.g., [5,6]. Nuclides measured in several large spherical target isotropically irradiated with monoenergetic protons also are good tests [25]. 3.2. Proton cross sections Measured proton cross sections were recently compiled and evaluated. Those for 10Be, 26Al, and 36Cl were reported in [18]. Cross sections for making 14C are from [26] and references therein. For oxygen, the dominant target element in most media, cross sections from several other sources agree with those in [26]. The evaluated excitation functions for making 14C, 41Ca, and 53Mn are given in [27]. Cross sections for making 3He, 20Ne, 21Ne, and 22Ne by protons have been compiled from many sources and evaluated [28]. The cross sections for 3He are total for that mass and include the decay of 3H as well as direct production of 3He. 3.3. Neutron cross sections There are only a few nuclides for which neutron-induced cross sections have been measured and reported. The reaction with the
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best-determined cross sections is for the production of Ne isotopes from Mg with several sets in good agreement below 20 MeV [29], which includes the energy for the peak cross sections for making 21 Ne. For higher energies, the excitation function adopted for the Mg(n,x)Ne reactions were made to converge with the ones measured for protons [28]. Some neutron-induced cross sections have been measured for the O(n,x)14C and Si(n,x)26Al reactions [30]. Many decades ago, charged particles were measured for several neutron-induced reactions, such as 39K(n,a)36Cl and 24Mg(n,a)21Ne. Direct measurements of 21Ne from neutron-irradiated targets gave cross sections in good agreement with the measurements of the emitted a particle [31]. Many samples have been irradiated with quasi-mono-energetic or white neutrons in which the long-lived or stable products have not been measured e.g., [21,22]. Some irradiations with quasimono-energetic neutrons with energies of 100–400 MeV have been or are being done and will have their long-lived radionuclides or stable nuclide measured after non-destructive gamma-ray spectroscopy [32]. 3.3.1. Cross sections for making 3He The cross sections for 3He include both the direct production of 3 He and that made by the decay of 3H. This cumulative or total 3He is sometimes called 3THe. The cross sections used for neutrons making 3He were those evaluated by the author for protons over 3 decades ago [33] and are not very different from the recent evaluation for proton reactions making 3He [28]. Those cross sections were used for calculations for the Knyahinya L-chondrite but needed to have an effective proton flux that was 30% higher than for other cosmogenic nuclei [11]. The measured and calculated production profiles as a function of depth in Knyahinya were in good agreement. Rates for making 3He in terrestrial basalt were in good agreement with measurements [5]. The excitation functions for making 3He from O and Si are shown in Fig. 1.
Fig. 1. The elemental cross sections (in millibarns) as a function of neutron energy (in MeV) for total 3He from O and Si and for 21Ne from Mg and Si. The cross sections between points are a linear interpolation on a log–log plot.
3.3.2. Cross sections for making 21Ne The isotope of interest for cosmogenic neon is the total production of 21Ne, as it is only 1% of natural Ne and thus easiest to detect as cosmogenic. Its (and also the other Ne isotopes) production by neutrons from Mg, a major target in many materials, has been measured up to 19 MeV [29]. Above that energy, neutron cross sections were assumed to gradually merge to the proton-induced one. For silicon (the target for making 21Ne in terrestrial quartz), an older version of the proton cross sections was adopted for neutrons that is very similar to the current proton version. The rates for making 21Ne in terrestrial SiO2 and basalt were about 10% low [5]. Rates for 21Ne in Knyahinya were consistent with other nuclides [11]. The excitation functions for making 21Ne from O and Si are shown in Fig. 1. 3.3.3. Cross sections for making 10Be To fit measured 10Be profiles in samples from known locations of the St. Severin meteorite, the cross sections for making 10Be from oxygen, the dominant target, were adjusted up much for energies below a few 100 MeV from the existing O(p,x)10Be cross sections [19]. The excitation function for making 10Be from Si [19] was the one then estimated for proton reactions making 10Be, which were 0.3 of cross sections measured for the Si(p,x)7Be reaction. They are consistent with more-recently measured proton cross sections. Terrestrial rates for 10Be in SiO2 were in fairly good agreement with early work [5]. Rates for 10Be in Knyahinya [11] and Apollo 15 deep drill core [4] needed higher effective fluxes than other nuclides, suggesting the estimated cross sections are low by 10%. The excitation functions for making 10Be from O and Si are shown in Fig. 2.
Fig. 2. The elemental cross sections (in millibarns) as a function of neutron energy (in MeV) for 10Be and 14C from O and Si. The cross sections between points are a linear interpolation on a log–log plot.
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The excitation function for the Ca(n,x)36Cl was estimated from (p,an) cross sections, mainly Fe to 52Mn. In 1991, those cross sections were multiplied by about 0.8 to get a better agreement of calculated ratios with elemental production ratios estimated for Fe and Ca in meteorites. The Fe(n,x)36Cl excitation function was assumed to be the same as measured proton-induced cross sections. These cross sections are higher than those measured for Ca(p,x)36Cl reaction for 50–200 MeV because the neutron-induced reaction with 40Ca can emit an a particle whereas the proton-induced reaction with 40Ca cannot emit an a particle. Early calculated rates for Knyahinya and Apollo 15 deep drill core were consistent with measurements [9,10]. Calculations for rates for making 36Cl from Ca were 15% low relative to early terrestrial measurements [5]. 4. Summary and discussion
Fig. 3. The elemental cross sections (in millibarns) as a function of neutron energy (in MeV) for 26Al (0.7-Myr) from Al and Si and for 36Cl from K and Ca. The cross sections between points are a linear interpolation on a log–log plot.
3.3.4. Cross sections for making 14C For oxygen and neutron energies below 35 MeV, the measured cross sections for making 14C [30] were used. The higher energies were 1.1 times the version adopted by [3] for fitting 14C measured in lunar samples. The excitation functions for Si were based on Si(p,x)14C cross sections [26] shifted to lower energies by 5 MeV because of the different reaction threshold energies (for 3He emitted with incident neutrons). Calculated rates for making 14C in Knyahinya were consistent with measurements [9,11]. The excitation functions for making 14C from O and Si are shown in Fig. 2. 3.3.5. Cross sections for making 26Al The excitation functions for making 26Al (the 0.7-Myr groundstate isomer) are not easy to calculate because the short-lived isomer 26mAl beta decays directly to 26Mg and not to 26Al. Some proton cross sections for 26Al were measured using good gamma-ray detection systems prior to AMS. The early proton excitation functions were adopted for neutron reactions making 26Al from Al and Si [34] and are shown in Fig. 3. Calculated rates for making 26 Al in terrestrial SiO2 were possibly low compared to early work [5]. Rates in Knyahinya and Apollo 15 deep drill core are in good agreement with measurements [4,9,10]. 3.3.6. Cross sections for making 36Cl Cross sections for measured a particles emitted from 39K irradiated by neutrons with energies up to about 15 MeV determine the most important part of the K(n,x)36Cl excitation function. The K curve in Fig. 3 shows that the cross sections near 10 MeV are much higher than at higher energies, and those energies are the ones where neutron fluxes are very high. The cross sections above 30 MeV were based on estimates for similar reactions, and are about 0.6–0.7 of recently measured proton cross sections.
Cross sections for six of the main cosmogenic nuclides now being routinely used for extraterrestrial and terrestrial work, 3He, 10 Be, 14C, 21Ne, 26Al, and 36Cl, were reviewed. All were developed a decade or more ago for a variety of extraterrestrial studies. They also yielded production rates that were consistent with early work on in situ terrestrial cosmogenic nuclides [5]. All have given calculated production rates using a variety of models for cosmic-ray particle fluxes that are within 10% or so of most measurements. While the physical basis of this work and some tests with measurements are good, there is room for improvement. Work on cross sections for elemental production should be tested with accelerator irradiations for mono-elemental targets e.g., [25] or natural samples with a wide range of compositions, such as different classes of meteorites. For proton cross sections, the best agreements with measurements for natural samples were achieved using good experimentally-measured cross sections [18]. Cross sections for reactions for neutron energies above 30 MeV are needed. Some previously-irradiated samples e.g., [21,22] need to have their long-lived and stable product measured. Both samples irradiated by quasimono-energetic neutrons and by white neutrons from high-flux spallation neutron sources are needed. Some results from such irradiations should be reported in the next year or so. More tests of these cross sections are needed with document samples using good production-rate models. The best tests should use the latest and well-documented codes for particle production and transportation, such as MCNPX. Results from such tests will help to show where these cross sections needed to be adjusted. Acknowledgements Members of the CRONUS-Earth project encouraged the preparation of this paper. David Argento and a reviewer provided useful comments that improved the manuscript. The CRONUS-Earth project of the National Science Foundation supported the recent work, preparation, and writing of this paper. NASA’s Cosmochemistry Program supported earlier cross-section work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
R.C. Reedy, J.R. Arnold, D. Lal, Annu. Rev. Nucl. Part. Sci. 33 (1983) 505. J.C. Gosse, F.M. Phillips, Quatern. Sci. Rev. 40 (2001) 1475. R.C. Reedy, J.R. Arnold, J. Geophys. Res. 77 (1972) 537. K.J. Kim, J. Masarik, R.C. Reedy, Nucl. Instrum. Methods B 268 (2010) 1291. J. Masarik, R.C. Reedy, Earth Planet Sci. Lett. 136 (1995) 381. D.C. Argento, R.C. Reedy, J.O. Stone, Nucl. Instrum. Methods Phys. Res. B, in review. R.C. Reedy, Nucl. Instrum. Methods B 12 (2000) 782. I. Leya, J. Masarik, Meteorit. Planet. Sci. 44 (2009) 1061. R.C. Reedy, J. Masarik, K. Nishiizumi, J.R. Arnold, R.C. Finkel, M.W. Caffee, J. Southon, A.J.T. Jull, D.J. Donahue, Lunar Planet. Sci. 24 (1993) 1195. R.C. Reedy, J. Masarik, Lunar Planet. Sci. 25 (1994) 1119.
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[11] K.J. Kim, R.C. Reedy, Lunar Planet. Sci. 35 (2004) 1359. [12] K.J. Kim, I.J. Graham, J. Masarik, R.C. Reedy, Nucl. Instrum. Methods B 259 (2007) 642. [13] J. Masarik, K.J. Kim, R.C. Reedy, Nucl. Instrum. Methods Phys. Res. B 259 (2007) 637. [14] I. Leya, H-J. Lange, S. Neumann, R. Wieler, R. Michel, Meteorit. Planet. Sci. 35 (2000) 259. [15] J. Masarik, J. Beer, J. Geophys. Res. 114 (2009) D11103. [16] T. Sato, H. Yasuda, K. Niita, A. Endo, L. Sihver, Radiat. Res. 170 (2008) 244. [17] R.C. Reedy, S.C. Frankle, Atomic Data Nucl. Data Tables 80 (2002) 1. [18] K. Nishiizumi, C.P. Kohl, J.R. Arnold, M.W. Caffee, J. Masarik, R.C. Reedy, Geochim. Cosmochim. Acta 73 (2009) 2163. [19] C. Tuniz, C.M. Smith, R.K. Moniot, T.H. Kruse, W. Savin, D.K. Pal, G.F. Herzog, R.C. Reedy, Geochim. Cosmochim. Acta 48 (1984) 1867. [20] W.R. Webber, J.C. Kish, J.M. Rockstroh, Y. Cassagnou, R. LeGrain, A. Soutoul, O. Testard, C. Tull, Astrophys. J. 508 (1998) 949. [21] J.M. Sisterson, F.D. Brooks, A. Buffler, M.S. Allie, D.T.L. Jones, M.B. Chadwick, Nucl. Instrum. Methods Phys. Res. B 240 (2007) 617. [22] J.M. Sisterson, J. Ullmann, Nucl. Instrum. Methods Phys. Res. B 234 (2007) 419. [23] K. Ammon, I. Leya, B. Lavielle, E. Gilabert, J.-C. David, U. Herpers, R. Michel, Nucl. Instrum. Methods Phys. Res. B 266 (2008) 2.
[24] A.J.T. Jull, D.J. Donahue, R.C. Reedy, J. Masarik, Meteorit. Planet. Sci. 29 (1994) 649. [25] I. Leya, H-J. Lange, M. Lüpke, U. Neupert, R. Daunke, O. Fanenbruck, R. Michel, R. Rösel, B. Meltzow, T. Schiekel, et al., Meteorit. Planet. Sci. 35 (2000) 287. [26] A.J.T. Jull, S. Cloudt, D.J. Donahue, J.M. Sisterson, R.C. Reedy, J. Masarik, Geochim. Cosmochim. Acta 62 (1998) 3025. [27] R.C. Reedy, Lunar Planet. Sci. 38 (2007) 1192. [28] R.C. Reedy, Lunar Planet. Sci. 39 (2008) 1907. [29] B. Lavielle, H. Sauvageon, P. Bertin, G. Haouat, Phys. Rev. C 42 (1990) 305. [30] M. Imamura, H. Nagai, M. Takabatake, S. Shibata, K. Kobayashi, K. Yoshida, H. Ohashi, Y. Uwamino, T. Nakamura, Nucl. Instrum. Methods Phys. Res. B 52 (1990) 595. [31] R.C. Reedy, G.F. Herzog, E.K. Jessberger, Earth Planet. Sci. Lett. 44 (1979) 341. [32] K. Nishiizumi, K.C. Welten, H. Matsumura, M.W. Caffee, K. Ninomiya, T. Omoto, R. Nakagaki, T. Shima, N. Takahashi, S. Sekimoto, et al., Geochim. Cosmochim. Acta 73 (2009) A945. [33] R.C. Reedy, in Proceedings of the Twelfth Lunar and Planetary Science Conference, Part B, Section 2, Pergamon Press, 1981, p. 1809. [34] R.C. Reedy, Nucl. Instrum. Methods B 29 (1987) 251.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Cosmogenic-nuclide production rates: Reaction cross section update R.C. Reedy ⇑ Planetary Science Institute, 1700 E Fort Lowell, Suite 106, Tucson, AZ 85719-2395, USA
a r t i c l e
i n f o
Article history: Available online 21 September 2011 Keywords: Cosmogenic nuclides Cross sections Neutron reactions Production rates
a b s t r a c t Interpretations of cosmic-ray-produced nuclide measurements are dependent on the accuracy of the production-rate estimates. Most production rates are determined using particles fluxes and cross sections for the relevant reactions. The reaction cross sections used for the production of cosmogenic nuclides are discussed. Recently, many experimental cross sections for making cosmogenic nuclides by protons have been compiled, evaluated, and used to study cosmogenic nuclides made by solar energetic protons in lunar samples. Neutrons make most galactic-cosmic-ray-produced nuclides. There are only a few measurements of cross sections for neutrons making cosmogenic nuclides because it is hard to get good fluxes of energetic neutrons, especially with energies >50 MeV. Most neutron cross sections to date have been estimated by using measured proton cross sections, occasionally adjusting them for nuclear systematics or to fit measurements of cosmogenic nuclides in documented samples. The status of spallation cross sections for the main reactions making the six main cosmogenic nuclides (3He, 10Be, 14C, 21Ne, 26Al, and 36Cl) from their major target elements is presented. Some comparisons of production rates calculated with these cross sections with measured rates are presented. The need for additional work to improve these important cross sections is discussed. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Cosmic-ray-induced (cosmogenic) nuclides, such as 10Be, 26Al, and 3He, are important because of their broad applications to many extraterrestrial and terrestrial studies, such as dating exposure ages of solar-system matter [1] and of surface features on the earth’s surface [2]. Production profiles for cosmogenic nuclides are known to vary with depth in the moon [3] and meteorites [4]. In the earth’s atmosphere and in its top surface, production rates also vary with location [5,6]. These variations can be different depending on the nuclide because of different nuclear reactions. Much work has been and is being done on modeling production systematics for these nuclides. The basic expression for calculating the production rate of a nuclide at one location depends on the composition of the sample, the fluxes of the particles (mainly neutrons and protons) to which that sample is exposed, and the excitation functions (cross sections as a function of energy) for all important reactions. The target chemistry is usually well determined. In most cases, only one or two target elements dominate the production of a cosmogenic nuclide. Usually the dominant particle making nuclides is the neutron, with protons making fewer nuclides. (Production by muons in the earth’s surface is ignored here.) The particle intensities vary much ⇑ Address: 152 Monte Rey Dr., Los Alamos, NM 87544, USA. Tel.: +1 505 6729519. E-mail address: [email protected] 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.08.034
with location (such as depth). The spectral shape of these particles also changes inside an irradiated object [3,4]. Some general discussions have been done on the excitation functions used for such production-rate calculations e.g., [7,8] and of tests of their consistencies with measurements e.g., [4,5,9–11]. This work reviews existing work on cross sections used for six important cosmogenic nuclides, 3He, 10Be, 14C, 21Ne, 26Al, and 36Cl. 2. Fluxes of cosmic-ray particles The particle flux as a function of energy to which a sample is exposed depends on when the sample was irradiated (as the fluxes of cosmic-ray particles, mainly protons, can vary over time) and the location of the sample. GCR particles penetrate up to several meters of the surface of a solid object and produce numerous secondary particles via spallation processes [3]. For the earth, the flux of cosmic rays hitting the top of the atmosphere varies with geomagnetic location, with no particles scattering into space at the earth’s poles and most particles deflected into space by the strong magnetic fields near the equator [12]. For extraterrestrial matter, the size and geometry of the irradiated object and the location of a sample inside that object strongly affect the production and transport of particles. For terrestrial matter, fluxes vary with depth in the atmosphere and, for in situ nuclides, with depth in the surface [5,6]. The flux in a sample depends on the medium around the sample and can be affected by being
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near a boundary between two very different media (such as solid, water or ice, and the atmosphere) [13]. The spectral shapes of these particles often vary significantly, with higher-energy particles being less important away from an object’s surface [4,6]. In most cases, neutrons are the dominant particles because many neutrons are made per cosmic-ray interactions and charged particles are quickly slowed down and stopped by ionization energy losses. Particle fluxes (especially for protons and neutrons) are usually calculated using codes that model the production and transport of nuclear particles, such as the Monte Carlo N Particle eXtended (MCNPX) code [4,6,11], which is well documented and tested. Much early work was done with a semi-empirical GCR model [3]. Other particle production and transport codes used include the LAHET Code System e.g., [5], the HERMES code e.g., [14], the GEANT code [15], and PHITS [16]. These calculated particle fluxes are used with excitation functions for the nuclear reactions of interest. These cross sections usually control how well calculated production rates compare to measurements for all of these GCR models. 3. Cross sections The cross sections for the nuclear reactions that make cosmogenic nuclides in matter vary much. Some nuclides are made by the capture of low-energy (E 0.01–10 eV) neutrons, and those capture cross sections are usually well determined [17]. Most nuclides are made by spallation reactions induced by particles having energies above about 1 MeV, and cross sections are needed for energies from threshold to several GeV. Protons dominate production of almost all cosmogenic nuclides by solar energetic particles [18]. For nuclides made by galactic-cosmic-ray (GCR) particles, production is mainly by neutrons with a small portion (5%) made by protons. Protons can be important for a few reactions near the surface of an irradiated object for nuclides made mainly by higher-energy particles (such as 3He). Cross sections reported here are cumulative ones and include nuclides made by the decay of other radionuclides to the nuclide of interest, such as 3H decaying to 3He, often called 3THe. Here, 3He is the cumulative of direct production and the decay of 3H. 3.1. Sources of cross sections The best cross sections are those that are well measured by at least 2 groups for a range of energies. This is usually the case for proton-induced reactions because it is easy to accelerate protons to a wide range of energies. With the use of AMS or noble-gas mass spectroscopy, cosmogenic nuclides made by protons, cross sections have been well measured. Prior to AMS, very few cross sections for cosmogenic nuclides were measured, especially the longer-lived ones (e.g., 0.7-Myr 26Al [3]) and those that do not emit a gamma ray in their decay (such as 10Be [19]). The international cross-section compilation called Cross Section Information Storage and Retrieval System (CSISRS) at the National Nuclear Data Center of the Brookhaven National Laboratory was queried to get as many measured cross sections as possible. Some cross sections have been determined using inverse reactions, like high-energy 16O on a proton-rich target with the energetic products determined by a set of detectors down beam instead of energetic protons on a 16O target [20]. Some mirror reactions have been used, such as O(p,x)7Be cross sections used for O(n,x)10Be or (p,x) cross sections used for (n,x) reactions (where x is one or more emitted particles). Good fluxes of energetic neutrons are hard to produce. Bombarding a target containing tritium (3H) with energetic deutrons (2H) can make nearly mono-energetic neutrons with energies up to 20 MeV. Higher-energy neutrons can be made by irradiating certain targets (such as 7Li or 9Be) with intense beams of
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mono-energetic protons. Many neutrons are directly emitted with energies slightly below that of the protons, but some lower-energy neutrons are also emitted. This spectrum is called quasi-monoenergetic. Corrections for these lower-energy neutrons usually are needed [21], especially for nuclides that have their largest cross sections at relatively low energies. Bombarding a thick target of a heavy element like W with energetic protons produces a high flux of neutrons with a continuum of energies up to near that of the incident protons [22]. Such a spectrum of neutrons is called white because of the continuum of energies. Although the measured cross section is an average, those for white neutrons can serve as a check of a set of cross sections for that energy range. For neutrons making many nuclides, cross sections for protoninduced reactions are often used for neutron-induced reactions. This assumption of similar neutron and proton cross sections is fairly good for product nuclides like 26Al that are between two stable nuclides or that are similar in binding energy per nucleon to an adjacent stable nuclide. Occasionally, a particle-specific reaction such as 24Mg(n,a)21Ne, 39K(n,a)36Cl, or 56Fe(p,a)53Mn, needs to be added or deleted. The assumption of approximately equal proton and neutron cross sections fails for products far from the region of the stable isotopes, such as neutron-rich 14C and 10Be [3,19]. Cross sections for analogous reactions of the same reaction type can be used to estimate cross sections, such as those for 58 Ni(n,2n)57Ni and 59Co(n,2n)58Co reactions used for the 42 Ca(n,2n)41Ca reaction. Some adjustments, such as for the threshold energies of the reactions, often are needed. There are many formulae and codes that have been for calculating cross sections. For high-energy spallation reactions (above 100 MeV), several fairly-simple formulae were developed many decades ago. Several codes have been developed to calculate cross sections. However, most formula and codes give cross sections for an individual nuclide that typically differ from measured ones by factors of 2 [23], and the use of such codes for getting good cross sections is limited. Many early estimates for neutron cross sections were adjusted using measured concentrations of cosmogenic nuclides e.g., [14,19]. Such adjustments give a set consistent with the assumptions in the modeling of the particle fluxes for the object of interest and the code used. Much work has been done recently using the MCNPX code [4,11]. There are several good sets of documented samples that can be used to test excitation functions for making cosmogenic nuclides, especially the Apollo 15 deep drill core e.g., [4], the Knyahinya L-chondrite e.g., [4,11,24], and rates determined from terrestrial in situ cosmogenic nuclides e.g., [5,6]. Nuclides measured in several large spherical target isotropically irradiated with monoenergetic protons also are good tests [25]. 3.2. Proton cross sections Measured proton cross sections were recently compiled and evaluated. Those for 10Be, 26Al, and 36Cl were reported in [18]. Cross sections for making 14C are from [26] and references therein. For oxygen, the dominant target element in most media, cross sections from several other sources agree with those in [26]. The evaluated excitation functions for making 14C, 41Ca, and 53Mn are given in [27]. Cross sections for making 3He, 20Ne, 21Ne, and 22Ne by protons have been compiled from many sources and evaluated [28]. The cross sections for 3He are total for that mass and include the decay of 3H as well as direct production of 3He. 3.3. Neutron cross sections There are only a few nuclides for which neutron-induced cross sections have been measured and reported. The reaction with the
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best-determined cross sections is for the production of Ne isotopes from Mg with several sets in good agreement below 20 MeV [29], which includes the energy for the peak cross sections for making 21 Ne. For higher energies, the excitation function adopted for the Mg(n,x)Ne reactions were made to converge with the ones measured for protons [28]. Some neutron-induced cross sections have been measured for the O(n,x)14C and Si(n,x)26Al reactions [30]. Many decades ago, charged particles were measured for several neutron-induced reactions, such as 39K(n,a)36Cl and 24Mg(n,a)21Ne. Direct measurements of 21Ne from neutron-irradiated targets gave cross sections in good agreement with the measurements of the emitted a particle [31]. Many samples have been irradiated with quasi-mono-energetic or white neutrons in which the long-lived or stable products have not been measured e.g., [21,22]. Some irradiations with quasimono-energetic neutrons with energies of 100–400 MeV have been or are being done and will have their long-lived radionuclides or stable nuclide measured after non-destructive gamma-ray spectroscopy [32]. 3.3.1. Cross sections for making 3He The cross sections for 3He include both the direct production of 3 He and that made by the decay of 3H. This cumulative or total 3He is sometimes called 3THe. The cross sections used for neutrons making 3He were those evaluated by the author for protons over 3 decades ago [33] and are not very different from the recent evaluation for proton reactions making 3He [28]. Those cross sections were used for calculations for the Knyahinya L-chondrite but needed to have an effective proton flux that was 30% higher than for other cosmogenic nuclei [11]. The measured and calculated production profiles as a function of depth in Knyahinya were in good agreement. Rates for making 3He in terrestrial basalt were in good agreement with measurements [5]. The excitation functions for making 3He from O and Si are shown in Fig. 1.
Fig. 1. The elemental cross sections (in millibarns) as a function of neutron energy (in MeV) for total 3He from O and Si and for 21Ne from Mg and Si. The cross sections between points are a linear interpolation on a log–log plot.
3.3.2. Cross sections for making 21Ne The isotope of interest for cosmogenic neon is the total production of 21Ne, as it is only 1% of natural Ne and thus easiest to detect as cosmogenic. Its (and also the other Ne isotopes) production by neutrons from Mg, a major target in many materials, has been measured up to 19 MeV [29]. Above that energy, neutron cross sections were assumed to gradually merge to the proton-induced one. For silicon (the target for making 21Ne in terrestrial quartz), an older version of the proton cross sections was adopted for neutrons that is very similar to the current proton version. The rates for making 21Ne in terrestrial SiO2 and basalt were about 10% low [5]. Rates for 21Ne in Knyahinya were consistent with other nuclides [11]. The excitation functions for making 21Ne from O and Si are shown in Fig. 1. 3.3.3. Cross sections for making 10Be To fit measured 10Be profiles in samples from known locations of the St. Severin meteorite, the cross sections for making 10Be from oxygen, the dominant target, were adjusted up much for energies below a few 100 MeV from the existing O(p,x)10Be cross sections [19]. The excitation function for making 10Be from Si [19] was the one then estimated for proton reactions making 10Be, which were 0.3 of cross sections measured for the Si(p,x)7Be reaction. They are consistent with more-recently measured proton cross sections. Terrestrial rates for 10Be in SiO2 were in fairly good agreement with early work [5]. Rates for 10Be in Knyahinya [11] and Apollo 15 deep drill core [4] needed higher effective fluxes than other nuclides, suggesting the estimated cross sections are low by 10%. The excitation functions for making 10Be from O and Si are shown in Fig. 2.
Fig. 2. The elemental cross sections (in millibarns) as a function of neutron energy (in MeV) for 10Be and 14C from O and Si. The cross sections between points are a linear interpolation on a log–log plot.
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The excitation function for the Ca(n,x)36Cl was estimated from (p,an) cross sections, mainly Fe to 52Mn. In 1991, those cross sections were multiplied by about 0.8 to get a better agreement of calculated ratios with elemental production ratios estimated for Fe and Ca in meteorites. The Fe(n,x)36Cl excitation function was assumed to be the same as measured proton-induced cross sections. These cross sections are higher than those measured for Ca(p,x)36Cl reaction for 50–200 MeV because the neutron-induced reaction with 40Ca can emit an a particle whereas the proton-induced reaction with 40Ca cannot emit an a particle. Early calculated rates for Knyahinya and Apollo 15 deep drill core were consistent with measurements [9,10]. Calculations for rates for making 36Cl from Ca were 15% low relative to early terrestrial measurements [5]. 4. Summary and discussion
Fig. 3. The elemental cross sections (in millibarns) as a function of neutron energy (in MeV) for 26Al (0.7-Myr) from Al and Si and for 36Cl from K and Ca. The cross sections between points are a linear interpolation on a log–log plot.
3.3.4. Cross sections for making 14C For oxygen and neutron energies below 35 MeV, the measured cross sections for making 14C [30] were used. The higher energies were 1.1 times the version adopted by [3] for fitting 14C measured in lunar samples. The excitation functions for Si were based on Si(p,x)14C cross sections [26] shifted to lower energies by 5 MeV because of the different reaction threshold energies (for 3He emitted with incident neutrons). Calculated rates for making 14C in Knyahinya were consistent with measurements [9,11]. The excitation functions for making 14C from O and Si are shown in Fig. 2. 3.3.5. Cross sections for making 26Al The excitation functions for making 26Al (the 0.7-Myr groundstate isomer) are not easy to calculate because the short-lived isomer 26mAl beta decays directly to 26Mg and not to 26Al. Some proton cross sections for 26Al were measured using good gamma-ray detection systems prior to AMS. The early proton excitation functions were adopted for neutron reactions making 26Al from Al and Si [34] and are shown in Fig. 3. Calculated rates for making 26 Al in terrestrial SiO2 were possibly low compared to early work [5]. Rates in Knyahinya and Apollo 15 deep drill core are in good agreement with measurements [4,9,10]. 3.3.6. Cross sections for making 36Cl Cross sections for measured a particles emitted from 39K irradiated by neutrons with energies up to about 15 MeV determine the most important part of the K(n,x)36Cl excitation function. The K curve in Fig. 3 shows that the cross sections near 10 MeV are much higher than at higher energies, and those energies are the ones where neutron fluxes are very high. The cross sections above 30 MeV were based on estimates for similar reactions, and are about 0.6–0.7 of recently measured proton cross sections.
Cross sections for six of the main cosmogenic nuclides now being routinely used for extraterrestrial and terrestrial work, 3He, 10 Be, 14C, 21Ne, 26Al, and 36Cl, were reviewed. All were developed a decade or more ago for a variety of extraterrestrial studies. They also yielded production rates that were consistent with early work on in situ terrestrial cosmogenic nuclides [5]. All have given calculated production rates using a variety of models for cosmic-ray particle fluxes that are within 10% or so of most measurements. While the physical basis of this work and some tests with measurements are good, there is room for improvement. Work on cross sections for elemental production should be tested with accelerator irradiations for mono-elemental targets e.g., [25] or natural samples with a wide range of compositions, such as different classes of meteorites. For proton cross sections, the best agreements with measurements for natural samples were achieved using good experimentally-measured cross sections [18]. Cross sections for reactions for neutron energies above 30 MeV are needed. Some previously-irradiated samples e.g., [21,22] need to have their long-lived and stable product measured. Both samples irradiated by quasimono-energetic neutrons and by white neutrons from high-flux spallation neutron sources are needed. Some results from such irradiations should be reported in the next year or so. More tests of these cross sections are needed with document samples using good production-rate models. The best tests should use the latest and well-documented codes for particle production and transportation, such as MCNPX. Results from such tests will help to show where these cross sections needed to be adjusted. Acknowledgements Members of the CRONUS-Earth project encouraged the preparation of this paper. David Argento and a reviewer provided useful comments that improved the manuscript. The CRONUS-Earth project of the National Science Foundation supported the recent work, preparation, and writing of this paper. NASA’s Cosmochemistry Program supported earlier cross-section work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
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