Predicting the production rates of cosmogenic nuclides in extraterrestrial matter

Abstract The production rates of nuclides made by the galactic and solar cosmic rays are important in the interpretations of measurements made with lunar samples, meteorites, and cosmic spherules. Production rates of cosmogenic nuclides have been predicted by a variety of methods that are reviewed in this paper, ranging from systematic studies of one or a group of meteorites to purely theoretical calculations. Production rates vary with the chemical composition and the preatmospheric depth of the sample and with the size and shape of the object. While the production systematics for cosmogenic nuclides are fairly well known, our ability to predict their production rates can be improved, with a corresponding increase in the scientific return. Additional detailed studies of cosmogenic nuclides in extraterrestrial objects are needed, especially for fairly small and very large objects. Nuclides made in simulation experiments and cross sections for many major nuclear reactions should be measured. Such studies are especially needed for the long-lived radionuclides that have only recently become readily measurable by accelerator mass spectrometry.


Introduction
'ri]cinner solar system not cmly rontn. ins tile terrwtriil.i pian~ts iill(i t heir IIIW:IS, but niso a nun~twr of smaller objects an~i a variety of raciiat ions, Some of these oi)jccts rcvwh tho su rfac(? of tile varth wit II(JII I After the discovery ofqosmic-ray-produced (cosmogonic) nuclides about 40 years ago, a wide variety of studies soon were being done with them (see historical review in ref. [2]). These studies ranged from the nature of the cosmic-ray interactions with matter to studies of the histor;es of the cosmic rays and of the objects themselves (see, for example, the review in ref. [1]). The initial work on cosmogonic nuclidcs came soon after the first high-energy (above * 1 (;eV) accelerators were built, and studies of cosmogonic nuclides made by the GeV protons in the galactic cosmic rays (GCR ) with meteorites complimented work being done cm high-energy nuclear reactions at these accelerators (e.g., the work on spallation systcmatics vith iron b,y ref. [3]), Long-lived cosmogonic radionuclides showed that the intensities of CCR particles ha~! not varied much in the past. The lengths of tin~~that meteorites had been exposed to cosmic rays (called exposure ages) were determined to have been w iO Nla ( 107 years) fcr stony meteorites and w 100 Jla to 1 Ga for iron meteorites, much less than their formation ages 4.S Ga ago.
Very soon after the first observations of cosmogcrric nuclides, several systematic studies were done with meteoritic samples that helped to establish some initial production rates of cosmogonic nuclides in meteorites. Several models were soon dek'eloped for the prediction of the production ratw of cosmcqgenic nuclidcs (e.g., lunar samples, cosmic dust, and cosmic spherules. On!y passing reference will be made to the production of cosmogonic nuclides in the carth"s atmosphere and in terrestrial rocks. Ilccause of the limitations of space for this article, only a few rcfercncos will sections, cosmogonic-nuclide production rates, unfortunately can not ho disrussed or citm].

Solar Cosmic Rays
be given below, and many excellent works involving cross mcasurcmcnts of cosmogonic nuclidcs, and rclatecl work 2.1 Nature

of SCR particles and their interactions
The energetic partir.lcs from the sun that occasionally pass through ti]c inner solar system have cncrgim of* 1-50 MeV but usually not extending much above N 100 McV [1,8]. These energetic solar particle evet,ts mainly occur when the sun is rclatiwdy act ivc and not during periods of low solar activity [1,8,9].
The fluxes of particles (which arc * 98% protons, plus some alpha particles and a few heavier nuclei [13]) in these events vary from barely dctectahlc to up to N 106 protons cm-2 s-' at the peak of the largest events, Although first dctcctcd l~ygrrmnd.lewd instruments in 1942, the detailed study of S('R pilrti~lcs I)cga.n in the l!l(jf)s and was aided by stllflics rrf SCR-produced tiuclidcs in lunar samples (cf., [ (1) where the parameter RO describes the shape, Typical values of ROrange from -35-150 NV [9,9]. Over the last * 106 years, the average omnidirectional fluxes of solar protons abov~10, 30, 60, and 100 MeV have been about 70, 25, 9, and 3 protons cm-2 s-1, respectively [1].
Because the ranges of most SCR particles are much less than their nuclear interaction lengths. most SCR pmticles are stopped by ionization energy losses before they can react. 'Their ranges are short.. * 1 g cm-2 in silicate material, so the few rractions that they produce are mainly in the top centimeter of an extraterrestrial target [8,10]. The nuclear reactions induced by SCR. particles tend to be low-energy onos 2gAl am-f few high-energy reactions, such as those that produce 10De like 'GFe(p,n) 56C0 and 28Si(p,2pn) , from oxygen and heavier elements, arc induced [8]. Relatively few secondary particles, such as neutrons.
are produced in these reactions [10], so almost all nuclidcs are made by the primary SCR particles. SCRproduced nucl.ides were rwulily observed in lunar samples because little material had been lost by handling or by rnicromcteorite erosion on the lunar surface (which has rates of -1 mm Ma-*). The outer layers of meteorites that have the SCR-produced nuclidcs are usually removed by ablation. Only very recently have meteorites been found that have large concentrations of SCR-produced nuclides, such as ALHA77005 [15] and Salcm [16]. Concentrations of SCR.-produccd radionuclides should be very high in very small objects in space, such as those rccovcrwl in deep-sea sediments [17, 18].

Calculatiorw of the production rates of SCR-produced nuclides
Onc of the first published results for the production rates of SCR-produced nuclides in lunar samplm was the hInntc Carlo calculations of Armstrong and Alsmillcr [10], These purely theoretical calculati(llls tart,cd with the intranuclcar ca..cadc induced by the primary particle and followc(l the subsequent evaporation of partichw from the cxritod nuchws to get the rc~idual nqlclous, All of t ho omit tml smondr. ry particles were tracked until they eticapml frc)m tlw moon or were removed hy nurlww ronrt.inns or~topping, 'rhcmults reproduced the Iunar-sample mults fairly WCII.A dofirioncy of this approach is thnt tlw rmlr dirvctly cidrulatm tho production nf 7bllmidual nuctci without III{*IISOof ;Iny cxporimmtai rross soctiot]s, The other type of model, the one that has almost always been used for calculating the production rates of nuclides by SCR particles, ignores secondary particles and only [OI1OWS the primary particles. The first published paper using this approach for lunar samples was by Reedy and Arnold [8]. Using the incident flux and spectrum of SCR particles and the well-known relations for the slowing down of charged nuclei in matter, this model calculates the fluxes of SCR particles as a function of depth inside a target. These depth-dependent SCR-particle fluxes arc calculated well by this approach. The production rate of a nuclide is then calculated by integrating over energy the product of these particle fluxes and the cross sections for the reaction making that nuclide. Often a nuclide can bc made in appreciable yield from several different target elements, and this integration must be done for each element. The main limitation of this approach is the need for a detailed excitation function (cross sccticms as a function of energy) for each important reaction [8,14]. Using known excitation functions and satellite-measured fluxes of solar protons, this model has reproduced well the activities of 78-day 5gCo mcaaurcd in several lunar rocks [9]. This type of model has also been applied to sevcrid solar-proton-produced nuclides in meteorites by Michel :.nd coworkers [19].
The excitation functic,ls for the r)roduction of long lived *eAl by the reactions of protons with aluminum and silicon arc shown in Fig. 1. SUCII excitation functions, especially for energies below 100 MeV, are needed for calculating production rates by SCR particles. 13ecause of the rapid decre-in SCR-p=ticlc flIIXCS with increasing energy, the most important cross sections for nuclide production by SCR particles are those nearest the reaction thresholds. These excitation functions have been fairly well measured (especially by ref. [20]), although lhcrc arc no mcasurccl cross sections bctwccll 52 and 300 hfcV (which is not a scrioun p!oblcm, M the shape there can IN fairly WCII cstirnatcd from other similar excitation functions).
There is also a di:mgrmvnent bctwcm the nm,asurcmcnts hy the orsay [ '"Si(p n)2" Al rmction (whirh is rrllflvlv rwtitllafwl !II I,IIu ;I&)ptPJ crow svctions Id(nv 2.3 \fu V ff)r IIIIP , , rllrvo 011l.'ig, I ), and Arnold [8] after it was modified for spherical meteoroids and with the evaluated excitation functions shown in Fig. 1. The ranges of approximate *oAl GCR production rates are indicated by the X on the left axis and the '( GCR)" near the right axis and show that solar-proton production of 26AI in meteorites is important in all small meteoroids (radii less than N 15 g cm -2) and in the outer few centimeters of larger meteoroids. Similar production profiles for '6 Al and several other solar-proton-produced radionuclides were reported by ref. [19] for several types of meteorites. For all nuclicles made by such low-energy reactions, the production rates drop very rapidly from the surface of the extraterrestrial object, as shown in Fig. 2.
The observation of such high concentrations for nuclidcs made by Lv-energy proton-induced reactions is a strong indication that the sample had been very CIOSC to the surface. Rates for the SCR production of several nuclides in very small objects (such a.s indicated by the O in Fig. 2) have also be !Ccalculated (e.g., [18,19]).
Some cosmogonic nuclidcs can only be made by solar particles with fairly high energies, such as 10Be from oxygen and heavier target elements, Excitation functions for the production of 10Be were recently presented in ref. [25], and their proton cross sections at lower .?nergies are much less than those used previously by Reedy and Arnold [8]. The 10lle solar-proton production rates in lunar rock 6S815 arc shown in Fig. 3 for scvmd solar-proton sprct. ra.l shapes and a flux of 70 protons cm-2 s-~above 10 MeV.
The average spectral shape of solar protons for the last few million years have been determined by several groups to be about RO = 100 MV, although another group has reported higher values for RO (cf., [1]).
The production rate of 10Ilc in lunar rocks by GCR particles is _ 10 atoms rein-l kg-*, so solar-protonproduccd 10lle at the very surface would be hard to detect unless the precision of the analyses WM IOSR than w 10%, especially if the correct solar-proton spectral shape is R. = 100 Mlr or less. The use of 10Ilc along with a radionuclide mfi~!chy Iow-energy rc,actions (such as *~Al or s3~f11) could bc very Ilscflll in restricting the possible spectral shapes of the solar proton-, Onc limitation at present in Calrulntirms fbr sol;w-proton-produmvl 10fh is t hfit t hrrc arc no measured cross sin-lions for cnorgirs Imlow 135 MOV (d,, [25]), Solll(' '"11Pprmluction cross svrtions HhoIIlcl lIrI measured at srw=ral Iowor protcm mwrgim from ox}'gcn and the nvxt ll)Osllilllporl;~tlt. li~rg('t group (magnesium, nlumillum, and siliron ), in ref.
[19]). However, there is still a need for additional cross sections, such as mentioned above for 10Be, Cross sections for the 160( p,3p)14 C reaction have only been measured once, and some additional cross sections for this and other 14C-producing reactiorls should be measured to confirm those used in determining the fluxes of solar protons over the last w 10 ka from lunar *4C profiles [14]. The status of other excitation functions for several other solar-proton-produced radionuclides was ako reviewed in ref. [14].
The average fluxes of solar protons over several time periods have been determined from measurements of activity-versus-depth profiles of l~C, '* Kr, '6.41. and 53Mn in the top centimeter of lunar rocks. As mentioned above and discussed in refs. [1,14], there are some disagreements among the measurements, LNOW that the measurement of some of these long-lived radicmuclides by accelerator mass spectrometry The GCR particles with energies below a few GeV nucleon-1 arc most affected by solar modulation [l], and the integral flux above 1 Gel' nucleon-l varies by a factor of 2 between solar minimum and solar maximum [1!3]. The particles in the GCR are w 87% protons, w 12%, alpha particles, and w 1% heavier nuclei [26].
As the ranges of GCR protons and alpha particles are much longer than their interaction iengths.
almost all GCR particles induce nuclear reactions before they are stopped in matter. These high-energy reactions usually result in many secondary particles, especially pions and neutrons. On average, each GCR Because the types of the particles and their energies in this cascade are sensitive to the size of the object and the depth inside it, the production rate of a cosmogonic nuclide can vary considerably in extraterrestrial matter. This effect of depth, size, and shape on production rates is referred to as "shielding." In predicting the production rate of a nuclide by GCR particles, shielding needs to be considered along with the chemical composition of the sample. The effects of shielding vary considerably with the types of reactions that produce a cosmogonic nucllde, with the extremes being nuclides made only by highcncrgy reactions (e.g., 10Be) and those made by neutron-capture reactions (such as 5gNi and 60Co in large objects). The production-rates-versus-depth profiles shown in Fig. 4  meteorites, iron meteorites, lunar samples, and cosmic spherules) and the diversity in types and energies ef GCR particles inside these objects. Four approaches will be discussed in more detail in sections below: use of cosmogonic-nuclide systematic measured in extraterrestrial samples, theoretical calculations, models using inferred particle spectra and reaction cross sections, and laboratory simulation irradiations. Several other approaches will be briefly described in the next two paragraphs. These various approaches have their advantages and their limitations. Most models have fairly well reproduced the measured concentrations and profiles for cosmogonic nuclic!es in extraterrestrial matter.
One of the simpler approaches to predicting production rates has been to determine the production ratio of two cosmogonic nuclides and to get the rate for i taking one of these nuclides from this ratio and a known rate fcr the other nucUde. For many nuclides made by high-energy reactions (e.g., 36Cl, 37Ar, and 39Ar in the metal phases of meteorites), the cross section ratios measured at an accelerator with GeV protons can be used to predict production ratios. The cross sections for the production of most nuclides made by high-energy spallation reactions systematically vary with AA, the difference in the mass of the target to that of the product. For AA >5, the yield of all species with mass A, Y(A), can be expressed where the power k typically varies between 2 and 3 for GCR-part.icle reactions in iron meteorites [3]. To get the relative rate for a specific isotope, the isobaric yield of that isotope for that mass needs to be known showed that the activity of a radionuclide as a function of depth in most meteorites increased with increasing depth near the surface, then re~mained fairly constant in the central parts. Iron meteorites, which are usually much larger than stony meteorites, have production profiles that often decrease towards the center (e.g., [4]). The trend lines, such as a radionuclide activity versus the 22Ne/21 Ne ratio, for these cores or slabs sometimes have different slopes than did the same trend line for samples from different meteorites. Several studies used samples with different chemical compositions from one meteorite (such as mineral separates) or a group of meteorites to determine production rates from individual target elements, such as rates for producing 26A1 from aluminum, silicon, and other elements.
hfany of the results from these systematic studies, such as the trend lines, have been used in predicting production rates in meteorites, These measurements also have been valuable in developing and testing models for the production rates of cosmogonic nuclides (e.g., [4,12]). Often the calculated production rates for a nuclide from such models S11OUICI be normalized to experimentally determined production rates.
Additional systematic studies arc being done, especially for Iong-livmi radionuclides that have only recently been made easier to analyze by /111S. Some detailed studies of many cosmogonic nuclides in sev~rid samplw from a meteorite also arc being done, vspccially for meteorites with a wide range of prcatmosphcric sizws (e,g, [29]).

Theoretical calculations
The production rates for several cosmogonic nuclides have been calculated by computer codes that use only some basic nuclear data, such as scattering, capture, and reaction crow sections, and are not normalized to observations. As discussed abcve in the section on SCR calculaticms, Monte Carlo calculations have been done for cosmogonic nuclides in lunar samples by Armstrong and Alsmiller [10], For the GCR, they published production-rate-versus-depth profiles for 26Al and 22Na and the neutron fluxes as a function of' depth. The calculations followed the neutrons until they reached thermal (technically <0.4 eV) energies, The calculated 26A1 and 22Na production rates and the thermal-neutron fluxes were consistent with lunar measurements [10]. As with the SCR Monte Carlo calculations, these GZ'R calculations [10] show the basic processes involved but are of limited use in detailed studies of cosmogonic nuclides in lunar samples.
The one case where essentially pure theoretical calculations have been very useful in studies of cosmogonic nuclides is for nuclide production by the capture of neutrons with low (thermal and epithermal) energies.
The radionuc]ides that can be made in appreciable amounts by neutron-capture reactions in- for the low ratios of these long-lived radicmuclides to the stable isotopes of the same element, then these products with their very different production profiles could be used to help unfold the exposure histories of meteorites.

Inferred particle fluxes and reaction cross sections
This approach to calculating production rates is similar to the main one used for SCR.-produccd nuclides, except that the particle fluxes are not calculated by a simple relaticn like ionization energy loss but must be inferred by other m~ans. When Arnold, Honda, and Lal [5] used this approach in predicting t}~e production rates of cosmogonic nuclides in iron meteorites, they used particle fluxes deriv~d from 'mR particles, they used available experimental data.
For secondary several sources.
particles above 100 MeV, they used data from nuclear emulsions that had been exposed at high altitude and other measurements in the ea; th's atmosphere. The flux as a function of energy used for all particics with energies above 100 MeV was

E
(3) where a was 1,0, 0,4, and 0,2 GcV for the primary GCR particles and for depths of 10 and 100 g cm-z, respectively, and c was normalized to experimental cosmic-ray The Rcwly-Arnold modd was cxtcndwl to mctcoritcs hy ref. [12], Curves for n as a function of depth were deriwxl for two nl~teoritcs with dilTermlt prcatmospllcric rndii (St, !Wcrin an(i Jilin), i~ll(l aIi expression was dvvolopml tllilt could C:dclllalr.xi n for i~lly r;ulius 1111(1 (Ioptll [ 12]. The '"i\l prm!uction rates shown in 1~'ig.5 for 1, chon(!ritvs wore ('illClllilt(!(l with this model Bender [7] for converting thick-target rcs[llts into production profiles in iron metcoritesi Their production 28A1 in Fig, 5, The production rates from profiles for fairly low energy reactions look similar to that for three models for high-energy products show very little increase near the surface (:omewhat Iikc tho 10llc curve in Fig, 4) can occasionally show that the object had an unusual exposure history. Extending the range of half-lives available, such as with 16-Ma 1291, 32-Ma '29Nb, or 103-Ma l'lBSm, would be very useful in studies of most extraterrestrial materials, as these half-lives are similar to many exposure ages. Much of the more exciting work chat will be done during the next few years with extraterrestrial materials will involve measurements of long-lived radionuclides done with AMS. The symbols O and X on the left axis are the production rates calculated for L very small object of this composition by solar protons and GCR protons, respectively. The symbol (G CR) is tile GCR prt+uction rate of "A1 observed imide typica! L chondrites, which have radii greater than N 40 g cm-2. usir,g an earlier set of cross sections: t!]cy arc a factor of 2 higher than the present calculated production rates done with the 10'ile production cross sections given in ref. [25]. Only very hard spectra (high values of ROj yield signilirant amounts of 'qt3c ccmpared to chc * 10 atoms min -1 kg-l pwduced by GCR particles at these d~l~ths.