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Interpretation of cosmogenic in meteorites on the basis of accelerator experiments and physical model calculations

R MICHEL and S NEUMANN Center for Radiation Protection and Radioecology, University Hannover, Am Kleinen Felde 30, D-30167 Hannover, Germany e-mail: [email protected], uni-hannover.de

Cosmogenic nuclides in extraterrestrial matter provide a wealth of information on the exposure and collision histories of small objects in space and on the history of the solar and galactic cosmic radiation. The interpretation of the observed abundances of cosmogenic nuclides requires detailed and accurate knowledge of their production rates. Accelerator experiments provide a quantitative basis and the ground truth for modeling cosmogenic production by measurements of the relevant cross sections and by realistic simulations of the interaction of galactic with meteoroids under completely controlled conditions, respectively. We ' review the establishment of physical model calculations of cosmogenic nuclide production in extraterrestrial matter on the basis of such accelerator experiments and exemplify this approach by presenting new experimental and theoretical results for the cosmogenic nuclide aaTi. The model calculations describe all aspects of cosmogenic nuclide production and allow the determination of long-term solar and galactic spectra and a consistent interpretation of cosmogenic nuclides in extraterrestrial matter.

1. Introduction energies are a few GeV/n. GCR spectra are modulated by interaction of GCR particles with the solar mag- In the solar system, one observes two types of natural netic field and thus depend on the solar activity. medium- and high-energy corpuscular radiation, the Typical SCR and GCR spectra at 1 A.U. are solar cosmic radiation (SCR) and the galactic cosmic shown in figure 1. For both, SCR and GCR spectra, radiation (GCR). SCR particles are emitted during suitable mathematical parameterizations exist. energetic solar events from the sun and consist on the For SCR particles, it is convenient to describe the average of 98% protons and 2% a-particles (Goswami differential flux density OJ/OR as function of the rigi- et al 1988). Their spectral distributions and intensities dity R. R is the relativistic momentum of the particle vary from event to event, typical energies going up to over its charge. This means for SCR protons a few hundred MeV/n. GCR particles come from out- OJ,,scR side the solar system. They are injected into the inter- OR - J0,sCR(47r, Ep > 10 MeV)-exp(-R/R0) stellar medium by supernova explosions and are (1) accelerated stochastically by complicated processes (Bryant et al 1992) and occasionally attain extreme with a characteristic rigidity, R0 [MV], and a 4r- energies up to 1021 eV. GCR consists of 87% protons, integral flux density of protons with energies Ep above 12% s-particles and 1% heavier ions which show 10MeV, J0,sca (47r, Ep > 10 MeV) [am -2 s-l]. similar energy spectra when compared as function of The energy-differential flux densities of GCR energy per nucleon (Alsmiller et al 1972). Mean GCR spectra OJcca/OE can be parameterized according to

Keywords. Cosmogenic nuclides; meteorites; simulation experiments; cross sections; modeling of production rates.

Proc. Indian Acad. Sci. ( Planet. Sci.), 107, No. 4, December 1998, pp. 441-457 Printed in India 441 442 R Michel and S Neumann

,1_0 +2 called cosmogenic nuclides have found manifold appli- cations. On Earth, they are produced by interactions with the atmosphere and these cosmogenic nuclides are incorporated in the large scale environmental SCR protons processes. There they act as natural tracers for use in 10 +o [~,J0] (years) archaeology, hydrology, glaciology, climatology, and other environmental sciences (Finkel and Surer 1993). [75,200] (1954-1964) ,.7 ;:>r"'~ Cosmogenic nuclides produced in situ in the earth's - [70,110] (1954-1986) crust have a high potential for studying processes like

"7 erosion, deglaciation (Lal 1986; Lal et al 1987) and to [50,55] (1977-1986) I0-2 M [MeV] date individual events e.g. impacts of extraterrestrial (year) objects (Nishiizumi et al 1991b). Investigations of cosmogenic nuclides in extrater- 300 / restrial matter allow us to study the history of the -(1977) matter exposed to SCR and GCR particles as well as / the dependence on time of the spectral distribution of 9OO SCR and GCR over time scales of millions of years GCRprotons (1969) (Geiss et al 1962; Lal 1972). Cosmogenic nuclides in extraterrestrial matter provide a past record which can- 1 0 -6 not be retrieved by any other means. Already these very first reviews demonstrated the scientific potential of cosmogenic nuclides in extraterrestrial matter. The

10 *o 10 *2 10 +4 Table 1. List of cosmogenic nuclides in meteorites with half- lives above 0.5 month and their target elements. ENERGY [MeV] Nuclide Half-life Main target elements Figure 1. Free space GCR proton spectra at 1 A.U. for times of a quiet (1977) and an active sun (1969) and average SCR 48V 0.0438 a Ti, Fe, Ni proton spectra for three periods from 1954 to 1986. SCR spectra 51Cr 0.0759 a Fe, Ni can be parameterized for individual flares as well as for time- 3TAr 0.096 a Ca, Ti, Fe, Ni averaged spectra by exponentially falling rigidity spectra 7Be 0.146 a C,O, Mg, A1, Si, S*, P*, Ca, Ti, Fe, Ni (McGuire and yon Rosenvinge 1984) characterized by a char- 5SCo 0.194 a Fe~, Ni acteristic rigidity, R0 [MV], and a 41r integral flux density of 56Co 0.213a Fe, Ni protons with energies above 10MeV, J0(41r, E >10MeV) 46Sc 0.230 a Ti, Fe, Ni [cm-2 s-l]. Rigidities of the observed flare spectra show a much 57Co 0.743 a Fe, Ni broader range (20MV - 150MV) than shown here for solar 54Mn 0.855 a Fe, Ni, Mn cycle averaged SCR spectra (Shea and Smart 1990). According 22Na 2.6 a Mg, A1, Si, Ca, Ti, Fe, Ni to Castagnoli and Lal (1980), GCR spectra can be character- 55Fe 2.7a Mn, Fe, Ni ized by only one parameter M [MeV] which describes the 6~ " 5.26 a CoS, Ni modulation by the solar magnetic field of GCR particles when aH 12.3a C, O, Mg, A1, Si, S*, P*, Ca, Ti, Fe, Ni entering the solar system. M is equivalent to the energy a GCR 44Ti 59.2 a Ti, Fe, Ni particle looses when penetrating into the solar system to a 328i 133 a Ca, Ti, Fe, Ni given heliocentric distance. 39Ar 269 a Ca, Ti, Fe, Ni 14C 5.73ka O, Mg, A1, Si, S*, P*, Ca, Ti, Fe, Ni 59Ni 75 ka Feg, Ni Castagnoli and Lal (1980) using a modulation para- 41Ca 103ka Ca $, Ti, Fe, Ni meter M [MeV] which represents the energy loss which 81Kr 210ka Rb, Sr, Y, Zr a particle undergoes when it enters the solar system 36C1 300ka C1$, Ca, Ti, Fe, Ni 26A1 716ka Mg, A1, Si, S*, P*, Ca, Ti, Fe, Ni and propagates to a certain heliocentric distance. For ~~ 1.5 Ma Ni GCR protons one obtains 1~ 1.51 Ma C, O, Mg, A1, Si, S*, P*, Ca, Ti, Fe, Ni 53Mn 3.7 Ma Fe, Ni OJp,GCR Ep.(Ep+2mp . c2) (Ep + x + M) -2"65 129I 15.7Ma Te$, Ba, I~EE OEp ( Ep + M) . ( Ep + 2mp . c 2 + M) 4~ 1.28 Ga Ca, Ti, Fe, Ni He stable C, O, Mg, A1, Si, S*, P*, Ca, Ti, Fe, Ni (2) Ne stable Na, Mg, A1, Si, S*, P*, Ca, Ti, Fe, Ni with x = 780- exp(-2.5 104Ep) and c = 1.244- 106 Ar stable C1$, Ca, Fe, Ni Kr stable Br$, Rb, Sr, Y, Zr cm -2 s -1 MeV -1. For heavier GCR particles analogous Xe stable Te, I S, Ba $, REE parameterizations exist. In the solar system, SCR and GCR interact with Note: Special relevance of target elements (exclusively or also) with respect to production of cosmogenic nRclides by cosmic dust, meteoroids, asteroids, comets and lunar capture ($) or by a-induced reactions (~) are indicated. and planetary surfaces, thereby producing a wide range Elements marked with (*) are only relevant in meteorites of stable and radioactive nuclides (table 1). These so- or the metal phase of stony . Cosmogenic nuclides in meteorites 443 exploitation of this potential, however, suffered for a sophisticated chemical separation schemes (Vogt and long time from large experimental and theoretical Herpers 1988), AMS measurements can be performed uncertainties due to limited analytical techniques as on many of these nuclides simultaneously from one well as due to crude and empirical modeling. individual sample. AMS is sensitive enough to even Shortly after the discovery of the first cosmogenic allow for the determination of cosmogenic nuclides in (3H) in meteoritic material (Begemann individual grains of cosmic dust (Nishiizumi et a11991a) et al 1957; Fireman and Schwaxzer 1957), the whole and to investigate in situ produced cosmogenic nuclides variety of cosmogenic radio nuclides measurable in in terrestrial surface samples (Lal 1986, Lal et al 1987); meteorites became evident (Ehmann and Kohman see (Finkel and Suter 1993) for further references. 1958; Shedlovsky 1960; Arnold et al 1961). These Today, the advanced measuring techniques allow for investigations used radiochemical techniques to the determination of the whole suite of stable and extract the whole suite of cosmogenic long-lived cosmogenic nuclides in a single sample of from hundreds of grams or even kilograms of meteo- 500rag combining rare gas mass spectrometry and ritic materials to allow for the detection of their decay AMS by consortia studies by different laboratories. with the measuring techniques available at that time. With respect to the short-lived radionuclides with Stable cosmogenic nuclides in extraterrestrial matter half-lives between a few days and several decades, were observed as positive isotopic abundance anomalies measuring techniques also have improved. Large in rare gases (Begemann et al 1957; Ebert and Ws volume semiconductor detectors in low-background 1957; Gentner and Zs 1957; Voshage and active and passive shields are used to measure about Hintenberger 1959; Hoffmann and Nier 1958; Eber- 10 radionuclides in a single sample of freshly fallen haxdt and Eberhaxdt 1960; Signer and Nier 1960). The meteorites; this however requires masses of the order advantage of using mass spectrometry to determine of 100 g (Bhandari et al 1989; Jenniskens et al 1994; cosmogenic rare gases was that different cosmogenic Murty et al 1998). Even depth profiles of cosmogenic nuclides could be measured in single samples with nuclides in different fragments of a meteorite axe masses of the order of hundred milligrams with an measured. Though such measurements often have accuracy of the order of 3% and 1-2% if absolute some drawbacks due to the statistical uncertainties concentrations or isotopic ratios were considered, involved and the problem of determination of detector respectively. This measuring technique also allowed to efficiencies for laxge-volume samples, relatively short- distinguish depth and size effects of cosmogenic lived cosmogenic radionuclides such as 44Ti with half- nuclide production rates and to establish empirical life of 59.2 years (Ahmad et al 1998), provide the only shielding corrections to improve the determination of means to reconstruct the intensity and spectral distri- CR exposure ages (Signer and Nier 1962; Eberhaxdt bution of cosmic ray particles on time scales up to a et al 1966; Maxti 1967; Schultz and Signer 1976; few hundred years (Bonino et a11994, 1995; Neumann Eugster 1988; Eugster and Michel 1995). et al 1997a). Cosmogenic radionuclides were not efficiently used This paper deals with the interpretation of cosmo- due to a lack of sensitive and accurate measuring genic nuclides in meteorites on the basis of physical methods. Some improvements were made for special model calculations of their production rates. It reviews radionuclides. Thus, the application of 7-V-coinci- some aspects of the development of such models and dence techniques to measure nuclides such as 26A1, describes the present state of the art. A general proce- 22Na and 6~ allowed for a nondestructive analysis in dure is described to develop model calculations from samples of a few tens of grams (Anders 1960; Herpers basic physical principles, using accelerator experiments et al 1967). In addition, radiochemical neutron activa- to measure the relevant data and to tion analysis was used to determine 53Mn in 100 mg validate such model calculations by simulation experi- samples of meteorites and lunar surface materials ments. Since simulation experiments axe performed (Herpers et al 1967). These achievements together under controlled conditions, they yield ground truth for with further technical improvements caused by the the modeling of cosmogenic nuclides production in need to analyze cosmogenic nuclides in small aliquots space. Besides the review aspect of this work, it presents of the lunar samples from the Apollo Missions new data for the cosmogenic nuclide 44Ti and describes provided a wealth of information on stable and radio- the general procedures to perform physical model calcu- active cosmogenic nuclides in extraterrestrial matter, lations and to interpret cosmogenic nuclide abundances see (Reedy et al 1983; Vogt et al 1990) for reviews. on the basis of such model calculations. A break-through in the measurement of long-lived cosmogenic radionuclides, however, was only obtained when accelerator mass spectrometry (AMS) was first 2. Physical models of cosmogenic nuclide used for the measurement of 36C1 in meteorites production (Nishiizumi et al 1979). Today, AMS allows the deter- mination of radionuclides such as 1~ 14C, 2~A1, 36C1, The production rates of cosmogenic nuclides in 53Mn, 6~ 59Ni, and 129I in 100mg samples. Using meteorites (and other objects) depend on size and 444 R Michel and S Neumann

bulk chemical composition of the meteoroid, on the composition cb ={cbj,j = 1,..., m} determines the shielding depth and the chemical composition of a transport of particles and their resulting spectra (in sample in it, on spectral distribution, composition and case of GCR calculations also the production and intensity of the solar (SCR) and galactic (GCR) cosmic transport of secondary particles). The sample chemi- radiation and on the exposure history of the meteo- cal composition c8 = {cs,j,j = 1,..., n} is the vector of roid. Except for bulk and sample chemical composi- chemical abundances of those elements contributing tions, all these parameters are unknown for a given to the production of the particular cosmogenic nuclide. meteorite and must be reconstructed. To decipher the The depth dependent spectra OJp,scR/OEp can be cosmic ray records in meteorites it is thus necessary to calculated considering electronic stopping and nuclear determine the long-term spectral distributions and attenuation of the primary particles in an irradiated intensities of the cosmic radiation, to reconstruct the body with bulk chemical composition cb taking into preatmospheric shapes of the meteoroids and the loca- account the actual irradiation geometry Due to their tion of the samples in it and to untangle their exposure low energies the depth scales of SCR interactions are histories. For such interpretations reliable model calcu- restricted to the outer surfaces of the irradiated objects lations of production rates of cosmogenic nuclides are or to small objects 15 g cm -2 may be a good estimate a basic requirement. During recent years, physical of the maximum depth relevant for SCR interactions models of cosmogenic nuclide production without free irradiating an infinite plane. In a number of publica- parameters have been developed (Michel et al 1989b, tions this model has been used and there is an agree- 1991, 1995a, 1996; Bhandari et al 1993; Leya 1997; ment in the way of the calculational procedures as Leya et a11995, 1996; Masarik and Reedy 1993, 1994; well as in the results obtained for the depth- and size- Reedy and Masarik 1994) that describe all relevant dependent SCR spectra (Reedy and Arnold 1972; aspects of cosmogenic nuclide records in extraterres- Michel and Brinkmann 1980; Michel et al 1982; trial matter. Bhattacharya and Bhandari 1975). The differences in Physical models of cosmogenic nuclide production production rates between SCR model calculations in extraterrestrial matter were preceded by a large reported so far exclusively depend on the availability number of empirical and semi-empirical models of of reliable and high accuracy cross sections of the cosmogenic nuclide production rates. It would by far underlying nuclear reactions. exceed the scope of this paper to give a complete For the interaction of GCR particles with matter, review on such models. We therefore refer here to energies up to 10 GeV/n have to be considered. The earlier surveys and discussions of such models (Reedy particle spectra inside an irradiated object are followed 1987; Michel et a11991, 1995a) and refrain here from a by intra- and inter-nuclear cascade calculations using critical discussion of empirical and semi-empirical Monte Carlo techniques which also take into account models. an accurate description of the spectra of secondary In physical models of cosmogenic nuclide produc- particles (Armstrong and Alsmiller 1971; Michel et al tion, the production rates P of a cosmogenic nuclide i 1991, 1995a; Masarik and Reedy 1993, 1994; Reedy are calculated as the sum of the production rates by and Masarik 1994). The secondary particles, in parti- SCR and GCR cular , are produced in significant amounts Pi = P/,SCR + Pi,GCR. (3) during the high-energy interactions of the primaries and dominate the GCR production of cosmogenic Due to their relatively low energies of less then a few nuclides in meteorites and planetary surfaces 100 MeV/n, SCR primaries produce only negligible The depth scales on which GCR interactions occur amounts of secondary particles whose influence mostly extend to several hundreds of g cm -2, a typical can be neglected in SCR model calculations. SCR 4He interaction length of GCR primaries in stony material particles can also be neglected because of their low being about 100gcm -2. Except for situations with abundances. Only in rare cases, e.g. ~ZCo, 5SCo, and extremely deep shielding, such as in the terrestrial 59Ni, 4He-induced reactions have to be taken into underground, non-hadronic particles (such as electrons account. Thus, the production rate of a cosmogenic and muons) can be neglected as a source Of cosmo- nuclide i by irradiation with a SCR proton spectrum genic nuclide production. Further, since the produc- characterized by its spectral parameters J0 and R0 can tion of secondary complex particles such as 2H, 3H, be calculated straight forward via 3He, and 4He is lower by orders of magnitude than the Pi,scR(R,d, cb, c~,Jo,Ro) = NL. ~"~cs'j production of secondary protons and neutrons (Koch Aj 1989), calculation of secondary GCR production of OJp,scR cosmogenic nuclides can be restricted to proton- and f ai,j,,(Ep) OEp (Ep, d, R, cb, Jo, Ro)dEp (4) neutron-induced reactions. In addition to protons, GCR consists of 8% aHe with R being a shape parameter (radius) of the irradia- and 1% heavier nuclei (Alsmiller et al 1972), the ted object, d being the depth of a sample inside the spectra of all GCR particles being about the same if object and NL Avogadro's number. The bulk chemical the energy is measured in energy per nucleon. This Cosmogenic nuclides in meteorites 445

10 *0 I I I illItl'' [ I I I ll'i'l I I I I IlllIl I I I llIll]

H-chondrite, R = 25 co "7>

1 0 -2 secondaryneutrons sn e~

I I ....

...... - ...... --'*" ...... - ...... , ...... : totalprotons pp+sp ~..,..,.:.: I 0 -a

M = 650 MeV ~ :'! J0 = 1 cm ~ s"~ i I. 0 -6 l, l I 1,117 li I l i 11111 [ 1 t I i Ititl i I Jqzllli 10 § 10 +2 10 ,4 ENERGY [MeV] Figure 2. GCR spectra of total (- primary + secondary) protons and secondary neutrons in the center of a H-chondrite with a radius of 25 cm calculated by HETC within the HERMES code system. For the calculations a primary GCR proton spectrum with a modulation parameter M = 650MeV was assumed. The data are normalized to a flux density of primary particles of J0 = 1 cm -2 s -1 .

again facilitates the calculation of GCR production sections of the underlying nuclear reactions for x-- rates since the production of secondary nucleons pp, sp, sn according to depends in good approximation only on the total energy dissipated in an irradiated object. Only for Pi,oca,=(d,R,c~,cb, M) = NL" Z-~jc.,j " f special cases, e.g. 57Co, 58Co and 59Ni, production by 1 4He particles must be considered explicitly. In general, OJx (E~, d, R, Cb, M)dEx. (6) it is sufficient to consider particles heavier than OE~ protons only approximately by the number of primary Note that the spectra OJ~/OE~(Ex, d,R, cb, M) are nucleons in a GCR spectrum which differs from the normalized to unit flux density of primary GCR number of primary protons in it (Michel et al 1991; nucleons. The depth and size dependent spectra of Leya 1997). primary and secondary GCR nucleons OJ~/OE~(Ex, d, Since the GCR production by primary protons and R, cb, M) can be caIculated using Monte Carlo codes by secondary protons and neutrons depends linearly such as HETC within the HERMES code system on the number of primary GCR nucleons with energies (Cloth et al 1988) or LAHET (Prael and Lichtenstein above 10 MeV, J0,GCR, which itself is unambiguously 1989) which both originated from HET developed in connected to the modulation parameter M of the GCR the sixties by Armstrong and Chandler (1972). In proton spectrum, one can write: principle, these codes also allow for the direct calcu- P/,GcR(R, d, Cb, c~, M) = J0,GcR(M) lation of residual nuclide production However, as demonstrated e.g. by a recent International Model and (Pi,oCR,~ + P/,oca, s; + P/,OCR,s~) (5) Code Intercomparison for Medium Energy Activation with Pi,GCR: being the production rates due to a Yields organized by NEA/OECD, all available codes unit flux density of primary protons, secondary at best are capable of predicting residual nuclide cross protons and secondary neutrons for x-- pp, sp, sn sections with average deviations of a factor of two respectively In the context of analyzing cosmogenic (Michel and Nagel 1997) Often, however, such devia- nuclides in meteorites one has to consider that M and tions even exceed factors of ten. Medium-energy codes hence J0,GCR depend on the mean distance from the are much more capable of calculating the nucleon sun and on helio-latitude of the orbit of an object in spectra of secondary particles resulting from medium space energy nuclear reactions including their transport in The Pi,OCR: can be calculated in analogy to equa- matter, e.g. (Filges et al 1992) Moreover, the spectra tion 4 as folding integrals of the spectra of primary resulting from HETC and LAHET were found to be in and secondary GCR particles at the location of a good agreement as far as GCR model calculations for sample inside the irradiated body and of the cross meteorites and the lunar surface are concerned 446 R Michel and S Neumann

,J.O +2 I I I r I I I [ i I I I l l ~ I ( ( ~ I i f I I r ] I r I

~ <~..Cy ~ | .... Q--G .... E) '~ 1_0 +~

N--__

<> 0-~

[] pp: E > 10 H-chondrites ._0 -2 ~-"-" ? sp:E> 10MeV "~ M = 650 MeV r ~ ~ sn: E > 10 MeV "~ O sn: E <0.1MeV 1_0-~ I , , ~ ,,,,,,I ...... I , , ,r-.,..I, , , , , 0 50 100 150 RADIUS [cm] Figure 3. Flux densities of primary and secondary GCR particles in the center of H-chondrites irradiated by a M = 650 MeV GCR proton spectrum.

(Michel et al 1991, 1995a; Armstrong and Alsmiller is below 10% of the maximum center production rate 1971; Masarik and Reedy 1993). (Fanenbruck et al 1994). Such Monte Carlo calculations can describe particle It has to be emphasized that proton and neutron transport down to 1 MeV for charged particles and to flux densities have different dependence on depth 20 MeV for neutrons. For protons this is sufficient and size, a fact which emphasizes the importance to since Coulomb repulsion prevents charged particles of describe adequately the decrease of center production lower energies to induce nuclear reactions. However, rates for large meteoroid radii (c.f. Michel et a11995a). since neutrons of all energies can produce nuclear interactions, transport codes designed for low-energy neutrons such as MORSE (Emmet 1975) or MCNP 3. Cross sections for the production (Briesmeister 1993) have to be coupled to HETC or of cosmogenic nuclides LAHET to follow the neutrons down to thermal energies and to obtain the entire neutron spectra. Up to the middle of the seventies the situation for Using the spectra calculated in this way it is then cross sections of proton induced reactions was very possible to reliably calculate GCR production rates of unsatisfactory; see Michel et al (1995b) for a discus- cosmogenic nuclides with high accuracy of better than sion. Therefore, systematic and comprehensive inves- 10% provided cross sections for the production of tigations were started by the first author and various cosmogenic nuclide by proton- and neutron-induced collaborators in order to measure all relevant cross reactions are available. sections for the production of cosmogenic nuclides in In figure 2 we show GCR proton and neutron extraterrestrial matter. After an early phase of experi- spectra in the center of a H-chondrite with a radius of ments at KFA//Jiilich, UCL/Louvain La Neuve and 25 cm and in figure 3, the dependence of center flux IPN/Orsay, (Michel et al 1985b and references densities on meteoroid radii for the same meteorite therein), at CERN/Geneve (Michel et al 1989c) and class. Only in cosmic dust and presolar grains the at LANL/Los Alamos (Michel et al 1995b), a general built-up of secondary particles can be neglected. experimental routine was evolved to determine Already in meteoroids with radii of 5 cm production excitation functions from thresholds up to 2.6 GeV by by GCR secondaries becomes significant and in objects combining experiments at LNS/Saclay, TSL/Uppsala with radii between 40 and 50cm the internuclear and PSI/Villigen covering the energy ranges from cascade is fully developed and secondary particles, in 2.6 GeV to 200 MeV, from 180 MeV to 70 MeV and particular neutrons, dominate. Significant thermal below 70MeV, respectively, (Bodemann et al 1993, and epithermal neutron fields, however, are relevant Michel et al 1995b, 1997a, Schiekel et al 1996a and only in larger objects; in smaller ones leakage through references therein). the surface prevents their built-up. For example, the During the past two decades the target elements C, production of 6~ which is mainly due to 59Co(n,v) N, O, Mg, A1, Si, Ca, Ti, Mn, Fe, Co, Ni, Cu, Nb, Sr, 6~ has, in the center of H-chondrites, its maximum Y, Zr, Nb, Ba and Au have been investigated. at a radius of about 85 cm. Up to a radius of 30 cm, it Residual radionuclides and stable rare gas Cosmogenic nuclides in meteorites 447 were measured after irradiation by AMS, ?-spectro- metry and by conventional mass spectrometry 10ot .- covering most relevant cross sections for the produc- tion of cosmogenic nuclides. A collaboration of up to 13 institutes at Ahmedabad, Bordeaux, KSln, Hann- over, Jiilich, Mainz, New Brunswick, Philadelphia, 10"o Uppsala and Zfirich contributed to these investiga- [] 0 this * Ti(p , nXn~Tir. --- oMzso tions. In 1997, the database covered nearly 550 target/ o MI97 product combinations with about 15,000 cross sec- O BR7t 10-t tions. It is available in EXFOR format (McLane 1996) v MI89 at the Nuclear Data Bank of NEA/OECD/Paris or ~ DR72 X SU97 from the Nuclear Data Center of IAEA/Vienna. A ! I I I I I I I1 I I I I I I |1] II complete review of all related references including the ~0 .t 10 .2 10 03 relevant EXFOR numbers may be found elsewhere JD (Michel et al 1997a). Large number of targets have been irradiated and stored for the measurement of Fe(p 5pxn)"Ti long-lived and stable nuclides in the future. Recent analyses covered the production of long-lived radio- nuclides such as 14C (Neupert 1996), 36CI (Schiekel et 10'o al 1994, 1996b; Sudbrock et al 1997), 41Ca and 129I I [] this (Schnabel et al 1996, 1997) and of stable rare gas 0 M197 isotopes (Leya et al 1998b; Gilabert et al 1998a; N SU97 Neumann et al 1997b). V O GLgB In figure 4 we give a survey on the cross sections for v 8R71A T,.) I0 -I o RA77 the production of 44Ti from the relevant target X H064 elements titanium, iron and and present a large II[ I I I I I I I I number of new measurements. These data nearly 10 ,2 10 ~3 completely satisfy the data needs of cross sections for the proton induced production of 44Ti. 44Ti was measured by using Ge and Si detector by measuring the 67.85 keV and 78.38 keV ?-transitions of 44Ti, having ?-intensities of 94.4~ and 96.2%, respectively; O (see Gloris 1998; Sudbrock 1997 for details). Only a i0'o O few earlier measurements by other authors exist Nl(p,7pxn) 44 T! (Brodzinski et al 1971a, 1971b; Dropesky and O'Brien M 1972; Honda and Lal 1964; Raisbeck and Yiou 1977b). The cross sections of Brodzinski et al (1971a, 1971b) [] t~is deviate considerably from those measured by our 10-t OM197 collaboration. N SU97 ,I I i i i I I I I [ I i Though our various collaborations established most of the existing cross section data base for the pro- t0 ,3 duction of cosmogenic nuclides, significant contribu- ENERGY [MeV] tions by a few other groups must be mentioned. The Figure 4. Cross sections for the proton-induced production of Bordeaux group investigated the production of rare 44Ti from Ti, Fe and Ni. Except for a few measurements by gas isotopes from various target elements (Regnier other authors [BR71 (Brodzinski et al 1971a); BR71A et al 1982, and references therein) and Raisbeck and (Brodzinski et al 1971b); DR72 (Dropesky and O'Brien 1972); Yiou measured cross sections for long-lived radio- RA77 (Raisbeck and Yiou 1977b); HO64 (Honda and La11964)] nuclides (Raisbeck and Yiou 1977a). During recent the data are from work of our group: this and MI80 (Michel and Brinkmann 1980); MI89 (Michel et al 1989c); MI97 (Michel et years, Sisterson and coworkers also performed sys- al 1997a); SU97 (Sudbrock 1997); GL98 (Gloris 1998). tematic measurements at various accelerators in order to improve the availability of cross sections for interpretation of SCR effects (Sisterson et al 1992a, neutrons the data base is acceptable and physical 1992b, 1994, 1997). model calculations can be reliably performed (Fanen- For neutron-induced reactions the situation is much bruck et al 1994). Generally, most available data are worse. In spite of the fact that secondary neutrons for energies equal to or below 14.7MeV; and only a dominate the production of cosmogenic nuclides, there few investigations went up to 30 MeV. There are two is an extreme lack of experimental cross sections. Only reports on measurements of cross sections of neutron- for capture reactions of thermal and epithermal induced reactions relevant for the production of 448 R Michel and S Neumann

cosmogenic nuclides below 30 MeV (Reedy et al 1979; strated that even in small meteoroids GCR produc- Lavielle et al 1990). Above 30 MeV, there is nearly a tion of cosmogenic nuclides is dominated by secondary complete lack of production cross sections; only a few particles, mostly neutrons. measurements of production cross sections for cosmo- At Laboratoire National Saturne (LNS) at CEN genic nuclides exist (Nakamura et a11992). Therefore, Saclay/France this problem was overcome. Two simu- the only first hand sources of neutron cross sections at lation experiments were performed at the SATURNE medium energies are nuclear reaction models. As synchrotron of LNS in which an artificial stony mentioned above, however, these models and codes meteoroid made of gabbro with a radius of 25 cm and describe the production of residual nuclides by nuclear an artificial iron meteoroid made of steel with a radius reactions at best within a factor of two (Michel and of 10 cm were isotropically irradiated with 1.6 GeV Nagel 1997). protons. This energy matches the average GCR proton This causes uncertainties in the a pr/ori GCR model energy during times of quiet sun such as the Maunder calculations even if one uses the available high-quality Minimum (Castagnoli and Lal 1980). The isotropic proton cross sections. Also the assumption of equal irradiation was achieved by four simultaneous move- proton and neutron cross sections which is frequently ments during irradiation. By two translational move- made does not hold even at medium energies (Michel ments (up/down and left/right) the artificial et al 1998) and systematic measurements of neutron meteoroids were exposed to a parallel proton "rain" cross sections are just about to start (Neumann et al covering their total cross sections. In this parallel 1997c). The application of theoretical neutron cross proton beam the artificial meteoroids were rotated sections in model calculations calls for validation of around two perpendicular axes. During effective beam- the calculational methods and/or for other means to on-target times of 282.1 h and 125.7h, respectively, obtain information about the required neutron cross the artificial stony and iron meteoroid received proton sections. fluences of 1.3 x 1014 cm -2 and 2.4 x 1014 cm-2, that are approximately equivalent to 1.6 and 3.0 Ma expo- sure of real meteoroids in space. The measured produc- 4. Simulation of GCR interactions tion rates matched those observed in real meteorites with meteoroids within 10% (Michel et al 1995a; Leya 1997; Leya et al 19985). Such validations can be obtained from thick-target Inside the artificial stony and iron meteoroids, experiments which provide at the same time a solution several thousands of thin targets of most cosmochemi- of the problem of missing neutron cross sections. cally relevant target elements were irradiated and Simulation experiments on Earth, in which thick production rate depth profiles of all the relevant targets are irradiated under controlled conditions by cosmogenic nuclides (> 500 target/product combina- medium- and high-energy protons or 4He nuclei and in tions) were measured using 7-spectrometry as well as which the production of residual nuclides in the thick accelerator and rare gas mass spectrometry. A theore- targets are directly measured, have for a long time tical analysis of the experimental production rates was been regarded as a tool to directly measure cosmo- performed using depth- and size-dependent spectra of genic nuclide production rates. However, it turned out primary and secondary particles calculated by the that most such experiments could not satisfy this HERMES code system (Cloth et al 1988) and experi- expectation, see (Michel et a11985a, 1989a) for critical mental and theoretical thin-target cross sections of reviews of the historical development. A breakthrough the underlying nuclear reactions. However, these a was achieved several years ago (Michel et al 1985a, priori calculations were found to reproduce the experi- 1989a) when simulation experiments with 600MeV mental production rates in the 600MeV and protons were performed at the CERN synchrocyclo- 1600MeV simulation experiments only within 40% tron, during which an isotropic irradiation of artificial on the average. Since the cross sections of proton- stony meteoroids with radii of 5, 15 and 25cm was induced reactions are considered to be of high reliabi- performed for the first time by complex movements of lity, the discrepancies between experimental and a the targets during irradiation. However, the produc- priori calculated production rates was attributed to tion rates measured in these experiments turned out the poor quality of the neutron cross sections used. to be too low by factors between two and ten com- A solution of this problem, however, can be derived pared to those observed in real meteorites. This was from the thick-target experiments themselves. The due to the fact that 600 MeV was too low an energy to experimental production rates measured in the thick- simulate the mean GCR proton spectra whose average target experiments performed at different energies proton energy is above 1 GeV. The underestimate of and with different meteoroid radii and bulk chemical the production rates in the 600 MeV simulation experi- compositions contain information of the neutron- ments was thus due to the dependence of secondary induced production which can be extracted if the particle multiplicities on primary particle energy. proton-induced production can be reliably calculated Inspite of this limitation, these experiments demon- and subtracted from the experimental ones; see Cosmogenic nuclides in meteorites 449

(Michel 1998) for a complete list of up-to-date refe- 4 I ...... I ..... ' ' ' ' I rences. As discussed elsewhere in detail (Michel et al 1996; Leya 1997; Leya and Michel 1997) it is possible Ti-44 from titanium to adjust the a priori neutron excitation functions by taking into account all available experimental data by an energy dependent least squares fit using the code STAY'SL (Perey 1977) modified by Matzke (1979). 2 Using this method a self-consistent set of cross sections of the underlying neutron-induced reactions

was established (Leya and Michel 1997). With those ":c~.-: ...... new neutron cross sections, it is possible to describe by a posteriori model calculations simultaneously all 0 f ...... , I , , , , ~ , , , , I data from the simulation experiments with an accuracy better than 10% (Michel et al 1996, 1997b; Leya 1997; Leya et al 1998a). 1.5 As an example, in figure 5 we present the produc- Ti-44 from iron tion rates of 44Ti from titanium, iron and nickel measured in the artificial iron meteoroid together with ~ 1.0 the results of a posteriori model calculations. Further examples of experimental depth profiles in the arti- ficial meteoroids and of a priori and a posteriori model calculations may be found elsewhere (Michel et al 0,5 "-"-" 1993, 1994, 1995a, 1996, 1997b; Leya 1997; Leya and F,.,) ...... ".:.::.:..-..- ..... ~- r :. =-'." :'-'-"-"'.".'""'." Michel 1997). A comprehensive publication of all the :.:: ...... results obtained for radionuclides is presently under preparation (Leya et al 1998b). For rare gases only a 0 I ...... , I , ...... i r small part of the results were published up to now :' I ...... I ...... I

(Wieler et al 1992; Weber and Begemann 1992; 2,0 Mathews et al 1994; Gilabert et al 1994, 1996, 1997). Ti-44 from nickel The majority of results still remains to be published. As has been shown elsewhere (Michel et a11996) the proton and neutron spectra inside the artificial meteoroids irradiated isotropically with 1.6 GeV pro- .... SP tons are a good approximation of the actual spectra in 1.o -- sN '-., -- TO meteoroids. However, there remain distinct differences o o o. caused by the monoenergetic protons in the simula- 0.6 ~.~.~.:.'..:.::.== =:, = ...... -" tion experiments and the continuous spectrum of GCR ....,-..:".':.:::'::".~ ...... primaries in space. Therefore, production rates obtai- .... . o.-.- ned from simulation experiments cannot directly be 0 i , , , , , , J , I p , i , a i , , , I used for the interpretation of cosmogenic nuclide 0 5 10 abundances in meteorites. In order to derive reliable surface DEPTH [cm] center production rates of cosmogenic nuclides in meteoroids Figure 5. Depth profiles for the production of 44Ti from Ti, Fe one has to calculate the primary and secondary GCR and Ni in an artificial iron meteoroid with a radius of 10 cm spectra inside a meteoroid starting from continuous irradiated isotropically with 1.6 GeV protons. The theoretical and realistic free-space GCR spectra and then to production rates are from a posteriori calculations using the calculate production rates using the same proton and experimental proton cross sections shown in figure 3 and neutron cross sections used in the a posteriori neutron excitation functions extracted from thick-target simulation experiments. For the theoretical production rates calculations of the production rates in the artificial the total production as well as those due to primary protons, meteoroids. secondary protons and secondary neutrons are distinguished.

5. Cosmogenic nuclides in meteorites rates in real stony and iron meteoroids in space with the same claim of accuracy for each of the target/ Given the good agreement obtainable between the product combinations investigated in the terrestrial experimental and a posteriori theoretical production simulation experiments. depth profiles in the artificial meteoroids irradiated by Since the production rates of cosmogenic nuclides 0.6 GeV and 1.6 GeV protons, it is possible to calcu- strongly depend on the spectral distribution of late for a given GCR proton spectrum the production primary SCR and GCR particles, e.g. (Michel et al 450 R Michel and S Neumann

1982, 1991), one first has to determine the long-term 100 i i i , i i ~ i i I i i i i f i , i i j i i i r SCR and GCR spectra in order to calculate their 26A1 in Knyahinya dependencies on depth in and size of a meteoroid. (R = 45 cm, L-chondrite) 80 The dependence on the GCR modulation parameter of GCR production rates in meteorites is largest for cosmogenic nuclides which are preferably produced by ~ 50 ...... - .... ~N low-energy secondary particles. Consequently, the dependence on modulation decreases in the sequence oz

53Mn, 26A1, 2ZNe, 1~ The center production rates in ~ 40 -: ,- - J0,~cR = 4.06 cm -~ s -1 an undifferentiated stony meteoroid with a radius of M = 620 MeV 40 cm of these nuclides differ by factors of 3.1, 2.3, 1.6 ~" 20 L sP and 1.5, respectively, for modulation parameters ..;...... between 300MeV and 900MeV (Michel et al 1991; PP Leya 1997). o i I I I I I I I I J 1 i I I I I I I I [ r I I 20 40 The dependence of 44Ti production rates on solar DEPTH [era] modulation is in-between those of 26A] and 21Ne as a consequence of the large mass difference between 44Ti Figure 6. Modeling of 26A1 in Knyahinya is used to determine and its most important target element iron. But, it is the 47r integral flux density of GCR nucleons. The resulting value JO,GCR = 4.06cm-2s -1 is equivalent to a GCR proton not a real low-energy product and therefore not very spectrum with a modulation parameter of 620MeV. The sensitive to solar modulation. The production rates in experimental data are from Graf et al (1990). the center of a 40 cm radius H-chondrite are calcu- lated to be 0.92, 1.05, 1.09, 1.27, and 1.63dpmkg -1 for modulation parameters M of 900, 650, 620, 450, 20 ' ' ' '''"' ' ' ' ''"'1 ' ' ' ''"" ' ' ' '" and 300MeV, respectively, the production rate for M=300MeV being 1.8 times larger than for M [MeV] Integral GCR Proton Spectra M = 900MeV. Within the range of relevant para- ~ 15 0 A meters the dependence of 44Ti production rates as function of integral number of primary GCR protons ~. can well be approximated by a linear function. ~ I0 Having calculated the dependence of production mr~ 100 rates on solar modulation, long-term GCR spectra can be derived by fitting theoretical GCR production rate -i 5 300 depth profiles of long-lived radionuclides to those ones 620 long observed in extraterrestrial matter provided that the abundances of stable cosmogenic rare gases indicate 0 that the exposure ages are long enough to make sure 10 10~ 10 t 10' that the radionuclides are in saturation. Such experi- ENERGY Ep [MeV] mental data exist for 1~ ]4C, 26AI, 36Ci, and 53Mn in the lunar surface and in a number of well investigated Figure 7. The long-term averaged GCR proton spectrum meteorites as e.g. Knyahinya, St. Severin, and Keyes. with a modulation parameter M = 620MeV compared to observed spectra and to spectra derived by Castagnoli and Lal We used for this purpose 26AI in Knyahinya (Michel (1980) for the local interstellar spectrum (LIS) and for the et al 1996; Leya 1997). Figure 6 shows the best GCR Maunder minimum. production rate depth profile of 26AI in Knyahinya describing the experimental data by Graf et al (1990). The long-term GCR spectrum has a mean flux density and chemical compositions and in the lunar surface. of primary GCR nucleon J0,CCR ----4.06 cm -2 s -I which The production rate depth profiles calculated for H- is equivalent to J0,cac,pp = 2.62 cm -2 s -I and to a GCR chondrites are shown in figure 8. Provided that the modulation parameter M = 620 MeV in the meteoroid GCR stayed constant as function of time the calcu- orbits. In figure 7 the long-term spectrum is compared lation of production rates of other cosmogenic nuclides with the range of observed and deduced integral is fLxed at the same time. GCR spectra. This figure also demonstrates that the As shown elsewhere (Michel et al 1996; Leya 1997; flux densities of the individual spectra are hardly Neupert 1996), the depth profiles of 1~ 14C, 26A1, changing around 10MeV J0,pp(E > 10MeV) and 36C1, 41Ca and 53Mn measured in stony and iron that, consequently, J0,pp(E> 10MeV) is a better meteorites and in the lunar surface, adjusted for orbit choice to characterize a GCR spectrum than J0,pp dependence of GCR spectra and intensities, can also (E > 1 CeV). be described with this GCR spectrum. Thus, one can The determination of J0.CCR at the same time fixes conclude that the GCR flux was constant during the the production rates of 26A1 in meteorites of all sizes last ten million years and had a spectrum with a Cosmogenic nuclides in meteorites 451

Since the model calculations are based on the 60 evaluation of equation 6 and since the total produc- tion rates are a sum of elemental production rates, elemental composition of different meteoroid classes or individual objects can easily be taken into account. dO Also the dependence of production rates on bulk i B chemical composition, which was observed in stony irons by Begemann and Schultz (1988) and Jentsch 20 and Schultz (1996), is easily accounted for by indivi- dual calculation of the respective depth- and size- dependent spectra in different matrices (Michel et al

,,,JlJliDliliiai,,,I,~ 1990; Masarik and Reedy 1994; Leya 1997; Leya et al 1998b). At present, our model calculations cover the = , , , , , , , , [ , = ~ , = , , = ~ [ ~ , t , , cosmogenic nuclides 1~ 14C, 26A1, 36C1, 4]Ca, 53Mn 80 as well as He, Ne, Ar, Kr and Xe isotopes with an accuracy <10% for production rates and <3% for production rate ratios and allows a complete inter- oo ...... pretation of cosmogenic nuclides in stony and iron meteorites and lunar surface materials. 40 ,,' [ The determination of long-term SCR spectra is more complicated than for GCR spectra. SCR effects have been clearly distinguished in lunar surface samples for a wide variety of cosmogenic nuclides; e.g. (Finkel et al 1971; Bhandari et al 1976; Kohl et al 1978; Rao et al 1994). Only recently, a depth profile with a clear 0 ,,,,,,,,I ...... I ..... signature of SCR interactions was reported in meteo- C~ t.4 ...... t ...... I ..... rites by Nishiizumi et al (1990). There is, however, further evidence for a more general presence of SCR t. 2 contributions to cosmogenic nuclide production in to - *'Ti small meteoroids (Michel et al 1982; Michel and Stfick 1984) and in the outermost surface of meteorites where material from close to the preatmospheric surface O.B ~ : luckily survived atmospheric transit (Lal and Marti 0.6 1977). In order to determine long-term SCR spectra, 0.4 ' = - theoretical SCR production rates have to be fitted to "experimental" SCR production rates in order to find H.chondrt _ the best set of SCR spectral parameters describing the 0 i i i i i .~ i i i [ , , , , , , J , , I , , , I = latter data. However, "experimental" SCR produc- 50 100 tion rates do not exist. They have to be calculated by surface DEPTH [cm] center subtraction of a GCR contribution which itself is not Figure 8. GCR production rates of 14C, 26A1 and 44Ti in H- accessible experimentally but has to be derived from chondrites for the long-term averaged GCR spectrum. GCR model calculations which at best can be vali- dated by comparison with experimental GCR produc- tion rates measured at much larger depths where SCR modulation parameter of M = 620 MeV. Changes on contributions are negligible. Thus, the extraction of smaller time scales as seen in the terrestrial 14C record experimental SCR data is only possible if reliable do not show up in the long-lived radionuclides with GCR model calculations are at hand. half-lives exceeding 5 ka. There are, however, indica- There are two more difficulties when interpreting tions on short-term changes on a time scale of a few SCR effects in lunar surface material and meteorites. decades as deduced by Bonino et al (1994, 1995) from First, there is no unambiguous determination of SCR the analysis of 44Ti in stony meteorites. An extension spectral parameters since the spectra depend on two of the time scale up to 50 million years would be parameters, R0 and J0, and only best fit combinations possible by analyzing 129I in stony meteorites. How- can be obtained as demonstrated by Rao et al (1994) ever, since the nuclear data needed for such an after a proper analysis of GCR production rates is analysis are still incomplete the analysis of 129I in performed. Secondly, there is the problem that such extraterrestrial matter is still ambiguous (Schnabel analyses have to take into account space erosion, i.e. et al 1997). the change of the outermost surface of an object in 452 R Michel and S Neumann

space by CR sputtering and by impact of cosmic dust Thus, the fundamental assumptions of dating methods and micrometeorites. have to be scrutinized by physical model calculations But mainly the lack of high-quality cross sections as it was done e.g. for the SlKr/Kr method by Gilabert led to a number of widely disagreeing determinations et al (1996, 1997). This can be done by calculation of of long-term SCR parameters (Finkel et al 1971; Kohl production rates of the respective nuclide after careful et al 1978; Bhandari et al 1976; Reedy and Marti measurement and analysis of the relevant cross 1991). Uncertainties about erosion rates of extrater- sections and thick-target production rates from simu- restrial matter in space just added to ambiguities of lation experiments. Moreover, such a procedure is these determinations. Since short-lived cosmogenic applicable to arbitrary meteorite classes. For He, Ne, radionuclides are not affected by such uncertainties, Ar and Kr this was demonstrated with good success SCR effects observed for such nuclides can be consis- (Michel et al 1995a; Herpers et al 1995; Knauer et al tently described taking into account actual flare data 1995; Leya 1997; Leya et al 1995, 1996; Neupert 1996; (Bodemann 1993). Our determination of long-term Weigel et al 1997) and also the results for Xe are averaged SCR spectral parameters from 26A1 and promising (Gilabert et al 1994). 53Mn depth profiles in lunar rocks yielded long-term Extreme deviations from constant production rate averaged SCR parameters J0,scR = 5 5cm-2s-1 and ratios are observed e.g. for the nuclide pair 26A1 and R0 = 125 MV (Bodemann 1993; Michel et a11996). As 1~ (figure 9), the production modes of which differ discussed elsewhere in detail (Michel et al 1996) our strongly because of different energies at which these model calculations on the basis of the long-term SCR nuclides are produced. ~6A1 is a low-energy product in and GCR spectra given above reproduce the produc- stony meteorites while 1~ is a high-energy one. This tion rates of 1~ and 26A1 in the Salem meteorite is, however, an advantage since the location of mea- reported by Nishiizumi et al (1990) and exclude sured 1~ and 26A1 data in an 26A1 versus 1~ plot of smaller values for long-term-averaged rigidities of SCR production rates allows to constrain meteoroid size spectra. and sample shielding depth (Neupert 1996; Neupert There is still a discrepancy with respect to long- et al 1997; Merchel et al 1997; Scherer et al 1997). term SCR parameters derived from investigations of Combining such information with rare gas data, in 3He, 21Ne, 22Ne, and 3SAr in lunar rocks 68815 and particular with the dependence of shielding para- 61016 by Rao et al (1994). These authors concluded meters 3He/21Ne and 22Ne/21Ne and production rates that long-term SCR spectra with J0,sca -- 66 cm-2 s -1 on radius and depth allows the determination of the and R0--85 MV are needed to fit the experimental exposure history of a meteorite: the radius of the data, parameters which cannot explain the observed meteoroid, sample shielding depths, exposure and 26A1 profiles (Michel 1998). Whether there is a long- terrestrial age and the decision about pairing of term change in SCR and consequently GCR para- different finds and complex exposure histories. meters or whether this discrepancy is merely due to The exposure age can be derived both from radius unreliable cross sections is still open. This problem can and depth assignment or from the theoretical depen- be settled after remeasuring the respective cross dence of rare gas production rates on shielding para- sections which is underway (Leya et a11998b; Gilabert meters, which for medium sized meteoroids (25 to et al 1998b; see also Reedy, this volume). 50 cm radius) agree well with those obtained from Some conclusions about the production of cosmo- semi-empirical models (Eugster 1988). For larger radii genic nuclides in stony meteoroids maybe drawn here. the empirical shielding depth correlations of produc- There is evidence from the simulation experiments tion rates do not hold. It is to be noted that for smaller and from model calculations for real meteoroids in radii the production of cosmogenic nuclides by SCR space that the elemental production rates of different particles has also to be considered (Michel et a11995a) target elements contributing to the production of a which often shows up in 26A1 but not in 1~ In addi- particular cosmogenic nuclide do not have identical tion, due to the availability of the relevant elemental depth and size dependences. Therefore, empirical production rates, by physical model calculations, the corrections of production rates for different chemical differentiated meteorites can also be dated with compositions derived from meteorite data have respect to their exposure ages with similar accuracy inherent uncertainties since they neglect such depen- (Weigel et al 1997). dencies. Physical model calculations and the general The knowledge about radius and shielding depth is approach described here allow calculations of more also crucial for the determination of terrestrial ages reliable production rates for different meteorite classes. e.g. via 14C. Figure 8 shows the production rates of For determination of the production rates of stable 14C in H-chondrites. For radii between 5 and 50 cm cosmogenic nuclides, usually constant production rate these production rates vary by up to a factor of three. ratios of a stable and radioactive nuclide have to be For calculating a terrestrial age from a measured 14C assumed. Our model calculations show, however, that specific activity the proper saturation activity has to quite often, correlations between production rates of be derived on the basis of size and shielding infor- different cosmogenic nuclides deviate from linearity. mation obtained from other cosmogenic nuclides Cosmogenic nuclides in meteorites 453

...... ~,: 70 , , ' ' ' ' ' ' ' 1 ' +~ + ~ ,~ ++ • %~ ] Ij~j~ + X A H-chondritcs 5O | + X VO %8 + X%o El Xlgll ][I +

x, @ + A v~ [] 5 ,k,l, o lo A J, K X vO~ I N N !5 '7, 40 O 25 v 32 O ,, 40 U X 5O 30 @ + 65 Iz 85 s~ 'i00 D x 4,20 I I I'llliillll[ll[ i I I I I 20 ' ' ~o 15 2O P(Br [dprn/kg] Figure 9. Correlation of 2SAl and l~ production rates in H-chondrites for the long-term averaged GCR spectrum.

measured in the same sample, which are then inter- 6. Conclusions preted by physical model calculations. Considering the achievements made so far in the Making systematic use of accelerators to measure measurement and interpretation of cosmogenic nuclides the cross sections relevant for the production of in extraterrestrial matter, some future goals, both cosmogenic nuclides and to simulate the irradiation experimental and theoretical ones, can be defined. conditions which a meteoroid undergoes in space, it From the experimental point of view an extension of was possible to establish a physical model without the cosmogenic nuclide coverage during measurement free parameters which describes all aspects of the of any sample is desirable. This stresses the importance production of cosmogenic nuclides by solar and of consortium studies as a regular approach. galactic cosmic ray particles. Further extension and The time scales on which GCR spectra are investi- development of this model exclusively rest on the gated can be extended from about 10 Ma to 50 Ma by improvement of our knowledge about the nuclear analysis of 129I. Further, analyses of 59Ni in lunar reactions underlying the production of cosmogenic samples would be highly desirable since they provide nuclides. the only means to derive long term spectra of ener- getic solar 4He particles. Acknowledgement Though our physical model calculations also ade- quately describe cosmogenic nuclide production in iron This work was partially supported by the German meteoroids (Leya 1997), an extension of the model Science Foundation. The first author is grateful to a calculations to 41K/a~ of iron meteorites is large number of colleagues for collaboration over a desirable. In this context, it has to be mentioned that time period of two decades. Also the opportunity to for iron meteorites one faces particular problems since use a wide variety of accelerators and to enjoy the skill contributions to cosmogenic nuclide production by and assistance of the accelerator staff is gratefully trace elements such as and phosphorus are signi- acknowledged. Without the collaborators and the ficant (Leya 1997). Here further cross section data are accelerator staff the maturity of physical model calcu- needed. lations obtained today would not have been achieved. For a further development of the model calcula- tions, improvement in cross section data for the pro- duction of nuclides such as 3H, 53Mn, 6~ 129I and of References rare gase isotopes is the major task. Some systematic work in this direction is underway for proton-induced Ahmad I, Bonino G, Castagnoli G C, Fischer S M, Kutschera reactions and, hopefully, may begin soon for neutron- W and Paul M 1998 Three-laboratory measurement of the induced ones in the near future. a4Ti half-life; Phys. Rev. Left. 80 2550-2553 454 R Michel and S Neumann

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