ISSN 1068-3356, Bulletin of the Lebedev Physics Institute, 2013, Vol. 40, No. 5, pp. 126–131. c© Allerton Press, Inc., 2013.Original Russian Text c© A.B. Aleksandrov, A.V. Bagulya, M.S. Vladimirov, N.V. Galkina, L.A. Goncharova, G.V. Kalinina, L.L. Kashkarov, N.S. Konovalova,N.M. Okat’eva, N.G. Polukhina, N.I. Starkov, 2013, published in Kratkie Soobshcheniya po Fizike, 2013, Vol. 40, No. 5, pp. 29–38.

Simulation of Passage of Gallactic Cosmic Ray Nucleiin Meteorite-Pallasite Substance

A. B. Aleksandrova, A. V. Bagulyaa, M. S. Vladimirova,N. V. Galkinaa, L. A. Goncharovaa, G. V. Kalininab, L. L. Kashkarovb,

N. S. Konovalovaa, N. M. Okat’evaa, N. G. Polukhinaa, and N. I. Starkova

a P. N. Lebedev Physical Institute of the Russian Academy of Science,Russia 119991, Moscow, Leninsky prospect, 53; e-mail: okateva@sci.lebedev.ru

b V. I. Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academy of Science,Russia, 119991, Moscow, Kosygina street 19

Received April 22, 2013

Abstract—The results are presented of model calculation of the interaction and yield of galactic-cosmic-ray superheavy-element nuclear fragmentation products from the 50 < Z < 92 range oftheir charges as they pass through a certain meteorite-pallasite substance thickness.

DOI: 10.3103/S1068335613050059

Keywords: GCR charge spectrum, superheavy nuclei, meteorites.Different methods have been used in recent decades to investigate the nuclei of heavy (VH group

with charge in the range 23 ≤ Z ≤ 29) and superheavy (VVH, Z ≥ 30) galactic-cosmic-ray (GCR)elements. Within the framework of OLYMPIYA project [1], the charge spectrum of GCR nuclei has beenstudied by their tracks in olivine crystals from Eagle Station and Marjalahti meteorites whose radiationage is 300 million years and 185 million years, respectively. Research groups of the Lebedev PhysicalInstitute and Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academy ofSciences elaborated the method of GCR nucleus charge identification by tracks etched in olivine crystalsfrom meteorites. The method is based on the experimentally established dependence between the tracketching velocity along the nucleus deceleration trace and its residual range [2]. However, the studies ofcharge spectrum of GCR superheavy nuclei by their tracks registered in olivine crystals from pallasiteshave suggested the necessity of estimating corrections due to allowance for the fragmentation of primaryGCR nuclei in the substance of investigated meteorites. Important here is the fact that fragmentation ofGCR heavy nuclei results in both underestimation of the number of registered GCR nuclei of a certaintype and enhancement of the flow of lighter secondary nuclei, i.e., fragmentation products. Allowance forheavy nucleus interaction with meteorite substance, including nuclear fragmentation, and investigationof the effect of these processes on the GCR charge composition variation is one of the goals of performedmodel calculations.

The authors carried out a full-scale simulation of a real experiment using SRIM program package[3] and GEANT4 program complex [4]. The joint use of these programs makes it possible to comparethe results obtained thus improving their reliability. The SRIM package was mainly applied to calculatethe ionization loss of nuclear energy in the substance. The use of GEANT4 package for simulationof ion passage in a substance allowed the account of all possible interaction processes, in particular,fragmentation [5].

As the main simulation tool the iion package was built which is the version of the Hadr01 package(modified according to our tasks) entering in GEANT4 as an official example of its application. In theiion package the possibility was added of studying different parameters of nucleus penetration throughdifferent depths in the body of irradiated meteorite and of generating different energetic, spatial, andangular distributions of primary nuclei using G4GeneralParticleSource (GPS) subpackage which is partof Geant4 [6]. The model calculations give parameter distributions of both primary nuclei and secondarynuclei due to fragmentation, which make possible further analysis.

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Fig. 1. Charge spectra of nuclei after passage through different thicknesses (10/40/70/100 mm) of the nickel-irontarget for the set of nuclei from the charge range of 50 to 92 with primary energy of 1000 MeV/nucleon.

SRIM and GEANT4 programs were applied to calculate the passage of 131Xe, 207Pb, and 238Unuclei through substances of different compositions in a wide energy range [7]. The simulation resultsobtained were compared with the tabulated data [8] showing the stopping powers and the paths of ionswith charges 2 ≤ Z ≤ 103 for the energy range from 2.5 to 500 MeV/nucleon in different materials.The results of calculations showed good agreement within the statistical error, which suggested thepossibility of using the elaborated iion package in GEANT4 for the present experiment.

The pallasite-class meteorites used in this work consist of a nickel-iron matrix with polycrystallineinclusions of olivine which is a semitransparent yellowy mineral. Some inclusions reach 1 to 2 cm in sizeand are composed of smaller (0.5–1 mm) individual olivine crystals. In its crystallographic structure,natural olivine (Mg0.88Fe0.12)2SiO4 relates to silicates with isolated silicon-oxygen tetrahedrons (SiO4)joined by Mg or Fe cations [9]. Before getting into olivine crystals charged particles pass some distancethrough the nickel-iron matrix of the meteoroid (a meteoric body in cosmic space). According to theanalysis of VH nucleus track density, the depth of olivine crystal occurrence from the nearest point onthe pre-atmospheric surface of the meteoroid makes up (1.5–4) cm for the investigated sample of EagleStation meteorite and (4–8) cm for Marjalahti meteorite.

For model calculations we used a set of nuclei from the charge range (50 < Z < 92) whose relativecontent in the Solar system is taken according to H. Suess, H.S. Urey, and A.G.W. Cameron [10].Simulation was carried out for each nucleus separately, and then the contributions from individual nucleiwere summed up. Since the spread of values of relative abundance of nuclei under study makes up twoorders of magnitude and calculations for one type of nuclei, especially heavy ones, takes rather muchtime, for 238U, i.e., the nucleus with least abundance in the considered range, the initial amount of nucleiwas taken to be 1000. The number of other nuclei was calculated proportionally to the given number of238U nuclei and to the ratio of their relative abundances.

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Fig. 2. Energy dependence of the energy loss dE/dx of nuclei of different elements upon deceleration in olivine [11]and threshold energy values E1thresh and E2thresh for olivine, obtained for dE/dx = 18 MeV(mg·cm−2) in the chargerange of 50 to 92.

To implement the possibility of making allowance for different nuclear interaction processes and thenanalyzing the change in their amount depending on the distance from the surface of irradiated meteorite,we simulated passage of a set of nuclei (with the same energy for all the nuclei) through Fe0.9Ni0.1 (FeNi)targets with density of (7.9 ± 0.1) g/ cm3. Figure 1 demonstrates the results of simulation of passage ofsuch nuclei with energies of 500 MeV/nucleon to 1000 MeV/nucleon through FeNi targets of differentthicknesses (10, 40, 70 and 100 mm). The results obtained imply that, for example, uranium nuclei, ifthey have energy exceeding 1000 MeV/nucleon, can leave track in olivine after passage through a morethan 10-mm-thick substance layer of meteorite decelerating medium.

Olivine is known to be a threshold detector. The critical value of ionization energy loss for olivine is18 MeV/(mg·cm−2) [11]. In the calculations, the threshold energy values E1thresh and E2thresh (Fig. 2)were determined from the energy loss curve for a corresponding nucleus. Thus, only those nuclei can beregistered in olivine whose energy lies in the range (E1thresh − E2thresh). Having made such estimationfor the previous results, one should note that about 30% of the initial flow of all the nuclei get intothe calculated energy range. Thus, in most cases primary nuclei either are completely fragmented orpenetrate deep into the meteoroid when they have energy exceeding the threshold value (E2thresh)(Fig. 3).

Olivine crystals are located at different depths in the meteoroid body, and the primary GCR nucleiand the secondary nuclei-fragments are decelerated when they pass not only through the nickel-ironmatrix but also through the neighboring olivine crystals surrounding the crystal studied. Therefore,when simulating the passage of nuclei in the meteoroid body, calculations were also made for theaverage chemical composition of pallasite-meteoroid substance: 65 vol. % (Mgх, Fe1−х)2SiO4 and35 vol. % Fe0.7Ni0.3 (FeNi-Olivine). For comparison we simulated the passage of uranium nuclei (238U)with energies of 500 MeV/nucleon, 700 MeV/nucleon, and 1000 MeV/nucleon through a target withsuch average chemical composition. The data obtained are compared to the results for the FeNi target(Fig. 4). The results show that at energy of 500 MeV/nucleon uranium nuclei are completely fragmentedto form lighter nuclei with charge Z < 55 after they have passed through the FeNi target, whereasin the spectrum of secondary nuclei for FeNi-Olivine a small part of primary uranium nuclei is stillpresent. However, as the energy of primary uranium nuclei increases, it is evident that the contributionof secondary particles in the group of nuclei with Z = 60 − 75 is considerable for the FeNi target only.The calculations were continued for both types of targets, but greater attention was paid to the passageof nuclei through the FeNi-Olivine target.

To obtain more accurate numerical estimates of the contribution of different primary nuclei of GCRwhen they pass through a meteorite, one should allow for the shape of cosmic ray energy spectrum.At energies in the investigated range, the experimental data on the particle spectrum are typically

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Fig. 3. The decrease (in percent) of the number N of the nuclei passed through 10 mm of the nickel-iron targetsubstance with respect to the initial number of nuclei N0 for three values of simulated energies.

Fig. 4. Charge spectra after passage of uranium nuclei with energies of 500 and 1000 MeV/nucleon through 10 mm ofFeNi and FeNi-Olivine targets.

represented in the “power-law” form N(E) ∼ 1/Eγ , where N is the number of particles with a givenenergy E and γ is a differential spectral index. The experimental data available in the literature on thevalue of the spectral index have a considerable spread. In this work we took the value γ = 2.5 which issometimes used for the procedure of spectrum “smoothing” by the data of different experiments [12].

When recording tracks in individual olivine crystals it is important to know not only the number ofproduced nuclei (fragmentation products) in the braking layer of the meteorite substance of a certainthickness, but also the number of these nuclei with certain threshold energy (corresponding to trackformation in olivine) flying from the nickel-iron layer surface closely adjoining the olivine crystal –detector (registration under condition of 2π geometry). According to the proposed model, the energy ofeach nucleus distributed by the law ∼ E−2.5 in a specially calculated range must correspond to the meannucleus path exceeding the particular calculated thickness of the meteorite nickel-iron matrix. At theoutput of the target the nucleus energy must lie within the limits of threshold values of track formationfor olivine (E1thresh − E2thresh), i.e., it is only such a nucleus that can be registered in crystalline olivine.Thus number of incident nuclei of each sort was set proportional to their abundance in the GCRcomposition. The range of initial energies for each nucleus was calculated using the energy dependence

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Fig. 5. The decrease (in percent) of the number N of the nuclei passed through FeNi-Olivine and FeNi targets withrespect to the initial number of nuclei N0 for the energy range of nuclei that will stop in contacting olivine-detector oftracks. The thicknesses of the targets are shown in the figure.

of inverse energy loss. We calculated the integral

L =

E1entry∫

E1thresh

dE

(dE/dx),

where E1entry is the minimum input energy.Known the given target thickness L, the E1entry value was found after several iterations. The E2entry

value was determined analogously. The ranges of input energies E1entry − E2entry differ for differentnuclei, but if the general form of the energy dependence of the number of nuclei is known, one candetermine the scaler factor by which the number of primary nuclei should be multiplied. Thus, weconsiderably reduced the time of computation by excluding the cases when the nuclei that have passedthrough the nickel-iron matrix cannot form a track in olivine. The energies of registered nuclei from thecharge range 50 < Z < 92 at the input of FeNi and FeNi-Olivine targets of different thicknesses werecalculated.

Specifying the energy in the range of estimated values for the iion package, we managed to reducestill more the time of computations by excluding the case when a nucleus that has passed through the

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nickel-iron matrix cannot form a track in olivine. Further calculations with corrections were made fora 10-mm-thick FeNi target and also for 10-mm- and 40-mm-thick FeNi-Olivine targets (Fig. 5). Theresults show that now, with the initial data thus given, all the nuclei can actually be registered in olivinein all the cases. One can also estimate the decrease in the registered nuclear flow depending on the targetthickness.

Thus, we created and modified the program package from the GENAT4 complex with allowance forthe experimental data. The results obtained made it possible not only to analyze the character of thechange in the output of nuclei – the fragmentation products – with depth from the surface of irradiatedpallasite body, but also to make a quantitative estimate of the contribution to the group of nuclei withZ = 60 − 75 from nuclei of heavier GCR elements that decayed at fragmentation in the meteorite-pallasite substance. Using the calculation data we managed to determine the change in the chargedparticle spectra in order to correct the investigated cosmic ray spectrum. We obtained the calculatedcharacteristics of the charge and energy spectra of nuclei of superheavy GCR elements at the input ofthe registering olivine crystal after passage through a certain meteoroid thickness. The results of thepresent work can explain a whole number of events observed in satellite experiments in the study ofcosmic ray composition in the range of superheavy nuclei Z > 65 [13-15]. Along with stable nuclei withZ ≤ 92, some signals were registered in the experiments from particles with the charge in the range94 < Z < 100. Particles with such a charge cannot enter in the composition of primary cosmic raysbecause of their very short lifetime. The authors of the above-mentioned papers do not comment on theorigin of these particles. In our opinion events with Z > 92 are not due to methodical inaccuracies orequipment error, but are the result of fragmentation of heavier nuclei from the region of the “island ofstability”. Several such events were also discovered in our studies of tracks of superheavy particles inolivine from meteorites.

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