CHARGE SPECTRUM OF HEAVY AND SUPERHEAVY COMPONENTS OF GALACTIC COSMIC RAYS: RESULTS OF THE OLIMPIYA EXPERIMENT

Olivine is distributed through pallasites in the form of crystals ranging from several millimeters up to 1–2 cm in size (Figure 2). According to current concepts, pallasites are either a product of unfinished differentiation of matter into the silicate phase and metal in the gravitation field, or a result of agglomeration of a silicate substance with iron. There are several models describing the formation of pallasites, including crystallization near the surface of an externally heated asteroid, crystallization of an impact melt, and nebular condensation (Goldstein et al. 2014).

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By its crystal structure, olivine ((Mg_x Fe_1-x)₂SiO₄) is attributed to the silicates with an isolated island arrangement (nesosilicates) of silicon–oxygen tetrahedra (SiO₄) bonded by means of Mg or Fe cations (Birle et al. 1968).

When passing through matter, heavy ions (M > 20 amu) with specific energies E > 1 MeV nucleon⁻¹ lose the majority of their energy (>95%) due to the excitation of the electron subsystem of a material. Subsequent relaxation of the extremely excited electron subsystem, accompanied by the transfer of part of its excess energy to the lattice, leads to formation of ion tracks. The sizes of these tracks are a few nanometers in diameter and many tens or more micrometers in length. The tracks consist of materials that have been highly damaged (structural changes, broken bonds, etc.), resulting in an elevated level of chemical activity as compared with the undamaged surrounding matrix (Durrani & Bull 1987). The selectivity of the etching process (the etching rate of a track being significantly higher than that of the bulk) converts each individual track into an open channel (Fleischer et al. 1975; Kashkarov et al. 2009) that can be easily identified by optical microscopy.

It has been shown (Egorov et al. 2008, 2011; Aleksandrov et al. 2009b) that the etching efficiency of long path-length tracks in olivine crystals is the same for the polycrystalline highly oriented regular texture and the single-crystal texture, i.e., the etched track length and the etching rate do not depend on the orientation of tracks relative to the olivine crystallographic axes. This feature is of great significance for processing the experimental data because it enables precise measurements of etched GCR nuclear track parameters, as well as calibration measurements of tracks produced by high-energy nuclei at the accelerator facilities, without any additional crystallographic analysis.

The meteoritic olivine crystals used in this work were located relatively close (up to 5–6 cm depth) to the preatmospheric meteoroid surface. Thus, it is assumed that these crystals could register nuclei of superheavy GCR elements with energies up to ∼1.5–5 GeV/nucl (Aleksandrov et al. 2009a). According to estimates based on phenomenological models (Pellas et al. 1983; Alexandrov et al. 2013a), 1 cm³ of olivine crystals at a depth of about 5 cm from the preatmospheric meteoroid surface can contain 10²–10³ tracks of nuclei with Z > 90. Moreover, within a surface depth of about 1 cm, up to 10⁴ of ion tracks of the VH (20 < Z < 30) group may have been accumulated over 10⁸ years of exposure in cosmic space.

Unlike the other types of track detectors (nuclear emulsion, plastic), olivine is free from tracks of light nuclei with Z ≤ 24, because the energy-loss threshold for creating etchable tracks is sufficiently high in this material (about 18 MeV cm⁻² mg⁻¹ or 5 keV/nm) (Horn et al. 1967). Taking this threshold into account, only etched tracks from nuclei heavier than the iron group (24 ≤ Z ≤ 28) can be detected in olivine. This high threshold of the projectile charge for etched track developing in olivine enables studies of the nuclear charges of very very heavy (VVH group, 30 ≤ Z ≤ 50), superheavy (SH group, 50 ≤ Z ≤ 80), ultraheavy (UH group, 80 ≤ Z ≤ 92), and transuranium (Z > 92) elements in GCR. Glass track etch detectors can also be insensitive to light nuclei, but only meteorites are irradiated with cosmic rays for millions of years.

To date, supernovae are considered to be the most probable sources of heavy elements in GCRs (Ginzburg 1999). The evaluation of minimal possible lifetimes of those nuclei which have produced tracks in meteorites is discussed in Section 3.3.

Structure transformations generated in the vicinity of ion trajectories were investigated using transmission electron microscopy (TEM). A TITAN 80-300TEM/STEM (FEI, US) operating at 300 kV was applied for this purpose.

For these investigations, thin electron-transparent foils of olivine along the trajectories of ion tracks were prepared using the focused ion beam (FIB) technique in a HELIOS dual-beam SEM/FIB system (FEI, US) equipped with C and Pt gas injectors and a micromanipulator (Omniprobe, US). A 2 μm Pt layer was deposited on the surface of the specimen prior to the preparation of cross-sections. Sections approximately 8 × 5 μm² in size and 2 μm thick were cut by 30 kV Ga⁺ ions, removed from the sample, and then attached to an Omniprobe semi-ring (Omniprobe, US). Final thinning was performed with 5 kV Ga⁺ ions followed by cleaning by 2 keV Ga⁺ ions to electron transparency.

High-resolution images as well as conventional bright-field TEM images were recorded.

The diameters of structurally changed regions were measured from the recorded bright-field images and high-resolution TEM (HRTEM) images. HRTEM images of 2 GeV Au ion-induced tracks in plain view were obtained by carefully tilting the specimen to align the tracks parallel to the incident electron beam.

Figure 3(a) presents a typical HRTEM image of an ion track. The olivine crystal lattice was observed in [110] zone axis, and a fast Fourier transform (FFT) obtained from that image is shown in Figure 3(b). Close inspection of the track core shown in Figure 3(c), along with FFT analysis, indicated that the core is mostly amorphous, which is in good agreement with some other works (Szenes et al. 2010; Rodriguez et al. 2014; Park et al. 2015). However, in some areas of the track core, periodic features could be revealed in orientations that differed from the olivine crystal lattice. Because the scale bar can be precisely calibrated by the known olivine d-spacings (e.g., d₀₀₁ = 5.99(7) Å; Heuer 2001), the radii of individual tracks can be measured reliably.

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These results demonstrate that considerable structural transformations occur only in the close (<10 nm) vicinity of the projectile trajectory. Therefore, these structure changes cannot stimulate an enhancement of the etching rate of olivine at distances ∼1 μm from the trajectory, which results in the detected syringe-like shape of GCR nuclear tracks (see Figure 7(a), (b) below).

We suggest that the chemical activation of olivine at such large distances from the ion trajectory is caused by spreading and specific relaxation of electronic excitations generated in the track (Gorbunov et al. 2013, 2014, 2015). It is assumed that this activation results from the neutralization of metal atoms linking SiO₄ atomic groups that break up bonds providing this linking. In particular, we think that the change of the oxidation degree of polyvalent Fe cations by fast electrons appearing due to the excitation of the electronic subsystem of a target by a projectile is the most probable mechanism of the chemical activation of investigated iron-bearing olivine.

Indeed, Monte Carlo (MC) simulations based on the well-tested original TREKIS code describing the initial kinetics of excitation of the electronic subsystem of solids in swift heavy ion tracks (Medvedev et al. 2015) demonstrate that fast electrons generated in ion tracks in olivine may spread up to micrometers from the ion trajectory. Figure 4 illustrates this spreading at 100 fs after an impact of 11.1 MeV nucleon⁻¹ Au ion realizing the electronic stopping around the Bragg peak.

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Within the framework of the activated complex theory (Connors 1990; Berg et al. 2002) the change of the specific Gibbs energy determines the level of chemical activation of a modified material.

Figure 5 (Gorbunov et al. 2015) illustrates the increase of chemical activity (the relative reaction rates) of olivine due to changes of the Gibbs energy in the vicinity of the trajectory of a gold ion having the energy E = 11.1 MeV/nucl. At distances less than 5 nm from the trajectory, the Gibbs energy of the material increases due to structure transformations stimulated by relaxation of the energy and momentum transferred into the olivine lattice during the relaxation of the excited electron subsystem. These transformations are confirmed by TEM images (Figure 3), as well as by simulations of the coupled kinetics of the relaxing electronic subsystem and lattice in swift heavy ion tracks in olivine (Gorbunov et al. 2013, 2014). Chemical activation of olivine at distances r > 5 nm from the ion trajectory is caused by neutralization of Fe ions binding SiO₄ tetrahedra in an olivine lattice by fast electrons generated in an ion track.

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Due to numerous microcracks, only about a quarter of olivine crystals up to 2 mm in size extracted from the (Fe, Ni) pallasite matrix are sufficiently transparent for track analysis by optical microscopy.

Within the framework of the OLIMPIYA project, a special method of multi-stage grinding and etching of a certain thickness of crystal layer was developed yielding the most precise detection of the parameters of etched tracks and efficient use of each chosen crystal volume.

First, polishing is applied because the quality of the crystal surface determines the accuracy of geometrical track parameter measurements. After the first cut, the resulting surface of the crystal has a roughness of 20 ± 10 μm. Grinding and polishing are performed up to a roughness no larger than 3–5 μm and 1–2 μm, respectively. Such quality is achieved by polishing with diamond pastes using powder grains decreasing successively from 14 μm down to 1 μm.

Sets of polished crystals, several pieces per set, are embedded into epoxy tablets of a size corresponding to the slot on the microscope table.

The presented work makes use of the common standard WN technique for chemical track etching in olivine crystals from pallasites. This technique was first described in Krishnaswami et al. (1971) and refined at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research (Petrova et al. 1995). The WN solution is prepared in the proportion of 40 g of trilon B (disodium salt of ethylenediaminetetraacetic acid), 1 ml of orthophosphoric acid, and 1 g of oxalic acid for 100 ml of water. For optimum pH = 8.0 ± 0.1, the obtained original solution is gradually supplemented with aqueous NaOH (4:3), the amount of which is determined empirically for each solution preparation. The solution is usually prepared in a large volume (1–2 liters), and all the subsequent etching operations occur in almost identical conditions. The temperature of the etching solution is maintained with an accuracy of about 1% and is +(110 ± 1)°C at positive solution vapor pressure (up to ∼1.5 atm). It has been established empirically that (a) this mode provides constant concentration of the solution and (b) there is no need to bring the solution up to its boiling point. As a result, the etching process occurs under almost constant conditions without any variations over a very long (up to ∼100 hr) etching time. The etching time is determined by the necessity to detect, with utmost accuracy, the value of the track etching rate changing along the path of a charged particle. The minimum etching time is 8 hr; after checking whether it is possible to search for high-velocity etching tracks, the procedure is continued, with checks at 12, 24, and 36 hr.

Olivines from meteorites are able to conserve heavy GCR nuclear tracks for hundreds of millions of years. Experiments show that, at low temperatures in outer space, tracks in olivine can persist much longer than 10¹⁰ years (Maurette et al. 1964; Fleischer et al. 1967). Such resistance of olivine allows it to conserve tracks at a relatively low temperature of (110 ± 1)°C throughout the etching process in a boiling solution for several tens of hours (Goswami et al. 1984). Moreover, the tracks survive polishing of the crystals by hand at room temperature. In this regard, determination of the nucleus charge does not require any contributions from track temperature characteristics at space exposure, as well as at olivine processing in the laboratory.

2.4.1. Identification of Tracks

At high energies, the energy loss of a projectile is not high enough to produce sufficiently severe damage for tracks to be etchable. During the slowing down of a particle, its energy loss along the trajectory gradually increases, finally surpassing the threshold (about 18 MeV cm⁻² mg⁻¹ or 5 keV/nm in olivine) for the creation of etchable tracks. At higher energy losses, the track etching rates are higher. Within the region of a maximum energy loss (Bragg peak) the high etching rate leads to a maximum diameter of the etched channel. The cylindrical section of the etched track demonstrates a fivefold increase of the etching rate (Perron & Maury 1986; Perron & Bourot-Denise 1986) in this region. Close to the stopping end of the particle trajectory, the electronic energy loss drops below the etching threshold, and the channel ends with a short, sharp tip. This form of an etched track is illustrated in Figure 6.

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Micrographs of two types of etched tracks in olivine confirming the scheme of Figure 6 are presented in Figure 7. Figure 7(a), (b) (magnification 40×) refers to final segments of the trajectory of an incident particle. Therefore, we assume further that an etched track consists of two regions: syringe-like, with a cylindrical part at the end of the path (where the energy losses are maximum); and needle-like, corresponding to the high-energy segment of the trajectory. About 2% of the tracks in the total data set are syringe-like. On the other hand, needle-like tracks are predominant (98% in the total data set) which, it seems, can be described statistically by considering the small sizes of olivine crystals compared to the long paths of high-energy particles. Figure 7(c) (magnification 20×) and Figure 7(d) (magnification 40×) demonstrate both types (syringe and needle-like tracks) in the same crystal; Figure 7(e) (magnification 40×) demonstrates a needle-like track; Figure 7(f), presents the general view of an olivine crystal with a few heavy projectile tracks (magnification 8×).

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Being exposed to cosmic radiation, olivine crystals accumulate tracks from nuclei with trajectories coming in from different directions. During etching, only tracks whose trajectories intersect the specimen surface are affected by the etchant.

Successive step-by-step etching has demonstrated that the etching rate V_etch (that is, the increment of the length of a track divided by the time of etching) considerably decreases when the tracks achieve a length of 100–200 μm (Bagulya et al. 2009). At very long etching times (up to 96 hr), tracks of 300–400 μm either continue to slowly lengthen or remain invariable.

The uncertainty associated with this effect of an uncontrolled decrease of V_etch can be ruled out with the technique of multi-stage slicing of layers at the layer-by-layer etching of the crystal (Kashkarov et al. 2008; Aleksandrov et al. 2010). After etching and analysis of the crystal surface, a thin layer of 50–100 μm is removed from the crystal by grinding (to an accuracy of several microns), and the procedure is repeated. The thickness of the layer removed by precision grinding and polishing is established for each particular set of observed tracks. After each etching step, the geometrical parameters (length and diameter) of the developed etched tracks at a given processing stage are measured. The successive stages of the treatment are shown schematically in Figure 8.

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Recording the data of etched track segments in different layers allows us to reconstruct the full track length throughout all processed layers (Figure 8, tracks 1 and 3). Such reconstruction requires an accurate determination of the coordinates of the track ends and angles of inclination relative to the etched surface. In order to produce this reconstruction, the PAVICOM tool is applied.

2.4.2. PAVICOM Image Processing

The search for tracks of heavy and superheavy charged particles of GCRs crucially depends on the ability to identify individual particle tracks and separate them from the background, as well as on the accuracy of the track geometry data in the (x, y ) plane and along the depth (z) of the crystal.

The (x, y , z) coordinates of the etched tracks were analyzed by PAVICOM (Completely Automated Measuring Complex) (Aleksandrov et al. 2004, 2012; Polukhina 2012)—a multi-functional programmable measuring facility developed for processing data obtained in various types of solid-state track detectors.

The software identifies the etched tracks because they appear as dark objects in the transparent olivine crystal (Aleksandrov et al. 2009b). In a fully automated process, PAVICOM determines the coordinates of track segments and the angle of inclination of a track with respect to the crystal surface, thus reconstructing the complete track length within all processed layers. Automatic scanning of the track elements is performed by means of optical microscopy combined with a movable sample stage (MiCos, Germany): MS-8 (working range, 205 × 205 mm; lateral accuracy, 0.5 μm) and LS-110 (working range, 305 mm; depth accuracy, 0.2 μm). A CMOS camera is fixed on the z-axis stage, allowing variation of the focus at different depths with steps of about 3 μm. The images are recorded by a 1.3 MP camera with a frame rate of 376 fps while the x–y stage is at rest and the z stage moves at constant velocity (the so-called Stop-and-Go motion algorithm). The scanning speed of this system is about 20–80 cm²/h⁻¹. Mathematical processing of the digitized images is performed by using a library of C++ programs.

A problem associated with automated processing is the change of the optical properties of the etched tracks at different depths of view. Near the crystal surface, the etched track is rather dark and has clear-cut and sharp edges. However, when going deeper, the tracks become increasingly pale and blurred, and it becomes difficult to discriminate them from background features. In order to reliably determine the track parameters deep in the crystal, several parameters in the analysis program are adapted to the depth of the crystal by automatically changing, e.g., filters, or geometrical parameters of etched tracks.

For data processing, it is also taken into consideration that etched tracks represent open channels or cavities with uneven walls. The image of an etched track often looks like a series of dark, light, and very light spots. In particular, the image of the tracks under a small angle of incidence of a projectile with respect to the crystal surface is subjected to greatest distortions due to optical effects. As a result, these images, scattering into separate clusters, have segments of elongated shape with the direction of the axis close to the direction of track's axis. When reconstructing the track, these features are taken into account by extending the axis of an elongated cluster and considering other clusters close to this axis (Figure 9).

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The track analysis is difficult in some olivine crystals because of numerous extraneous spots from various sorts of inhomogeneities, microcracks, and optical effects (reflection, refraction, focusing etc.). To reduce this background and to increase the efficiency of track identification, the software is equipped with the ability to isolate an area of the image where the signal-to-noise ratio is most favorable. Spot-like features are separated from true tracks by a complete analysis through the entire crystal depth: the image of a real track shifts with depth in the direction of the particle trajectory, whereas the positions of extraneous objects remain fixed at a certain depth in the crystal. This additional test enables a more efficient selection and identification of real tracks.

2.4.3. Etching Rate as an Important Track Parameter

The main and only parameter measured after chemical track etching of olivine crystals, used in previous experiments on the search for heavy nuclei in meteorites (Otgonsuren et al. 1976; Flerov & Ter-Akopian 1981), was the length of etched tracks, i.e., the segment of charged particle deceleration path along which a region with increased chemical activity is formed. Within the approach developed in the OLIMPIYA experiment, we record the etching rate V_etch along the projectile trajectory as the second main track characteristic used for determination of the nuclear charges (Aleksandrov et al. 2008). This additional parameter provides quite essential information, because the crystals accessible for the experiments are sometimes too small to observe the complete length of tracks. Particularly for VH nuclei, the track length may exceed the size of a crystal and even multiple step-wise etching does not allow the measurement of the complete track length by the available technique (Figure 10). For example, the full length of an etched uranium track reaches 10 mm (at U energy of about 400 MeV nucleon⁻¹), whereas the average thickness of a crystal is at least 10 times smaller.

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Experiments with ion beams of various elements of fixed energy available at accelerator facilities were carried out within the framework of this project. They demonstrated (Alexandrov et al. 2013a) that the etching rate V_etch along the projectile trajectory changes noticeably following changes in the energy loss of a projectile, as well as in the spectrum of electrons generated in a track. For instance, for U ions, the track etching rate V_etch = (7 ± 1) μm h⁻¹ at the trajectory fragment corresponding to the residual path length R ≅ 1000 μm increases up to (25 ± 2) μm h⁻¹ at R ≅ 200 μm.

In general, because the projectiles are not always stopped in a crystal, the measured segment L of the nucleus deceleration path does not coincide with the residual path length R, so it might be either L ≅ R or L < R. The former case is attributed to tracks etched up to the stopping point. In the latter case, the projectile passes through the crystal without being stopped and the analysis of the registered segment of the track must be based on accurate measurements of the etching rates. In this case, use of the developed method of multi-stage etching process and the automated track parameter measurements make it possible to determine V_etch with good accuracy.

It should also be noted that most tracks exit from olivine before the particle comes to a halt. Due to this, track lengths L registered in our experiments are, in most cases, less than the values of R, and the measured parameters L and V_etch give the lower estimates of nuclear charges.

In summary, in combination with the results of the calibration experiments (see the next section) these two parameters of etched tracks in olivine crystals from meteorites, i.e., the measured length of the etched track L and the etching rates V_etch, form a database which can be used for determination of GCR nuclear charges.

Using the above-mentioned parameters (L and V_etch, see Section 2.4) charges of nuclei Z can be uniquely determined only when (Z–V_etch–L) dependence is determined from the calibration experiments.

A series of such calibration irradiations were performed at the UNILAC and SIS accelerators (GSI Helmholtz Centre for Heavy Ion Research, Darmstadt, Germany) with Kr, Xe, Au, Bi, and U ions, as well as at the accelerator complex of the Institute of Modern Physics (Lanzhou, China) with Bi ions.

The calibration campaign included the irradiation of olivine crystals from Marjalahti and Eagle Station pallasites, as well as Earth olivine samples, with Kr, Xe, Au, Bi, and U ions of 11.1 MeV nucleon⁻¹ and 150 MeV nucleon⁻¹ (for U ions), and Bi with energies of 2.5, 4.5, and 9.4 MeV nucleon⁻¹. The irradiations were made at incident angles of 90° and 45° to the normal of the sample surfaces, with fluences varied between 10⁵ and 10¹² ions cm⁻².

For uranium, the data obtained by Perron & Maury (1986) were also used.

Figure 11 presents optical micrographs of olivine crystals containing various almost-parallel etched ion tracks. The detected density of registered tracks varies from 30 to 80 tracks per crystal.

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As an example, some of the calibration results are presented in Table 1 and Figure 12. The majority of our results are in good agreement within the errors with the calculations by SRIM-2008. The agreement of the results at energies of 2.5 and 4.3 MeV nucleon⁻¹ is worse, which may be associated with a wider spectrum shape after particle deceleration to the desired energy.

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The experimentally measured lengths of tracks in the irradiated olivine crystals show a good agreement with the corresponding values calculated using the SRIM-2008 code (Ziegler et al. 1985, 2008).

Based on the results of the calibration experiments, the charge of the projectiles can be plotted as a function of the track lengths and track etching rates measured in the experiments (Figure 13). The accuracy of charge determination by this technique ranges in ±1 to ±2 charge units.

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Within the charge range of 67 < Z < 93, this calibration surface can be fitted by a five-parameter function given by Equation (1),

$$\begin{eqnarray}&&{V}_{\mathrm{etch}}(Z,L)=\displaystyle \frac{A(Z)\cdot (1+E(Z)\cdot {L}^{2})}{1+B(Z)\cdot \exp \left[\tfrac{L-C(Z)}{D(Z)}\right]}.\end{eqnarray} \tag{ 1 }$$

The fitting parameters A, B, C, D, and E of the function depend smoothly on charge Z and were approximated by a linear function with a small quadratic term. This allows a good extrapolation of charge values to several units beyond the limits of the calibration experiments (Z > 92).

Figures 14 and 15 present the results of the calibration experiments and their fitting by Equation (1).

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The application of our layer-by-layer grinding and etching method, in combination with the system of automatic detection of etched tracks (PAVICOM), has allowed us to analyze a large set of experimental track data. Within the OLIMPIYA project, a total of 442 crystals of meteoritic olivine crystals (264 crystals from the Marjalahti meteorite and 178 crystals from the Eagle Station meteorite) were investigated. Using the technique of projectile-charge determination described in Sections 2.4 and 2.5, and based on the data on the track length and the track-etching rate, in combination with calibration results, 11,647 tracks were assigned to GCR nuclei having charges Z > 20 (in accordance with Otgonsuren (1973), uranium content in terrestrial olivines is 10⁻¹¹–10⁻¹² g/g, whereas the concentration of uranium in the surrounding rock minerals is about 10⁻⁷–10⁻⁹ g/g, and occasional spontaneous or induced fission tracks in meteorite olivine was evaluated at the same level of uranium content, 10⁻¹¹–10⁻¹² g/g). Out of them, 10,283 tracks were produced by nuclei with Z ≥ 50, 1233 tracks by nuclei with Z ≥ 70, 384 tracks with charges assessed as Z ≥ 75, and 9 tracks by nuclei with Z ≥ 88. Compared to other studies, the OLIMPIYA experiment has yielded a huge number of GCR tracks, providing one of the best-sampled data sets (see Table 2).

Currently, there are three sets of results obtained in the largest satellite experiments registering cosmic heavy ions: ARIEL-6 (Fowler et al. 1987), HEAO-3 (Binns et al. 1985), and UHCRE (Donnelly et al. 2012). These experimental data sets available to date and our results are presented in Figure 16, showing the relative abundances of nuclei with Z ≥ 48; the data were normalized by the content of iron nuclei A(₂₆Fe) = 10⁶. The nuclei charge determination accuracy in OLYMPIYA is determined by the geometric parameters of tracks, measured on the automated microscope with precision German mechanics (it is 0.5 μm for all coordinates). ARIEL-6, HEAO-3m and UHCRE data show a peak at Z = 79, 77, and 78, respectively, and the height of the UHCRE peak is two times higher than the others. The existing disagreement between the available results requires further research. The results of this work within the errors have the best agreement with HEAO data, although the decline of the distribution is steeper in the region of Z > 80.

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Registrations of transuranium nuclei with charges of 92 < Z < 100 were mentioned in experiments by Shirk & Price (1978), Donnelly et al. (2001), and Perelygin et al. (2003a, 2003b). Unfortunately, these papers do not comment on the nature of these events.

It should also be noted that transuranium nuclei with charges of 92 < Z < 100 registered in ARIEL-6 and UHCRE experiments have lifetimes that would be too short to reach our solar system, starting from the nearest supernova.

We think that events with Z > 92 appear, not due to inaccuracies of the applied method or instrumental failures, but as the result of the fragmentation of heavier, more stable nuclei from the region of the Island of Stability.

Analyzing the superlong particle tracks in meteoritic olivines, we also found several events that can be attributed to particles with Z > 92.

Three superlong tracks with lengths of more than 500 μm and etching rates exceeding 35 μm h⁻¹ were detected when analyzing the data accumulating during the OLIMPIYA experiment, see Figures 17(a)–(d) below.

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Taking into account that the maximum value of the experimentally measured etching rate for tracks of uranium nuclei in olivine before their stoppage point is V_etch,U = 26 ± 1 μm h⁻¹, this indicates that the charges of these registered nuclei significantly exceed the charge of uranium.

The charge assessment for these nuclei is based on the dependence of the etching rate V near the stoppage point of the charge value. For nuclei with Z ≤ 92, we used the empirical function V(L, Z) to determine, by interpolation, the charges of the nuclei, Parameters of this function were determined by comparison with experimental data on nuclei up to Z = 92. At present, we cannot pronounce upon how well this function works for Z > 92 because insufficient experimental data make it impossible to extrapolate the function to this region. In any event, the curves obtained for higher Z, up to 100, are shown in Figure 15, as illustrated. The parameter V was used for charge determination near the stoppage point to evaluate our data in the larger charge region. The etching rate V is almost independent from the residual length L in this area. The character features of our tracks demonstrate that the nuclei are only located near the stoppage. Figure 18 shows that, in this case, the V dependence from the charge is well-approximated by a straight line (there are five experimental points well-approximated by a straight line at our disposal). Thus, charge determination by extrapolation in the region up to Z = 110–120 is more reliable than using empirical function V(L, Z). The obtained approximation is quite accurate and possesses a great level of confidence (95%). Further extrapolation of the straight line and the corridor of errors to an etching rate of 35 μm h⁻¹ gives the required evaluation. The performed regression analysis of the etching rate near the stoppage point (Alexandrov et al. 2013a) made it possible to refine the assessment of charge of one of these nuclei to ${119}_{-6}^{+10}$ with a 95% probability (Figure 18). The obtained nucleus charge error estimation is carried out by extrapolation of the characteristics of a complex chemical process (etching) with the use of the results of previously performed calibration measurements. The error estimation is made with consideration of the calibration errors by means of approximation of the experimental points by a straight line, and building an error corridor with a specified confidence level.

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Thus, it seems that the data obtained in the OLYMPIA experiment can supply arguments supporting the existence of the theoretically predicted Island of Stability for long-lived transfermium nuclei of natural origin. Estimates of their minimum lifetimes are presented in Section 3.3.

In order to reach our solar system and form tracks in meteorite olivine, nuclei registered in pallasites should exist for a sufficiently long time. Their average lifetimes should, as a minimum, be equal to the time necessary for their flight from their point of origin to our solar system's asteroid belt, from where a predominant number of meteorites come. The minimum estimate of the lifetimes of the nuclei registered in pallasites can be determined as the time of their flight from the closest supernova (SN) to our solar system, which depends on the velocity V to which a nucleus could accelerate after being formed and on the distance to our solar system.

Generally, the trajectory of a nucleus in space is not a straight line due to the existence of the galactic magnetic field. In a homogeneous magnetic field, the trajectory of a charged particle is a spiral with a Larmor radius, which in the relativistic case appears (in the SI system) as shown in Landau & Lifshitz (1975):

$$\begin{eqnarray*}&&R=\displaystyle \frac{{{Ev}}_{\perp }}{{c}^{2}{eB}},E=\displaystyle \frac{{{mc}}^{2}}{\sqrt{1-\tfrac{{v}^{2}}{{c}^{2}}}},\end{eqnarray*}$$

where m is the particle mass, e is its charge, ${v}_{\perp }$ is the initial part of the velocity in perpendicular to the field direction, B is the magnitude of a homogeneous magnetic field, and E is the particle relativistic energy.

This radius will depend on (1) the magnetic field strength, (2) charge of projectile (a cosmic nucleus may bear some electrons, and we cannot say how many electrons it bears), (3) direction of the magnetic field, which may change during the meteorite exposition (exposition time of a meteorite is comparable to the period of rotation of our solar system in the galaxy), (4) the kinetic energy of the nucleus and (5) ratio between initial components of nucleus velocity in perpendicular and parallel directions to the magnetic field's.

Taking into account all of these factors requires special calculations. We would like to estimate the minimum life time;  so, in the limit case, when ${v}_{\perp }$ in the initial timepoint is zero, and the particle velocity is directed along the magnetic field, ${v}_{\perp }$ will be zero at every other timepoint. In this case, the trajectory coincides with a straight line, which gives an assessment of a minimum possible flight time for a nucleus. If ${v}_{\perp }\gt 0$, the time of flight will only be greater.

As for nucleus collisions with particles of the galactic interstellar medium, it should be considered that up to 70% of the volume of galaxy is a hot ionized gas with particle density n = 65·10⁻⁴ atoms cm⁻³ (meaning dimensionless probability [n] = 65·10⁻⁴ to find an interstellar atom in one cubic centimeter) (Ferriere 2001). Half of these particles are fully ionized hydrogen and helium atoms, and the other half consists of electrons of these atoms. An estimation of the collision probability can be obtained using the experimental data on the scattering of relativistic nuclei on hydrogen and helium targets. Without going into the details of the dependence of the total cross-section of the charge and mass of the projectile nucleus, one can say that, for nuclei with energies above 500 MeV per nucleon, the collision cross-section is limited by the value of 1 barn (Webber et al. 1990). Therefore, the likelihood for the incident nucleus to scatter on a gas particle in each cubic centimeter is equal to w = (σ·[n])/(1 cm²) = 65·10⁻²⁸. For example, the probability for a nucleus to scatter on a distance of 20 pc = 6·10¹⁹ cm equals W  = w·6·10¹⁹ = 3.6·10⁻⁷, and thus can obviously be neglected.

To assess the velocity of a nucleus hitting an olivine crystal from a meteorite, a specific feature of olivines' etching mechanism can be used, namely the existence of the threshold value of the ionization losses (about 18 MeV cm⁻² mg⁻¹) of projectiles, below which no etched channel emerges. For a uranium nucleus, losses above this threshold value occur at ion energies E < 500 MeV per nucleon; for a lead nucleus, at E < 300 MeV per nucleon. Herewith, the residual path length of a uranium nucleus with energy of 500 MeV per nucleon in olivine is 14 mm; it is 7 mm for a lead nucleus with energy of 300 MeV per nucleon.

The meteorite represents a nickel–iron matrix with olivine cells up to 1 cm in size. The matrix wall thickness ranges from 2 to 5 mm. Using the SRIM-2008 code, we calculate the specific losses and path lengths of uranium nucleus for a solid material, including olivine and nickel. Table 3(a) presents such values of initial kinetic energy E_kin of uranium nuclei, prior to their entry into the meteorite at which, at a corresponding preatmospheric depth PD, their energy will equal 500 MeV per nucleon—this represents the upper boundary where energy E_max will result in an etchable track. The lower boundary E_min corresponds to nuclei that approach the crystal at a corresponding depth with almost zero energy. Figure 19 shows the intervals E_min and E_max as functions of depth PD for the uranium nucleus. Only nuclei with energy E within the range E_max < E < E_min can produce an etched channel in the crystal at a preatmospheric depth PD. The width of this range is essentially constant and equals approximately 300 MeV/nucleon. Thus, there is a relation between PD and energy and, therefore, the velocity of a penetrating nucleus.

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Table 3 shows the velocities v for various values of preatmospheric depth PD for preselected kinetic energies E_kin = E_max (PD). By setting the distance DD from a particle's point of origin to our solar system, we can find the time of flight and recalculate it with account for the effect of deceleration into the particle's time of flight T (c is the speed of light):

$$\begin{eqnarray*}&&T=\mathrm{DD}/v\cdot \sqrt{1-{(v/c)}^{2}}.\end{eqnarray*}$$

There are different experimental estimations of the distance to the closest supernovae, based on direct observations of supernova remnants in space. They range from ∼200 pc (Aschenbach 1998) up to ∼1 Kpc (Badenes et al. 2006). However, it is known that supernovae have appeared within every 30 years, and it may be some are closer to Earth, but not all of them are registered. For example, there is an estimation based on measurements of ⁶⁰Fe abundance in the samples from the deep ocean estimating the distance to be ∼30pc (Fields & Ellis 1999). Table 3 presents the time-of-flight values for uranium (a) and lead (b) assessed using this technique, for DD = 100 pc.

OLIMPIYA experiments detected a transfermium nucleus with Z = 119. Assessment of its minimal lifetime T_min by the considered method (time-of-flight evaluation) requires extrapolation into the region of large charges. To carry it out, we performed necessary calculations for three heavy nuclei: Ra, Pb, and W. Figure 20 shows the summary results of extrapolation for four values of charge and various depths of PD, at a distance DD = 100 pc to a supernova. Figure 20 demonstrates that T_min for Z = 119 falls into the interval of 50 years < T_min < 100 years. Note that, for uranium nuclei, the corresponding value of T ranges from 150 years < T_min < 300 years. It should be mentioned that the estimated time-of-flight for a uranium nucleus is many orders of magnitude shorter than the lifetime of uranium nuclei. Thus, the real lifetime of a nucleus detected in the experiments with Z = 119 can also be larger than its assessed T_min. It is important that these estimated minimal lifetimes taken as the times-of-flight are many orders of magnitude larger than the lifetimes of transfermium nuclei produced artificially at accelerators.

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