Introduction

The isotopic compositions of a natural sample can provide useful information on the origin and/or physicochemical processes such as evaporation, condensation, diffusion, isotopic exchange and radiometric decay. To determine such an isotopic composition, a mass spectrometers have been widely used over several decades, which requires a destructive/consuming treatment such as sputtering, laser ablation and thermal ionization. Since the highly intense muon beam can be produced (Miyake et al 2009), muon-induced characteristic X-ray analysis has attracted interest because this brand-new analytical method has significant potential to determine the isotope ratios without any destruction, which is desirable for rare and precious samples such as planetary samples and/or archaeological artefacts.

The muon is one of the charged leptons with a mass of 105.7 MeV/c2, approximately 200 times heavier than the electron. In the classical Bohr model, orbital radii of negative leptons (electron and/or muon) around an atomic nucleus are inversely proportional to the lepton mass. Because the energy gaps between orbits are also proportional to the lepton mass, cascade transitions of the trapped muon from higher- to lower-energy states emit the muonic characteristic X-ray with c.a. 200 times higher energy than that associated with the orbital transition of electrons. (For instance, electron-induced Kα–X-rays of C and O have energies of 0.3, 0.5 keV, respectively, whereas muonic Kα–X-rays of C and O have energies of 75, 134 keV, respectively.) We have successfully applied this sophisticated non-destructive elemental analysis to various meteorites and the returned sample from C-type asteroid Ryugu (Terada et al. 2014, 2017; Osawa et al. 2015, 2022; Nakamura et al. 2022, Chiu et al. 2023; Ninomiya et al. 2024).

Interestingly, the innermost orbit of the muon (the 1 s orbit) is extremely close to the nucleus and tends to be affected by the distribution of the nuclear charge. Therefore, the energy of characteristic X-ray changes depending on the mass of nuclides, which is called “isotope shift”. So far, energy shifts of some enriched isotope metals have been confirmed: Zn (Jenkins et al. 1970), Sn & Nd (Macagno et al. 1970), Ba (Kunold et al. 1983), Mo (Schellenberg et al. 1984), Ba (Kunold et al. 1983), Te (Shera et al. 1989), Sm (Strasser et al. 2009) and so forth. Recently, our research team also successfully demonstrated that the energy shifts of “normal” Pb metal (Ninomiya et al. 2019) and “normal” Ag metal (Osawa et al. 2020) can be detected using the pulsed muon beam at J-PARC (the Japan Proton Accelerator Complex (J-PARC)). It is well known that the Pb isotopic ratios are very informative not only for chronology in Earth and planetary science but also for identification of the production area of archaeological artefacts in archaeology. As a next step, we have applied this sophisticated method to natural terrestrial samples, specifically to galena (PbS) to determine the Pb isotope ratios non-destructively using a direct current (DC) muon beam (Fig. 1).

Fig. 1
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Schematic view of the principle of muon-induced characteristic X-ray

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Method and experiment

The MUon Science Innovative Channel (MuSIC) facility at Research Center for Nuclear Physics (RCNP), Osaka University, Japan, was designed to produce a direct current (DC) muon beam with an extremely high proton-to-muon yield (108 muons/s with a 0.4 kW proton beam, 392 MeV proton energy with a current of 1 μA (Fig. 2a). In order to produce an intense muon beam from the 0.4 kW proton beam, a novel pion capture system has been employed (Hino et al. 2014). A continuous proton beam extracted by a cyclotron accelerator bombards a cylindrical graphite target (4 cm in diameter and 20 cm in length) to produce pions that decay into muons and two neutrinos with a very short lifetime (26 ns). The momentum peak of the MuSIC muon beam at the current setting is ~ 70 MeV/c with a beam size of 5 cm. Since the first light of a muon beam in 2014, MuSIC has provided an intense DC muon beam with a momentum range of 20–120 MeV/c (Kohno 2015; Cook et al. 2017), which can also be applicable for non-destructive elemental analysis (Terada et al. 2017).

Fig. 2
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a An entire view of the MuSIC (Muon Science Innovative Channel) beamline at RCNP (Research Centre for Nuclear Physics), Osaka University. b Outlet of the muon beam at the MuSIC. c A schematic illustration of an analytical setting

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In this study, we conducted a muonic X-ray measurement of two samples: an enriched 208Pb sample (Φ30 mm × 0.35 mm: Pb ingot from ISOFLEX USA, 208Pb: 99.57%, 207Pb: 0.35%, 206Pb: 0.01% and 204Pb: 0.07%) and natural galena (PbS) from the Osarizawa mine, Japan (15 mm × 25 mm × 13 mm: 208Pb: 52.8%, 207Pb: 20.9%, 206Pb: 24.9% and 204Pb: 1.4% determined by LA-ICP mass spectrometry). The samples were placed in the centre of the muon beamline, 135 mm from the beamline exit. For X-ray detection, two high-purity germanium detectors were used for X-ray detection. One is the GC6020 (CANBERRA) with a diameter of 51.8 mm, and another is the BE3830 (CANBERRA) with a diameter of 30 mm.

Figure 2b, c illustrates the geometry of the analytical setting. Two Ge detectors were oriented at 90 degrees to the muon beam and GC6020 and BE3830 were placed at distance of 90 mm and 80 mm from the sample, respectively. A pair of plastic scintillators with the size of 30 mm × 30 mm that detect the muon passage was also placed in front of the sample to trigger the X-ray counting system. By counting X-ray signals coincident with the signal from the plastic scintillators, we were able to reduce the signal-to-noise ratio dramatically. More details of the analytical setting are written in Ninomiya et al. (2022).

The muon flux on the sample was estimated as 500 muons/s by the counting rate of the plastic scintillation counters. The muon momentum was set to 60 MeV/c to obtain enough muon intensity. The exposure times to the muon beam were 2.0 h for the enriched 208Pb sample and 6.4 h for the natural PbS, respectively.

Results and discussion

Figure 3a, b shows the muonic X-ray spectra obtained from an enriched 208Pb sample and the natural galena (PbS) using the Ge-detector GC6020. Various muonic X-rays of Pb, such as Pb2-1, Pb3-2, Pb5-3, Pb4-3 and Pb5-4, are detected due to a muon cascade process. On the other hand, the S2-1 peak at 516 keV appears only in the energy spectra of PbS (Fig. 3c). Other sulphur peaks are not shown because the energy of their muonic X-rays are too low (for example, 100 keV for S4-2 and/or 133 keV for S3-2) in this experimental setting. Some gamma rays from the decay of thallium (Tl), which was a by-product of the muon nuclear capture such as 208Pb (μ−, 0n) 208Tl, were also detected. The details of gamma rays from the decay of thallium (Tl) were discussed in Kudo et al. (2019).

Fig. 3
figure 3

a, b Whole muonic X-ray spectra of an enriched 208Pb sample and the natural galena (PbS) obtained by Ge-detector GC6020. Cascading muonic Pb X-rays such as Pb2-1, Pb3-2, Pb5-3, Pb4-3 and Pb5-4 lines were clearly observed. c Enlarged X-ray spectrum around 510 keV. Due to the S2-1 X-rays (516 keV), it can be observed that the peak width of PbS is broadened in comparison with that of the enrich 208Pb sample

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Figure 4a shows an enlarged view of the muonic Pb2-1 X-ray spectra (Kα1(2p3/2-1s1/2) and Kα2(2p1/2-1s1/2)) obtained by the Ge-detector GC6020. The enriched 208Pb sample shows a sharp peak, whereas the natural galena (PbS) has broad peaks with a tail on the high-energy side. It is noted that the low-energy component of the spread peak was consistent with the peak of the enriched 208Pb sample and that the higher energy of the spread peak was consistent with the expected energy of the muonic X-ray of 207Pb, 206Pb and 204Pb (Kessler et al. 1975).

Fig. 4
figure 4

a Enlarged view of the muonic Pb2-1 X-ray region. Due to the large energy splitting between muonic 2p1/2 and 2p3/2 states, Kα1(2p3/2-1s1/2) and Kα2(2p1/2-1s1/2) X-rays appear in two different energy regions. Each peak was a single sharp component in the enriched 208Pb sample (blue line); on the other hand, it was broadening due to the presence of the lighter isotope of Pb in the PbS sample (red line). b, c Expanded spectrum of muonic Kα1 X-ray and Kα2 X-ray of Pb with the fitting component by four Gaussian functions with fixed peak width for 208Pb, 207Pb, 206Pb and 204Pb, where the peak centres of 206Pb, 207Pb and 204Pb were also assumed to be the literature values (Kessler et al. 1975)

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Because the muon capture probability for each lead isotope is the same, that is, the sensitivity of each isotope is identical, the intensity ratio of muonic X-rays from 208Pb, 207Pb, 206Pb and 204Pb must be consistent with the isotopic composition. In order to derive the Pb isotopic composition, we carried out the deconvolution of the broad peaks by four muon-induced characteristic X-ray peaks as follows. First, the single peaks of the Kα1(2p3/2-1s1/2) and Kα2(2p1/2-1s1/2) X-rays of the enriched 208Pb sample were fitted with a single Gaussian function, determining the peak centre and peak width. Then, the broad Kα X-rays peaks of the natural galena (PbS) were fitted with four Gaussians functions for 208Pb, 207Pb, 206Pb and 204Pb with fixed the peak width, where the peak centres of 207Pb, 206Pb and 204Pb were also assumed to be the literature values (Kessler et al. 1975). The obtained isotope ratios of Pb of the natural galena from the two X-ray peaks of two detectors are summarized in Tables 1 and 2, respectively. As shown in Fig. 5, the four-averaged isotope ratios obtained from the muonic Pb characteristic X-ray are in close agreement with those determined by the LA-ICP mass spectrometer within one sigma level. Thus, this study has demonstrated for the first time that the DC muon beam analysis is feasible for non-destructive isotope measurement of heavy elements in the natural samples, although the accuracy and precision are still insufficient for conducting the latest research in the research field of Earth and planetary science and archaeology (Table 3).

Table 1 Observed peak area and Pb isotope ratios from transition of 2p1/2-1s1/2
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Table 2 Observed peak area and Pb isotope ratios from transition of 2p3/2 → 1s1/2
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Fig. 5
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Comparison with the four-averaged isotope ratios obtained from muonic characteristic X-ray with those determined by the LA-ICP mass spectrometer of the natural PbS (galena). Error bars are one sigma level

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Table 3 Comparison of Pb isotope ratios of PbS obtained by muon analysis and LA-ICP mass spectrometer
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Finally, we emphasize that the isotopic shift in the energy of the muon-induced characteristic X-rays occurs for all isotopes (Wu and Wilets 1969; Engfer et al. 1974). This means that with further development of detectors, isotopic measurements of all natural samples (not only solid samples but also liquids and gases) can be taken non-destructively. Recently, advanced spectroscopy utilizing a transition edge sensor (TES) has been developed for harder X-ray spectroscopy (Guruswamy et al. 2018; Tatsuno et al. 2016; Okada et al. 2016). Great advantages of TESs are to provide an order of magnitude better energy resolution than semiconductor-based detectors (for instance, the achieved energy resolution is 5.2 eV FWHM at Co Kα (6.9 keV) by Tatsuno et al. (2016) and 22 eV at 97.43 keV by Bacrania et al. (2009). That means TESs and/or cryogenic microcalorimeter have a great potential to distinguish the muonic Kα peak for lighter elements such as C (75.26 keV for 12C and 75.31 keV for 13C) and O (133.544 keV for 16O and 133.572 keV for 18O), and determine the isotope ratios not only heavy elements but also lighter elements without any destructive analysis. MuSIC facility also plans to increase the beam intensity by 15 times by reconstruction of the AVF cyclotron accelerator, which would improve the counting statistics problem. Thus, interdisciplinary further development such as higher-intensity DC muon beams and higher-energy-resolution detectors for hard X-rays would bring new “eyes” to see through the isotopic composition of planetary materials and/or archaeology artefacts non-destructively.