Development of non-destructive isotope measurement of the natural galena (PbS) using negative muon beams

In Earth and planetary science, Pb isotopic composition is well known to play a key role in deciphering the origin and evolution of materials because they provide unique chronological and/or indigenous regional information as a radiogenic daughter nuclide from U and Th. To determine such an isotopic composition, mass spectrometers have been widely used over several decades, which requires a destructive/consuming treatment such as sputtering, laser ablation and thermal ionization. Here, we first report the non-destructive Pb isotopic measurement of natural galena (PbS) using the energy shift of muon-induced characteristic X-rays. The observed Pb isotopic composition of the natural galena is in good agreement with that obtained by conventional mass spectrometry. Such a muon-based Pb isotopic analysis method is expected to be applied to identify the production area of archaeological artefacts (e.g. bronze products), where non-destructive analysis is highly desirable compared to conventional mass spectrometry


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/c 2 , 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-Xrays 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(Terada et al. , 2017;;Osawa et al. 2015Osawa et al. , 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).

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 (10 8 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).
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

Results and discussion
Figure 3a, b shows the muonic X-ray spectra obtained from an enriched 208 Pb sample and the natural galena (PbS) using the Ge-detector GC6020.Various muonic X-rays of Pb, such as Pb 2-1 , Pb 3-2 , Pb 5-3 , Pb 4-3 and Pb 5-4 , are detected due to a muon cascade process.On the other hand, the S 2-1 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 S 4-2 and/or 133 keV for S 3-2 ) 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 208 Pb (μ − , 0n) 208 Tl, were also detected.The details of gamma rays from the decay of thallium (Tl) were discussed in Kudo et al. (2019).
Figure 4a shows an enlarged view of the muonic Pb 2-1 X-ray spectra (K α1(2p3/2-1s1/2) and K α2(2p1/2-1s1/2) ) obtained by the Ge-detector GC6020.The enriched 208 Pb 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 208 Pb sample and that the higher energy of the spread peak was consistent with the expected energy of the muonic X-ray of 207 Pb, 206 Pb and 204 Pb (Kessler et al. 1975).
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 208 Pb, 207 Pb, 206 Pb and 204 Pb 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 K α1(2p3/2-1s1/2) and K α2(2p1/2-1s1/2) X-rays of the enriched 208 Pb 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 208 Pb, 207 Pb, 206 Pb and 204 Pb with fixed the peak width, where the peak centres of 207 Pb, 206 Pb and 204 Pb 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).
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 K α (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 K α peak for lighter elements such as C (75.26 keV for 12 C and 75.31 keV for 13 C) and O (133.544 keV for 16 O and 133.572 keV for 18 O), 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.

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

Fig. 2 a
Fig. 2 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

Fig.
Fig. Whole muonic X-ray spectra of an enriched 208 Pb sample and the natural galena (PbS) obtained by Ge-detector GC6020.Cascading muonic Pb X-rays such as Pb 2-1 , Pb 3-2 , Pb 5-3 , Pb 4-3 and Pb 5-4 lines were clearly observed.c Enlarged X-ray spectrum around 510 keV.Due to the S 2-1 X-rays (516 keV), it can be observed that the peak width of PbS is broadened in comparison with that of the enrich 208 Pb sample

Fig. 5
Fig. 5 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

Table 1
Observed peak area and Pb isotope ratios from transition of 2p1/2-1s1/2

Table 2
Observed peak area and Pb isotope ratios from transition of 2p3/2 → 1s1/2

Table 3
Comparison of Pb isotope ratios of PbS obtained by muon analysis and LA-ICP mass spectrometer