GermanIum array for non-destructive testing (GIANT) setup for muon-induced x-ray emission (MIXE) at the Paul Scherrer Institute

The field of elemental composition analysis can draw from a rich set of techniques. However, there is a lack of depth-dependent analysis beyond the surface, i.e., below the first 100 µm. Although one can cut or destroy an object of interest and fall back to the surface-sensitive methods, this is clearly not an option for numerous objects, e.g., precious samples such as cultural heritage artifacts or in situ and operando studies of Li-ion batteries. Muon-induced x-ray emission (MIXE), however, is a non-destructive technique with access to the bulk and depth-profiling capabilities.^1–5 

The required negative muon beams only exist at a few large-scale accelerator facilities such as the following: (1.) Paul Scherrer Institute (PSI), Switzerland; (2.) ISIS, Rutherford Appleton Laboratory (RAL), United Kingdom; (3.) TRI University Meson Facility (TRIUMF), Canada; (4.) Japan Proton Accelerator Research Complex, MUon Science Establishment (J-PARC MUSE), Japan; and (5.) MUon Science Innovative Channel (MuSIC), Japan. Among those, a proof-of-concept study showed that the continuous high-flux Swiss Muon Source (SμS) at PSI is highly suited to host an experimental MIXE station.⁶ Therefore, the Laboratory of Muon-Spin Spectroscopy (LMU) at PSI set out to develop a dedicated experimental station. The goal was to build a platform solution to fulfill the following conditions:

• It can be used in different configurations, e.g., number of detectors,

• It has a well-defined geometry for reproducibility (in following campaigns and simulations)

• It has an operation as a non-stationary experiment

• It has a high-beam (-time) utilization

The resulting setup presented here, the GermanIum Array for Non-destructive Testing (GIANT), marks the continuation of the development of state-of-the-art equipment like the μSR spectrometers at PSI by LMU.⁷ 

The interaction of negative muons with matter provides unique elemental sensitivity. Muons are transported by static electromagnetic optics and implanted into an object with a given momentum (typically 20–50 MeV/c). When implanting negative muons in the matter, the first deceleration processes taking place are similar to those for positive muons, i.e., electrostatic interaction with the outer electrons of the target atoms. This leads, for a large range of momentum, to a similar stopping power as the one for positive muons. Hence, negative muons exhibit a proton-like Bragg peak-stopping profile. The implantation depth spans from as little as 0.01 cm for 20 MeV and heavy elements like lead up to 1 cm for 50 MeV and typical plastics.⁸ The mean depth of resulting distributions is predominantly dependent not only on the object’s density ρ but also on its heterogeneity ρ(x). The spread of the implantation profile (straggling) is additionally dependent on the muon-beam momentum distribution. Common achievable depth resolutions range from 50 to 1000 µm, whereby a better resolution can be achieved at a cost of reduced muon-beam intensities, i.e., longer acquisition times.

A typical beam spot diameter, i.e., sample area illuminated, is of the order of 2 cm. The setup imposes little constraints on the upper limit of the overall object size. Typically, the samples are mounted in the air. However, measurements in different gas atmospheres or vacuum are also possible. Smaller samples with areas down to mm can be measured through collimation of the beam with the downside of a lower signal rate.

Another feature of MIXE is the ability to distinguish individual isotopes. Heavy elements like Ag have line splitting due to isotopic shifts on the order of several keV and are easily detectable. Even for lighter elements, recent advances with precise higher-order calculations of the transition energies¹¹ open up the possibility to analyze isotopes with overlapping lines. More detail and example are given in Sec. V D.

An example spectrum in Cu is shown in Fig. 1, where the peaks corresponding to different transition series are clearly visible. To acquire such spectra, the probability to measure the emitted muonic x-ray photons is a convolution of multiple factors. Depending on its energy, a photon will experience an attenuation by the sample itself, which will depend on the elements and density ρ(x) of the sample. Moreover, the geometrical configuration of the sample and the detectors may lead to different path lengths for the x-rays through the sample and solid angles covered by the detectors. Last, but not least, the detection efficiency and resolution of the detector are a function of the photon energy and require proper calibration protocols.

To assess the elemental composition of an object, there are generally two paths. One has to either apply several corrections or work with a set of reference samples such that the effects mostly cancel out. More details are presented in Sec. V.

The SμS at the Paul Scherrer Institute (PSI, Switzerland) encompasses the muon beamlines and instrument complex at PSI. It is fed by the three-stage high-intensity proton accelerators (HIPA) complex. The protons start with a pre-acceleration to 870 keV before being boosted to 72 MeV in the first cyclotron. The heart of the HIPA is the final acceleration with the main ring cyclotron to 590 MeV. With proton currents of up to 2.4 mA, it is one of the most powerful (1.4 MW) accelerators in the world.

The protons are utilized for the secondary particle production of neutrons, pions, and muons by the subsequent decay of the pions. Among the several beamlines capturing the produced particles, the five beamlines of the SμS (πM3, πE1, πE3, μE4, and μE1) hosting the experimental stations of the Laboratory of Muon Spin Spectroscopy (LMU) sit at the two-pion/muon production targets E and M. A schematic of the area is shown in Fig. 2.

All MIXE campaigns at PSI so far have been conducted at the πE1.2 beamline. The beamline can be operated both for negative and positive decay muons and pions and has two branches through the last three port dipole magnets. It hosts the permanently installed DOLLY μSR spectrometer in the πE1.1 area at the 90° port.¹² Using the second πE1.2 area, at the 38° branch, temporary experiments can also be installed. The current layout of the beamline is shown in Fig. 2. After capturing muons from the production target, a W-section of quadrupole and dipole elements allows the operation of an overall achromatic mode with a momentum dispersion within the second dipole. This second 30° dipole has an integrated horizontal slit system that is used to block parts of the muon beam, effectively reducing the momentum bite Δp/p by sacrificing rates. After the W-section, a spin rotator with up to ±250 kV serves not only for spin rotation for μSR experiments but also as a Wien filter, reducing the electron or positron contamination.

Momenta for negative muons with acceptable rates are between 20 and 50 MeV/c (see Fig. 3). This corresponds to a penetration of 0.04–1 g/cm².

The beam spot was characterized by a particle-tracing detector consisting of a quartet of micromega detectors. The Micromegas (MICRO MEsh GAseous Structure) is a type of micropattern gaseous detector, invented by Giomataris et al. in 1995.¹³ To study the size of the muon beam spot at the sample position, four Micromegas detectors (MMDs) arranged in a telescope were set up (see Fig. 4). These MMDs have an active area of 80 × 80 mm² and were originally used by the NA64 experiment at CERN.¹⁴ The MMDs were continuously flushed with a gas mixture of Argon/CO2 (82%/18%).

To reconstruct the beam spot, the muon beam was stopped at the sample position in a beam dump. Once the muons decayed, their decay electrons then traversed through the telescope and ionized the gas mixture. The freed electrons were guided by an electrical field of the order of 500 V cm⁻¹ through the micro-mesh into a second region, where a strong electrical field was applied (50 kV cm⁻¹). The free electrons were accelerated and gained enough energy to further ionize the gas, kicking off an avalanche process. At the end of this region, the local avalanche reached two differently oriented planes (X and Y) with each 320 readout strips, where the amplified signal could be read out, allowing for a hit reconstruction in 2D with a spatial resolution of the order of 100 µm. When at least three of the four detectors of the telescope had a hit recorded, a track could be fitted and extrapolated onto the sample position. The beam spot was reconstructed for different momenta, shown in Fig. 5. By fitting a Gaussian distribution in both the horizontal and vertical axes of the beam spot, its standard deviation was taken as a figure of merit for the beam spot size. The results are summarized in Table I.

The GIANT setup was built under the constraints mentioned in the introduction Sec. I. Not being a permanently installed experimental setup at PSI, but only used during beam times of a week length, quick setup times for high beam time utilization were required. Practically, it meant to develop a platform where electronics, cabling, and options for the alignment of the detectors and the overall setup relative to the beam could be prepared offline prior to the actual beam times. The requirement of reproducibility comes in two-fold. First, a preparation including cooling of the detectors and calibration of the setup outside the experimental area, transportation, and recommissioning requires to separate the fragile HPGe detectors from the setup for transportation. Hence, a quick and straightforward re-installation of the detectors at identical positions is compulsory. Second, to be able to correct the effects on the x-ray spectrum acquisition discussed in Sec. II, precise knowledge about the positions of the detectors is required. Last, but not least, an optimum use of the beam times is meant to reduce the duration of costly interruptions, e.g., sample changes and detector refills.

for a large number of photons (i.e., n_μ > 1), the detector size and quantum efficiency determine the maximum single-photon detection efficiency for a given detector. In the scenario of detector radius 5 cm and 100% interaction efficiency, the maximum single-photon probability is reached at P₁ ≈ 37%. One can imagine that the distance of a detector can always be tuned such that it covers the solid angle that corresponds to the highest probability to encompass only one photon. Needless to say that at high numbers of muons, this distance quickly becomes ridiculously large, e.g., n_μ = 100 corresponds to d = 1 m for this thought experiment. The overall DAQ rate of a setup is then merely an economical question by scaling through the number of present HPGe detectors.

Independent of the beam type (pulsed or continuous), care should be taken that the HPGes are not exposed to large backgrounds from beam halos, misguided, or secondary particles and their bremsstrahlung that are typically about FWHM ≈ 108 cm for the here addressed muon beams that all have beam spots in the cm range.

These considerations give a very rough understanding of how different muon beams, facilities, and/or setups could be compared in terms of maximum achievable DAQ rates for a given muon rate (and/or pulse rate) per single detector.

• The ideal facility would deliver 1 muon every 10 us, i.e., be a pulsed muon beam with n_μ = 1 on target for any given momentum (consider in-flight decays to determine the muon rate at the source or elsewhere) with a repetition rate of 100 kHz. The HPGe detector placement can then be tuned for maximum efficiency to achieve a signal detector DAQ rate of 38% · 100 kHz = 38 kHz.

• At the Swiss Muon Source (SμS) at PSI a typical muon rate of 50 kHz for momenta used for archaeological samples gives a singe-detector DAQ rate of ≈108 kHz.

• ISIS at RAL is based on a pulsed beam with a 50 Hz repetition rate and a maximum total $≈5MHz$ negative muon rate.³ Thus, the DAQ rate for a single detector is about 20 Hz for this approximation.

• MUSE at J-PARC provides up to 10 MHz of muons as a pulsed beam with about 4 *10⁴ muons per spill at a repetition rate of 25 Hz.^17,18 Therefore, the maximum DAQ rate per detector is ≈10 Hz.

• MuSIC at RCNP delivers around 500 Hz of continuous negative muons according to a work done by Ninomiya et al.¹⁹ Therefore, the DAQ rate would be ≈190 Hz.

• TRIUMF has a beamline (M9H) with negative cloud muons under construction with a beam expected in 2024.²⁰ An experiment from Grossheim et al. in 2009 reported a negative muon rate of 80 Hz for the study of ²⁷Al²¹ at another beamline. However, currently, no MIXE negative muon program is active.

A true comparison would, however, require a standard set of samples to be studied and compared across facilities and should encompass other variables such as depth resolution, i.e., momentum bite, beam spot, etc., or at least a report on the DAQ rate. It leaves to say that of course, a pulsed beam has advantages when studying short-timescale (∼ us) dynamic phenomena because of the ease to trigger a reaction in relation to the trigger pulse. At a continuous source, mere random sampling only becomes advantageous when the higher rate and wanted sampling rate give an advantage in terms of the underlying Poisson probability. However, for the case of MIXE, no experimental interest in a US scale application has been done yet. The only time-dependent study to date is the characterization of Li-ion batteries during cycling²² on an hourly scale. Moreover, the higher overall rate at the pulsed muon beam facilities ISIS and MUSE can allow more stringent collimation and reduction of the beam without losing single-detector DAQ rates than at the continuous muon beam facilities. The interested reader may inform themselves further with the following publications that provide a more detailed sample-dependent description of the measurement conditions at the individual facilities; with this general review about muon spectroscopy,²³ measurements at ISIS; a review of performed measurements,²⁴ instrument characterizations,^3,25 precious metal objects,^2,5,25,26 at MUSE at J-PARC; on meteorites,¹⁷ batteries,²⁷ precious metal objects,^28,29 at MuSIC at RCNP; study of meteorites,³⁰ and at SμS at PSI; proof-of-concept,⁶ meteorites,³¹ batteries,²² and archaeological precious metal objects.³² 

The considerations and the comparisons above highlight that for proper optimization of a MIXE setup, a set of rigorous simulations is required. For the case of the GIANT setup at PSI, limited development time led to the construction of a versatile instrument that fulfills the stated requirements and allows a later optimization. A picture of the setup is shown in Fig. 6. Most of the mechanics were done with aluminum construction profiles. The maximum capacity of the system is to host 22 HPGes. The first campaign in 2021 only used six detectors, with later increments to 11 and 14 HPGes for the latest 2022 measurement period. Performance and detection efficiencies are presented in Sec. V. The used HPGe detectors are from Mirion Technologies with 7 l liquid nitrogen (LN₂) BigMac cryostats. To have proper detection efficiency and energy resolution over the full-energy range, both planar (low-energy) and co-axial (high-energy) detectors are used. Each detector is held in a frame that allows easy (dis-) mounting and distance adjustment. The angular alignment is solved by combining multiple detectors on vertical arms. An arm can be freely positioned at a wanted angle in the horizontal plane θ and carry up to four detectors. The angle between two detectors in the vertical plane of an arm has to be Δϕ ≥ 35°. Maximum angles are ϕ = ±55° with ϕ = 0 being horizontal. The arms are fixed on a central axis to create a common focal point for all detectors. Models of the individual elements are presented in Fig. 7. Such an ensemble is mounted to a larger platform that also hosts the electronics and LN₂ distribution. The platform runs on rails parallel to the beam axis to easily (dis-)engage the beam port with the whole setup. On starting the beam time, the reproducibility and integration of electronics allow us to push the setup time (mechanical, electrical, and cryogenic setup and commissioning) down to ≈4 h.

To reduce the background of uncorrelated signals in the germanium detectors a typical scheme for continuous beams is to use muon tagging. All MIXE campaigns at PSI so far were making use of the plastic scintillator setup developed originally for the muX experiment.³³ It is composed of a 200 µm × 25 mm × 25 mm scintillating plastic polyvinyltoluene (BC-400), called M-counter, masked with an 8 mm × 10 cm × 10 cm BC-400 veto counter with an 18 mm central hole. The scintillators are paired with Silicon Photomultipliers (SiPMs) and in-house developed pre-amplifiers.

With samples of various dimensions and compositions, each sample requires individual alignment. To maximize the beam utilization, the time-intensive sample mounting and alignment are not performed on the instrument itself. A copy of the sample mount and a laser mimicking the focal point of the detectors and muon beam allows us to prepare the sample without interrupting the beam. On sample change, the prepared adapter only needs to be transferred to the setup in the experimental area resulting in a downtime of less than 5 min.

Common materials hosting the often-fragile samples (e.g., archaeological objects) are low-density polyethylene (PE) foam, Al, or Cu wires. If a sample has (partial) transparency for muons, a controlled beam dump of 1 cm PE or 5 mm Al to stop 45 MeV/c muons can be used. For small objects and especially for the measurements of lateral sub-regions of a larger object, the mounts can be combined with a collimator out of PE or Al.

The efficiency and energy calibration of the setup was done with a large set of radioactive sources in combination with measurements of pure samples. Details are presented in Sec. V A.

Another potential beam time interruption is the filling of the LN₂ dewars of the HPGe detectors. Remedy comes by remote control of the refilling process. The cryostats are connected through a network of relay-switched solenoid valves to a 200 l storage dewar at 1.5 bar. To monitor the filling process K-type thermocouples installed in the LN₂ return lines serve as a cost-effective reading to distinguish N₂ from LN₂. A time series of the filling process and the temperature-calibrated thermocouple values are shown in Fig. 8.

All detectors, HPGe and plastic scintillators, are connected to 16-channel SIS3316 14 bit 250 MSamples Versa Module Europa (VME) digitizers from Struck Innovative Systems (SIS). The communication with the DAQ computer is done via glass fibers between a VME communication module SIS3104 and a PCI card SIS1100. All software front- and back-ends are based on the maximum integrated data acquisition system (MIDAS).³⁴ Signals from the detectors are passed through a trapezoidal filter on the field-programmable gate array (FPGA) chip of the SIS3316 module with parameters optimized for each channel to provide analog digital converter (ADC) values related to the energy of the signal. In parallel, the rising edge of the HPGe waveforms is digitized for the 300 − 400 × 4 ns samples to allow later timing, pile-up, and energy corrections. Such corrections and coincidence handling between plastic scintillators and HPGes are performed offline on another analysis server.

The energy and efficiency calibrations of the HPGe detectors are performed using standard radioactive gamma-emitting sources with known activities and reference dates. As an example, the calibrations performed during the first MIXE campaign in 2021, when there were six HPGe detectors placed in the GIANT setup, are shown in Fig. 9. The distance between the focal point and the surface of the detectors was ∼145 mm. The standard radioactive sources (with a 3% error on the activities from the manufacturer) of ⁸⁸Y, ¹⁵²Eu, ²⁴¹Am, ²¹⁰Pb, ⁶⁰Co, ¹³³Ba, ⁵⁷Co, and ¹⁰⁹Cd were used for calibration purposes. With these sources, the calibrations could be performed only up to ∼1.8 MeV. Hence, the 2614.511(10) keV of ²⁰⁸Tl (produced during the decay of ²²⁸Th), present in the natural background run, was also taken into account. In addition, the K_α1 muonic x-ray of 208Pb (present in natural-Pb) at 5963.77(45) keV (determined precisely in 1970s³⁵) was used to extend the calibration points up to ∼6.0 MeV. Figure 9(a) shows the energy calibration data points along with the fits (using a quadratic polynomial function) for the six detectors, the details of which are shown in the figure legend. The data points for absolute efficiency and the sigma of the peaks (fit with a Gaussian function) until ∼1.8 MeV are shown in Figs. 9(b) and 9(c), respectively. The data points in Fig. 9(c) are also fit with a quadratic polynomial function. From Fig. 9(b), it is evident that the “GR” detectors have higher efficiency than the “BE” detectors at higher energies. However, the “BE” detectors have much better resolution than the “GR” detectors at all energies, as evident from the plots in Fig. 9(c).

In the offline analysis, before analyzing the in-beam spectra from the actual samples, two different corrections are employed, by using the digitized preamplifier pulses of each HPGe detector: (i) baseline corrections and (ii) timing corrections. The details on these corrections can be found in Ref. 36.

A typical HPGe preamplifier pulse/waveform, corresponding to a single muon event, is shown in Fig. 10(a), with the three different parts indicated. An important feature to be noted is the constant baseline of the preamplifier pulse, as shown in the inset of Fig. 10(a). The maximum amplitude of this pulse is proportional to the energy of the muonic x-ray for that particular muon event. At high muon momentum, the muon rate increases (see Fig. 3), and pile-up effects in the HPGe detectors are visible. One effect is the partial overlapping of the preamplifier pulses from two consecutive muon events, leading to a non-constant baseline, as shown in Fig. 10(b) and the inset within. This effect leads to an underestimation of the energy deposited by the muonic x-ray in the detector, resulting in a pronounced low-energy tail on the peak in the energy spectra. By performing baseline correction, the true height of the pulse (i.e., the muonic x-ray energy) can be reconstructed. These tails are not only seen in the in-beam spectra but also in radioactive sources with very high activity. As an example, the uncorrected ADC spectrum from one single detector, obtained from a highly active ²²⁸Th radioactive source has been shown by the black spectrum in Fig. 10(c). As can be seen from the red spectrum in Fig. 10(c), the baseline correction not only removes the low-energy tails but also improves the peak-to-background ratio. A notable feature worth mentioning is the peak hidden within the tail marked by the black arrow [see Fig. 10(c)]. The inset of Fig. 10(c) shows the energy-calibrated baseline-corrected spectrum with all the peaks from the different decay products of ²²⁸Th marked [see Fig. 10(d) for the decay chain of ²²⁸Th].³⁷ 

The SIS3316 digitizer uses the Leading Edge Threshold (LET) algorithm to extract the time from the pre-amplifier pulse, which is unfortunately very sensitive to jitter and walk effects. Hence, in the current analysis, the Extrapolated Leading Edge Threshold (ELET) algorithm has been used in the offline analysis to achieve better timing information. The measured time t_diff of a muonic x-ray event is determined with respect to the observed time of a muon detected in the muon entrance detector. The 2D plot of the muonic x-ray energy vs the measured time for one of the HPGe detectors, obtained during the experiment, is shown in Fig. 11(a). The time offset and ELET corrections ensure that all the detectors are properly time aligned and that the time resolution is reasonable at all energies [see Fig. 11(b)]. The best-timing resolution we could achieve is ∼20 ns at 1 MeV. Such good timing resolution of detectors is necessary to discriminate between background, prompt and delayed signals.

Once all the calibrations and the offline corrections are performed, the spectra can be analyzed to quantitatively determine the elemental compositions of the investigated samples. For this step, one makes use of the existing databases and/or software to determine the muonic x-ray energies and compare them with the experimental spectra to deduce the elements present in the sample.^11,38 To determine the elemental composition, two different approaches can be followed: (i) to make use of the calibration curves (i.e., the ratio of K_α or L_α lines vs ratio of at. % of the two different elements), obtained from reference standards, which have a similar elemental composition to the investigated sample, or (ii) to directly determine the at. % from the intensities of K_α muonic x-ray peaks of the different elements present in the sample. For the later approach, great care must be taken to correct the observed intensities for the effects of the detector efficiency, the muon capture probability, and the branching ratio of the K_α peak.

In both the above approaches, one would need to take into account the mass attenuation of the muonic x-rays inside the sample itself [see Eq. (10)]. For the mass-attenuation effects, there are many added complications that need to be taken into account for an accurate analysis, like (i) beam-spot size on the sample, (ii) distribution of muons across the beam-spot, (iii) scattering of muons with the sample, (iv) contribution of attenuation due to additional collimators/beam dumps, (v) non-uniform density of the sample, (vi) porosity of the sample, (vii) complicated geometry of the sample, (viii) position of the individual detectors on the array, etc. Since attenuation coefficient is dependent on the density of the sample, which may not be known for many of the samples, one needs to perform an iterative analysis to arrive at the precise composition. This calls for an extensive dedicated Geant4 simulation framework, which is currently under development.

As mentioned in Sec. V B 2 and in Ref. 6, time-cuts can be performed to separate the prompt and delayed events. Figures 12(a) and 12(b) show the prompt spectra (−50 < t_diff < 50 ns), from a single HPGe detector, obtained from a B30 aluminum bronze alloy from Schmelzmetall AG³⁹ in the energy ranges 250–600 and 1100–2200 keV, respectively. The peaks from the elements Cu, Al, Fe, and Ni can be identified, shown by brown, green, red, and blue colors, respectively. According to the company’s datasheet,³⁹ the guaranteed ranges of the chemical composition (in wt. %) for this sample is 10.5%–12.5% Al, 5.0%–7.0% Fe, 5.0%–7.0% Ni, max. 1.5% Mn, others 0.5%, and the rest is Cu. The inset in Fig. 12(b) shows the delayed spectrum (100 < t_diff < 200 ns), where the muonic x-rays are no longer observed, and only the gamma-rays from the different isotopes of Ni (nuclear capture of muon by Cu nucleus results in Ni nucleus) are seen. The gamma-rays are marked with brown arrows in Fig. 12(b) and the inset. The gamma-rays thus act as an additional confirmation to the muonic x-rays on the most abundant elements in the sample.

In addition to the elemental analysis, the MIXE technique also allows one to identify the isotopic ratios of elements. Besides the other advantages mentioned above, this is an additional pro over the usually used non-destructive x-ray fluorescence technique (XRF), which cannot identify the isotopes. The techniques used nowadays for isotopic analysis are multiple-collector inductively coupled plasma mass spectrometry (MC-ICP-MS), thermal ionization mass spectrometry (TIMS), and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS), all of which are destructive methods but provide highly precise isotopic ratios.^40–42 

With the GIANT setup, it has now been possible to determine the isotopic ratios of elements with atomic number Z > 20 by using the K_α muonic x-ray peak. An example of such a spectrum, obtained from an individual HPGe detector, for a pure Cu sample, along with the fits, is reported in Fig. 13. Natural-Cu has two stable isotopes ⁶³Cu and ⁶⁵Cu with natural abundances of 69.15(15)% and 30.85(15)%, respectively.³⁷ This corresponds to an isotopic ratio ⁶⁵Cu/⁶³Cu = 0.446(2). The K_α1 and K_α2 muonic x-ray energies for these isotopes were determined using Mudirac software,¹¹ as shown in the third column of Table III. The fourth column shows that the ratio K_α2/K_α1 ∼ 0.5 for both the Cu isotopes, which is the expected value from theoretical considerations. The isotopic ratio obtained for both K_α1 and K_α2 transitions, shown in the fifth column, is ∼0.4, which is in reasonable agreement with the experimental value of 0.446(2). However, for the proper characterization of the GIANT setup for these isotopes, it is necessary to measure industrial standards and also compare the ratios obtained with samples measured with the other destructive methods. In addition, the ability to disentangle between muonic x-rays and gamma-rays opens up an alternative route to use gamma-rays (see Sec. V C) to determine the isotopic ratios.

An important application of isotopic ratio determination is in the field of archaeology to deduce the provenance of an excavated artifact. An important element used in such provenance studies is to determine the isotopic ratios of Pb (which has four stable isotopes ^{204,206,207,208}Pb) present in the artifact.⁴³ The natural abundances of these isotopes are ²⁰⁸Pb(52.4(1)%), ²⁰⁶Pb(24.1(1)%), ²⁰⁷Pb(22.1(1)%), and ²⁰⁴Pb(1.4%).³⁷ However, since K_α muonic x-ray energy of Pb isotopes is at ∼6 MeV, where the efficiencies of the HPGe detectors is low and since Pb content in such artifacts is also low (usually less than 5%), this calls for long measurement times in order to determine precise ratios.

From the above sections, it is evident that the usage of MIXE with GIANT using the continuous muon beam at PSI is most suitable for doing applied research. The areas of applied physics, where MIXE has already been used in the campaigns so far, are (i) Li-ion batteries from Empa, Switzerland,²² (ii) metallic archaeological artifacts from the Augusta Raurica Museum, Switzerland,³² and (iii) meteorites from the Natural History Museum, Bern.³¹ 

The MIXE activities at PSI are ongoing with several projects in the pipeline. A collaborative effort for an AI-based automatized muon beam tuning to rapidly change between momentum settings at optimal conditions has started. To further optimize the utilization and reduce the workload for users, an automatic sample changer is being planned. This empowers recent collaborations with industry via ANAXAM (Non-profit technology transfer and access point of large-scale research infrastructure at PSI to industry). Moreover, work on a full-scale Geant4 model of the setup and MIXE physics is underway to allow for a rigorous systematic study and a higher level of corrections and optimization of MIXE.

The GIANT setup was built at PSI and successfully used in multiple MIXE campaigns acquiring up to 500 spectra per year with about three weeks of beam time. With a strong focus on versatility and reproducibility, it is forming the basis of the ongoing developments and improvements at LMU. A single spectrum with decent statistics to reach a sensitivity of ≈1 at. % is possible within about 1 h of data taking. This is thanks to the high rate but low pile-up of the continuous muon beam at the SμS (compared with pulsed beams). The calibration with a set of radioactive sources results in an average detector photo peak efficiency $ϵ̄≈0.11$ % and energy resolution σ_E = 0.8 keV at E = 1000 keV. During the last campaign (09.2022), a mix of planar and coaxial, totally 14, detectors were used. Initial corrections using digitized waveforms of the rising edge of the detector signal already proved to be valuable. For example, isotope fractions of elements like copper with overlapping lines, i.e., isotope shift smaller than the energy resolution, can be readily resolved. The availability of the MIXE technique at PSI has led to a rich user base engaged in various lines of research. Among already measured samples are archaeological objects, several series of Li-ion battery studies, meteorites, oxidation states of metals, and environmental samples showing unprecedented results.

Our research was funded by the Swiss National Science Foundation, Sinergia project “Deepμ,” Grant No. 193691 (https://www.psi.ch/en/smus/muon-induced-X-ray-emission-mixe-project, accessed on 30 August 2022). The realization of the MIXE project own thanks to numerous people at PSI as also external. Initial concepts and design choices for the structure profited from discussions with the technical staff of the LMU Hans-Peter Weber and Matthias Elender. Enormous effort for the operation of the setup during the beam times was done by numerous people from the LMU; Zurab Guguchia, Charles Hillis Mielke III, Debarchan Das, Fabian Hotz, Zaher Salman, Toni Shiroka, and Chennan Wang. Putting the setup together and getting necessary customs parts would have not been possible without the great infrastructure at PSI, i.e., the Workshop, Lager/Shop, Liquid Gases Group, Electricians and the Hallendienst with a special shoutout to Roger Schwarz. A huge thanks goes to Andrea Raselli, Andreas Suter, and Robert Scheuermann for the continued IT, DAQ and MIDAS support. In general, the collaboration with the muX experiment allowed us to kick-start the MIXE endeavor at PSI. A special thanks within the muX team goes to Frederik Wauters for his nuanced help with the software side of the DAQ. The mutual assistance with the muMASS experiment for the micromegas and the OMC4DBD collaboration, Osaka university, Tokyo University and RIKEN Nishina Center for Accelerator-Based Science and the Radiochemistry Group of PSI for the mutual lending of HPGes. Moreover, no research at the HIPA facilities would work without the PSI Division GFA, a tremendous acknowledgment to all personnel involved in the operation of the main proton beam and the secondary beamlines with special mention of Thomas Rauber and Patrick Simon for on-site support at the πE1 beamline. Last, but not least, technical and physics discussions with Aldo Antognini, Paolo Crivelli, and Anna Soter helped to shape the GIANT setup.

The authors have no conflicts to disclose.

Lars Gerchow: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Sayani Biswas: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Gianluca Janka: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Carlos Vigo: Formal analysis (equal); Investigation (equal); Software (equal); Validation (equal); Writing – review & editing (equal). Andreas Knecht: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal). Stergiani Marina Vogiatzi: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal). Narongrit Ritjoho: Data curation (equal); Investigation (equal); Writing – review & editing (supporting). Thomas Prokscha: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Hubertus Luetkens: Investigation (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Alex Amato: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.