## 3 Experimental Details and Results  
The MIXE experiment was performed using the \(\pi\)E1 beamline, fed by the High Intensity Proton Accelerator (HIPA) [50] of the Paul Scherrer Institute (PSI), Switzerland. This beamline is capable of delivering positive or negative muons [51]. With this beamline, we could achieve typical muon rates of \(\sim\)1.5 kHz and \(\sim\)60 kHz at momentum \(p=20\) and 45 MeV/c, respectively, with momentum bite \(\Delta p/p=2\%\) (\(\sigma=\Delta p\)). We also observed a pile-up of \(\sim\)1% with the muon rates of \(\sim\)60 kHz. Even at momentum bite of 0.5%, we could obtain reasonable muon rates, which would be ideal for the investigation of thin samples. As the \(\pi\)E1 beamline of the HIPA accelerator complex at PSI delivers a continuous beam, one has to detect the individual arrival time of each muon using a muon entrance detector, made of polyvinyltoluene (BC-400), and of \(\sim\)200 \(\upmu\)m thickness. In addition, a 5 mm thick BC-400 muon counter with a 18 mm (diameter) hole was placed just before the muon entrance counter. This detector served as a collimator and veto detector at the same time. Together with a 1.5 m drift tube, from the last quadrupole of the beamline to the muon detector arrangement, this guaranteed that the long focal distance resulted in a similar sized beam spot on target. The experimental apparatus (see Figure 1 and [52]) was originally developed for the muX experiment [53]. It consisted of a planar detector and a stand-alone coaxial detector (efficiency, \(\epsilon\sim\)70%) from PSI; a stand-alone coaxial detector (\(\epsilon\sim\)75%) from KU Leuven; one MINIBALL cluster module, with three detector crystals (\(\epsilon\sim\)60% each), from KU Leuven [54]; seven compact coaxial detectors (\(\epsilon\sim\)60%) from the IN2P3/STFC French/UK Ge Pool [55]; and a low-energy detector from ETH Zurich. So, in total we had twelve coaxial and two low-energy Ge detectors. Out of the above-mentioned detectors, two of these had a BGO anti-Compton shield. The timing resolution of this setup was \(\sim\)50 ns and \(\sim\)20 ns at 200 keV and 1 MeV, respectively. The energy and efficiency calibrations for this detector setup was done using the standard radioactive sources of \({}^{152}\)Eu, \({}^{88}\)Y, \({}^{60}\)Co and \({}^{137}\)Cs. The target consisted of a three-layered sandwich sample of iron (Fe), titanium (Ti), and copper (Cu) plates and was placed in vacuum. Each layer was 500 \(\upmu\)m thick with a diameter of 26.5 mm. There were two main purposes of measuring such a sandwich sample consisting of pure elements: (i) to demonstrate the possibility of measuring the different \(\mu\)-X rays and gamma-rays for different elements, (ii) to determine if by changing the muon momentum, we are able to probe the element present at different depths inside the sample and how such measurements correlate with simulations for penetration depths of negative muons. Hence, the measurement of such a simple sample acts as proof of principle for later precise measurements on actual samples like archaeological artefacts, battery and meteorite samples where the depth-dependent elemental compositions are of interest. The simple geometry of the sample was also chosen to benchmark our results with the ones obtained in a similar sample at the pulsed muon source ISIS [29]. Figure 1: A photograph of the experimental setup showing the assembly of the detectors. The sample was measured at six different muon momenta, \(p\) = 28.6, 35.0, 37.5, 40.0, 42.5, and 45.0 MeV/c, with momentum bite \(\Delta p/p\) = 2% (\(\sigma=\Delta p\)). A data collection time of \(\sim\)30 min was used for each muon momentum. The statistical uncertainty of the presented raw spectra follows the Poisson statistics (\(\sigma=\sqrt{N}\)) and is therefore omitted in the figures for visibility of the smaller peaks. A comparison of the presented spectra to data, taken at other facilities can be performed, by taking into account the according bin widths (stated in the y-labels).