## 3 Experimental Details and Results
Therefore, by applying a time-cut of \(-50\) ns \(<t_{diff}<50\) ns one selects primarily the  
Figure 3: **(top panel)** Percentage of muons stopping in each layer of the sandwich sample obtained from simulations (shown by solid lines) and experiment (points) for the three different layers Fe (blue line and blue filled circles), Ti (green line green filled squares) and Cu (red line and red filled diamonds). The inset shows a sketch of the orientation of the sandwich sample with respect to the negative muon beam and the thickness of the individual layers. Two black dashed lines are drawn at the intersection of the simulated curves. (**bottom** panel) The residuals (experimental-simulated) in percentage for the different data points. \(\mu\)-X rays of Fe (see Figure 4(ai), where the \(\mu\)-X rays of the N-series at 65.6, and 79.6 keV and of the M-series at 92.6, 134.9, 157.8, and 172.3 keV are observed, already reported in Refs. [59,62]). Here, \(t_{diff}\) is the time difference between the muon entrance counter and the germanium detector. Similarly, by using a time cut of 100 ns \(<\)\(t_{diff}\)\(<\) 200 ns, i.e., a time range where the \(\mu\)-X rays have already been emitted, the \(\mu\)-X rays are no more present in the histogram and solely the gamma-rays are obtained (see Figure 4(ai)). Figure 4(ai), exhibits the gamma-rays from the \({}^{54-56}\)Mn nuclei. None of those have been reported in previous works, probably because these transitions are at low energy. The energy values of these gamma-rays were taken from the adopted level schemes in National Nuclear Data Center (NNDC) [63]. Some uncertainty was related to the existence of the 126 keV state [61], as the observation of a 858 keV gamma-ray was reported, which is a result of the decay from 984 keV state to the 126 keV state. Our present data clearly confirms the existence of the 126 keV state, since we observed the 126 keV gamma-ray. Since the time difference between the emission of the \(\mu\)-X rays and the gamma-rays is very small, one would still observe the gamma-rays (but with much lower intensity compared to the \(\mu\)-X rays) also in the prompt \(\mu\)-X ray spectrum. We observe this in Figure 4a and some of these peaks are marked with a black dashed line. Figure 4(bi,ii) shows the \(\mu\)-X ray and gamma-ray spectra from Fe in the energy range 200-500 keV, measured using all the twelve coaxial detectors. We observe \(\mu\)-X rays of the L-series at 265.3, 268.9, 358.0, 362.0, 400.6, 404.6, 423.8, 427.8, 437.8, 442.5, 447.3, and 451.5 keV, as observed in Ref. [47]. The gamma-rays are from the \({}^{53,54,56}\)Mn isotopes. Figure 4c shows the \(\mu\)-X ray and gamma-ray spectra from Fe in the energy range 500-1000 keV, measured using again all the twelve coaxial detectors. Figure 4(ci) shows a \(\mu\) X-ray of 578.9 keV, but this does not belong to Fe. This is the muonic \(K_{a}\) line of Cl, which is present in the plastic (PVC), a cylindrical shaped plastic sample holder. It is to be noted that we also observed the muonic \(K_{\alpha}\) line of C at 75.2 keV (Figure 4(ai)). The gamma-rays are from \({}^{54,55}\)Mn, \({}^{53,54}\)Cr, and \({}^{56}\)Fe isotopes, as shown in Figure 4(ci). All these gamma-rays, except those of \({}^{53}\)Cr, were observed in the previous references. Figure 4d exhibits the \(\mu\) X-ray and gamma-ray spectra from Fe in the energy range 1000-2000 keV. The \(\mu\) X-rays of the K-series at 1253.06, 1257.19, 1522.3, 1615.3, 1658.2, 1681.7, 1695.7, and 1704.7 keV are observed (see also Ref. [60]). The gamma-rays originate from \({}^{53,54,55}\)Mn and \({}^{53}\)Cr isotopes. All these gamma-rays, except those of \({}^{53}\)Cr, were observed in the previous references. With respect to the muon lifetime (\(\tau_{\mu}=2.2\)\(\upmu\)s), the emission of muonic X-rays (\(\tau_{\text{X-ray}}<10^{-13}\) s) can be seen as in coincidence with the formation of the muonic atom, while the emission of gamma-rays (\(\tau_{\gamma}<10^{-12}\) s) in coincidence with the nuclear capture of the muon.