## 3 Experimental Details and Results
This opens the possibility of statistically intense applications like an elemental 3D-tomography employing a transmission muon tracker (a hodoscope similar to the one described in Ref. [18]). The continuous muon beam of PSI will allow the unique feature of individual muon tracking. Therefore, in contrast to scanning techniques by collimation, a 3D tomography at PSI will not hamper any rates or efficiencies discussed in this manuscript. Thus, the overall acquisition time scales only with the chosen discretization. The use of such a hodoscope would also allow a superior offline collimation compared to the common practice of physical collimation, as employed with our veto counter. An adapted collimation on a sample-by-sample basis is e.g., important for cases of in-planar inhomogeneity and/or for a region-of-interest smaller than the beam spot. Figure 2: The counts (N) of the muonic X-ray spectrum in the energy range 900 to 2150 keV, from all the twelve coaxial Ge detectors, for the six different muon momenta (\(p\)) (**a**) 28.6 MeV/c, (**b**) 35.0 MeV/c, (**c**) 37.5 MeV/c, (**d**) 40.0 MeV/c, (**e**) 42.5 MeV/c, and (**f**) 45.0 MeV/c. The data accumulation time for each momentum was \(\sim\)30 min. The \(\mu\)-X rays of Fe, Ti and Cu are labelled in blue, green, and red colors, respectively. The energies of the \(\mu\)-X rays were taken from [59; 60]. The inset in panel (a) shows the zoomed portion of the spectrum (from 1240 to 1270 keV), to emphasize the fine structure of the muonic \(K_{x}\) lines in Fe. A statistical error of the data points (\(\sqrt{N}\)) is not shown for visibility of the smaller peaks. In addition to the \(\mu\)-X rays, the gamma-rays produced after the nuclear capture of muons have also been observed in the present experiment. We show this for the data measured at the muon momentum of \(p=28.6\) MeV/c, where all the muons stop in the very first Fe layer. The gamma-rays, resulting from the nuclear capture in Fe, were previously studied in Ref. [61] and Ref. [60]. In Ref. [61], only six gamma-rays were detected in the Fe spectrum, resulting from the isotopes \({}^{56}\)Fe (\(\mu^{-},\
u\gamma\)) \({}^{56}\)Mn, \({}^{56}\)Fe (\(\mu^{-},\
u\pi\gamma\)) \({}^{55}\)Mn, \({}^{56}\)Fe (\(\mu^{-},\
u 3n\gamma\)) \({}^{53}\)Mn, and \({}^{56}\)Fe (\(\mu^{-},\
u pn\gamma\)) \({}^{54}\)Cr. A gamma-ray at 847 keV was observed, due to the decay of the first excited state of \({}^{56}\)Fe, in both the prompt \(\mu\)-X ray and the delayed gamma-ray spectra. The presence of this 847 keV in the delayed spectrum was explained to be arising due to the inelastic scattering of the \({}^{56}\)Fe nucleus by neutrons following the muon capture. In the other Ref. [60], up to forty-nine gamma-rays originating from the de-excitation of the \({}^{56}\)Fe (\(\mu^{-},\
u\gamma\)) \({}^{56}\)Mn, \({}^{56}\)Fe (\(\mu^{-},\
u 2n\gamma\)) \({}^{54}\)Mn, \({}^{56}\)Fe (\(\mu^{-},\
u 3n\gamma\)) \({}^{53}\)Mn and \({}^{56}\)Fe (\(\mu^{-},\
u pn\gamma\)) \({}^{54}\)Cr isotopes were observed. From our analysis, we observed all the gamma-rays mentioned in the previous two references. In addition, we also observe the gamma rays from \({}^{56}\)Fe (\(\mu^{-},\
u p2n\gamma\)) \({}^{53}\)Cr or \({}^{54}\)Fe (\(\mu^{-},\
u p\gamma\)) \({}^{53}\)Cr. Figure 4a shows the \(\mu\)-X ray and gamma-ray spectra from Fe in the energy range 0-200 keV, measured using the two low-energy germanium detectors. In order to differentiate between these two spectra, a time-gate cut has been applied. As the muon cascade down to the 1s ground state is almost instantaneous after its capture by an atom, the associated \(\mu\)-X ray emission will happen basically in coincidence with the muon entrance time.