Angular distribution of low momentum atmospheric muons at ground level

We report measurements of the angular distributions of low momentum atmospheric muons at 38 m above sea level for zenith angles $\theta$ between -60 and 60 degrees in the south-north direction. The muon detection was performed with two NaI(Tl) scintillation detectors mounted in coincidence. An adjustable lead thickness placed between the detectors allowed to select muons with a minimal momentum ranging from 0.3 to 0.9 GeV$/$c. The integrated and the differential muon flux were determined by analyzing the deposited energy spectra in the scintillators backed up by a Geant4 simulation of the experimental setup. The results are consistent with the $\cos^{n}(\theta)$ distribution in good agreement with the literature. These data contribute to fill the gap in the geomagnetic cutoff rigidity interval 8~GV$<P_c<$14~GV where no similar measurements were performed before. We found that $n=1.88-0.12~P_{\mu}^c$ in this domain of muon momenta cutoff $P_{\mu}^c$<1 GeV$/$c. The present measurements are useful for many muon studies requiring an accurate integrated flux.