One of the uncertainties in the interpretation of ultra-high-energy cosmic-ray (UHECR) data comes from the high-energy hadronic interaction models used for air shower Monte-Carlo (MC) simulations. A long-standing problem of the so-called "muon excess", the discrepancy of number of muons predicted by simulations and observed in the data, is believed to be caused by the incompleteness of modern hadronic interaction models, all of which are known to use the extrapolated values of the parameters of hadronic interactions, such as cross sections and multiplicities. The present work is dedicated to the study of muon densities in UHE extensive air showers from the Telescope Array experiment surface detector data. In the 7-year-data from the Telescope Array experiment, we find that the number of particles observed for signals with an expected muon purity of similar to 65% at a lateral distance of 2000 m from the shower core is 1.72 +/- 0.10(stat.) +/- 0.37(syst.) times larger than the MC prediction value using the QGSJETII-03 model for the proton-induced showers. A similar effect is also seen in comparison with other hadronic models such as QGSJETII-04, which shows a 1.67 +/- 0.10 +/- 0.36 excess. We also studied the dependence of these excesses on lateral distances and found a slower decrease of the lateral distribution of muons in the data as compared to the MC, causing larger discrepancy at the larger lateral distances.
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