The all-particle spectrum of primary cosmic rays in the wide energy range from 10¹⁴ to 10¹⁷ eV observed with the Tibet-III air-shower array

We present an updated all-particle energy spectrum of primary cosmic rays in a wide range from 10¹⁴ to 10¹⁷ eV using 5.5 × 10⁷ events collected from 2000 November through 2004 October by the Tibet-III air-shower array located 4300 m above sea level (an atmospheric depth of 606 g cm^-2). The size spectrum exhibits a sharp knee at a corresponding primary energy around 4 PeV. This work uses increased statistics and new simulation calculations for the analysis. We discuss our extensive Monte Carlo calculations and the model dependencies involved in the final result, assuming interaction models QGSJETO1c and SIBYLL2.1, and heavy dominant (HD) and proton dominant (PD) primary composition models. Pure proton and pure iron primary models are also examined as extreme cases. A detector simulation was also performed to improve our accuracy in determining the size of the air showers and the energy of the primary particle. We confirmed that the all-particle energy spectra obtained under various plausible model parameters are not significantly different from each other, which was the expected result given the characteristics of the experiment at high altitude, where the air showers of the primary energy around the knee reach near-maximum development, with their features dominated by electromagnetic components, leading to a weak dependence on the interaction model or the primary mass. This is the highest statistical and the best systematics-controlled measurement covering the widest energy range around the knee energy region.