We have observed Markarian 421 in 2001 January and March with the CANGAROO-II imaging Cerenkov telescope during an extraordinarily high state at TeV energies. From 14 hr of observations at very large zenith angles, ∼70°, a signal of 298 ± 52 gamma-ray-like events (5.7 σ) was detected at E > 10 TeV, where a higher sensitivity is achieved than those of usual observations near the zenith, owing to a greatly increased collecting area. Under the assumption of an intrinsic power-law spectrum, we derived a differential energy spectrum dN/dE = (3.3 ± 0.9stat ± 0.3syst) × 10-13(E/10 TeV) -(4.0-0.6+0.9, stat±0.3syst) photons cm-2 s -1 TeV-1, which is steeper than those previously measured around 1 TeV and supports the evidence for a cutoff in the spectrum of Mrk 421. However, the 4 σ excess at energies greater than 20 TeV in our data favors a cutoff energy of ∼8 TeV, at the upper end of the range previously reported from measurements at TeV energies.
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