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The LOw-Frequency ARray (LOFAR) is used to make precise measurements of radio emission from extensive air showers, yielding information about the primary cosmic ray. Interpreting the measured data requires an absolute and frequency-dependent calibration of the LOFAR system response. This is particularly important for spectral analyses, because the shape of the detected signal holds information about the shower development. We revisit the calibration of the LOFAR antennas in the range of 30–80 MHz. Using the Galactic emission and a detailed model of the LOFAR signal chain, we find an improved calibration that provides an absolute energy scale and allows for the study of frequency dependent features in measured signals. With the new calibration, systematic uncertainties of 13% are reached, and comparisons of the spectral shape of calibrated data with simulations show promising agreement. [ABSTRACT FROM AUTHOR]

The energy reconstruction of extensive air showers measured with the LOFAR Radboud Air Shower Array (LORA) is presented in detail. LORA is a particle detector array located in the center of the LOFAR radio telescope in the Netherlands. The aim of this work is to provide an accurate and independent energy measurement for the air showers measured through their radio signal with the LOFAR antennas. The energy reconstruction is performed using a parameterized relation between the measured shower size and the cosmic-ray energy obtained from air shower simulations. In order to illustrate the capabilities of LORA, the all-particle cosmic-ray energy spectrum has been reconstructed, assuming that cosmic rays are composed only of protons or iron nuclei in the energy range between ∼2 × 10 16 and 2 × 10 18 eV. The results are compatible with literature values and a changing mass composition in the transition region from a Galactic to an extragalactic origin of cosmic rays. [ABSTRACT FROM AUTHOR]