Detection of reflected Cherenkov light from extensive air showers in the SPHERE experiment as a method of studying superhigh energy cosmic rays

Although a large number of experiments were carried out during the last few decades, the uncertainty in the spectrum of all nuclei of primary cosmic rays (PCRs) with superhigh energies is still high, and the results of many experiments on nuclear composition of PCRs are contradictory. An overview of the SPHERE experiment on detecting Vavilov-Cherenkov radiation from extensive air shower (EAS) reflected from a ground snow surface is given. A number of experimental studies implementing this method are presented and their results are analyzed. Some other popular methods of studying PCRs with superhigh energies (E0 > 1015 eV) and their main advantages and drawbacks are briefly considered. The detecting equipment of the SPHERE-2 experiment and the technique of its calibration are considered. The optical properties of snow, which are important for experiments on reflected Cherenkov light (CL) from EAS, are discussed and the history of observing reflected EAS CL is described. The algorithm of simulating the detector response and calculating the fiducial acceptance of shower detection is described. The procedure of processing the experimental data with a subsequent reconstruction of the spectrum of all PCR nuclei and analysis of the mass composition is shown. The first results of reconstructing the spectrum and separating groups of cosmic-ray nuclei with high energies in the SPHERE-2 experiment are presented. Main sources of systematic errors are considered. The prospects of developing the technique of observation of reflected EAS CL in future experiments are discussed.