Calculation of the Exposure of GRANDProto300 to Cosmic Rays

GRANDProto300 is one of the prototype experiments of the Giant Radio Array for Neutrino Detection. It will feature about 300 radio antenna detectors in Xiaodushang in Dunhuang, China, covering a total geometrical area of about 200 km$^2$. A main scientific goal of GRANDProto300 is the study of cosmic rays in the transition region (10$^{17}$ eV < 𝐸 < 10$^{18.5}$ eV). Our study calculates the exposure of GRANDProto300 to cosmic rays and estimates the number of cosmic-ray events to be detected during a fixed observation period. The trigger efficiency reaches 50, 80, and 90% at 10$^{17.5}$, 10$^{17.9}$, and 10$^{18.3}$ eV, respectively. The exposure of GRANDProto300 is 50 km$^2$ day sr at around 10$^{17.5}$ eV, and the expected number of observed cosmic rays with energies above 10$^{17}$ eV and zenith angles above 65$^{\circ}$ is about 130 events per day. GRANDProto300 will be able to measure the cosmic-ray energy spectrum in 10$^{17.2}$ eV $<E<$ 10^{19.5} eV through one-year observation, with a statistical precision about five times better than the previous spectral measurement by a mono-fluorescence detector of the Telescope Array Low-Energy Extension. The statistical uncertainty in the measurement of the mean depth of the air-shower maximum $X_{\rm max}$ is about five times better than the previous measurements using radio detectors at 10$^{17.5}$ eV; systematic uncertainties should be a dominant contribution limiting our interpretation of the chemical composition of cosmic rays in the transition region.