A new semi-empirical model for cosmic ray muon flux estimation

Cosmic ray muons have emerged as a non-conventional high-energy radiation probe to monitor dense and large objects. Muons are the most abundant cosmic radiation on Earth; however, their flux at sea level is approximately 104 min-1m-2, much less than that of induced radiation. In addition, cosmic ray muon flux depends on not only various natural conditions, e.g., zenith angle, altitude, or solar activity, but also the geometric characteristics of detectors. Since the low muon flux typically results in long measurement times, an accurate estimation of measurable muon counts is important to improve the efficiency of muon applications. Here we propose a simple and versatile semi-empirical model to improve the accuracy in muon flux estimation at all zenith angles by incorporating the geometric parameters of detectors, and we name this the 'effective solid angle model.' To demonstrate the functionality of our model, it is compared with (i) the cosine-squared model, (ii) the PARMA model, (iii) Monte Carlo simulations, and (iv) experimental measurements. Our results show that the muon count rate estimation capability is significantly improved, resulting in increasing a mean C/E level from 0.7 to 0.95. In addition, by selecting an appropriate intensity correlation, the model can be easily extended to estimate muon flux at various altitudes and also underground.