Atmospheric Effects on Cosmic-Ray Intensity Near Sea Level

The effects of atmospheric temperature and pressure on the $\mu$-meson intensity are studied theoretically for locations near sea level. The analysis is based on a unidimensional equation for the vertical differential intensity of $\mu$ mesons, studied originally by Sands. The treatment is rigorous in the sense that it includes the continuous production as well as the ionization losses of $\mu$ mesons in the atmosphere. With the help of a newly derived range spectrum of $\mu$ mesons at production and the exact expression for the survival probability of $\mu$ mesons, a three-term regression formula for the relative changes of the $\mu$-meson intensity is derived and discussed in detail. According to this formula, the relative intensity changes are correlated not only with the average production height and the ground pressure (a customarily employed two-term correlation) but also with the average tropospheric temperature. This additional correlation, resulting from the ionization losses of $\mu$ mesons in the air, seems to remove some apparent difficulties in the interpretation of experimental data. In particular, it seems to explain the discrepancies found in the decay coefficients determined from diurnal and seasonal observations, respectively.