Correlation of Long-term Cosmic-Ray Modulation with Solar Activity Parameters

In this work, we analyze the long-term cosmic-ray modulation observed by the Hermanus neutron monitor, which is the detector with the longest cosmic-ray record, from 1957 July. For our study we use the force-field approximation to the cosmic-ray transport equation, and the newest results on the mean free paths from the scattering theory. We compare the modulation parameter (phi) with different rigidity (P) dependences: P, P-2, and P-2/3. We correlate them with solar and interplanetary parameters. We found that (1) these rigidity dependences properly describe the modulation, (2) long-term cosmic-ray variations are better correlated with the magnitude of the heliospheric magnetic field (HMF) than the sunspot number, solar wind speed, and tilt angle of the HMF, and (3) the theoretical dependence of the parallel mean free path on the magnetic field variance is in agreement with the modulation parameter and therefore with the neutron monitor record. We also found that the force-field approximation is not able to take into account the effects of three-dimensional particle transport, showing a poor correlation with the perpendicular mean free path.