“…This relationship is expected owing to the dependence of the diffusion coefficient K of GCR particles on the rigidity R, K ∝ R α ; here the coefficient α depends on the exponent ν of the PSD of the IMF turbulence according to the quasi-linear theory (QLT) as α = 2 -ν (Jokipii, 1966(Jokipii, , 1971Hasselman and Wibberentz, 1968;Toptygin, 1985). As was shown by Wawrzynczak and Alania (2005a, 2005b, Wawrzynczak (2008, 2012), and Alania, Iskra, andSiluszyk (2008, 2010), the exponent γ is related to α. Namely, γ ≈ 2 -ν in the range of frequency of the IMF turbulence f ≈ ∼ 10 −6 -10 −5 Hz, to which the neutron monitors and muon telescopes respond. The validity of the QLT (Jokipii, 1966(Jokipii, , 1971 for the GCR particles with energy ≥ 1 GeV is confirmed by the weakly nonlinear theory (WNLT; Shalchi et al, 2004), nonlinear parallel diffusion theory (NLPA; Qin, 2007) and by Droge (2003), Shalchi andSchlickeiser (2004), andShalchi (2009).…”