Implications of the cosmic-ray radial intensity gradients observed during minimum solar modulation

We have already reported the cosmic-ray radial intensity gradients for both protons and helium nuclei measured over two decades in Rβ (magnetic rigidity R times velocity β) on the Mariner IV space probe in 1965 which showed that the modulating function is separable into the product of a function of particle parameters and a function of the time t and the heliocentric radius r for the observations (O'Gallagher and Simpson 1967). The modulating function can be written as exp (−η(r, t)/ƒ(R, β)) where η(r, t) is the modulating parameter and ƒ(R, β) = Rβ for [Formula: see text] and ƒ(R, β) [Formula: see text] β for [Formula: see text]. The magnitude of the observed gradient corresponds to a change Δη = −0.2 ± 0.05 GV for Δr = 0.4 AU and at 1 GV yields a value for the diffusion coefficient in Parker's model of 3.2 × 1021 cm/s. If the value of η in 1965 is small [Formula: see text], the observed value of Δη/Δr implies that the greatest part of the modulation takes place within 5 AU at solar minimum. The value of Δη; derived from these gradient measurements is compared with estimates of the change in η required to produce the observed time–intensity variations during the solar cycle.