The phenomenon that galactic proton spectra measured during two consecutive solar minimum modulation periods intersect at a particular energy was studied with a drift model for the modulation of cosmic rays in the heliosphere. This effect causes cosmic rays at neutron monitor energies to behave differently than at lower energies during these periods. Gradient and curvature drifts of charged particles in the global heliospheric magnetic field give a natural explanation for this feature. The model shows that the crossover energy depends primarily on the particle species, the radial distance from the Sun, the minimum value of the ''tilt angle'' during the A<0 minimum period, and the amount of drifting that occurs during consecutive solar minimum modulation periods.