a softening of the diffusion coefficient to explain this feature, such that we can already anticipate that $\delta_{\rm h}<\delta$. The normalization of the diffusion coefficient $K_{10}$ (which carries the physical units) is another free parameter. Mind the difference with the convention used in most past analyses, where the normalization was instead $K_0$ and was defined at a rigidity $R_0=1\,{\rm GV}$. Note also that $K_{10}\simeq K(10\,{\rm GV})$, not a strict equality, because of the influence of the other terms.

We further introduce the spectral-change parameters \[eq:Delta\] \_[l]{} &=& - \_[l]{} ,\
\_[h]{} &=& - \_[h]{}, As already mentioned above, $\Delta_{\rm h}$ is expected to be positive. A positive $\Delta_{\rm l}$ is also expected from damping arguments and from the flattening of the primary CR spectra observed by Voyager I, as CRs may diffuse mostly on self-generated turbulence—see the discussion above. Notice that in the low-rigidity regime, additional non-relativistic processes might further be considered in an effective way by raising the velocity $\beta$ to the power $\eta$, an effective index which—it has been argued—might take negative values in some regimes [@PtuskinEtAl2005; @PtuskinEtAl2006a].

A comment on $\eta$ is in order: since the rigidity range of CR data analyzed in this article is always 