Revisit cosmic ray propagation by using $^{1}$H, $^{2}$H, $^{3}$He and $^{4}$He

The secondary-to-primary ratios are unique tools to investigate cosmic ray propagation mechanisms. In this work, we use the latest data of deuteron-to-helium 4 ratio and helium 3-to-helium 4 ratio measured by PAMELA combined with other Z≤2 primary fluxes measured by PAMELA and Voyager-1, to constrain the cosmic ray acceleration and propagation models. The analysis is performed by interfacing statistical tools with the GALPROP propagation package. To better fit both the modulated and unmodulated low energy cosmic ray data, we find that a time-, charge- and rigidity-dependent solar modulation model is better than the force-field approximation. Among all the studied cosmic ray propagation models, the diffusion–reacceleration–convection model is strongly supported by the derived Bayesian evidence. The robustness of the estimated diffusion slope δ is cross-checked by another low-mass secondary-to-primary ratio, i.e. the antiproton-to-proton ratio. It is shown that the diffusion–reacceleration–convection model can reconcile well with the high energy antiproton-to-proton ratio. This indicates that the estimated value of δ is reliable. The well constraint δ from the “best” model is found to be close to 1/3, inferring a Kolmogorov-type interstellar magnetic turbulence.