A Possible Approach to Three-dimensional Cosmic-Ray Propagation in the Galaxy. II. Stable Nuclei with Energy Change

We extend our model of three-dimensional cosmic-ray propagation without energy change to that including energy change due to reacceleration and ionization energy loss. We assume that there is no boundary in both the radial spread of the disk and the latitudinal spread of the halo, and that the three critical parameters, the diffusion coefficient D, the gas density n, and the cosmic-ray source density Q, depend on both the space position r and the rigidity R of the cosmic-ray particle. It is possible to apply the weighted slab technique to the transport equation, even including the energy change process, if the diffusion coefficient is separable in r and R, i.e., D(rR)=(v/c)R^αD(r), and combining it with the first-pole approximation in the path length distribution, we can obtain the analytical solution rather easily. We show that the rigidity dependence of the secondary-to-primary ratio behaves as R^-α in the high-energy region and as vR^α in the low-energy region. We compare our numerical results with experimental data in both the low- and the high-energy regions and find that our model reproduces all components over the wide energy range 1 GeV nucleon^-1 to 100 TeV nucleon^-1, with the adoption of appropriate scale heights in D, n, and Q. We also confirm that the reacceleration process actually occurs during the propagation in the Galaxy and that its magnitude is comparable with that expected from reasonable numerical choices for three parameters, D, n, and the velocity of the hydromagnetic turbulence v_M.