Cosmic-ray propagation in the Galaxy: Techniques and the mean matter traversal

After examining the techniques used for solving the equations describing th e propagation of cosmic-ray nuclei in the Galaxy, we have introduced a tech nique that yields exact numerical solutions for the steady state equations. We have implemented this in a new code, which uses the Runge-Kutta numeric al method and incorporates current knowledge of relevant physical parameter s to carry out simultaneous integration of the steady state equations. Comp aring results from the steady state solution with those obtained using the weighted-slab approximation, we find that the weighted slab underestimates the equilibrium flux at low energies for all nuclei and does so most severe ly for secondary nuclei. At high energies, the fluxes of secondary nuclei a lso differ from the steady state results, depending upon the value of the p arameter U, the ratio of the of the daughter and parent nuclei (A/Z). R-asy , the high-energy asymptotic ratio of the secondary fluxes obtained from th e weighted-slab and steady state solutions, is well parameterized by the us eful relationship R-asy = U-0.53. Our results are in qualitative, but not q uantitative, agreement with the seminal work of Ptuskin, Jones & Ormes. We have determined the path length traversed by cosmic rays by making use of t he steady state technique and the observed B/C ratio for various compositio ns of interstellar gas. Our results agree well with those derived by Webber , but vary from those of Heinbach & Simon.