Steady State of Cosmic-Ray Nuclei—Their Spectral Shape and Path Length at Low Energies

The steady state of cosmic-ray nuclei in interstellar space is discussed. It is shown that for a steady-state situation (or for any mode of propagation in which the allowed path lengths between the source and observer have a wide distribution), the generally used matter-slab approximation for the interstellar matter traversed by cosmic rays leads to erroneous conclusions. The steady-state energy spectra of heavy nuclei are found to have negative slopes down to energies $\sim 50 \frac{\mathrm{MeV}}{N}$, if the injection spectra are like a rigidity power law; this offers an explanation for the apparently surprising observation of flat spectra for heavy nuclei down to energies $\sim 50 \frac{\mathrm{MeV}}{N}$. Further it is found that the $\frac{L}{M}$ ratio cannot keep on increasing at low energies but must decrease continuously below a few hundred $\frac{\mathrm{MeV}}{N}$, even for energy-independent fragmentation cross sections; this also is in accord with recent experimental results.