Mapping the AMS-02 and CALET Data onto the Source Spectra and Residence Times of Galactic Cosmic Rays

The recent measurements of the spectral intensities of cosmic-ray nuclei have suggested that the ratio of Boron to Carbon nuclei, $R(E)$, comprises two components, $R_1(E)$ which carries all of the energy dependence and the other $R_A$, a constant independent of energy per nucleon. This finding supports the earlier theoretical expectations and results of gamma-ray astronomy that one of these components is attributable to spallation in a cocoon like region surrounding the sources and the other in the general interstellar medium before cosmic rays leak away from the Galaxy. A new model-independent way of analyzing cosmic-ray spectra is presented here to shed light on the recent findings: Imposing the single constraint that the source function of B nuclei is minimal we use a cascade of rate equations to map point-by-point the observed cosmic ray spectra of p, B, C, O and Fe on to their source spectra and the two life-times of cosmic rays $\tau_G$ in the Galaxy and $\tau_S$ in the cocoons surrounding the sources. The model independent results show that the appropriate choice is $\tau_S(E)$ is responsible for $R_1(E)$ and the source spectra are power laws with indices of $\sim-2.7$.