Under ideal conditions, the shock acceleration theory of cosmic rays predicts that the spectral indices (γ) of different elements after acceleration should be consistent. However, studies of the spectra of elements with $\mathrm{A}/\mathrm{Z}\approx 2$, as measured by the AMS-02 experiment, confirm the existence of differences in spectral indices among these elements. In this work, based on a spatially dependent propagation model, we utilize observational data from AMS-02 and DAMPE to constrain $\gamma$. To avoid the influence of solar modulation and due to the lack of precise, high-energy component-resolved spectra, this study utilizes data only within the energy range of 3 GeV/n to 10 TeV/n. We determine that for elements with $\mathrm{A}/\mathrm{Z}\approx 2$, $\gamma$ is positively correlated with both Z and A, likely due to A- or Z-dependent fragmentation cross sections. We anticipate that the observed spectra of Ni and Zn will be consistent with that of Fe, while their injection spectra are expected to be slightly softer than that of Fe. We look forward to further measurements from AMS-02, DAMPE, and HERD to verify these findings, and we also hope for theoretical frameworks that can systematically explain this phenomenon.

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• Cosmic ray acceleration
• Cosmic ray composition & spectra
• Cosmic ray propagation