  Precise measurements of energy spectra of different cosmic ray species were
obtained in recent years, by particularly the AMS-02 experiment on the
International Space Station. It has been shown that apparent differences exist
in different groups of the primary cosmic rays. However, it is not
straightforward to conclude that the source spectra of different particle
groups are different since they will experience different propagation processes
(e.g., energy losses and fragmentations) either. In this work, we study the
injection spectra of different nuclear species using the measurements from
Voyager-1 outside the solar system, and ACR-CRIS and AMS-02 on top of
atmosphere, in a physical framework of cosmic ray transportation. Two types of
injection spectra are assumed, the broken power-law and the non-parametric
spline interpolation form. The non-parametric form fits the data better than
the broken power-law form, implying that potential structures beyond the
constrained spectral shape of broken power-law may exist. For different nuclei
the injection spectra are overall similar in shape but do show some differences
among each other. For the non-parametric spectral form, the helium injection
spectrum is the softest at low energies and the hardest at high energies. For
both spectral shapes, the low-energy injection spectrum of neon is the hardest
among all these species, and the carbon and oxygen spectra have more prominent
bumps in 1-10 GV in the R2dN/dR presentation. Such differences suggest the
existence of differences in the sources or acceleration processes of various
nuclei of cosmic rays.
