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Description
In unstable nuclei, single particle orbits undergo rearrangement, leading to various shell evolution phenomena, such as the new magic number $N=14$ and $N=16$ observed in neutron-rich O isotopes [1]. But in $^{16,17}\mathrm{C}$, the $N=14$ magic number disappear, and the $2s_{1/2}$ and $1d_{5/2}$ neutron orbits are nearly degenerate, which were proved by the close s- and d-wave states of them [2]. However, whether the $N=16$ magic number existing in $^{16,17}\mathrm{C}$ or not is still unclear in experiment, since the excited states with the valence neutron dominated by the $1d_{3/2}$ orbit (using “the $1d_{3/2}$ state” for short in the following text) in $^{16,17}\mathrm{C}$ were unbound states, and they were not observed in previous experiments.
In order to search for such kind of excited states in $^{16,17}\rm{C}$, we conducted the $^{15,16}\mathrm{C}(d,p) ^{16,17}\mathrm{C}$ experiments in inverse kinematics at the Radioactive Beam Line at Lanzhou (RIBLL1) in the Institute of Modern Physics (IMP) in 2022 [3,4]. As of now, we have completed the particle identification, and reconstructed the excitation energy spectra of $^{16,17}\mathrm{C}$ using the energies and angles of the recoil protons emitting to the backward angles with the missing mass method. According to the differential cross sections of each populated state comparing to the distorted wave Born approximation (DWBA) calculations, we found some candidates for the $1d_{3/2}$ state in the unbound states of $^{16,17}\mathrm{C}$. For $^{16}\mathrm{C}$, $1d_{3/2}$ states may lie around 8~10 MeV, and for $^{17}\mathrm{C}$ they may lie around 4~6 MeV. Further data analysis and theoretical calculations to determine if they are the $1d_{3/2}$ states or not are still in progress.
Reference:
[1] A. Schiller, N. Frank et al., Phys. Rev. Lett. 99, 112501 (2007).
[2] M. Stanoiu, D. Sohler et al., Phys. Rev. C 78, 034315 (2008).
[3] Pu W. L., Ye Y. L. et al., Nucl. Sci. Tech. 35, 12 (2024).
[4] Zhu H. Y., Lou J. L., et al. Nucl. Sci. Tech. 34, 159 (2023).
