Cross-shell states in ${}^{15}$C: a test for p-sd interactions

Abstract

The low-lying structure of ${}^{15}$C has been investigated via the neutron-removal ${}^{16}$C$(d,t)$ reaction. Along with bound neutron sd-shell hole states, unbound p-shell hole states have been firmly confirmed. The excitation energies and the deduced spectroscopic factors of the cross-shell states are an important measure of the $[(p{)}^{-1}(sd{)}^2]$ neutron configurations in ${}^{15}$C. Our results show a very good agreement with shell-model calculations using the SFO-tls interaction for ${}^{15}$C. However, a modification of the $p$-$sd$ and $sd$-$sd$ monopole terms was applied in order to reproduce the $N=9$ isotone ${}^{17}$O. In addition, the excitation energies and spectroscopic factors have been compared to the first calculations of ${}^{15}$C with the $abinitio$ self-consistent Green's function method employing the NNLO${}_{sat}$ interaction. The results show the sensitivity to the size of the $N=8$ shell gap and highlight the need of going beyond the current truncation scheme in the theory.