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

TL;DR

This study investigates the low-lying structure of $^{15}$C through neutron-removal reactions, confirming unbound p-shell states and comparing experimental data with shell-model and ab initio calculations to test p-sd interactions.

Contribution

It provides new experimental data on cross-shell states in $^{15}$C and compares these with advanced theoretical models, highlighting the sensitivity to shell gaps and the need for improved calculations.

Findings

Confirmation of unbound p-shell hole states in $^{15}$C

Good agreement with shell-model calculations after monopole term adjustments

Sensitivity of results to the $N=8$ shell gap and theoretical truncation schemes

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 $ab~ initio$ 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.