Constraining the $N=16$ Shell Gap in $^{17}$C via Transfer to the Continuum in the $^{16}$C$(d,p)^{17}$C Reaction

TL;DR

This study extends a semi-microscopic model to unbound states of $^{17}$C, using transfer reactions to constrain the $N=16$ shell gap, finding it to be larger than 5 MeV, consistent with recent reports.

Contribution

The work advances the modeling of unbound nuclear states and provides new constraints on the $N=16$ shell gap in $^{17}$C through transfer reaction analysis.

Findings

A large $N=16$ shell gap (>5 MeV) is necessary to match experimental data.

The extended model successfully describes unbound states of $^{17}$C.

Results support a significant shell gap consistent with recent literature.

Abstract

Recently, a semi-microscopic structure model has been presented to study the structure of a weakly-bound, two-body nucleus with a deformed core, including Pauli-blocking effects. The model has been successfully applied within the adiabatic distorted wave approximation (ADWA) reaction framework to study the reactions $^{16}$C(d, p)$^{17}$C, restricting the analysis to bound states of the residual $^{17}$C nucleus. In these calculations, the structure of $^{17}$C is described using the recently presented semimicroscopic Nilsson+AMD model (NAMD), considering different Pauli-blocking methods. In the present work, the analysis is extended to unbound states of this nucleus with the aim of constraining the location of the $1d_{3/2}$ single-particle strength and infer the $N=16$ shell-gap. Comparing the measured energy differential cross section for this reaction with calculations in which the position of the $1d_{3/2}$ orbital is arbitrarily varied, we conclude that a large shell-gap (>5 MeV) is required, in agreement with recently reported value from [J. Lois-Fuentes et al., Phys. Lett. B 867, 139600 (2025)].