Unbound neutron $\nu0d_{3/2}$ strength in $^{17}$C and the N=16 shell gap

TL;DR

This study investigates the unbound neutron $0d_{3/2}$ strength in $^{17}$C, revealing continuum states, shell gap size, and comparing experimental results with shell model predictions to enhance understanding of nuclear structure near the neutron drip line.

Contribution

The paper provides the first detailed experimental measurement of unbound neutron strength in $^{17}$C and compares it with advanced shell model calculations, refining the understanding of the N=16 shell gap.

Findings

Identification of a 3/2$^+$ state at 4.40 MeV with significant continuum strength.

Determination of the N=16 shell gap as approximately 5.08 MeV.

Shell model predictions are in reasonable agreement but underestimate the shell gap.

Abstract

Significant continuum strength has been observed to be populated in $^{17}$C produced in the d($^{16}$C,p) reaction at a beam energy of 17.2~MeV/nucleon. The strength appears at greater than $\sim$2~MeV above the single-neutron decay threshold and has been identified as arising from transfer into the neutron $0d_{3/2}$ orbital. Guided by shell model predictions the greater majority of the strength is associated with a 3/2$^+$ state at an excitation energy of 4.40$_{-0.14}^{+0.33}$ MeV and a much weaker 3/2$^+$ level at 5.60$_{-0.45}^{+1.35}$ MeV. The corresponding total widths were determined to be 3.45$_{-0.78}^{+1.82}$ and 1.6$_{-1.4}^{+4.6}$ MeV, respectively. From the backward angle proton differential cross sections and the branching ratios for neutron decay to the $^{16}$C(2$_{1}^{+}$) level, the corresponding spectroscopic factors to the ground state were deduced to be 0.47$\pm{10}$ and $<$0.09. Shell-model calculations employing the phenomenological SFO-tls interaction as well as Gamow Shell-Model calculations including continuum effects are in reasonable agreement with experiment, although the predicted strength lies at somewhat lower energy. The size of the N=16 shell gap ($\varepsilon_{ \nu0d_{3/2}}-\varepsilon _{\nu 1s_{1/2}}$) was estimated to be 5.08$_{-0.33}^{+0.43}$~MeV - some 1.3~MeV larger than found in the SFO-tls shell model calculation.