Unbound neutron ν0d3/2 strength in 17C and the N=16 shell gap

Abstract

Significant continuum strength has been observed to be populated in ¹⁷C produced in the d(¹⁶C,p) reaction at a beam energy of 17.2 MeV/nucleon. The strength appears at greater than ∼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 ¹⁶C(2${}_1^{+}$) level, the corresponding spectroscopic factors to the ground state were deduced to be 0.47±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 (${\epsilon }_{\nu 0d_{3/2}}-{\epsilon }_{\nu 1s_{1/2}}$) 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.