Single-Neutron Adding on $^{34}$S

TL;DR

This study investigates the distribution of single-neutron strength in $^{34}$S by measuring the $^{34}$S($d$,$p$)$^{35}$S reaction, revealing fragmented strength and resolving previous discrepancies in neutron orbital occupancies.

Contribution

It provides detailed measurements of single-neutron spectroscopic overlaps and energies in $^{35}$S, clarifying the neutron distribution and shell structure near $N=28$.

Findings

Determined single-neutron centroids for orbitals in $^{35}$S.

Resolved previous discrepancies in $1p_{1/2}$ strength distribution.

Highlighted reduction in the $N=28$ shell gap.

Abstract

Purpose: Single-neutron adding data was collected in order to determine the distribution of the single-neutron strength of the $0f_{7/2}$, $1p_{3/2}$, $1p_{1/2}$ and $0f_{5/2}$ orbitals outside of $Z=16, N=18$, $^{34}$S. Methods: The $^{34}$S($d$,$p$)$^{35}$S reaction has been measured at 8 MeV/u to investigate cross sections to excited states in $^{35}$S. Outgoing proton yields and momenta were analyzed by the Super-Enge Split-Pole Spectrograph in conjunction with the CeBrA demonstrator located at the John D. Fox Laboratory at Florida State University. Angular distributions were compared with Distorted Wave Born Approximation calculations in order to extract single-neutron spectroscopic overlaps. Results: Spectroscopic overlaps and strengths were determined for states in $^{35}$S up through 6 MeV in excitation energy. Each orbital was observed to have fragmented strength where a single level carried the majority. The single-neutron centroids of the $0f_{7/2}$, $1p_{3/2}$, $1p_{1/2}$ and $0f_{5/2}$ orbitals were determined to be $2360^{+90}_{-40}$ keV, $3280^{+80}_{-50}$ keV, $4780^{+60}_{-40}$ keV, and $\gtrsim7500$ keV, respectively. Conclusion: A previous discrepancy in the literature with respect to distribution of the neutron $1p_{1/2}$ strength was resolved. The integration of the normalized spectroscopic strengths, up to 5.1 MeV in excitation energy, revealed fully-vacant occupancies for the $0f_{7/2}$, $1p_{3/2}$, and $1p_{1/2}$ orbitals, as expected. The spacing in the single-neutron energies highlighted a reduction in the traditional $N=28$ shell-gap, relative to both the $1p$ spin-orbit energy difference ($N=32$) and the lower limit on the $N=34$ shell spacing.