First in-beamγ-ray study of the level structure of neutron-richS39

The neutron-rich $^{39}\mathrm{S}$ nucleus has been studied using binary grazing reactions produced by the interaction of a 215-MeV beam of $^{36}\mathrm{S}$ ions with a thin $^{208}\mathrm{Pb}$ target. The magnetic spectrometer, PRISMA, and the $\ensuremath{\gamma}$-ray array, CLARA, were used in the measurements. Gamma-ray transitions of the following energies were observed: 339, 398, 466, 705, 1517, 1656, and 1724 keV. Five of the observed transitions have been tentatively assigned to the decay of excited states with spins up to ($11/{2}^{\ensuremath{-}}$). The results of a state-of-the-art shell-model calculation of the level scheme of $^{39}\mathrm{S}$ using the SDPF-U effective interaction are also presented. The systematic behavior of the excitation energy of the first $11/{2}^{\ensuremath{-}}$ states in the odd-$A$ isotopes of sulfur and argon is discussed in relation to the excitation energy of the first excited ${2}^{+}$ states of the adjacent even-$A$ isotopes. The states of $^{39}\mathrm{S}$ that have the components in their wave functions corresponding to three neutrons in the $1{f}_{7/2}$ orbital outside the $N=20$ core have also been discussed within the context of the 0 $\ensuremath{\hbar}\ensuremath{\omega}$ shell-model calculations presented here.