First in-beam $\gamma$-ray study of the level structure of neutron-rich ${}^{39}\mathrm{S}$

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 $\gamma$-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 ($11/2^{-}$). 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 $11/2^{-}$ 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 $1f_{7/2}$ orbital outside the $N=20$ core have also been discussed within the context of the 0 $\hslash \omega$ shell-model calculations presented here.

Figure 1

Mass spectrum for sulfur $(Z=16)$ isotopes (measured in coincidence with $\gamma$ rays) populated in the present work. See text for details.

Figure 2

Gamma-ray singles energy spectrum observed in coincidence with ${}^{39}\mathrm{S}$ ions detected at the focal plane of PRISMA.

Figure 3

One-dimensional Doppler-corrected $\gamma$-ray energy spectrum from targetlike fragments observed in association with ${}^{39}\mathrm{S}$ ions detected at the focal plane of the PRISMA spectrometer. All but one of the observed photopeaks can be associated with known $\gamma$-ray transitions in ${}^{205}\mathrm{Pb}$. See text for details.

Figure 4

Partial level schemes of the $N=23$ isotones, ${}^{37}\mathrm{Si}$ and ${}^{41}\mathrm{Ar}$, together with the proposed level scheme of ${}^{39}\mathrm{S}$. The results of shell-model calculations based on the SDPF-U effective interaction are also presented. See text for details.

Figure 5

Excitation energies of the first $2^{+}$ states of the even-$A$ isotopes of sulfur and argon for neutron numbers in the range from 14 to 28 (red triangles connected by red lines). Also shown are the excitation energy differences between the first $11/2^{-}$ and first ${7/2}^{-}$ states of the odd-$A$ isotopes (blue squares connected by blue lines). See text for details.

Figure 6

Shell-model wave-function components corresponding to states of ${}^{39}\mathrm{S}$ for which three neutrons in the $1f_{7/2}$ orbital outside a closed $N=20$ core are coupled to an inert $Z=16$ proton core (blue). The red histograms correspond to the coupling of the three $f_{7/2}$ neutrons to protons with a ($2s_{1/2}$)${}^1$($1d_{3/2}$)${}^1$ configuration. See text for details.