In-beam $\gamma$-ray spectroscopy of ${}^{38–42}\mathrm{S}$

The low-energy excitation level schemes of the neutron-rich ${}^{38–42}\mathrm{S}$ isotopes are investigated via in-beam $\gamma$-ray spectroscopy following the fragmentation of ${}^{48}\mathrm{Ca}$ and ${}^{46}\mathrm{Ar}$ projectiles on a ${}^{12}\mathrm{C}$ target at intermediate beam energies. Information on $\gamma \gamma$ coincidences complemented by comparisons to shell-model calculations were used to construct level schemes for these neutron-rich nuclei. The experimental data are discussed in the context of large-scale shell-model calculations with the SDPF-MU effective interaction in the $sd\text{−}pf$ shell. For the even-mass S isotopes, the evolution of the yrast sequence is explored as well as a peculiar change in decay pattern of the second $2^{+}$ states at $N=26$. For the odd-mass ${}^{41}\mathrm{S}$, a level scheme is presented that seems complete below 2.2 MeV and consistent with the predictions by the SDPF-MU shell-model Hamiltonian; this is a remarkable benchmark given the rapid shell and shape evolution at play in the S isotopes as the broken-down $N=28$ magic number is approached. Furthermore, the population of excited final states in projectile fragmentation is discussed.

Figure 1

Particle identification spectra for the reaction residues produced in ${}^{12}\mathrm{C}({}^{46}\mathrm{Ar},X)Y$ (upper panel) and ${}^{12}\mathrm{C}({}^{48}\mathrm{Ca},X)Y$ (lower panel). The energy loss was measured with the ionization chamber of the S800 focal plane. The time-of-flight was taken between plastic scintillators in the beam line and in the back of the S800 focal plane. The S isotopes of interest are unambiguously identified and separated.

Figure 2

Doppler-corrected $\left(v/c=0.357\right)$ $\gamma$-ray spectrum taken with GRETINA in coincidence with ${}^{38}\mathrm{S}$ as identified with the S800 spectrograph. The inset expands the energy range from 2 to 4 MeV.

Figure 3

Background-subtracted $\gamma \gamma$ coincidence spectra for ${}^{38}\mathrm{S}$. Coincidence spectra for the 1282, 1515, and 1534 keV transitions are shown. The small number of counts observed agrees with expectations based on the statistics of the measurement.

Figure 4

Proposed experimental level schemes for ${}^{38}\mathrm{S}$ based on previous data and coincidence relationships. The experimental level scheme is confronted with shell-model calculations using the SDPF-MU Hamiltonian.

Figure 5

Doppler-reconstructed $\gamma$-ray spectrum in coincidence with ${}^{39}\mathrm{S}$ $\left(v/c=0.348\right)$. The inset expands the higher-energy region of the spectrum.

Figure 6

Background-subtracted $\gamma \gamma$ coincidence spectra for ${}^{39}\mathrm{S}$. Software gates on the 337, 466, and 533 keV transitions are displayed. The coincidence spectra shown in the left and in the middle panel investigate the previously claimed 337-466 keV coincidence [19], which seems plausible based on our low-statistics data. The right panel provides weak evidence for a coincidence between the newly observed 533 and 370 keV transitions.

Figure 7

Predicted level scheme and nanosecond lifetimes for ${}^{39}\mathrm{S}$ from shell-model calculations using the SDPF-MU effective interaction.

Figure 8

Doppler-reconstructed $\gamma$-ray spectrum in coincidence with ${}^{40}\mathrm{S}$ (with $v/c=0.341$ for ${}^{40}\mathrm{S}$ from ${}^{48}\mathrm{Ca}$ beam and $v/c=0.350$ for ${}^{40}\mathrm{S}$ from ${}^{46}\mathrm{Ar}$ beam).

Figure 9

Background-subtracted $\gamma \gamma$ coincidence spectra for ${}^{40}\mathrm{S}$. Spectra in coincidence with the strongest transitions at 902, 1350, and 1572 keV are shown.

Figure 10

Proposed experimental level scheme for ${}^{40}\mathrm{S}$ compared to the SDPF-MU shell-model calculations. The level scheme is based on the $\gamma \gamma$ coincidence spectra and intensities. The tentative placement of the 2057 keV transition is indicated. The tentative identification of the low-lying even-spin yrast sequence is based on comparison with the shell model and the population pattern of excited states observed throughout this work.

Figure 11

Doppler-reconstructed $\gamma$-ray spectrum in coincidence with ${}^{41}\mathrm{S}$ $\left(v/c=0.342\right)$. The spectrum is expanded with changed binning beyond 500 keV to highlight the high density of small peaks up to $\sim 3.2$ MeV.

Figure 12

Background-subtracted $\gamma \gamma$ coincidence spectra for ${}^{41}\mathrm{S}$. Spectra in coincidence with 451, 536, 1099, and 1633 keV are shown.

Figure 13

Background-subtracted $\gamma \gamma$ coincidence spectra for ${}^{41}\mathrm{S}$. Spectra gated on 1611 and 1302 keV transitions in ${}^{41}\mathrm{S}$ are shown. These transitions do not appear in coincidence with 451 keV (see also Fig. 12) or any other transitions that they would feed.

Figure 14

Proposed experimental level schemes for ${}^{41}\mathrm{S}$ based on the observed coincidences, intensities, energy sums, and comparison to the shell model (SDPF-MU Hamiltonian). Solid lines and filled arrows indicate firm level and transition assignments, the dashed line and unfilled arrows indicate a tentative placement. Given that the 1611 and 1302 keV $\gamma$-ray transitions are strong and not in coincidence with 451 keV, we argue that they likely populate the ground state directly. Comparison to shell-model energies, decay branchings, and systematics was used to assign tentative $J^{\pi }$ values (see text).

Figure 15

Doppler-reconstructed $\gamma$-ray spectrum in coincidence with ${}^{42}\mathrm{S}$ $\left(v/c=0.335\right)$. The insets expand energy regions of the spectrum with weaker intensity transitions. Transitions at 1143 and 2154 keV are tentative.

Figure 16

Background-subtracted $\gamma \gamma$ coincidence spectra for ${}^{42}\mathrm{S}$. Spectra in coincidence with 902, 1787, 1820, and 2803 keV are shown.

Figure 17

Background-subtracted $\gamma \gamma$ coincidence spectra for ${}^{42}\mathrm{S}$. Spectra in coincidence with 949, 992, and 2677 keV are shown.

Figure 18

Proposed experimental level scheme for ${}^{42}\mathrm{S}$ based on the $\gamma \gamma$ coincidence spectra, intensities, and energy sums. The experimental data is confronted with shell-model calculations using the SDPF-MU effective interaction. Comparison to shell-model energies and decay branchings was used to assign tentative $J^{\pi }$ quantum numbers (see text).

Figure 19

Comparison of the excitation energy ratios of the first excited $2^{+},4^{+}$, and $6^{+}$ states across the neutron-rich sulfur isotopes. For ${}^{36}\mathrm{S}$, the $6_1^{+}$ state has not yet been identified in the literature [23], and is expected at high excitation energy where the level density is significant. The collective $4^{+}$ and $6^{+}$ states of ${}^{44}\mathrm{S}$ have not yet been observed either. For the calculated ${}^{44}\mathrm{S}$ $E\left(4^{+}\right)/E\left(2^{+}\right)$ ratio, the shell-model energy of the second $4^{+}$ state is used since the $6_1^{+}\to 4_2^{+}\to 2_1^{+}\to 0_1^{+}$ cascade is connected by the strongest $E2$ transitions. However, the energy ratios would not change if the $4_1^{+}$ or $6_2^{+}$ energies were used instead since $E\left(6_2^{+}\right)-E\left(6_1^{+}\right)=56$ keV and $E\left(4_2^{+}\right)-E\left(4_1^{+}\right)=134$ keV. The tentative $6_1^{+}$ assignments for ${}^{40,42}\mathrm{S}$ stem from the measurements presented here.

Figure 20

Shell-model (SDPF-MU) neutron $p_{3/2}$ occupancy for the $0^{+}$ (red) and $2^{+}$ (blue) states of ${}^{38–44}\mathrm{S}$ below 4.5 MeV. The rapid onset of neutron $p_{3/2}$ occupancy together with the dramatic increase in the level density of $0^{+}$ and $2^{+}$ states in ${}^{44}\mathrm{S}$ signals a sudden transition into the $N=28$ “island of inversion” in the S isotopic chain. The role of ${}^{42}\mathrm{S}$ as a sensitive probe for the neutron configurations is discussed in the text.