Lifetime measurements of states of ${}^{35}\mathrm{S}$, ${}^{36}\mathrm{S}$, ${}^{37}\mathrm{S}$, and ${}^{38}\mathrm{S}$ using the AGATA $\gamma$-ray tracking spectrometer

Lifetimes or lifetime limits of a small number of excited states of the sulfur isotopes with mass numbers $A=35$, 36, 37, and 38 have been measured using the differential recoil-distance method. The isotopes of sulfur were populated in binary grazing reactions initiated by a beam of ${}^{36}\mathrm{S}$ ions of energy 225 MeV incident on a thin ${}^{208}\mathrm{Pb}$ target which was mounted in the Cologne plunger apparatus. The combination of the PRISMA magnetic spectrometer and an early implementation of the AGATA $\gamma$-ray tracking array was used to detect $\gamma$ rays in coincidence with projectile-like nuclear species. Lifetime measurements of populated states were measured within the range from about 1 to 100 ps. The number of states for which lifetime measurements or lifetime limits were possible was limited by statistics. For ${}^{35}\mathrm{S}$, the lifetime was determined for the first $1/2^{+}$ state at 1572 keV; the result is compared with a previous published lifetime value. The lifetime of the $3^{-}$ state of ${}^{36}\mathrm{S}$ at 4193 keV was determined and compared with earlier measurements. No previous lifetime information exists for the ($6^{+}$) state at 6690 keV; a lifetime measurement with large associated error was made in the present work. For ${}^{37}\mathrm{S}$, the states for which lifetime limits were established were those at 646 keV with $J^{\pi }=3/2^{-}$ and at 2776 keV with $J^{\pi }=11/2^{-}$; there are no previously published lifetime values for excited states of ${}^{37}\mathrm{S}$. Finally, a lifetime limit was established for the $J^{\pi }=\left(6^{+}\right)$ state of ${}^{38}\mathrm{S}$ at 3675 keV; no lifetime information exists for this state in the literature. Measured lifetime values were compared with the results of state-of-the-art shell-model calculations based on the PSDPF, SDPF-U, and FSU effective interactions. In addition, nuclear magnetic-dipole and electric-quadrupole moments, branching ratios, mixing ratios, and electromagnetic transition rates, where available, have been compared with shell-model values. The current work suffers from poor statistics; nevertheless, lifetime values and limits have been possible, allowing a useful discussion of the ability of state-of-the-art shell-model calculations to reproduce the experimental results.

Figure 1

Mass spectrum of the sulfur isotopes produced in the present work.

Figure 2

Gamma-ray singles spectrum measured in coincidence with ${}^{35}\mathrm{S}$ ions detected at the focal plane of the PRISMA spectrometer. The photopeaks labeled with a triangle and star correspond to $\gamma$ rays from the associated target-like ${}^{208,209}\mathrm{Pb}$ isotopes, respectively.

Figure 3

The level scheme for ${}^{35}\mathrm{S}$ observed in the earlier ${}^{36}\mathrm{S}+{}^{208}\mathrm{Pb}$ experiment [10].

Figure 4

A section of a measured ${}^{35}\mathrm{S}\gamma$-ray spectrum which shows the 1423-keV ${}^{209}\mathrm{Pb}$ contaminant $\gamma$-ray photopeak (in red), and the same spectrum (in blue) with the photopeak removed through the application of a $Q$ gate. This spectrum is a sum of spectra corresponding to all five target to degrader distances.

Figure 5

Section of the measured $\gamma$-ray spectra for target-degrader distances of 20, 35, 65, and $120\mu \mathrm{m}$, which shows the two components of the 1572-keV photopeak corresponding to the $1/2^{+}$ to $3/2^{+}$ (ground state) transition in ${}^{35}\mathrm{S}$. The black curve corresponds to a fit to the data (Gaussian peaks plus linear background). Background-subtracted photopeaks are shown in green (corresponding to $\gamma$-ray emission between the target and absorber) and in blue (corresponding to $\gamma$-ray emission after the decaying nucleus has passed through the degrader foil).

Figure 6

The decay curve corresponding to the $1/2^{+}\to 3/2^{+}$ transition in ${}^{35}\mathrm{S}$. See text for details.

Figure 7

Gamma-ray singles spectrum measured in coincidence with ${}^{36}\mathrm{S}$ ions detected at the focal plane of the PRISMA spectrometer. The photopeaks labeled with a circle, square, and triangle correspond to $\gamma$ rays from the associated target-like ${}^{206,207,208}\mathrm{Pb}$ isotopes, respectively.

Figure 8

The level scheme for ${}^{36}\mathrm{S}$ observed in the earlier ${}^{36}\mathrm{S}+{}^{208}\mathrm{Pb}$ experiment [10].

Figure 9

Section of the ${}^{36}\mathrm{S}\gamma$-ray energy spectrum with and without $Q$ conditions set to remove feeding from higher-lying states and from unobserved side-feeding states.

Figure 10

Section of the measured $\gamma$-ray spectra for target-degrader distances of 7, 20, 35, and $120\mu \mathrm{m}$ which shows the two components of the photopeak corresponding to the 902-keV $3_1^{-}\to 2_1^{+}$ transition in ${}^{36}\mathrm{S}$. See also caption to Fig. 5.

Figure 11

Decay curve for the ${}^{36}\mathrm{S}{3}_1^{-}\to 2_1^{+}$ transition. See text for details.

Figure 12

Section of the measured $\gamma$-ray spectra for target-degrader distances of 7, 35, and $120\mu \mathrm{m}$ which shows the two components of the 1484-keV photopeak corresponding to the ($6_1^{+}$) $\to 5_1^{-}$ transition in ${}^{36}\mathrm{S}$.

Figure 13

The decay curve corresponding to the ($6^{+}$) $\to 5_1^{-}$ transition in ${}^{36}\mathrm{S}$. See text for details.

Figure 14

Gamma-ray singles energy spectrum observed in coincidence with ${}^{37}\mathrm{S}$ ions detected at the focal plane of the PRISMA spectrometer. The photopeaks labeled with a circle and asterisk correspond to $\gamma$ rays from the associated target-like ${}^{206,207}\mathrm{Pb}$ isotopes, respectively.

Figure 15

The level scheme for ${}^{37}\mathrm{S}$ based on the earlier ${}^{36}\mathrm{S}+{}^{208}\mathrm{Pb}$ experiment [6].

Figure 16

A section of the ${}^{37}\mathrm{S}\gamma$-ray spectrum showing the 646-keV $\gamma$-ray photopeak. The spectrum corresponds to a sum of spectra measured at all target-degrader distances. Only one component of the photopeak is observed: that corresponding to $\gamma$-ray emission after the degrader foil.

Figure 17

Results of the calculation of the percent of $\gamma$ rays emitted before passage through the degrader foil for target-degrader distances up to $250\mu \mathrm{m}$. Calculations have been performed for lifetimes in the range from 1 to 100 ps.

Figure 18

Section of a $\gamma$-ray spectrum for ${}^{37}\mathrm{S}$ which shows the 2776-keV photopeak and corresponding to a sum of all spectra measured at the five different target-to-degrader distances.

Figure 19

A partial level scheme for ${}^{38}\mathrm{S}$ based on the earlier ${}^{36}\mathrm{S}+{}^{208}\mathrm{Pb}$ experiment [10, 58].

Figure 20

Gamma-ray singles spectrum measured in coincidence with ${}^{38}\mathrm{S}$ ions detected at the focal plane of the PRISMA spectrometer. The photopeaks labeled with an asterisk and a circle correspond to $\gamma$ rays from the associated target-like nuclei, namely, ${}^{206}\mathrm{Pb}$ and ${}^{207}\mathrm{Pb}$ isotopes, respectively.

Figure 21

A section of the ${}^{38}\mathrm{S}\gamma$-ray spectrum showing the 849-keV $\gamma$-ray photopeak. The spectrum corresponds to a sum of spectra measured at all target-degrader distances. Only one component of the photopeak is observed: that corresponding to $\gamma$-ray emission after the degrader foil.