Proton Shell Gaps in $N=28$ Nuclei from the First Complete Spectroscopy Study with FRIB Decay Station Initiator

The first complete measurement of the $\beta$-decay strength distribution of ${}_{17}{}^{45}{\mathrm{Cl}}_{28}$ was performed at the Facility for Rare Isotope Beams (FRIB) with the FRIB Decay Station Initiator during the second FRIB experiment. The measurement involved the detection of neutrons and $\gamma$ rays in two focal planes of the FRIB Decay Station Initiator in a single experiment for the first time. This enabled an analytical consistency in extracting the $\beta$-decay strength distribution over the large range of excitation energies, including neutron unbound states. We observe a rapid increase in the $\beta$-decay strength distribution above the neutron separation energy in ${}_{18}{}^{45}{\mathrm{Ar}}_{27}$. This was interpreted to be caused by the transitioning of neutrons into protons excited across the $Z=20$ shell gap. The SDPF-MU interaction with reduced shell gap best reproduced the data. The measurement demonstrates a new approach that is sensitive to the proton shell gap in neutron rich nuclei according to SDPF-MU calculations.

Figure 1

Top view of the FDSi two-focal plane system, sliced to see the implantation locations. The beam comes from the left, passing through the first diagnostic cross, and can follow the blue (red) path to implant into the first (second) focal plane. In the first focal plane, south of the beam path is the neutron detector array, while north of the beam is the $\gamma$-ray detection system. The second focal plane consists of an implantation detector inserted into MTAS, preceded by an accompanying diagnostic cross.

Figure 2

Panel (a) shows the particle identification corresponding to implanted nuclei from chlorine to potassium. The atomic number ($Z$) was determined from the energy loss in the pin detector, with the time of flight between upstream timing scintillators. The black circle represents the location for ${}^{45}\mathrm{Cl}$. Panel (b) shows the decay curve for ${}^{45}\mathrm{Cl}$ from the first focal plane. The blue line shows the decay of the main isotope, and the green (yellow) line shows the inclusion of the $P_{0n}$ ($P_{1n}$) child decays. The total fit, including a constant background, $P_{0n}$, and $P_{1n}$ decays, is shown by the pink line. The inset plot compares experimental values for the half-life of ${}^{45}\mathrm{Cl}$, including literature from Refs. [27, 38, 47], with the weighted average shown as the black line with a gray band.

Figure 3

Decay signatures within 1800 ms of ${}^{45}\mathrm{Cl}$ implantation obtained using all three parts of the FDSi. (a) shows the high-resolution $\gamma$-ray data, with the singles shown in black and the $\gamma \text{−}\gamma$ spectrum gated on the 542 keV transition shown in red. The most prominent peaks assigned to ${}^{45}\mathrm{Ar}$ have been marked with the corresponding $\gamma$-ray energy. (b) shows the MTAS data and deconvolution, where the different color lines represent feeding to individual states and the pink line is the total fit as the sum of the paths. States above $S_n$ were not considered due to low statistics. (c) shows the results of the neutron deconvolution, measuring neutron energies ($E_n$) via the time-of-flight ($n\mathrm{TOF}$) method. The red (blue) peaks are neutrons that feed to the ground (excited) state(s) in ${}^{44}\mathrm{Ar}$. The deconvolution data for (b) and (c) has been shifted down on the $y$ axis for visualization purposes, but the total fit (pink) has not been shifted.

Figure 4

(a) A comparison of experimental $S_{\beta }$ (black) to theoretical predictions from LSSM using the SD-PF-SDG [20] (red) and SDPF-MU (blue, green, pink) interactions. In this figure, SDPF-MU (dec.) represents calculations done with the $Z=20$ shell gap decreased by 1 MeV (blue) and SDPF-MU (inc.) $Z=20$ shell gap increased by 1 MeV (pink dotted), compared to the reference gap shown by SDPF-MU (ref.) (green dashed curve). (b) The number of protons (gray) and neutrons (black) excited from the $sd$ to $pf$ shell, as a function of energy, for states in ${}^{45}\mathrm{Ar}$ after $\beta$ decay. The solid and dashed were obtained with decreased shell gap and reference SDPF-MU interactions, respectively. See text for more details.

Figure 5

The cumulative $S_{\beta }$ for odd-$Z$ decays along $N=28$, calculated using the SDPF-MU interaction. Solid and dashed lines refer to the decreased (dec.) and reference (ref.) shell gaps, respectively. Vertical lines indicate $Q_{\beta }$ values [59].