$\beta$ decay of ${}^{36}\mathrm{Mg}$ and ${}^{36}\mathrm{Al}$: Identification of a $\beta$-decaying isomer in ${}^{36}\mathrm{Al}$

The level structure of ${}^{36}\mathrm{Al}$ has been studied via $\beta$ decay of ${}^{36}\mathrm{Mg}$ at the Facility for Rare Isotope Beams (FRIB) and the National Superconducting Cyclotron Laboratory (NSCL). A long-lived isomer in ${}^{36}\mathrm{Al}$ was identified which decays by $\beta$ to an excited state of ${}^{36}\mathrm{Si}$. The ground state and the isomeric state of ${}^{36}\mathrm{Al}$ were found to populate different energy levels of ${}^{36}\mathrm{Si}$. The results from the two data sets in the present work complement each other. Configuration interaction calculations performed with the FSU shell-model Hamiltonians provide reasonable descriptions to the experimental observations and offer insight into future improvements of the theoretical interpretation.

Figure 1

(a) The $\beta$-delayed $\gamma$-ray spectrum observed in the FRIB experiment within the 100 ms time window following the arrival of an ion of ${}^{36}\mathrm{Mg}$. (b) The $\beta$-delayed $\gamma$-ray spectrum of the same isotope within the 100 ms time window as observed in the NSCL experiment. (c) The spectrum in the inset shows the 1109 keV gate confirming the $\gamma \text{−}\gamma$ coincidence with the 1408 keV peak in the NSCL data. The peaks labeled in red are newly assigned (or observed) in the current analysis.

Figure 2

(a) $\beta$-delayed $\gamma$-ray spectrum of ${}^{36}\mathrm{Al}$ decay achieved from the FRIB experiment. A 100 ms time window between the ${}^{36}\mathrm{Al}$ ions and the subsequent decays was considered. (b) $\beta$-delayed $\gamma$-ray spectrum of ${}^{36}\mathrm{Al}$ decay obtained from the NSCL experiment. A temporal correlation of 100 ms between the implants and the decay events was considered. The peaks labeled in red are newly assigned (or observed) in the current analysis.

Figure 3

Decay schemes of mass $A=36$ nuclei proposed from the current analysis. Only the $\beta \text{−}0n$ branches are shown here. The levels and $\gamma$-ray transitions shown in red and green are newly assigned. We propose that the isomeric state of ${}^{36}\mathrm{Al}$ is favorably populated by the $\beta$ decay of ${}^{36}\mathrm{Mg}$ (a similar procedure of the $\beta$ decay of ${}^{34}\mathrm{Mg}$ [9, 27]) and the ground state is strongly populated in the fragmentation reaction. However, the possibility of a vice-versa scenario cannot be excluded.

Figure 4

(a) ${}^{36}\mathrm{Al}$ decay curve for a correlation time of 1500 ms between the implants and the $\beta$ decay within 1 pixel. (b) Decay curve gated by the 2316 keV $\gamma$-ray transition from the $\beta \text{−}0n$ daughter ${}^{36}\mathrm{Si}$.

Figure 5

Decay curve of ${}^{36}\mathrm{Mg}$ gated by the 657 keV $\gamma$-ray transition from the $\beta \text{−}0n$ daughter ${}^{36}\mathrm{Al}$.

Figure 6

Half-life of the suggested isomeric state of ${}^{36}\mathrm{Al}$ has been extracted from the $\gamma$-peak gated time distribution of the (a) 1408 keV and (b) 1109 keV transitions, populated via $\beta$ decay of ${}^{36}\mathrm{Mg}$.

Figure 7

Experimental energy states of ${}^{36}\mathrm{Al}$ observed in the present work are compared with those predicted by using the FSU shell-model interaction. We note that the relative ordering of the two $\beta$-decaying states could not be determined from the current analysis. Unmixed $0\hslash \omega$ (0p0h) and $1\hslash \omega$ (1p1h) states were calculated for the negative and positive parity levels, respectively, of ${}^{36}\mathrm{Al}$. The levels in red have been newly observed in the current analysis and the spin-parity are suggested according to the shell-model predictions.

Figure 8

Experimental energy states of ${}^{36}\mathrm{Si}$ observed in the present analysis as well as in the previous work [34] are compared with those predicted by using the FSU shell-model interaction. Unmixed $0\hslash \omega$ (0p0h) and $1\hslash \omega$ (1p1h) states were calculated for the positive and negative parity levels, respectively, of ${}^{36}\mathrm{Si}$. The levels in red have been observed for the first time in the current analysis and the spin-parity are suggested according to the shell-model predictions.