Identification of the crossing point at $N=21$ between normal and intruder configurations

The ${\beta }^{-}$ decay of ${}^{34}\mathrm{Mg}$ was used to study the ${}^{34}\mathrm{Al}$ nucleus through $\gamma$ spectroscopy at the Isotope Separator On-Line facility of CERN. Previous studies identified two $\beta$-decaying states in ${}^{34}\mathrm{Al}$ having spin-parity assignments $J^{\pi }=4^{-}$ dominated by the normal configuration $\pi {\left(d_{5/2}\right)}^{-1}\otimes \nu \left(f_{7/2}\right)$ and $J^{\pi }=1^{+}$ by the intruder configuration $\pi {\left(d_{5/2}\right)}^{-1}\otimes \nu {\left(d_{3/2}\right)}^{-1}{\left(f_{7/2}\right)}^2$. Their unknown ordering and relative energy have been the subject of debate for the placement of ${}^{34}\mathrm{Al}$ inside or outside the $N=20$ “island of inversion.” We report here that the $1^{+}$ intruder lies only 46.6 keV above the $4^{-}$ ground state. In addition, a new half-life of $T_{1/2}=44.9\left(4\right)\mathrm{ms}$, that is twice as long as the previously measured 20(10) ms, has been determined for ${}^{34}\mathrm{Mg}$. Large-scale shell-model calculations with the recently developed sdpf-u-mix interaction are compared with the new data and used to interpret the mechanisms at play at the very border of the $N=20$ island of inversion.

Figure 1

(a) $\beta$-gated $\gamma$-ray spectrum of the ${}^{34}\mathrm{Mg}$ decay recorded in the first 300 ms after the proton impact. The most intense transitions in ${}^{34}\mathrm{Al},{}^{34}\mathrm{Si}$, and ${}^{33}\mathrm{Al}$ are labeled. (b) Time distribution, relative to the proton impact, of the 364.5-keV $\gamma$ ray from ${}^{34}\mathrm{Al}$ with a corresponding decay half-life of $T_{1/2}=44.3\left(3\right)\mathrm{ms}$. An exponential together with a constant background were used as the fitting function, shown in red. The vertical dashed line indicates the closing of the beam gate, 40 ms after the proton impact.

Figure 2

Background-subtracted $\beta$-gated $\gamma$-ray spectra in coincidence with $\gamma$ rays at (a) 414.2, (b) 492.9, and (c) 975.0 keV obtained from the decay of ${}^{34}\mathrm{Mg}$. The 597.5-, 970.4- and 487.7-keV transitions feeding the $4^{-}$ ground state are observed in the top, middle, and bottom spectra, respectively.

Figure 3

Level scheme of ${}^{34}\mathrm{Al}$ populated in the $\beta$ decay of ${}^{34}\mathrm{Mg}$ including absolute intensities per 100 decays (left) and shell-model calculation using the sdpf-u-mix interaction [23] (right: negative- and positive-parity states in red and black, respectively). The levels and transitions indicated in red in the experimental level scheme are linked directly to the newly identified $4^{-}$ ground state and assumed to be of negative parity. Tentative spins and parities are assigned based on $\gamma$-ray branching ratios and $log\mathit{\text{ft}}$ values. The half-lives of the $4^{-}$ and $1^{+}$ states are taken from Ref. [21]. The calculated excitation energy of the $1_1^{+}$ state of ${}^{34}\mathrm{Al}$ is $\sim 500\mathrm{keV}$. However, for display purposes all the positive-parity states were shifted down in energy so that the energy of the $1_1^{+}$ state matches its experimental counterpart.