High-sensitivity study of levels in ${}^{30}\mathbf{Al}$ following $\beta$ decay of ${}^{30}\mathbf{Mg}$

$\gamma$-ray and fast-timing spectroscopy were used to study levels in ${}^{30}\mathrm{Al}$ populated following the ${\beta }^{-}$ decay of ${}^{30}\mathrm{Mg}$. Five new transitions and three new levels were located in ${}^{30}\mathrm{Al}$. A search was made to identify the third $1^{+}$ state expected at an excitation energy of $\sim 2.5$ MeV. Two new levels were found, at 3163.9 and 3362.5 keV, that are firm candidates for this state. Using the advanced time-delayed (ATD) $\beta \gamma \gamma$(t) method we have measured the lifetime of the 243.8-keV state to be $T_{1/2}=15\left(4\right)\mathrm{ps}$, which implies that the 243.8-keV transition is mainly of $M1$ character. Its fast $B(M1;2^{+}\to 3^{+})$ value of 0.10(3) W.u. is in very good agreement with the USD shell-model prediction of 0.090 W.u. The 1801.5-keV level is the only level observed in this study that could be a candidate for the second excited $2^{+}$ state.

Figure 1

HPGe singles energy spectrum, with ${}^{30}\mathrm{Al}$ peaks identified. A time gate of 300–1200 ms after the proton impact on target was selected to enhance the ${}^{30}\mathrm{Mg}$ activity. In this time range the ${}^{30}\mathrm{Na}$ has decayed away. In a second step, the ${}^{30}\mathrm{Al}$ decay to ${}^{30}\mathrm{Si}$ was subtracted. This did not suppress the ${}^{29}\mathrm{Al}$ peaks (the $A=29$ chain was present in the experiment due to the $\beta -n$ branch in ${}^{30}\mathrm{Na}$ [13]) but oversubtracted the peaks in ${}^{29}\mathrm{Si}$.

Figure 2

HPGe-HPGe coincidences energy spectrum with a condition on the 243.8-keV transition.

Figure 3

${}^{30}\mathrm{Al}$ activity gated on the 243.8-keV transition. The red (gray) dots show the activity before the dead-time correction and the black dots after the off-line correction. The green (light gray) line is a fit to the dead-time-corrected activity and the purple vertical line shows the fitting-range limit. The Bateman equation for a decay chain [20] was used for the fit, with the half-life of ${}^{30}\mathrm{Na} [T_{1/2}=49.4\left(20\right)$ ms 13] as a fixed parameter and a constant background, a normalization factor, and the ${}^{30}\mathrm{Mg}$ half-life as free ones.

Figure 4

Partial level scheme of ${}^{30}\mathrm{Al}$ populated following the ${\beta }^{-}$ decay of ${}^{30}\mathrm{Mg}$ from this work. For absolute intensity per 100 decays, multiply by 0.94(5). ${\mathrm{Q}}_{\beta }$ value was obtained from [24].

Figure 5

Time difference of the $\beta -{\mathrm{BaF}}_2$(t) coincidence with a gate on the 243.8-keV transition, shown for the second ${\mathrm{BaF}}_2$. To precisely select a particular $\gamma$-cascade decay, an additional coincidence with the 443.8-keV transition was made with the HPGe detectors. To obtain the final $\tau =21\left(8\right)$ ps, the centroid shift $\mathrm{\Delta }C$ shown must be corrected by the energy-dependent time walk of the ${\mathrm{BaF}}_2$ crystal, $-7\left(7\right)$ ps in this case, and the Compton contribution, $+2\left(1\right)$ ps.