Experimental study of $\beta$-delayed proton decay of ${}^{23}\mathrm{Al}$ for nucleosynthesis in novae

The $\beta$-delayed $\gamma$ and proton decay of ${}^{23}\mathrm{Al}$ has been studied with an alternative detector setup at the focal plane of the momentum achromat recoil separator MARS at Texas A&M University. We could detect protons down to an energy of 200 keV and determine the corresponding branching ratios. Contrary to results of previous $\beta$-decay studies, no strong proton intensity from the decay of the isobaric analog state (IAS) of the ${}^{23}\mathrm{Al}$ ground state at $E_x=7803$ keV in ${}^{23}\mathrm{Mg}$ was observed. Instead we assign the observed low-energy group $E_{p,\mathrm{c}.\mathrm{m}.}=206$ keV to the decay from a state that is 16 keV below the IAS. We measured both proton and gamma branches from the decay of this state at $E_x=7787$ keV in ${}^{23}\mathrm{Mg}$, which is a very rare case in the literature. Combining our data with its measured lifetime, we determine its resonance strength to be $\omega \gamma ={1.4}_{-0.4}^{+0.5}$ meV. The value is in agreement with older direct measurements, but disagrees with a recent direct measurement. This state is the most important resonance for the radiative proton capture ${}^{22}\mathrm{Na}$($p,\gamma$)${}^{23}\mathrm{Mg}$ in some astrophysical environments, such as novae.

Figure 1

NeNa cycles and possible depleting reactions for stable (black boxes) and $\beta$-emitting (red boxes) nuclei.

Figure 2

Secondary-beam identification with the $\Delta$E-E target telescope at the focal plane of MARS. The vertical bars represent the position of the momentum-defining slits in MARS during the production of ${}^{23}\mathrm{Al}$. This setting yields $\Delta p/p=\pm 0.6\%$ and a purity of better than $90\%$.

Figure 3

Schematic representation of the detector setup at the focal plane of MARS: (1) Separator $\mathit{XY}$ slits, (2) $\Delta$E-E detector for beam tuning, (3) Rotatable aluminum degrader, (4) $45{}^{°}$ wedge with the detector stack, (5) HPGe detector, (6) Cabling connections, and (7) Cooling system. See text for more details.

Figure 4

The $\gamma$-ray spectrum following the $\beta$ decay of ${}^{23}\mathrm{Al}$ from 0–4 MeV (upper panel, log scale) and 4–8 MeV (lower panel, linear scale). Major $\gamma$ lines relevant for the states near $S_p$ are identified, as well as the only major contaminant present, ${}^{14}\mathrm{O}$ ($E_{\gamma }=2313$ keV). See text for more details.

Figure 5

Partial level scheme of ${}^{23}\mathrm{Mg}$. The transition intensities (in italics, percents relative to the 451-keV line) for the astrophysically relevant 7787-keV state are shown; $\gamma$ intensities and energies are from Ref. [25] and the proton intensity from this work.

Figure 6

A sample $\beta$-delayed proton spectrum obtained from the decay of ${}^{21}\mathrm{Mg}$. The ${}^{21}\mathrm{Mg}$ ions were deposited midway through the DSSSD and the decay spectrum was acquired with one strip over about 8 hours of beam time. The known 1257(10), 1773(2), and 1939(5)-keV lines [27] are highlighted with arrows.

Figure 7

Full collected statistics for the ${}^{23}\mathrm{Al}$ data (black solid line) and the ${}^{22}\mathrm{Mg}$ data (blue dashed line). The energy is the total measured decay energy. The smoothed ${}^{22}\mathrm{Mg}$ spectrum, scaled to match the ${}^{23}\mathrm{Al}$ spectrum at 150 keV, is shown with red dots and corresponding uncertainties. The upper panel shows only the low-energy part where the proton group at $~270$ keV is clearly visible on top of the $\beta$ background, whereas the lower panel shows the total spectra.

Figure 8

Comparison of the $\beta$-delayed proton spectrum of ${}^{23}\mathrm{Al}$ obtained in this experiment (black solid line) and the spectrum published in [15], which has been magnified 15 times (red dash line). The peaks from this work are slightly higher in energy because they represent the total measured decay energy, whereas in [15], the spectrum was obtained from a detector outside the source, which recorded only the proton energy. The original data for this plot is courtesy of Peräjärvi [30].

Figure 9

Spectrum for $\beta$-delayed protons from ${}^{23}\mathrm{Al}$ obtained after background subtraction. The energy shown is the total measured decay energy. The fits appear as solid lines. The inset shows the composite fit consisting of presumed peaks in the low-energy part where significant background subtraction was required.

Figure 10

Upper panel: The contribution of the 7787-keV state to the ${}^{22}\mathrm{Na}$($p,\gamma$) reaction rate at typical nova peak temperatures. Lower panel: Ratio ($R=N_a\langle \sigma \nu \rangle /N_a\langle \sigma \nu \rangle {}_{\mathrm{adopted}}$) of the rate deduced in the present work (see text) and the adopted rate [40].