Constraining the Neutron Star Compactness: Extraction of the ${}^{23}\mathrm{Al}\mathbf{(}p,\gamma \mathbf{)}$ Reaction Rate for the $rp$ Process

The ${}^{23}\mathrm{Al}(p,\gamma ){}^{24}\mathrm{Si}$ reaction is among the most important reactions driving the energy generation in type-I x-ray bursts. However, the present reaction-rate uncertainty limits constraints on neutron star properties that can be achieved with burst model-observation comparisons. Here, we present a novel technique for constraining this important reaction by combining the GRETINA array with the neutron detector LENDA coupled to the S800 spectrograph at the National Superconducting Cyclotron Laboratory. The ${}^{23}\mathrm{Al}(d,n)$ reaction was used to populate the astrophysically important states in ${}^{24}\mathrm{Si}$. This enables a measurement in complete kinematics for extracting all relevant inputs necessary to calculate the reaction rate. For the first time, a predicted close-lying doublet of a $2_2^{+}$ and $(4_1^{+},0_2^{+})$ state in ${}^{24}\mathrm{Si}$ was disentangled, finally resolving conflicting results from two previous measurements. Moreover, it was possible to extract spectroscopic factors using GRETINA and LENDA simultaneously. This new technique may be used to constrain other important reaction rates for various astrophysical scenarios.

Figure 1

Top: Doppler-corrected $\gamma$-ray spectrum of decays in ${}^{24}\mathrm{Si}$ in the 1400–2000 keV range measured with GRETINA when gating on ${}^{24}\mathrm{Si}$ ions in the S800 focal plane (inset: full spectrum). The dotted histogram displays the scaled background induced by transferlike reactions on carbon atoms in the target (see text). Bottom: The $\gamma$-ray coincidence spectrum gated on the $E_{\gamma }$ region between 1550 to 1610 keV. The coincidence with the $\gamma$ rays at 1874 keV can be clearly identified.

Figure 2

Differential cross section in the center-of-mass system measured with the LENDA detector. Shown is the sum of all states compared to a detailed ADWA calculation (purple line; see text). Error bands (dotted lines) are due to the uncertainty in the experimental spectroscopic factors.

Figure 3

The $1\text{−}\sigma$ uncertainty band of the current rate (black lines) due to the conflicting results of Refs. [18] and [19]. Also shown is the $1\text{−}\sigma$ rate uncertainty calculated within this work (gray band). The calculations include the $Q$-value uncertainty of 20 keV. Moreover, the recommended REACLIB (green) and REACLIB/30 (blue) rates are shown.