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The abundance of $^{26}$Al carries a special role in astrophysics, since it probes active nucleosynthesis in the Milky Way and constrains the Galactic core-collapse supernovae rate. It is estimated through the detection of the 1809~keV $\gamma$-line of the daughter $^{26}$Mg and from the superabundance of $^{26}$Mg in comparison with the most abundant Mg isotope (A=24) in meteorites. For this reason, high precision is necessary not only in the investigation of $^{26}$Al nucleosynthesis process but also in the investigation of the stable $^{27}$Al and $^{24}$Mg [1,2].
Moreover, these nuclei enter the so-called MgAl cycle playing an important role in the production of Al and Mg [3]. Recently, high-resolution stellar surveys have shown that the Mg-Al anti-correlation in red-giant stars in globular clusters may hide the existence of multiple stellar populations, and that the relative abundances of Mg isotopes may not be correlated with Al.
The common thread running through these astrophysical scenarios is the $^{27}{\rm Al}(p,\alpha)^{24}{\rm Mg}$ fusion reaction, which is the main $^{27}$Al destruction channel and directly correlates its abundance with the $^{24}{\rm Mg}$ one. Since available spectroscopic data and tabulated reaction rates show large uncertainties owing to the vanishingly small cross section at astrophysical energies, we have applied the Trojan Horse Method (THM) to the three-body quasi-free reaction $d(^{27}{\rm Al},\alpha{}^{24}{\rm Mg})n$. This has allowed us to perform high precision spectroscopy on the compound nucleus $^{28}$Si, from which we extracted important information on the $^{27}{\rm Al}(p,\alpha)^{24}{\rm Mg}$ fusion cross section in the energy region of interest for astrophysics, not accessible to direct measurements.
All details can be found in refs.[4,5].
In particular, the indirect measurement made it possible to assess the contribution of the 84~keV resonance and to lower upper limits on the strength of nearby resonances.
About the impact of the measurement, in this work we have evaluated the effect of the THM recommended rate on intermediate-mass asymptotic giant branch stars experiencing hot bottom burning. Here, a sizeable increase in surface aluminum abundance is observed at the lowest masses due to the modification on the fusion cross section, while $^{24}$Mg is essentially unaffected by the change we determined.
[1] S. Palmerini et al., Monthly Notices of the Royal Astronomical Society 467, 1193 (2017).
[2] C. Iliadis et al., The Astrophysical Journal Supplement 193, 23 (2011).
[3] C. Iliadis et al., Nuclear Physics A 841, 3 (2010).
[4] M. La Cognata et al., The Astrophysical Journal 941, 96 (2022).
[5] M. La Cognata et al., Physics Letters B 826, 136917 (2022).
