We report the first (in)elastic scattering measurement of ${}^{25}\mathrm{Al}+p$ with the capability to select and measure in a broad energy range the proton resonances in ${}^{26}\mathrm{Si}$ contributing to the ${}^{22}\mathrm{Mg}(\alpha ,p)$ reaction at type I x-ray burst energies. We measured spin-parities of four resonances above the $\alpha$ threshold of ${}^{26}\mathrm{Si}$ that are found to strongly impact the ${}^{22}\mathrm{Mg}(\alpha ,p)$ rate. The new rate advances a state-of-the-art model to remarkably reproduce light curves of the GS $1826–24$ clocked burster with mean deviation $<9\%$ and permits us to discover a strong correlation between the He abundance in the accreting envelope of the photospheric radius expansion burster and the dominance of ${}^{22}\mathrm{Mg}(\alpha ,p)$ branch.

• Received 22 June 2020
• Revised 22 December 2020
• Accepted 5 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.172701