Advancement of photospheric radius expansion and clocked type-I x-ray burst models with the new $^{22}$Mg$(\alpha,p)^{25}$Al reaction rate determined at Gamow energy

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 $^{26}$Si contributing to the $^{22}$Mg$(\alpha,p)$ reaction at type I x-ray burst energies. We measured spin-parities of four resonances above the $\alpha$ threshold of $^{26}$Si that are found to strongly impact the $^{22}$Mg$(\alpha,p)$ rate. The new rate advances a state-of-the-art model to remarkably reproduce lightcurves 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 photospheric radius expansion burster and the dominance of $^{22}$Mg$(\alpha,p)$ branch.