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.

Background: In presolar low-density graphite grains, an extraordinarily large ${}^{22}$Ne/${}^{20}$Ne ratio or even nearly pure ${}^{22}$Ne is found, pointing to the condensation of radioactive ${}^{22}$Na in grains. Supernovae and neon-rich novae are the main events that produce ${}^{22}$Na via the explosive hydrogen burning process. The ${}^{22}$Na($p$, $\gamma$)${}^{23}$Mg reaction is one of the key reactions that influences the ${}^{22}$Na abundance in ejecta.

${}^{13}\mathrm{N}$($p,\gamma$)${}^{14}\mathrm{O}$ is one of the key reactions in the hot CNO cycle which occurs at stellar temperatures around $T_9⩾0.1$. Up to now, some uncertainties still exist for the direct capture component in this reaction, thus an independent measurement is of importance. In present work, the angular distribution of the ${}^{13}\mathrm{N}$($d,n$)${}^{14}\mathrm{O}$ reaction at $E_{c.m.}=8.9$ MeV has been measured in inverse kinematics, for the first time. Based on the distorted-wave Born approximation (DWBA) analysis, the nuclear asymptotic normalization coefficient (ANC), $C_{1,1/2}^{{}^{14}O}$, for the ground state of ${}^{14}\mathrm{O}$ $\to$ ${}^{13}\mathrm{N}$ + $p$ is derived to be $5.42\pm 0.48$ ${\mathrm{fm}}^{-1/2}$. The ${}^{13}\mathrm{N}$($p,\gamma$)${}^{14}\mathrm{O}$ reaction is analyzed with the $R$-matrix approach, its astrophysical $S$ factors and reaction rates at energies of astrophysical relevance are then determined with the ANC. The implications of the present reaction rates on the evolution of novae are then discussed with the reaction network calculations.

The ${}^{18}\mathrm{O}(\alpha ,\gamma ){}^{22}\mathrm{Ne}$ reaction is critical for AGB star nucleosynthesis due to its connection to the abundances of several key isotopes, such as ${}^{21}\mathrm{Ne}$ and ${}^{22}\mathrm{Ne}$. However, the ambiguous resonance energy and spin-parity of the dominant 470 keV resonance leads to substantial uncertainty in the ${}^{18}\mathrm{O}(\alpha ,\gamma ){}^{22}\mathrm{Ne}$ reaction rate for the temperature of interest. We have measured the resonance energies and strengths of the low-energy resonances in ${}^{18}\mathrm{O}(\alpha ,\gamma ){}^{22}\mathrm{Ne}$ at the Jinping Underground Nuclear Astrophysics experimental facility (JUNA) with improved precision. The key 470 keV resonance energy has been measured to be $E_{\alpha }=474.0\pm 1.1\mathrm{keV}$, with such high precision achieved for the first time. The spin-parity of this resonance state is determined to be $1^{-}$, removing discrepancies in the resonance strengths in earlier studies. The results significantly improve the precision of the ${}^{18}\mathrm{O}(\alpha ,\gamma ){}^{22}\mathrm{Ne}$ reaction rates by up to about 10 times compared with the previous data at typical AGB temperatures of 0.1–0.3 GK. We demonstrate that such improvement leads to precise ${}^{21}\mathrm{Ne}$ abundance predictions, with an impact on probing the origin of meteoritic stardust SiC grains from AGB stars.