The ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction is the main neutron source for the slow-neutron-capture process in asymptotic giant branch stars and for the intermediate process. Direct measurements at astrophysical energies in above-ground laboratories are hindered by the extremely small cross sections and vast cosmic-ray-induced background. We performed the first consistent direct measurement in the range of $E_{\mathrm{c}.\mathrm{m}.}=0.24$ to 1.9 MeV using the accelerators at the China Jinping Underground Laboratory and Sichuan University. Our measurement covers almost the entire intermediate process Gamow window in which the large uncertainty of the previous experiments has been reduced from 60% down to 15%, eliminates the large systematic uncertainty in the extrapolation arising from the inconsistency of existing datasets, and provides a more reliable reaction rate for the studies of the slow-neutron-capture and intermediate processes along with the first direct determination of the alpha strength for the near-threshold state.

${}^{13}\mathrm{N}$($p,\gamma$)${}^{14}\mathrm{O}$ 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.

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.

${}^{26}\mathrm{Al}$ with a half-life of $7.17\times {10}^5$ years is one of the most significant nuclides in $\gamma$-ray astronomy and presolar grains of meteorites. Its main production mechanism in the $\mathrm{H}$-burning MgAl cycle is the ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ reaction. In the temperature region of 0.05–0.3 GK of astrophysical interest, the astrophysical ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ reaction rate is dominated by the resonant capture of several low-energy resonances. In this work, we report the results of a complete experimental investigation of the $E_{\mathrm{c}.\mathrm{m}.}=92$, 130, and 189 keV resonances in the ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ reaction with the Jinping Underground Nuclear Astrophysics Experimental Facility. The updated thermonuclear ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ reaction rate is (32–39)% higher than that obtained at the Laboratory for Underground Nuclear Astrophysics around 0.07–0.09 GK, mainly due to the 32% enhancement of the 92-keV resonance strength. The astrophysical impact of our new rate on the ${}^{26}\mathrm{Al}$ yield in a 5 ${\mathrm{M}}_{\odot }$ low-metallicity asymptotic giant branch star is investigated, in which an increase of (45–79)% in the ${}^{26}\mathrm{Al}$ yield is found by adopting our new ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ rates.

The ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction substantially influences the abundance ratios of the main isotopes of carbon and oxygen and hence has been regarded as the holy grail in nuclear astrophysics. Its importance lies in the fact that it significantly affects the yield of key elements and that it plays a crucial role in the study of the mass gap of black holes. This reaction's cross section is greatly influenced by the subthreshold state 7.117-MeV $1^{-}$ of ${}^{16}\mathrm{O}$, which is challenging to determine. To study such states the $\alpha$-cluster transfer reaction can be helpful. In this work, the angular distribution of the ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^7\mathrm{Li}){}^{16}\mathrm{O}$ reaction was measured, leading to the 7.117-MeV $1^{-}$ state at $E_{{}^{11}\mathrm{B}}\left(\mathrm{lab}\right)=50$ MeV. By using the finite-range distorted-wave Born approximation and coupled-reaction-channel analysis, we obtained the asymptotic normalization coefficient (ANC) to be $(2.54\pm 0.40)\times {10}^{28}$ ${\mathrm{fm}}^{-1}$ and the reduced $\alpha$ width to be $4.92\pm 0.77$ keV at a channel radius of 6.5 fm. Then, by using the $R$-matrix code azure, we calculated the astrophysical $S$ factor of the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction and found that the astrophysical $S_{E1}$ (300) factor of the ground-state transitions is $55.3\pm 9.0$ keV b. This value is lower than what was found in previous works, indicating that the $S$ factor is highly sensitive to the ANC.