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Here we report on the direct measurement of the resonance strengths of the $E_{\mathrm{R}}^{\mathrm{lab}}=647\mathrm{keV}$and 1842 keV resonances in the ${}^{40}\mathrm{Ca}(p,\gamma ){}^{41}\mathrm{Sc}$reaction. At novae temperatures, $0.2<T_9<0.7$, the ${}^{40}\mathrm{Ca}(p,\gamma ){}^{41}\mathrm{Sc}$reaction is governed by the low energy resonance at $E_{\mathrm{R}}^{\mathrm{lab}}=647\mathrm{keV}$, whereas the $E_{\mathrm{R}}^{\mathrm{lab}}=1842\mathrm{keV}$resonance serves as a normalization standard for nuclear reaction experiments within the astrophysically relevant energy range. For the $E_{\mathrm{R}}^{\mathrm{lab}}=647\mathrm{keV}$resonance, we obtain a resonance strength $\omega \gamma =(2.51\pm 0.{09}_{\mathrm{stat}}\pm 0.{22}_{\mathrm{syst}})\mathrm{meV}$, with an uncertainty a factor of 2.5 smaller than the previous direct measurement value. For the $E_{\mathrm{R}}^{\mathrm{lab}}=1842\mathrm{keV}$resonance, we obtain a resonance strength $\omega \gamma =(0.148\pm 0.{006}_{\mathrm{stat}}\pm 0.{013}_{\mathrm{syst}})\mathrm{eV}$, which is consistent with previous studies but deviates by $2\sigma$from the most recent measurement. Our results suggest ${}^{40}\mathrm{Ca}$to be a strong waiting point in the nucleosynthesis path of oxygen-neon (ONe) novae. Published by the American Physical Society2025 

: The ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the ${}^{16}\mathrm{O}$nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, $2^{+}$) and (7.12 MeV, $1^{-}$), that dominate the behavior of the low-energy $S$factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy. : The objective of this research is to examine how the subthreshold and ground-state ANCs impact the low-energy $S$factor, especially at the key astrophysical energy of $300\mathrm{keV}$. The $S$factors are calculated within the framework of the $R$-matrix method using the code. Our total $S$factor takes into account the $E1$and $E2$transitions to the ground state of ${}^{16}\mathrm{O}$including the interference of the subthreshold and higher resonances, which also interfere with the corresponding direct captures, and cascade radiative captures to the ground state of ${}^{16}\mathrm{O}$through four subthreshold states: $0_2^{+},3^{-},2^{+}$, and $1^{-}$. To evaluate the impact of subthreshold ANCs on the low-energy $S$factor, we employ two sets of the ANCs. The first selection, which offers higher ANC values, is attained through the extrapolation process [Blokhintsev , ]. The set with low ANC values was employed by deBoer []. A detailed comparison of the $S$factors at the most effective astrophysical energy of 300 keV is provided, along with an investigation into how the ground-state ANC affects this $S$factor. : The contribution to the total $E1$and $E2S$factors from the corresponding subthreshold resonances at $300\mathrm{keV}$are $(71–74)\%$and $(102–103)\%$, respectively. The correlation of the uncertainties of the subthreshold ANCs with the $E1$and $E2S\left(300\mathrm{keV}\right)$factors is found. The $E1$transition of the subthreshold resonance $1^{-}$does not depend on the ground-state ANC but interferes constructively with a broad $(9.585\mathrm{MeV};1^{-})$resonance giving (for the present subthreshold ANC) an additional $26\%$contribution to the total $E1S\left(300\mathrm{keV}\right)$factor. Interference of the $E2$transition through the subthreshold resonance $2^{+}$with direct capture is almost negligible for small ground-state ANC of $58{\mathrm{fm}}^{-1/2}$. However, its interference with direct capture for higher ground-state ANC of $337{\mathrm{fm}}^{-1/2}$is significant and destructive, contributing $-27\%$. The low-energy $S_{E2}\left(300\mathrm{keV}\right)$factor experiences a smaller increase when both subthfreshold and the ground-state ANCs rise together due to their anticorrelation, compared to when only the subthreshold ANCs increase. Published by the American Physical Society2024 

Abstract The interplay and correlation between the $$^{22}$$ 22 Ne $$(\alpha ,\gamma )^{26}$$ ( α , γ ) 26 Mg and the competing $$^{22}$$ 22 Ne $$(\alpha ,n)^{25}$$ ( α , n ) 25 Mg reaction plays an important role for the interpretation of the $$^{22}$$ 22 Ne $$(\alpha ,n)^{25}$$ ( α , n ) 25 Mg reaction as a neutron source in the s - and n -processes. This paper provides a summary and new data on the $$\alpha $$ α -cluster and single-particle structure of the compound nucleus $$^{26}$$ 26 Mg and the impact on the reaction rate of these two competing processes in stellar helium burning environments.