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The ^{22}Ne(p,γ)^{23}Na reaction, part of the neon-sodium cycle of hydrogen burning, may explain the observed anticorrelation between sodium and oxygen abundances in globular cluster stars. Its rate is controlled by a number of low-energy resonances and a slowly varying nonresonant component. Three new resonances at E_{p}=156.2, 189.5, and 259.7 keV have recently been observed and confirmed. However, significant uncertainty on the reaction rate remains due to the nonresonant process and to two suggested resonances at E_{p}=71 and 105 keV. Here, new ^{22}Ne(p,γ)^{23}Na data with high statistics and low background are reported. Stringent upper limits of 6×10^{-11} and 7×10^{-11} eV (90% confidence level), respectively, are placed on the two suggested resonances. In addition, the off-resonant S factor has been measured at unprecedented low energy, constraining the contributions from a subthreshold resonance and the direct capture process. As a result, at a temperature of 0.1 GK the error bar of the ^{22}Ne(p,γ)^{23}Na rate is now reduced by 3 orders of magnitude.

The $^{17}$O(p,$\alpha$)$^{14}$N reaction plays a key role in various astrophysical scenarios, from asymptotic giant branch stars to classical novae. It affects the synthesis of rare isotopes such as $^{17}$O and $^{18}$F, which can provide constraints on astrophysical models. A new direct determination of the $E_{\rm R}~=~64.5$~keV resonance strength performed at the Laboratory for Underground Nuclear Astrophysics accelerator has led to the most accurate value to date, $\omega\gamma = 10.0 \pm 1.4_{\rm stat} \pm 0.7_{\rm syst}$~neV, thanks to a significant background reduction underground and generally improved experimental conditions. The (bare) proton partial width of the corresponding state at $E_{\rm x} = 5672$~keV in $^{18}$F is $\Gamma_{\rm p} = 35 \pm 5_{\rm stat} \pm 3_{\rm syst}$~neV. This width is about a factor of 2 higher than previously estimated thus leading to a factor of 2 increase in the $^{17}$O(p,$\alpha$)$^{14}$N reaction rate at astrophysical temperatures relevant to shell hydrogen-burning in red giant and asymptotic giant branch stars. The new rate implies lower $^{17}$O/$^{16}$O ratios, with important implications on the interpretation of astrophysical observables from these stars.