Thermonuclear reaction rate of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">O</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>17</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">F</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>18</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>

The $^{17}\mathrm{O}(p,\ensuremath{\gamma})^{18}\mathrm{F}$ and $^{17}\mathrm{O}(p,\ensuremath{\alpha})^{14}\mathrm{N}$ reactions have a profound influence on hydrogen-burning nucleosynthesis in a number of stellar sites, including red giants, asymptotic giant branch (AGB) stars, massive stars, and classical novae. Previously evaluated thermonuclear rates for both reactions carry large uncertainties. We investigated the proton-capture reaction on $^{17}\mathrm{O}$ in the bombarding energy range of ${E}_{p}^{\mathrm{lab}}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}180\text{\ensuremath{-}}540\phantom{\rule{0.3em}{0ex}}\text{keV}$. We observed a previously undiscovered resonance at ${E}_{R}^{\mathrm{lab}}\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}193.2\phantom{\rule{0.3em}{0ex}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0.3em}{0ex}}0.9\phantom{\rule{0.3em}{0ex}}\text{keV}$. The resonance strength amounts to $(\ensuremath{\omega}\ensuremath{\gamma}){}_{p\ensuremath{\gamma}}=\phantom{\rule{0.3em}{0ex}}(1.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. With this value, the uncertainties of the $^{17}\mathrm{O}(p,\ensuremath{\gamma})^{18}\mathrm{F}$ reaction rates are reduced by orders of magnitude in the peak temperature range of classical novae $(T=0.1\text{\ensuremath{-}}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{GK})$. We also report on a reevaluation of the $^{17}\mathrm{O}(p,\ensuremath{\gamma})^{18}\mathrm{F}$ reaction rates at lower temperatures that are pertinent to red giants, AGB stars, or massive stars. The present work establishes the $^{17}\mathrm{O}(p,\ensuremath{\gamma})^{18}\mathrm{F}$ reaction rates over a temperature range of $T=\phantom{\rule{0.3em}{0ex}}0.01\text{\ensuremath{-}}1.5\phantom{\rule{0.3em}{0ex}}\mathrm{GK}$ with statistical uncertainties of 10--50%. The new recommended reaction rates deviate from the previously accepted values by an order of magnitude around $T\ensuremath{\approx}0.2\phantom{\rule{0.3em}{0ex}}\mathrm{GK}$ and by factors of 2--3 at $T\phantom{\rule{0.3em}{0ex}}&lt;\phantom{\rule{0.3em}{0ex}}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GK}$.