<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>17</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>He,<i>d</i><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>18</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>F reaction and its implication in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>17</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>destruction in the CNO cycle in stars

The proton stripping reaction $^{17}\mathrm{He}$,d${)}^{18}$F has been used to reinvestigate the proton widths of the states in $^{18}\mathrm{F}$ near the proton threshold. Distorted-wave angular distributions were calculated using appropriate methods for stripping to unbound states. The deduced proton width for the level at ${E}_{x}$=5.673 MeV (${J}^{\ensuremath{\pi}}$${=1}^{\mathrm{\ensuremath{-}}}$) is significantly larger than a previous value obtained from a direct radiative capture experiment. A subthreshold state at ${E}_{x}$=5.603 MeV (${J}^{\ensuremath{\pi}}$${=1}^{+}$) was found to have a rather large proton reduced width so that this state contributes significantly to the astrophysical S factor at low energy. These measurements lead to substantial changes in the stellar reaction rate for the $^{17}(\mathit{p}$,\ensuremath{\alpha}${)}^{14}$N reaction. This result is discussed in relation to recent observation of the isotopic abundance ratio $^{16}\mathrm{O}$${/}^{17}$O in red giant stars. In addition, the nuclear structure of $^{18}\mathrm{F}$ is studied via the measurement of spectroscopic factors for most of the levels in $^{18}\mathrm{F}$ bound against proton decay.