Observation of the Astrophysically Important<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>State in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>18</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow><mml:mi>e</mml:mi></mml:math>via Elastic Scattering of a Radioactive<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>F</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>Beam from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

The ${}^{17}\mathrm{F}(p,\ensuremath{\gamma}{)}^{18}\mathrm{Ne}$ reaction is important in stellar explosions, but its rate has been uncertain because of an expected ${3}^{+}$ state in ${}^{18}\mathrm{Ne}$ that has never been conclusively observed. This state would provide a strong $\ensuremath{\ell}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ resonance and, depending on its excitation energy, could dominate the stellar reaction rate. We have observed this missing ${3}^{+}$ state by measuring the ${}^{1}\mathrm{H}{(}^{17}\mathrm{F},p{)}^{17}\mathrm{F}$ excitation function with a radioactive ${}^{17}\mathrm{F}$ beam at the ORNL Holifield Radioactive Ion Beam Facility. We find that the state lies at a center-of-mass energy of ${E}_{r}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}599.8\ifmmode\pm\else\textpm\fi{}1{.5}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{2.0}_{\mathrm{sys}}\phantom{\rule{0ex}{0ex}}\mathrm{keV}$ ( ${E}_{x}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4523.7\ifmmode\pm\else\textpm\fi{}2.9\mathrm{keV}$) and has a width of $\ensuremath{\Gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}18\ifmmode\pm\else\textpm\fi{}{2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{1}_{\mathrm{sys}}\phantom{\rule{0ex}{0ex}}\mathrm{keV}$.