Direct Measurement of Astrophysically Important Resonances in ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{C}\mathrm{a}$

According to sensitivity studies, the $^{38}$\mathrm{K}$\left( p, \gamma \right){}^{39}$\mathrm{C}\mathrm{a}$$reactionhasasignificantinfluenceon$$\mathrm{A}\mathrm{r}$$,$$\mathrm{K}$$,and$$\mathrm{C}\mathrm{a}$$ production in classical novae. In order to constrain the rate of this reaction, we have performed a direct measurement of the strengths of three candidate $\mathrm{\ell }=0$ resonances within the Gamow window, at $386\pm 10\mathrm{k}\mathrm{e}\mathrm{V}$, $515\pm 10\mathrm{k}\mathrm{e}\mathrm{V}$, and $689\pm 10\mathrm{k}\mathrm{e}\mathrm{V}$. The experiment was performed in inverse kinematics using a beam of unstable ${}^{38}\mathrm{K}$ impinged on a windowless ${\mathrm{H}}_2$ target. The ${}^{39}\mathrm{C}\mathrm{a}$ recoils and prompt $\gamma$ rays from ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{C}\mathrm{a}$ reactions were detected in coincidence using a recoil mass separator and a BGO array, respectively. For the $689$ keV resonance, we observed a clear recoil-$\gamma$ coincidence signal and extracted resonance strength and energy values of $120_{-30}^{+50}{(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})}_{-60}^{+20}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{.})\mathrm{m}\mathrm{e}\mathrm{V}$ and $679_{-1}^{+2}(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 1(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{.})\mathrm{k}\mathrm{e}\mathrm{V}$, respectively. We also performed a singles analysis, extracting a resonance strength of $120\pm 20(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 15(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{.})\mathrm{m}\mathrm{e}\mathrm{V}$, consistent with the coincidence result. For the $386$ keV and $515$ keV resonances, we extract $90\mathrm{\%}$ confidence level upper limits of $2.54$ meV and $18.4$ meV, respectively. We have established a new recommended ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{C}\mathrm{a}$ rate based on experimental information, which reduces overall uncertainties near the peak temperatures of nova burning by a factor of $\sim 250$. Using the rate obtained in this work in model calculations of the hottest oxygen-neon novae reduces overall uncertainties on $\mathrm{A}\mathrm{r}$, $\mathrm{K}$, and $\mathrm{C}\mathrm{a}$ synthesis to factors of $15$ or less in all cases.