Direct Measurement of Astrophysically Important Resonances in ${}^{38}\mathrm{K}(p,{\hat{I}}^3){}^{39}\mathrm{Ca}$

Abstract

According to sensitivity studies, the ${}^{38}\mathrm{K}\left(p,{\hat{I}}^3\right){}^{39}\mathrm{Ca}$ reaction has a significant influence on $\mathrm{Ar}$, $\mathrm{K}$, and $\mathrm{Ca}$ 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 $\ell =0$ resonances within the Gamow window, at $386\pm 10\mathrm{keV}$, $515\pm 10\mathrm{keV}$, and $689\pm 10\mathrm{keV}$. The experiment was performed in inverse kinematics using a beam of unstable ${}^{38}\mathrm{K}$ impinged on a windowless ${\mathrm{H}}_2$ target. The ${}^{39}\mathrm{Ca}$ recoils and prompt ${\hat{I}}^3$ rays from ${}^{38}\mathrm{K}\left(p,{\hat{I}}^3\right){}^{39}\mathrm{Ca}$ 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-${\hat{I}}^3$ coincidence signal and extracted resonance strength and energy values of $120_{-30}^{+50}{(stat.)}_{-60}^{+20}(sys.)\mathrm{meV}$ and $679_{-1}^{+2}(stat.)\pm 1(sys.)\mathrm{keV}$, respectively. We also performed a singles analysis, extracting a resonance strength of $120\pm 20(stat.)\pm 15(sys.)\mathrm{meV}$, consistent with the coincidence result. For the $386$ keV and $515$ keV resonances, we extract $90\%$ confidence level upper limits of $2.54$ meV and $18.4$ meV, respectively. We have established a new recommended ${}^{38}\mathrm{K}(p,{\hat{I}}^3){}^{39}\mathrm{Ca}$ 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 $\mathrm{Ar}$, $\mathrm{K}$, and $\mathrm{Ca}$ synthesis to factors of $15$ or less in all cases.

11 pages, 6 figures, accepted for publication in Phys. Rev. C