Branching ratio Γ α / Γ γ of the 4.033 MeV 3 / 2 + state in 19 Ne

The branching ratio ${\\ensuremath{\\Gamma}}_{\\ensuremath{\\alpha}}/{\\ensuremath{\\Gamma}}_{\\ensuremath{\\gamma}}$ of the 4.033 MeV ${3/2}^{+}$ state in ${}^{19}\\mathrm{Ne}$ plays a crucial role in the breakout from the hot CNO cycle into the rapid proton capture process. This ratio has been studied by making use of the advantages of inverse kinematics. The state was populated via the ${}^{3}\\mathrm{He}{(}^{20}\\mathrm{Ne},\\ensuremath{\\alpha}{)}^{19}{\\mathrm{Ne}}^{*}$ reaction and its decay via $\\ensuremath{\\gamma}$ or $\\ensuremath{\\alpha}$ emission was measured by detecting the heavy reaction products ${(}^{19}\\mathrm{Ne}$ or ${}^{15}\\mathrm{O})$ in coincidence in a magnetic spectrograph. An upper limit ${\\ensuremath{\\Gamma}}_{\\ensuremath{\\alpha}}/{\\ensuremath{\\Gamma}}_{\\ensuremath{\\gamma}}l~6\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}4}$ has been obtained. With these results, the astrophysical reaction rate for the ${}^{15}\\mathrm{O}$ $(\\ensuremath{\\alpha},\\ensuremath{\\gamma})$ ${}^{19}\\mathrm{Ne}$ reaction has been calculated. Its influence on the breakout at various astrophysical sites, novas, x-ray bursts, and supermassive stars, is discussed.