Background: The ${}^{15}\mathrm{O}(\alpha ,\gamma ){}^{19}\mathrm{Ne}$ bottleneck reaction in Type I x-ray bursts is the most important thermonuclear reaction rate to constrain experimentally, to improve the accuracy of burst light-curve simulations. A proposed technique to determine the thermonuclear rate of this reaction employs the ${}^{20}\mathrm{Mg}\left(\beta p\alpha \right){}^{15}\mathrm{O}$ decay sequence. The key ${}^{15}\mathrm{O}(\alpha ,\gamma ){}^{19}\mathrm{Ne}$ resonance at an excitation of 4.03 MeV is now known to be fed in ${}^{20}\mathrm{Mg}\left(\beta p\gamma \right){}^{19}\mathrm{Ne}$; however, the energies of the protons feeding the 4.03 MeV state are unknown. Knowledge of the proton energies will facilitate future ${}^{20}\mathrm{Mg}\left(\beta p\alpha \right){}^{15}\mathrm{O}$ measurements.

Purpose: To determine the energy of the proton transition feeding the 4.03 MeV state in ${}^{19}\mathrm{Ne}$.

Method: A fast beam of ${}^{20}\mathrm{Mg}$ was implanted into a plastic scintillator, which was used to detect $\beta$ particles. 16 high purity germanium detectors were used to detect $\gamma$ rays emitted following $\beta p$ decay. A Monte Carlo method was used to simulate the Doppler broadening of ${}^{19}\mathrm{Ne}\gamma$-ray lines and compare to the experimental data.

Results: The center of mass energy between the proton and ${}^{19}\mathrm{Ne}$, feeding the 4.03 MeV state, is measured to be $1.21{}_{-0.22}^{+0.25}\mathrm{MeV}$, corresponding to a ${}^{20}\mathrm{Na}$ excitation energy of $7.44{}_{-0.22}^{+0.25}\mathrm{MeV}$. Absolute feeding intensities and $\gamma$-decay branching ratios of ${}^{19}\mathrm{Ne}$ states were determined including the 1615 keV state, which has not been observed before in this decay. A new $\gamma$ decay branch from the 1536 keV state in ${}^{19}\mathrm{Ne}$ to the ground state is reported. The lifetime of the 1507 keV state in ${}^{19}\mathrm{Ne}$ is measured to be $4.3{}_{-1.1}^{+1.3}$ ps resolving discrepancies in the literature. Conflicting ${}^{20}\mathrm{Mg}(\beta p$) decay schemes in published literature are clarified.

Conclusions: The utility of this Doppler broadening technique to provide information on $\beta$-delayed nucleon emission and excited-state lifetimes has been further demonstrated. In particular, knowledge of the proton energies feeding the 4.03 MeV ${}^{19}\mathrm{Ne}$ state in ${}^{20}\mathrm{Mg}\beta$ decay will facilitate future measurements of the $\alpha$-particle branching ratio.

• Received 7 January 2019

DOI:https://doi.org/10.1103/PhysRevC.99.065801