Doppler broadening in Mg 20 ( β p γ ) Ne 19 decay
The $^{15}$$\textbf{O}$$\Big({α,γ}\Big)$$^{19}$$\textbf{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}$$\textbf{Mg}$$\Big({βpα}\Big)$$^{15}$$\textbf{O}$ decay sequence. The key $^{15}$$\textbf{O}$$\Big({α,γ}\Big)$$^{19}$$\textbf{Ne}$ resonance at an excitation of 4.03 MeV is now known to be fed in $^{20}$$\textbf{Mg}$$\Big({βpγ}\Big)$$^{19}$$\textbf{Ne}$ however, the energies of the protons feeding the 4.03 MeV state are unknown. Knowledge of the proton energies will facilitate future $^{20}$$\textbf{Mg}$$\Big({βpα}\Big)$$^{15}$$\textbf{O}$ measurements. To determine the energy of the proton transition feeding the 4.03 MeV state in $^{19}$$\textbf{Ne}$. A fast beam of $^{20}$$\textbf{Mg}$ was implanted into a plastic scintillator, which was used to detect $β$ particles. 16 high purity germanium detectors were used to detect $γ$ rays emitted following $βp$ decay. A Monte Carlo method was used to simulate the Doppler broadening of $^{19}$$\textbf{Ne}γ$-ray lines and compare to the experimental data. The center of mass energy between the proton and $^{19}$$\textbf{Ne}$, feeding the 4.03 MeV state, is measured to be $1.21^{+0.25}_{-0.22}$ $\textbf{MeV}$, corresponding to a $^{20}$$\textbf{Na}$ excitation energy of $7.44^{+0.25}_{-0.22}$$\textbf{MeV}$. Absolute feeding intensities and $γ$-decay branching ratios of $^{19}$$\textbf{Ne}$ states were determined including the 1615 keV state, which has not been observed before in this decay. A new $γ$ decay branch from the 1536 keV state in $^{19}$$\textbf{Ne}$ to the ground state is reported. The lifetime of the 1507 keV state in $^{19}$$\textbf{Ne}$ is measured to be $4.3^{+1.3}_{-1.1}$ ps resolving discrepancies in the literature. Conflicting $^{20}$$\textbf{Mg}$$\Big({βp}\Big)$ decay schemes in published literature are clarified.The utility of this Doppler broadening technique to provide information on $β$-delayed nucleon emission and excited-state lifetimes has been further demonstrated. In particular, knowledge of the proton energies feeding the 4.03 MeV $^{19}$$\textbf{Ne}$ state in $^{20}$$\textbf{Mg}$ $β$ decay will facilitate future measurements of the $α$-particle branching ratio.