High-precision 28 Si( p , t ) 26 Si reaction to determine 22 Mg( α , p ) 25 Al reaction rates

The rise time of stellar x-ray bursts is a signature of thermonuclear runaway processes in the atmosphere of neutron stars and is highly sensitive to a series of ($\ensuremath{\alpha}$,$p$) reactions via high-lying resonances in $sd$-shell nuclei. Lacking data for the relevant resonance levels, the stellar reaction rates have been calculated using statistical, Hauser-Feshbach models, assuming a high-level density. This assumption may not be correct in view of the selectivity of the ($\ensuremath{\alpha}$,$p$) reaction to natural parity states. We measured the ${}^{28}$Si($p$,$t$)${}^{26}$Si reaction with a high-resolution spectrometer to identify resonance levels in ${}^{26}$Si above the $\ensuremath{\alpha}$-emission threshold at 9.164 MeV excitation energy. These resonance levels are used to calculate the stellar reaction rate of the ${}^{22}$Mg($\ensuremath{\alpha}$,$p$)${}^{25}$Al reaction and to test the validity of the statistical assumption.