Search for $^{22}$Na in novae supported by a novel method for measuring femtosecond nuclear lifetimes

Classical novae are thermonuclear explosions in stellar binary systems, and important sources of $^{26}$Al and $^{22}$Na. While γ rays from the decay of the former radioisotope have been observed throughout the Galaxy, $^{22}$Na remains untraceable. Its half-life (2.6 yr) would allow the observation of its 1.275 MeV γ-ray line from a cosmic source. However, the prediction of such an observation requires good knowledge of its nucleosynthesis. The $^{22}$Na(p, γ)$^{23}$Mg reaction remains the only source of large uncertainty about the amount of $^{22}$Na ejected. Its rate is dominated by a single resonance on the short-lived state at 7785.0(7) keV in $^{23}$Mg. Here, we propose a combined analysis of particle-particle correlations and velocity-difference profiles to measure femtosecond nuclear lifetimes. The application of this method to the study of the $^{23}$Mg states, places strong limits on the amount of $^{22}$Na produced in novae and constrains its detectability with future space-borne observatories.