$\beta$-decay Measurements Near the $N=40$ Island of Inversion to Quantify Cooling of Accreted Neutron Star Crusts

Understanding the thermal structure of the outer crust of accreting neutron stars is important to interpret astronomical X-ray observations. Ground-state to ground-state $\beta$-decay transitions of neutron-rich nuclei comprising the crust enable Urca neutrino cooling processes that affect this thermal structure. Here we constrain the ground-state to ground-state transition strengths for the decays of $^{57}$Sc, $^{57}$Ti, and $^{59}$Ti based on experimental data. The data were obtained by combining total absorption $\gamma$-spectroscopy data from the SuN detection system with $\beta$-delayed neutron emission data from the NERO detection system at Michigan State University's National Superconducting Cyclotron Laboratory. We find $\log ft=$5.8$^{+0.3}_{-0.2}$ and $\log ft=$5.34$^{+0.08}_{-0.24}$ for the decays of $^{57}$Ti and $^{59}$Ti, respectively, and find no evidence for ground-state feeding in the decay of $^{57}$Sc. The results indicate weaker transitions than predicted by theory and indicated by previous measurements, resulting in reduced efficiency of neutrino cooling in accreted neutron star crusts in systems that exhibit X-ray superbursts.