The location of electron capture heat sources in the crust of accreting neutron stars depends on the masses of extremely neutron-rich nuclei. We present first results from a new implementation of the time-of-flight technique to measure nuclear masses of rare isotopes at the National Superconducting Cyclotron Laboratory. The masses of 16 neutron-rich nuclei in the scandium -- nickel range were determined simultaneously, improving the accuracy compared to previous data in 12 cases. The masses of $^{61}${V}, $^{63}${Cr}, $^{66}${Mn}, and $^{74}${Ni} were measured for the first time with mass excesses of $-30.510(890)$ MeV, $-35.280(650)$ MeV, $-36.900(790)$ MeV, and $-49.210(990)$ MeV, respectively. With the measurement of the $^{66}$Mn mass, the locations of the two dominant electron capture heat sources in the outer crust of accreting neutron stars that exhibit superbursts are now experimentally constrained. We find that the location of the $^{66}$Fe$rightarrow^{66}$Mn electron capture transition occurs significantly closer to the surface than previously assumed because our new experimental Q-value is 2.1 MeV (2.6$sigma$) smaller than predicted by the FRDM mass model.
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