β-delayed neutron emission of Mn64, Cr62, and Fe65

The $\beta$-decay properties of nuclei near the second nuclear “island of inversion” around neutron rich nuclei with neutron number 40 are important tests of nuclear structure models and interactions. In particular, the $\beta$-delayed neutron emission branch ($P_{\mathrm{n}}$), is useful for investigating $\beta$-strength and neutron-$\gamma$ competition above the neutron separation energies of the daughter nuclei. We report new constraints for $P_{\mathrm{n}}$ values for three nuclei in the region: ${}^{62}\mathrm{Cr}$ ($P_{\mathrm{n}}<1\%$), ${}^{64}\mathrm{Mn}$ ($P_{\mathrm{n}}=1.5\left(6\right)\%$), and ${}^{65}\mathrm{Fe}$ ($P_{\mathrm{n}}<1\%$), measured with the Neutron Emission Ratio Observer (NERO) neutron long counter system and the Beta Counting Station (BCS) at the National Superconducting Cyclotron Laboratory (NSCL). Our results resolve the large discrepancy between previous direct and indirect measurements for ${}^{64}\mathrm{Mn}$ and confirm the predictions of global theoretical models when a statistical treatment of the $\gamma$ and neutron decays of the daughter states is included. We also obtain improved half-lives for ${}^{62}\mathrm{Cr}$ [206(5) ms] and the short-lived isomer in the ${}^{62}\mathrm{Fe}$ daughter [112(7) ms] from $\beta$-delayed $\gamma$ emission data obtained in the same experiment with the Summing NaI (SuN) total absorption spectrometer. Finally, we use $\gamma$ emission data to obtain a new upper limit for the ${}^{62}\mathrm{Cr}\beta$-decay population of the long-lived isomeric state in ${}^{62}\mathrm{Mn}$.