Search for a low-energy enhancement in the $\gamma$-decay strength of neutron-rich $^{64}$Fe

Far from stability, little is known about $\gamma$ strength functions ($\gamma$SFs) and nuclear level densities (NLDs). In certain isotopes, e.g., in the Fe-Cd region, an unexpected increase in the low energy $\gamma$-decay probability has been observed. The presence of this enhancement, or upbend, can have a significant influence on neutron capture rates. These rates are crucial for nucleosynthesis models. Recently, the upbend was found in $^{70}$Ni, the first time in a neutron-rich nucleus. It is unknown how this feature evolves throughout the nuclear landscape. An indirect method known as the $\beta$-Oslo method has been developed to constrain neutron capture rates for radioactive nuclei. With the $\beta$-Oslo method, the reaction product is populated in $\beta$-decay, and the NLD and $\gamma$SF are extracted simultaneously. At the NSCL, excited states were populated via $\beta$-decay for neutron-rich $^{64}$ Fe. $\gamma$-rays are recorded with the 4$\pi$ Summing Na(I) (SuN) segmented total absorption spectrometer, which allows a simultaneous extraction of the NLD and $\gamma$SF. These results will be presented for $^{64}$Fe, a nucleus expected to exhibit an upbend in the $\gamma$SF.