Low-energy enhancement in the magnetic dipole $\gamma$-ray strength functions of heavy nuclei

A low-energy enhancement (LEE), which was observed experimentally in the $\gamma$-ray strength function ($\gamma \mathrm{SF}$) describing the decay of compound nuclei, would have profound effects on $r$-process nucleosynthesis if it persists in heavy neutron-rich nuclei. The LEE was shown to be a feature of the magnetic dipole ($M1)$ strength function in configuration-interaction shell-model calculations in medium-mass nuclei. However, its existence in heavy open-shell nuclei remains an open question. Here, using a combination of many-body methods, we identify a LEE in the $M1\gamma \mathrm{SFs}$ of heavy samarium nuclei. In particular, we use the static-path plus random-phase approximation ($\text{SPA}+\text{RPA}$), which includes static and small-amplitude quantal fluctuations beyond the mean field. Using the $\text{SPA}+\text{RPA}$ strength as a prior, we apply the maximum-entropy method to obtain finite-temperature $M1\gamma \mathrm{SFs}$ from exact imaginary-time response functions calculated with the shell-model Monte Carlo method. We find that the slope of the LEE in samarium isotopes is roughly independent of the average initial energy over a wide range below the neutron separation energy. As the neutron number increases, strength transfers to a low-energy excitation, which we interpret as the scissors mode built on top of excited states.