Low-energy enhancement of the magnetic dipole radiation in odd-mass lanthanides

We compute the magnetic dipole ($M1$) $\ensuremath{\gamma}$-ray strength functions ($\ensuremath{\gamma}\mathrm{SF}\text{s}$) for the odd-mass lanthanides $^{143--151}\mathrm{Nd}$ and $^{147--153}\mathrm{Sm}$ using the shell-model Monte Carlo method in combination with the static-path approximation and the maximum-entropy method. In particular, we quantify the statistical uncertainties in the calculated $M1\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}\mathrm{SFs}$ and show that they are under control for the excitation energies relevant to the experiments despite a Monte Carlo sign problem that originates in the projection onto an odd number of neutrons. We identify a low-energy enhancement (LEE) in the $M1\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}\mathrm{SFs}$ of these odd-mass lanthanides, which was recently observed experimentally in some of them. We also find a scissors mode resonance (SR) in the strongly deformed isotopes. We observe that the decrease in the LEE strength with neutron number along an isotopic chain is compensated for by an increase in the SR strength in the deformed nuclei. We compare our results with recent experiments.