  Heavy even-even nuclei exhibit low-energy collective excitations that are
separated in scale from the microscopic (fermion) degrees of freedom. This
separation of scale allows us to approach nuclear vibrations within an
effective field theory (EFT). In odd-mass nuclei collective and single-particle
properties compete at low energies, and this makes their description more
challenging. In this article we describe odd-mass nuclei with ground-state spin
$I=\sfrac{1}{2}$ by means of an EFT that couples a fermion to the collective
degrees of freedom of an even-even core. The EFT relates observables such as
energy levels, electric quadrupole ($E2$) transition strengths, and magnetic
dipole ($M1$) moments of the odd-mass nucleus to those of its even-even
neighbor, and allows us to quantify theoretical uncertainties. For isotopes of
rhodium and silver the theoretical description is consistent with data within
experimental and theoretical uncertainties. Several testable predictions are
made.
