  The orbital Feshbach resonance (OFR) is a novel scheme for magnetically
tuning the interactions in closed-shell fermionic atoms. Remarkably, unlike the
Feshbach resonances in alkali atoms, the open and closed channels of the OFR
are only very weakly detuned in energy. This leads to a unique effect whereby a
medium in the closed channel can Pauli block, or frustrate, the two-body
scattering processes. Here, we theoretically investigate the impact of
frustration in the few- and many-body limits of the experimentally accessible
three-dimensional $^{173}$Yb system. We find that by adding a closed-channel
atom to the two-body problem, the binding energy of the ground state is
significantly suppressed, and by introducing a closed-channel Fermi sea to the
many-body problem, we can drive the system towards weaker fermion pairing.
These results are potentially relevant to superconductivity in solid-state
multiband materials, as well as to the current and continuing exploration of
unconventional Fermi-gas superfluids near the OFR.
