  Recently a new type of Feshbach resonance, i.e., orbital Feshbach resonance
(OFR) was proposed for the ultracold alkali-earth (like) atoms, and
experimentally observed in the ultracold gases of $^{{\rm 173}}$Yb atoms.
Unlike most of the magnetic Feshbach resonances of ultracold alkali atoms, when
the OFR of $^{{\rm 173}}$Yb atoms appears, the energy gap between the
thresholds of the open channel (OC) and the closed channel (CC) is much smaller
than the characteristic energy of the inter-atomic interaction, i.e., the van
der Waals energy. In this paper we study the OFR in the systems with small
CC-OC threshold gap. We show that in these systems the OFR can be induced by
the coupling between the OC and either an isolated bound state of the CC or the
scattering states of the CC. Moreover, we also show that in each case the
two-channel Huang-Yang pesudopoential is always applicable for the approximate
calculation of the low-energy scattering amplitude. Our results imply that in
the theoretical calculations for these systems it is appropriate to take into
account the contributions from the scattering states of the CC.
