  We report on the first proton-induced single proton- and neutron-removal
reactions from the neutron-deficient $^{14}$O nucleus with large Fermi-surface
asymmetry $S_n-S_p$ = 18.6 MeV at $\sim$100 MeV/nucleon, a widely used energy
regime for rare-isotope studies. The measured inclusive cross sections and
parallel momentum distributions of the $^{13}$N and $^{13}$O residues are
compared to the state-of-the-art reaction models, with nuclear structure inputs
from many-body shell-model calculations. Our results provide the first
quantitative contributions of multiple reaction mechanisms including the
quasifree knockout, inelastic scattering and nucleon transfer processes. It is
shown that the inelastic scattering and nucleon transfer, usually neglected at
such energy regime, contribute about 50% and 30% to the loosely bound proton
and deeply bound neutron removal, respectively. These multiple reaction
mechanisms should be considered in analyses of inclusive one-nucleon removal
cross sections measured at intermediate energies for quantitative investigation
of single-particle strengths and correlations in atomic nuclei.
