  We propose a new neutron-capture site in early metal-poor and metal-free
stars of $\sim 20$--$30 \,\mathrm{M}_\odot$ that results from proton ingestion
in the He shell during late stages of the stars' lives. Most of the neutron
capture occurs in the first $\lesssim 10^6\,$s following proton ingestion when
$^{13}{\rm C}(\alpha,\mathrm{n})^{16}\mathrm{O}$ produces neutron densities
typical of the intermediate neutron-capture process. This phase may be followed
by another lasting $\gtrsim 10^7\,$s with
$^{17}\mathrm{O}(\alpha,\mathrm{n})^{20}\mathrm{Ne}$ producing much lower
neutron densities typical of the slow neutron-capture process. We explore the
dependence of the proposed neutron-capture nucleosynthesis on the amount and
time of proton ingestion, the initial metallicity, and the ensuing supernova
shock. We obtain a range of heavy element abundance patterns including those
attributed to the slow neutron-capture process or a combination of the slow and
rapid neutron-capture processes. Our results can account for the observed
ubiquity of heavy elements such as Sr and Ba in the early Galaxy and explain
puzzling abundance patterns of these elements in at least some very metal-poor
(VMP) stars including those of the carbon-enhanced varieties. In the latter
case, the explanation by the single site proposed here differs from the
existing paradigm that attributes various classes of VMP stars to enrichment by
multiple different sites.
