  Data from KEK on subthreshold $\bar{\mrm{p}}$ as well as on $\pi^\pm$ and
$\mrm{K}^\pm$ production in proton-, deuteron- and $\alpha$-induced reactions
at energies between 2.0 and 12.0 A GeV for C, Cu and Pb targets are described
within a unified approach. We use a model which considers a nuclear reaction as
an incoherent sum over collisions of varying numbers of projectile and target
nucleons. It samples complete events and thus allows for the simultaneous
consideration of all final particles including the decay products of the
nuclear residues. The enormous enhancement of the $\bar{\mrm{p}}$ cross
section, as well as the moderate increase of meson production in deuteron and
$\alpha$ induced compared to proton-induced reactions, is well reproduced for
all target nuclei. In our approach, the observed enhancement near the
production threshold is mainly due to the contributions from the interactions
of few-nucleon clusters by simultaneously considering fragmentation processes
of the nuclear residues. The ability of the model to reproduce the target mass
dependence may be considered as a further proof of the validity of the cluster
concept.
