Inclusive K+-meson production in proton-nucleus collisions in the near-threshold and subthreshold energy regimes is analyzed with respect to the one-step (pN → K+YN, Y=Λ, Σ) and two-step (pN → NNπ, NN2π; πN → K+Y) incoherent production processes. An appropriate folding model is used that properly takes into account the struck-target-nucleon-removal energy and the momentum distribution (nucleon spectral function), novel elementary cross sections for proton-nucleon reaction channel close to threshold, as well as nuclear-mean-field-potential effects on the one-step and two-step kaon-creation processes. A detailed comparison of the model calculations of the K+ total and differential cross sections for the p+9Be and p+12C interactions with the existing experimental data is given, which displays both the relative role of the primary and secondary production channels at considered incident energies and those features of the cross sections that are sensitive to the high-momentum and high-removal-energy parts of the nucleon spectral function. It is found that, contrary to previous studies known in the literature, the pion-nucleon production channels do not necessarily dominate in pA collisions at subthreshold energies and that the relative strength of the proton-and pion-induced reaction channels for light target nuclei in the subthreshold energy regime is governed by the kinematics of the experiment under consideration.
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