  The energy dependence of the total kaon production cross sections in baryon
baryon ($N$ and $\Delta$) collisions are studied in the resonance model, which
is a relativistic, tree-level treatment. This study is the first attempt to
complete a systematic, consistent investigation of the elementary kaon
production reactions for both the pion baryon and baryon baryon reactions. Our
model suggests that the magnitudes of the isospin-averaged total cross sections
for the $N N \to N Y K$ and $\Delta N \to N Y K$ ($Y = \Lambda$ or $\Sigma$)
reactions are almost equal at energies up to about 200 MeV above threshold.
However, the magnitudes for the $\Delta N$ reactions become about 6 times
larger than those for the $N N$ reactions at energies about 1 GeV above
threshold. Furthermore, the magnitudes of the isospin-averaged total cross
sections for the $N N \to \Delta Y K$ reactions turn out to be comparable to
those for the $N N \to N Y K$ reactions at $N N$ invariant collision energies
about 3.1 GeV, and about 5 to 10 times larger at $N N$ invariant collision
energies about 3.5 GeV. The microscopic cross sections are parametrized in all
isospin channels necessary for the transport model studies of kaon production
in heavy ion collisions. These cross sections are then applied in the
relativistic transport model to study the sensitivity to the underlying
elementary kaon production cross sections.
