In a resonance model the reactions pi N -> Y K and pi Delta -> Y K are studied. For the reactions pi N -> Lambda K and pi Delta -> Lambda K, the resonances N(1650)(J^P=1/2^-), N(1710)(1/2^+) and N(1720)(3/2^+) are included as intermediate states. For the reactions pi N -> Sigma K, the resonances N(1710)(1/2^+), N(1720)(3/2^+) and Delta(1920)(3/2^+) are considered, while for the pi Delta -> Sigma K reactions the intermediate resonances are N(1710)(1/2^+) and N(1720)(3/2^+). Besides these resonances in the s-channel, the t-channel K^*(892) exchanges are also taken into account as a smooth background. The relevant coupling constants for the meson-baryon vertices are obtained (except for Delta(1920)) from the experimental decay branching ratios of the relevant resonances. All isospin channels of the pi N -> Y K and pi Delta -> Y K cross sections are calculated. By comparing the calculated results with the available experimental data, we find that the total cross sections of the pi N -> Y K reactions can be explained by the resonance model. The pi Delta -> Y K cross sections, for which no experimental data are available, are predicted theoretically. Parametrizations of the calculated total cross sections for all different isospin channels are given for the use of kaon productions in heavy ion collisions. The differential cross sections are also studied.
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