Analysis of Kaon Production at SIS Energies

We analyse the production and propagation of pions and kaons in heavy-ion reactions from 0.8 -- 1.8~A$\cdot$GeV within a coupled channel transport approach including the kaon production channels $BB \to K^+YN, \pi B\to K^+Y, BB \to NN K \bar{K}, \pi B\to N K\bar{K}, K^+B\to K^+B $ and $\pi \pi\to K \bar{K}$. Assuming the hyperon selfenergy to be 2/3 of the nucleon selfenergy we find that all inclusive experimental $K^+$ spectra at SIS energies can be reproduced reasonably well without any selfenergies for the kaons although a slightly repulsive kaon potential cannot be excluded by the present data on kaon spectra and flow.