Antikaon production in A+A collisions at SIS energies within an off-shell G-matrix approach

The production and propagation of antikaons -- described by dynamical spectral functions $A_h(X,\vec{P},M^2)$ as evaluated from a coupled channel $G$-matrix approach -- is studied for nucleus-nucleus collisions at SIS energies in comparison to the conventional quasi-particle limit and the available experimental data using off-shell transport theory. We find that the $K^-$ spectra for $^{12}C + ^{12}C$ and $^{58}Ni + ^{58}Ni$ at 1.8 A$\cdot$GeV remain underestimated in the $G$-matrix approach as in the on-shell quasi-particle approximation whereas the preliminary spectra for $Au + Au$ at 1.5 A$\cdot$GeV are well described in both limits. This also holds approximately for the $K^-$ rapidity distributions in semi-central collisions of $Ni+Ni$ at 1.93 A$\cdot$GeV. However, in all limits considered there is no convincing description of all spectra simultaneously. Our off-shell transport calculations, furthermore, demonstrate that the strongest in-medium effects should be found for low antikaon momenta in the center-of-mass frame, since the deceleration of the antikaons in the attractive Coulomb and nuclear potentials and the propagation to the on-shell mass induces a net shift and squeezing of the $K^-$ spectra to the low momentum regime.