On the momentum-dependence of $K^{-}$-nuclear potentials

The momentum dependent $K^{-}$-nucleus optical potentials are obtained based on the relativistic mean-field theory. By considering the quarks coordinates of $K^-$ meson, we introduced a momentum-dependent "form factor" to modify the coupling vertexes. The parameters in the form factors are determined by fitting the experimental $K^{-}$-nucleus scattering data. It is found that the real part of the optical potentials decrease with increasing $K^-$ momenta, however the imaginary potentials increase at first with increasing momenta up to $P_k=450\sim 550$ MeV and then decrease. By comparing the calculated $K^-$ mean free paths with those from $K^-n$/$K^-p$ scattering data, we suggested that the real potential depth is $V_0\sim 80$ MeV, and the imaginary potential parameter is $W_0\sim 65$ MeV.