- th / 9 90 90 24 v 1 1 3 Se p 19 99 1 The antikaon potential in nuclear matter at finite momentum ∗

We study the antikaon potential at finite momentum for proton and neutron nuclear matter. Our approach is based on the momentum dependence of the real part of the total K − N scattering amplitude, which is fixed in free space by experimental data, using the dispersion relation approach. We decompose the contributions to the scattering amplitude from different processes and consider the Λ(1405) and Σ(1385) to be dissolved in nuclear matter at density ρ0. Within this approach the K − potential is found to be attractive up to high kaon momenta. Our result is in line with the data on the antikaon potential evaluated from the analysis of kaonic atoms (low momenta), heavy-ion (interdmediate momenta) and proton-nucleus (high momenta) collisions. The antikaon potential in nuclear matter at finite relative momentum at present is a question of vivid interest, which is partly discussed in a controversal manner. The analysis [1] of data on kaonic atoms leads to an antikaon potential of ≃–180 MeV at normal nuclear density ρ 0 , while the studies [2] of K −-meson production from heavy-ion collisions [3] suggest an attractive potential ≃–100÷120 MeV. We have proposed in Ref. [4] to attribute this discrepancy to the momentum dependence of the antikaon potential, since the kaonic atoms explore stopped antikaons with p K ≈0, while the heavy-ion experiments have probed the range 300≤p K ≤600 MeV/c. The evaluation of the momentum-dependent potential is a rigorous problem and substantially depends on the model applied. Here we discuss a dispersive approach in which the uncertainties are under theoretical and experimental control. Within the low density theorem the real part of the antikaon potential at baryon density ρ B is given in terms of the real forward K −-nucleon scattering amplitude D as U (ρ B , E K) = − 2π m K ρ B D(E K), (1) where E K is the kaon energy relative to the nuclear matter rest frame. It is important to note * Supported by Forschungszentrum Jülich that D here is the total scattering amplitude including all possible processes available at given antikaon energy E K. It is obvious that with increasing E K the number of open reaction channels becomes very large such that all channels cannot be calculated separately anymore. The contribution from the individual reaction channels then can be controlled only by the relative saturation of the total cross section. In case …