NORDITA 95/47-N, nucl-th/9507023 Kaon Energies in Dense Matter

We discuss the role of kaon-nucleon and nucleon-nucleon correlations in kaon condensation in dense matter. Correlations raise the threshold density for kaon condensation, possibly to densities higher than those encountered in stable neutron stars. PACS numbers: 13.75.Jz, 21.65.+f, 97.60.Jd Typeset using REVTEX 1 The possibility of kaon condensation in dense matter was suggested by Kaplan and Nelson [1], and it has been discussed in many recent publications. [2{7]. The basic idea is that the energy of a K , K, is lowered by interaction with nucleons, and in neutron star matter in beta equilibrium one expects negative kaons to be present if the energy to create one in the medium is less than the electron chemical potential, e, the energy required to add an extra electron. One complication in determining the low energy interactions of kaons with nucleons is that the interactions of kaons with protons in vacuo is dominated by the (1405) resonance. Fortunately this does not a ect the K interaction with neutrons, which is expected to dominate in neutron stars. In dense matter the e ects of the (1405) are likely unimportant, because the kinematic region of interest is far from the resonance. To describe the KN interactions Brown, Lee, Rho, and Thorsson [5], herafter denoted by BLRT, employed an e ective Lagrangian based on chiral perturbation theory. To circumvent the di culties with the resonance, parameters of the Lagrangian were tted to KN; (N = n or p), data, which are una ected by the resonance. The Lagrangian was treated in mean eld theory, and the density for condensation was found to be 3 4 0, where 0 = 0:16fm 3 is nuclear matter density. This is to be compared with the central density of about 4 0 for a neutron star of mass 1:4M according to the estimates of Wiringa, Fiks and Fabrocini [8] using realistic models of nuclear forces. The conclusion was that kaon condensation could a ect the structure, maximum mass and cooling rates of neutron stars signi cantly. In this Letter, we rst show that an important contribution to the kaon energy in the BLRT treatment is the rst term in an expansion in powers of the particle density, with a strength proportional to kaon-nucleon scattering lengths. We then argue that kaon-nucleon correlations in the medium will be reduced compared with those for a kaon and nucleon in vacuo, and that consequently the attraction experienced by a kaon in matter will be smaller that earlier estimates indicated. BLRT use the Lagrangian of Jenkins and Manohar [9] containing terms of the two lowest orders in the chiral expansion, and the nucleons are treated in mean eld theory, that is 2 their densities are assumed to be uniform, and equal to n and p. The spatially uniform state, which is the one of lowest energy in this model, is given by