Kaon polarization in nuclear matter

Abstract

The kaon-nucleon interaction in nuclear matter is considered by taking into account tree graphs, p-wave interaction, pionic intermediate states, kaon fluctuations and some residual interaction. The latter one is constrained by Adler's consistency condition. The K −, K +, K 0, K 0 polarization operators are calculated in cold nuclear matter with arbitrary isotopic composition. An extra s-wave repulsion is found, which probably shifts the critical point of a K − condensation with vanishing kaon momentum to large nucleon densities. Oppositely, an extra p-wave attraction is obtained, which may lead to a K − condensation at vanishing temperatures and densities ϱ ⩾ ϱ c − ∼ (4–6) ϱ 0. The spectrum of the kaonic excitations in nuclear matter is analyzed and a new low-lying branch in the K − (and also K 0 ) spectrum is found. Its presence may lead to interesting observable consequences, such as the enhancement of the K − yields in heavy-ion reactions. At ϱ ⩾ ϱ c − the frequency of this low-lying branch becomes negative at non-vanishing momentum; that signals the onset of a new type inhomogeneous K − condensation. The K − condensate energy is calculated in the approximation of a small KK coupling constant. Accordingly, neutron star matter may undergo a first-order phase transition to proton matter with K − condensate at ϱ > ϱ c − due to p-wave interaction. The temperature dependence of the most important terms of the K − polarization operator is discussed. In a rather wide temperature region 0 < T < 1 2 m π a growing temperature enlarges the K − N attraction and promotes the kaon condensation. The possibility of p-wave K 0 condensation is also considered. The question is qualitatively discussed whether proton matter with K − condensate or neutron matter with K 0 condensate is energetically more favorable.