Λ-hyperons in symmetric nuclear matter

The study of the hyperon-nucleon ( YN ) interaction is essential to an understanding of the physics of octet baryons and nuclear systems with strangeness. In addition, the YN interactionalso determinesthepropertiesof hyper- nuclei, double hypernuclei and the behavior of dense nu- clear matter. Unfortunately, experimental data of the YN interaction are rare compared to the nucleon-nucleon case. There exist only a very limited amount of scattering data with which one constructs high quality potentials such as the Nijmegensoft corepotentialNSC97, NSC89, the Jülich one-boson-exchangepotential and the recently constructed chiral effective field theory potential with cutoffs between 550 and 700 MeV (1). The focus of this work is a comparative analysis of all these various potentials and determine their differences as well as their similarities. Based on a Renormalization Group (RG) approach an effective low-momentum YN interaction Vlow k is obtained by using these potentials as initial condition for solving the corresponding RG equa- tions (2). From these different Vlow k's we calculate in Hartree-Fock approximation the single particle potential (SPP) for the Λ-hyperon in symmetric non-strange nuclear matter. This allows us to investigate the density depen- dence of the SPP without any hyperon-hyperon ( YY )i n- teractions, which are not well known generally. The re- sulting various SPP's for vanishing hyperon momentum as function of the density are shown in Fig. 1. The SPP is given by an integration over the diagonal elements of the effective low-momentum potential ma- trix. This also establishes a simple connection between the SPP and the Vlow k. In addition, some experimental data e.g. from the (π � ,K + ) spectra are available and allow a comparison. It is found that the depth of the SPP at satura- tion density ρ0 is �30 MeV (3). As one can see in the figure most of the different effec- tive YN interactions give different result in magnitude as well as the shape of the curves. The common feature is that all Nijmegen models and the chiral effective theory agree up to, and slightly above, the saturation density. The agree- ment of all the Nijmegen models is expected since all are based on a similar footing. Interesting is the agreement with the model using chiral effective theory in leading or- der. Thischiralpotentialandall NSC97 potentialscrossthe only known experimental point at saturation density ρ0. For higher densities it is obvious that none of the po- tential agree with each other. Note, that these differences do not influence the behavior of hypernuclei strongly. But on the other hand, these differences can have drastic con-