Formula omitted]–nuclear bound states in a dynamical model

Abstract

A comprehensive data base of K − –atom level shifts and widths is re-analyzed in order to study the density dependence of the K ¯ –nuclear optical potential. Significant departure from a t eff ρ form is found only for ρ ( r ) / ρ 0 ≲ 0.2 and extrapolation to nuclear-matter density ρ 0 yields an attractive potential, about 170 MeV deep. Partial restoration of chiral symmetry compatible with pionic atoms and low-energy pion–nuclear data plays no role at the relevant low-density regime, but this effect is not ruled out at densities of order ρ 0 and beyond. K ¯ –nuclear bound states are generated across the periodic table self consistently, using a relativistic mean-field model Lagrangian which couples the K ¯ to the scalar and vector meson fields mediating the nuclear interactions. The reduced phase space available for K ¯ absorption from these bound states is taken into account by adding an energy-dependent imaginary term which underlies the corresponding K ¯ –nuclear level widths, with a strength required by fits to the atomic data. Substantial polarization of the core nucleus is found for light nuclei, and the binding energies and widths calculated in this dynamical model differ appreciably from those calculated for a static nucleus. A wide range of binding energies is spanned by varying the K ¯ couplings to the meson fields. Our calculations provide a lower limit of Γ K ¯ = 50 ± 10 MeV on the width of nuclear bound states for K ¯ -binding energy in the range B K ¯ ∼ 100 – 200 MeV . Comments are made on the interpretation of the FINUDA experiment at DAΦNE which claimed evidence for deeply bound K − p p states in light nuclei.