Calculations of nuclear quasi-bound states based on chiral meson–baryon amplitudes

Abstract

In-mediumKN scattering amplitudes developed within a new chirally motivated coupled-channel model due to Cieplý and Smejkal that fits the recent SIDDHARTA kaonic hydrogen 1s level shift and width are used to construct K − nuclear potentials for calculations of K − nuclear quasi-bound states. The strong energy and density dependence of scattering amplitudes at and near threshold leads to K − potential depths −ReV K ≈ 80−120 MeV. Self-consistent calculations of all K − nuclear quasibound states, including excited states, are reported. Model dependence, polarization effects, the role of p-wave interactions, and two-nucleon K − N N → Y N absorption modes are discussed. The K − absorption widths Γ K are comparable or even larger than the corresponding binding energies B K for all K − nuclear quasi-bound states, exceeding considerably the level spacing. This discourages search for K − nuclear quasi-bound states in any but lightest nuclear systems.

η -nuclear bound states revisited

“…The latter procedure requires a self-consistent calculation to ensure that the B η argument of the input f ηN coincides with the B η output of the binding energy calculation. However, it was shown in our recent studies of K − -nuclear dynamics [18,19,20,21,22,23] that a more involved self-consistent calculation is required to correctly implement the subthreshold energy dependence, and it is this self-consistent procedure that is applied here to calculate η-nuclear bound states. This procedure results in imposing stronger constraints than ever on the onset of η-nuclear binding.…”

In-medium $\mathaccent "7016\relax K$- and $\eta $-meson Interactions and Bound States

“…Yet, systematic treatments of energy dependence within dynamical and self-consistent calculations ofK and η bound states in nuclei have been lacking until recently. The present overview is focused on recent progress made by the Prague-Jerusalem Collaboration towards incorporating medium modifications, particularly those implied by the energy dependence of the corresponding scattering amplitudes [4,5,6,7,8,9,10,11].…”

\(\bar{K}\)N Interactions in the Nuclear Medium and \(\bar{K}\) Nuclear Quasi-Bound States

“…In our calculations [4][5][6][7][8] we applied meson-baryon coupled-channel separable s-wave interactions by Cieplý and Smejkal [3,9] which are matched to equivalent chiral SU(3) scattering amplitudes derived from the chiral effective Lagrangian at up to next-to-leading order (NLO). Solving the coupled-channel Lippmann-Schwinger equations F = V + VGF with the potential kernels leads to a separable in-medium scattering amplitudes F i j , given in the two-body cm system by…”

“…[4][5][6]. The point is that in the nuclear medium (for A ≫ 1 approximated by the lab system) the argument √ s in the scattering amplitudes is given by…”

“…[4][5][6] for details). The interaction of K − with a nucleus is described by the Klein-Gordon equation of the form…”