Abstract
Current algebra sum rules for kaon-nucleus elastic-scattering amplitudes are re-written as off-mass-shell, finite-contour forward dispersion relations. Saturating these latter with narrow levels, both in the meson-nucleus continua and in the bound-state spectra, we produce a general formula for the dependence of the real parts of kaon-nucleus scattering lengths on the target quantum numbers. We introduce explicitly a shell-model description of nuclear ground-states, which was instrumental in reproducing with satisfactory accuracy the corresponding pion-nucleus data: most of the effects observed there (up to and including the 2s−1d shell) were consistent with a naive spherical-harmonic-oscillator picture. An output of this analysis is the (average) kaon-nucleon sigma-term: the value derived here stays as large as found in two previous estimates by ourselves, the first from a slightly less sophisticated analysis of (mostly) the same data, the second derived from the dispersion-relation evaluations of the zero-energy, fixed-t kaon-nucleon scattering amplitudes made by Oades. Such a large value (about 640 MeV) confirms the hypothesis, advanced by Donoghue and Nappi, of a large, nonperturbative, strange-quark scalar density in the nucleon.
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