Abstract
A density expansion of the ${K}^{+}$-nucleus optical potential is used within a momentum-space approach to analyze the experimental total and elastic differential cross section data. We add to the microscopic first-order optical potential a phenomenological higher-order term proportional to the nucleon density raised to a power $\ensuremath{\alpha}.$ A fit to the total cross section data yields a value for $\ensuremath{\alpha}$ of $2.85\ifmmode\pm\else\textpm\fi{}0.25$ and a strength for the potential that decreases slightly faster than the inverse of the kaon laboratory momentum. To obtain a higher-order potential compatible with all the data and with parameters that are target independent, a renormalization of the differential cross section data by 30%, consistent with our estimate of systematic errors, is made. The need for such a large renormalization is explained.
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