Abstract
Optical potentials for $K^+$-nucleus interactions are constructed from $K^+$-nucleon amplitudes using recently developed algorithm based on $K^+$-N kinematics in the nuclear medium. With the deep penetration of $K^+$ mesons into the nucleus at momenta below 800~MeV/c it is possible to test this approach with greater sensitivity than hitherto done with $K^-$ and pions. The energy-dependence of experimental reaction and total cross sections on nuclei is better reproduced with this approach compared to fixed-energy amplitudes. The inclusion of Pauli correlations in the medium also improves the agreement between calculation and experiment. The absolute scale of the cross sections is reproduced very well for $^6$Li but for C, Si and Ca calculated cross sections are (23$\pm4$)\% smaller than experiment, in agreement with earlier analyses. Two phenomenological models that produce such missing strength suggest that the imaginary part of the potential needs about 40\% enhancement.
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