$K^+$-nucleus potentials from $K^+$-nucleon amplitudes

TL;DR

This paper develops a new method to construct optical potentials for $K^+$-nucleus interactions from $K^+$-nucleon amplitudes, improving agreement with experimental data across various nuclei and energies.

Contribution

It introduces an algorithm based on $K^+$-N kinematics in the nuclear medium to better model $K^+$-nucleus interactions, incorporating energy dependence and Pauli correlations.

Findings

Improved reproduction of reaction and total cross sections with energy-dependent amplitudes.

Inclusion of Pauli correlations enhances agreement with experimental data.

Discrepancies in cross sections for heavier nuclei suggest the need for a 40 ext{%} increase in the imaginary potential component.

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.