K−Mesonic X Rays and theK¯−NScattering Lengths

Abstract

$K^{-}$ mesonic x rays from helium have recently been observed and their energies and intensities measured. The strong-interaction effects on these lines appear to be an order of magnitude smaller than expected on the basis of simple considerations. We discuss a model for the strong $K^{-}-\alpha$ interaction effects assuming dominance of two-body $\overline{K}-N$ interactions and based upon the representation of the $\overline{K}-N$ interactions by complex central Yukawa potentials adjusted to the experimental scattering lengths. For ranges associated with any known particle exchanges, the results, although very different from those obtained previously in Born approximation, still disagree by an order of magnitude with experiment. After considering various alternative explanations of this disagreement, we note that a $\overline{K}-N$ scattering-length solution having a value for Im $A_1$ considerably smaller than that currently favored would allow agreement of our model with experiment.