K−-Mesonic Atoms

Abstract

Computational techniques previously used by the authors for the treatment of ${\mu }^{-}$- and ${\pi }^{-}$-mesonic atoms are extended to $K^{-}$-mesonic atoms and x-ray yields for the most important transitions are calculated as a function of atomic number. It is shown that the experimental measurement of these yields will provide a sensitive determination of the imaginary part of the $K^{-}$-nucleus optical potential. The level shifts due to the meson scattering interaction are also discussed. In principle, one can relate the level shifts to the real part of the zero-energy scattering lengths with the help of the theory of Deser et al.; however, the calculations show that, for the ground state, such measurements will be more difficult to perform than in ${\pi }^{-}$-mesonic atoms because of the low yields of the $K$ lines. Therefore, an attempt was made to predict the shifts of the $2p$ state. It turns out that these shifts are expected to be measurable, both from the point of view of magnitude and yield, for the elements from carbon to fluorine. The Auger electron spectra from stopping $K^{-}$ mesons in nuclear emulsion are derived from the cascade calculations. In particular, it is shown that the expected fraction of $K^{-}$ captures associated with at least one Auger electron of more than 15-keV energy is 4% in the light (C,N,O) and 88% in the heavy (AgBr) emulsion elements. An experiment on Auger electrons in nuclear emulsion is described. Whereas the theoretical and experimental numbers of $K^{-}$ stoppings associated with electrons are in good agreement, there are systematic discrepancies in the details of the energy and multiplicity spectra which are, most probably, due to experimental uncertainties. The level shifts in $\pi$-mesonic atoms are briefly discussed in an Appendix.