K−-Meson Absorption in Nuclei with Below-Threshold Effects

Energy level widths and level shifts of $K^{-}$-mesonic atomic levels corresponding to terminal atomic transitions preceding nuclear capture are calculated for ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$. In this calculation we have considered the effects on the $\overline{K}N$ system arising from the presence of the $Y_0^{*}\mathrm{}\left(1405\right)\mathrm{}$ quasibound state below threshold as well as the momentum distribution of the nucleons in the nucleus. The mass difference between the ${\overline{K}}^{0}n$ and $K^{-}p$ channels is also taken into account. The Klein-Gordon equation for the $K^{-}$ meson is solved by an iterative procedure in the presence of the nuclear optical potential and the Coulomb potential. Results are seen to compare quite favorably with experimental values given by Backenstoss et al.