Comparison ofΣ+pandΣ−nSystems

Assuming that the nuclear interactions between ${\Sigma }^{-}n$ and ${\Sigma }^{+}p$ are charge-symmetric, the effect of the Coulomb potential in the ${\Sigma }^{+}p$ system on the binding energy and wave function of a possible bound state of the ${\Sigma }^{+}p$ system is calculated. Using a phenomenological square-well potential the binding energies, ${\epsilon }_{+}$ and ${\epsilon }_{-}$, of the ${\Sigma }^{+}p$ and ${\Sigma }^{-}n$ systems are determined. In particular, it is found that the limiting condition, ${\epsilon }_{+}\to 0$, implies that ${\epsilon }_{-}$ is 0.38, 0.47, 0.62 Mev when the square-well range parameter, $b$, equals 1.4×${10}^{-13\mathrm{}}$, 1.0×${10}^{-13\mathrm{}}$, 0.6×${10}^{-13\mathrm{}}$ cm respectively. If the ${\Sigma }^{-}n$ interaction determines ${\epsilon }_{-}$ to lie in the small but finite region $0<\mathrm{}{\epsilon }_{-}<{\overline{\epsilon }}_{-}$, then the ${\Sigma }^{-}n$ system is bound and the ${\Sigma }^{+}p$ system unbound. Conversely, if ${\Sigma }^{+}p$ is bound, then ${\epsilon }_{-}>{\overline{\epsilon }}_{-}$. A brief discussion of the experimental situation with regard to these hyperon compounds is given.