Effect of the Pauli exclusion principle in the electric dipole moment of ${}^9$Be with $\mathrm{\mid }\mathrm{\Delta }S\mathrm{\mid }=1$ interactions

We calculate the contribution of the $\mathrm{\mid }\mathrm{\Delta }S\mathrm{\mid }=1$ $K$ meson exchange process generated by the Cabibbo-Kobayashi-Maskawa matrix to the electric dipole moment (EDM) of the ${}^9$Be nucleus by considering the $\alpha n - \alpha \Lambda$ channel coupling. It is found that the effect of the Pauli exclusion principle is not important intermediate $S=-1$ state, and that the result is consistent with the EDM of ${}^9$Be calculated with the $\mathrm{\mid }\mathrm{\Delta }S\mathrm{\mid }=1$ interactions as a perturbation without considering the nucleus-hypernucleus mixing. Our result suggests that the effect of the $\mathrm{\mid }\mathrm{\Delta }S\mathrm{\mid }=1$ interactions is neither suppressed nor enhanced in nuclei, if the difference of binding energies between the nucleus and the hypernucleus is small compared to the hyperon-nucleon mass difference.