Possible effect of the three-nucleon force on the virtual state of the triton and the correlated n-d doublet scattering length

The energy $E_v$ of the virtual state of the triton on the second sheet is calculated. The inclusion of a three-nucleon force moves $E_v$ towards the n-d threshold. The n-d doublet scattering length $a_2$ is strongly correlated with $E_v$. This offers a possible explanation for the improvement of the theoretical value for $a_2$ when a three-nucleon force is included.