Comparison of realistic local and one-boson-exchange potentials in the three-nucleon system

The disagreement that currently exists regarding the calculated and experimental values of the triton binding energy ($E_T$) and the doublet scattering length (${}_{}{}^2{}_{}{}^{}a$) is analyzed in considerable detail. Using the unitary pole approximation, which has previously been tested with great success, we have calculated $E_T$ and ${}_{}{}^2{}_{}{}^{}a$ for a large class of realistic potentials. The results show that the one-boson-exchange potentials (OBEP) give in general ∼1 MeV more binding for ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and correspondingly smaller ${}_{}{}^2{}_{}{}^{}a$ than the local hard- and soft-core potentials. This difference is shown to be partly due to the fact that the OBEP have in general smaller deuteron $D$-state probability, and partly due to the fact that they fit the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ $n-p$ rather than the $p-p$ data. Finally, we demonstrate that the correlation between $E_T$ and ${}_{}{}^2{}_{}{}^{}a$, predicted by Phillips on the basis of separable potential calculations, has validity for the more realistic interactions.