Comparison of the unitary pole and Adhikari-Sloan expansions in the three-nucleon system

The binding energy of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, the percentage $S$-, $S^{\prime }$-, and $D$-state probability, and the charge form factor of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are calculated using the unitary pole and Adhikari-Sloan separable expansions to the Reid soft core potential. Comparison of the results for the two separable expansions show that the expansion of Adhikari and Sloan has the better convergence property, and the lowest rank expansion considered (equivalent to the unitary pole approximation) gives a good approximation to the binding energy of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and the charge form factor of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, even at large momentum transfer ($K^2<20\mathrm{}$ ${\mathrm{fm}}^{-2\mathrm{}}$).