Trinucleon Coulomb energy with inclusion of a three-nucleon force

We calculate binding energy difference between ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ using the exact hyperspherical harmonics method where Coulomb force is treated nonperturbatively. A variety of two-nucleon potentials with or without a two-pion-exchange three-body force (Fujita-Miyazawa type) has been used properly. We compare our results with the "hyperspherical formula" and previous calculations. Calculated Coulomb energy agrees roughly with the hyperspherical formula; but the significant difference indicates that the perturbative treatment is not sufficient.