T-Matrix Perturbation Theory for the Three-Nucleon System with the Reid Potential

The binding energy of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ for the Reid soft-core ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ potentials was determined, using $T$-matrix perturbation theory, to be 7.02 MeV. The one-term separable approximation to the Reid potential, constructed using the deuteron wave function in the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ channel and the form factor associated with the antibound state in the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ channel, gave a binding energy of 7.15 MeV. This is close enough to the exact answer to be very useful in realistic three-nucleon calculations. It also demonstrates the important contribution that the two-body bound state wave functions make to the triton binding energy.