Three-body unitary transformations, three-body forces, and trinucleon bound state properties

A three-body unitary transformation method for the study of three-body forces is presented. Starting with a three-body Hamiltonian with two-body forces, unitary transformations are introduced to generate Hamiltonians that have both two- and three-body forces. For cases of physical interest, the two-body forces of the altered Hamiltonians are phase equivalent (for two-body scattering) to the original and the three-body force vanishes when any interparticle distance is large. Specific examples are presented. Applications for studying the possible role of three-body forces in accounting for trinucleon bound state properties are examined. Calculations of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ charge form factors and Coulomb energy difference with hyperspherical radial transformations and with conventional $N$-$N$ potentials are performed. The form factor calculations demonstrate how the proposed method can help obtain improved agreement with experiment by the introduction of appropriate three-body forces. Calculations of the Coulomb energy difference confirm previous estimates concerning charge symmetry breaking in the $N$-$N$ interaction.