Contribution of three-body force to the trinucleon problem by an essentially exact calculation

The hyperspherical harmonic method has been used to calculate the effect of two-pion exchange three-body force (Fujita-Miyazawa type) on trinucleon systems, with the $N-N$ Afnan- Tang S3 potential. The Coulomb force and three-body force have been taken into account nonperturbatively. Simplification in the numerical calculation has been achieved through the use of an adiabatic approximation in order to decouple the system of differential equations. Binding energy, charge form factor, and pointlike proton density of both ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ have been calculated for various values of the cutoff parameter in the three-body force. Results indicate that the inclusion of the three-body force improves agreement with experiment. An interesting feature is the possible appearance of nodes near origin in the hyper-radial wave function.