Energy Dependence of the πN Amplitude and the Three-Nucleon Interaction

Abstract.

By calculating the contribution of the ππ three-body force to the three-nucleon binding energy in terms of the πN amplitude using perturbation theory, we are able to determine the importance of the energy dependence and the contribution of the different partial waves of the πN amplitude to the three-nucleon force. A separable representation of the non-pole πN amplitude allows us to write the three-nucleon force in terms of the amplitude for NN → NN*, propagation of the NNN* system, and the amplitude for NN* → NN , with N* being the πN quasi-particle amplitude in a given state. The division of the πN amplitude into a pole and non-pole part gives a procedure for the determination of the πNN form factor within the model. The total contribution of the three-body force to the binding energy of the triton for the separable approximation to the Paris nucleon-nucleon potential (PEST) is found to be very small mainly as a result of the energy dependence of the πN amplitude, the cancellation between the S- and P-wave πN amplitudes, and the soft πNN form factor.