The three nucleon system including one dynamical pion: A one dimensional test case

The Padova model, describing piNNN scattering, is discussed in a new partition notation and a new approximation scheme is proposed. The resulting equations are recast in a standard AGS-form with the inclusion of correction terms to the two-cluster effective potential. These correction terms describe the explicit degree of freedom for one pion. It is shown that one set of correction terms can be interpreted as three-nucleon corrections of the Tucson-Melbourne type. A second set of correction terms is discovered that was previously not included in three-nucleon force calculations. In order to investigate the effect of the correction terms a one-dimensional system is developed that mimics standard two-nucleon physics. The corresponding three-nucleon system is investigated in respect to the 1D-triton binding energy. It is demonstrated that the TM-type correction terms depend significantly on an adjustable parameter. The range of the effect on the 1 D-triton binding energy makes it possible to correct the underbinding discovered in the standard calculation. However, it is also shown that the new type of correction terms has a non-negligible effect on the 1 D-triton binding energy. Therefore, the adjustment parameter should take this effect into account when gauged to the 1D-triton binding energy.