Integro-differential equation approach. III. Triton and α-particle bound states. Realistic forces and two-body correlations

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Abstract
Four-nucleon binding energies and Faddeev amplitudes are calculated in the integro-differential equation approach, which neglects all N-body correlations with N≥3, for realistic forces in the three-channel approximation. Good agreement is obtained with corresponding results recently obtained by means of the Faddeev-Yakubovsky equations. Thereby, the dominance of two-body correlations, even for realistic forces, is established. The effect of the inclusion of the hypercentral potential in the definition of the (modified) Faddeev amplitudes for realistic forces is investigated and found to be of less importance for realistic forces than for central spin-dependent forces. The three- and four-nucleon modified Faddeev amplitudes are also compared. We found that the D-state Faddeev amplitudes are less sensitive to the number of nucleons, to the inclusion of the hypercentral potential, and to the nucleon-nucleon force than the mixed symmetry S’-state amplitudes.