A Realistic Formalism for 4 N Bound State in a Three - Dimensional Yakubovsky Scheme

A spin-isospin dependent Three-Dimensional formalism based on the momentum vectors for the four-nucleon bound state is presented. The four-nucleon Yakubovsky equations with twoand three-nucleon interactions are formulated as a function of the vector Jacobi momenta. Our formalism, according to the number of spin-isospin states that one takes into account, leads to only a strictly finite number of the coupled three dimensional integral equations to be solved. The evaluation of the transition and permutation operators as well as the coordinate transformations due to considering the continuous angle variables instead of the discrete angular momentum quantum numbers are less complicated in comparison with partial wave representation. With respect to partial wave the present formalism with the smaller number of equations leads to higher dimensionality of the integral equations. We have concluded that three dimensional formalism is less cumbersome for considering the three-nucleon forces.