Few-body bound states in a three dimensional approach

Recently the three dimensional (3D) approach has been successfully applied for three- and four-body bound states, where it greatly simplifies the numerical calculations without using the PW decomposition. The Faddeev-Yakubovsky equations with two- and three-nucleon interactions are formulated as a function of the vector Jacobi momenta. This formalism, according to the number of spin-isospin states that one takes into account, leads to only a strictly finite number of 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 is less complicated in comparison with partial wave representation. With respect to the partial wave representation the 3D formalism with the smaller number of equations leads to higher dimensionality of the integral equations.