Low-momentum effective interaction in the three-dimensional approach

The formulation of the low-momentum effective interaction in the model space Lee-Suzuki and the renormalization group methods is implemented in the three-dimensional approach. In this approach the low-momentum effective interaction V_{low k} has been formulated as a function of the magnitude of momentum vectors and the angle between them. As an application the spin-isospin independent Malfliet-Tjon potential has been used into the model space Lee-Suzuki method and it has been shown that the low-momentum effective interaction V_{low k} reproduces the same two-body observables obtained by the bare potential V_{NN}.