A technique to perform few-nucleon calculations in momentum space without employing partial wave (PW) decompositions is developed. It is shortly called the 3D technique, and is intended to be a viable alternative to the successful PW technique, especially for higher energies.

The development begins with the nucleon-nucleon (NN) system, where antisymmetric momentum-helicity basis states are defined, which are constructed using momentum vector states and helicity states of NN total spin. Appropiate for the momentum-helicity basis a set of six independent operators is defined to express any NN potential, which is given in operator form. Representative potentials are the modern AV18 and Bonn-B potentials, which are used in this work. The 3D technique is applied to both NN scattering and the deuteron. Comparison with PW calculations is performed to test the formulation and numerical realization of the 3D technique. In addition for the deuteron, an "operator form" of the deuteron wave function is presented, allowing for investigating some momentum dependent spin densities with analytic angular behavior.

The development and application of the 3D technique is extended to the Nd break-up process, in which the Faddeev's scheme is used. In this work only the leading term of the full Nd break-up amplitude is considered to describe the process at higher energies, beyond ~ 200 MeV projectile laboratory energy. For simplicity the deuteron state is kept being expanded in its partial wave components, s and d waves. The leading term of the amplitude in the 3N basis states is derived in a so called physical representation, where spins and isospins of the individual nucleons are taken, and the spins are quantized along an arbitrary but fixed z axis. For the NN system a connection between the physical representation and that in the momentum-helicity basis has been obtained. This leads then to an expression for the leading term of the full Nd break-up amplitude in terms of the NN T-matrix element in the momentum-helicity basis, with which 3N observables are calculated. These are the differential cross section, the neutron polarization, the proton analyzing power and the polarization transfer coefficients. The formulation is applied to the (p,n) charge exchange reaction in the semi-exclusive pd break-up process d(p,n)pp for energies up to ~ 500 MeV. For energies below ~ 200 MeV comparison with PW calculations is performed, as well as with the ones taking the full Nd break-up amplitude to see rescattering effects. Finally relativistic kinematics is introduced into the formulation, allowing to observe some relativistic effects. Comparisons are also performed with experimental data.

Results in this work show that the 3D technique has proven to be a good alternative to the PW decomposition and appears to be necessary at higher energies, where the PW technique is no longer feasible. In contrast to the PW decomposition the 3D technique requires much less algebraic work. For lower energies, where the PW calculations are still reliable, the 3D calculations show perfect agreement with the PW calculations.

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