The nucleon-nucleon ͑NN͒ t matrix is calculated directly as function of two vector momenta for different realistic NN potentials. To facilitate this a formalism is developed for solving the two-nucleon LippmannSchwinger equation in momentum space without employing a partial wave decomposition. The total spin is treated in a helicity representation. Two different realistic NN interactions, one defined in momentum space and one in coordinate space, are presented in a form suited for this formulation. The angular and momentum dependence of the full amplitude is studied and displayed. A partial wave decomposition of the full amplitude it carried out to compare the presented results with the well-known phase shifts provided by those interactions.PACS number͑s͒: 21.45.ϩv, 13.75.Cs

A recently developed formulation for treating two-and three-nucleon bound states in a threedimensional formulation based on spin-momentum operators is extended to nucleon-nucleon scattering. Here the nucleon-nucleon t-matrix is represented by six spin-momentum operators accompanied by six scalar functions of momentum vectors. We present the formulation and provide numerical examples for the deuteron and nucleon-nucleon scattering observables. A comparison to results from a standard partial wave decomposition establishes the reliability of this new formulation. 21.45.Bc

An operator form of the 3N bound state is proposed. It consists of eight operators formed out of scalar products in relative momentum and spin vectors, which are applied on a pure 3N spin 1/2 state. Each of the operators is associated with a scalar function depending only on the magnitudes of the two relative momenta and the angle between them. The connection between the standard partial wave decomposition of the 3N bound state and the operator form is established, and the decomposition of these scalar function in terms of partial wave components and analytically known auxiliary functions is given. That newly established operator form of the 3N bound state exhibits the dominant angular and spin dependence analytically. The scalar functions are tabulated and can be downloaded. As an application the spin dependent nucleon momentum distribution in a polarized 3N bound state is calculated to illustrate the use of the new form of the 3N bound state.

A three-dimensional approach based on momentum vectors as variables for solving the three-nucleon Faddeev equation in first order is presented. The nucleon-deuteron breakup amplitude is evaluated in leading order in the nucleon-nucleon ͑NN͒ T matrix, which is also generated directly in three dimensions avoiding a summation of partial wave contributions. A comparison of semiexclusive observables in the d͑p, n͒pp reaction calculated in this scheme with those generated by a traditional partial wave expansion shows perfect agreement at lower energies. At about 200 MeV nucleon laboratory energies deviations in the peak of the cross section appear, which may indicate that special care is required in a partial wave approach for energies at and higher than 200 MeV. The role of higher order rescattering processes beyond the leading order in the NN T matrix is investigated with the result that at 200 MeV rescattering still provides important contributions to the cross section and certain spin observables. The influence of a relativistic treatment of the kinematics is investigated. It is found that relativistic effects become important at projectile energies higher than 200 MeV.

A recently developed helicity basis for nucleon-nucleon (NN) scattering is applied to the deuteron bound state. Here the total spin of the deuteron is treated in such a helicity representation. For the bound state, two sets of two coupled eigenvalue equations are developed, where the amplitudes depend on two and one variable, respectively. Numerical illustrations based on the realistic Bonn-B NN potential are given. In addition, an 'operator form' of the deuteron wave function is presented, and several momentum dependent spin densities are derived and shown, in which the angular dependence is given analytically.