First-order neutron-deuteron scattering in a three-dimensional approach

The description of the neutron-deuteron scattering process has been possible using the partial wave approach since the 1980s (Few-Body Syst. 3 , 123 (1988); Phys. Rep. 274 , 107 (1996); Acta Phys. Pol. B 28 , 1677 (1997)). In recent years the so-called “three-dimensional” formalism was developed, where the calculations are performed with operators acting directly on the three-dimensional degrees of freedom of the nucleons. This approach avoids a tedious step of the classical calculations, the partial wave decomposition of operators, and in this paper is applied to the neutron-deuteron scattering process. The calculations presented here are a first step toward a new calculation scheme that would make it possible to easily produce precise predictions for a wide range of nuclear force models. This paper is a continuation of the work presented in Eur. Phys. J. A 43 , 339 (2010) where the breakup channel was considered in detail. The theoretical formulation used in this paper is very closely related to the formalism introduced in Eur. Phys. J. A 43 , 339 (2010) and Phys. Rev. C 68 , 054003 (2003), however, we work directly with the matrix representation of operators in the joined isospin-spin space of the three-nucleon system and use only the driving term of the three-nucleon Faddeev equations. This greatly simplifies the numerical realization of the calculation and allows us to consider also the elastic channel of the reaction.