Accurate Three-Nucleon Bound-State Calculation with an Extended Separable Expansion of the Two-Body T-Matrix

Abstract.

An accurate solution for the three-nucleon bound state is obtained within 1 keV in the binding energy and, on the whole, better than 1% in the wave function, using a new systematic and efficient method. The method is based on a recently developed separable expansion for any finite-range interaction, in which a rigorous separable series for the two-body t-matrix is obtained by expanding the wave function in terms of a complete set of basis functions inside the range of the potential. In order to treat a potential with a strong repulsive core, as in the case of the Argonne potential, we develop a two-potential formalism. The expansion starts with a few EST (Ernst, Shakin, and Thaler) terms in order to accelerate the convergence and continues with an orthogonal set of polynomials, avoiding the known difficulties of a pure EST expansion. Thus, several techniques are combined in the present extended separable expansion (ESE). In this way, the method opens a new systematic treatment for accurate few-body calculations resulting in a dramatic reduction in the CPU time required to solve few-body equations.