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

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. Received November 6, 1996; revised April 14, 1997; accepted for publication April 30, 1997     

Sum rules for forward elastic pion-nucleon scattering

A number of energy weighted sum rules relating amplitudes and differential cross sections for forward elastic and charge exchange scattering to the total pion-nucleon cross section are derived from dispersion relations.     

Sum rules for forward elastic photon scattering

Relations between integrals over forward elastic photon scattering amplitudes, forward elastic cross sections and total cross sections are derived from dispersion relations. A new photon-proton interaction sum rule is derived and evaluated.     

Quality of the three-nucleon bound-state wave function from a two-nucleon separable expansion method

The numerical quality of the³H wave function obtained by the separable expansion method of Ernst, Shakin, and Thaler is examined. Separable approximations to the Paris potential with increasing accuracy are used in the¹ S ₀ and³ S ₁-³ D ₁ partial waves to calculate the binding energy, wave function, wave-function component percentages, and theS- andD-wave asymptotic normalization constants of³H. The results are compared with existing five-channel calculations obtained directly (without expansion) from the Paris potential to determine convergence. It is found that the results converge rapidly to the right values, indicating that the³H wave function thus obtained is of high quality and essentially indistinguishable from that obtained directly from the Paris interaction.Dedicated to Profs. Erich Schmid and Ivo laus on the occasion of their 60th birthdays