Analyses of the energy-dependent single-separable-potential models for the $$\mathcal{N}\mathcal{N}$$ scattering

Abstract

By starting from a systematic study of the salient features regarding the quantum-mechanical two-particle scattering off an energy-dependent (ED) single separable potential and its connection with the rank-2 energy-independent (EI) separable potential in theT-(K-) amplitude formulation, the present status of the ED single-separable-potential models due to Tabakin (M1), Garcilazo (M2) and Ahmad (M3) has been discussed. It turned out that the incorporation of a self-consistent optimization procedure improves considerably the results of the1S0 and3S1 scattering phase shifts for the models (M2) and (M3) up to the c.m. wave numberq=2.5 fm−1, although the extrapolation of the results up toq=10 fm−1 reveals that the two models follow the typical behaviour of the well-known supersoft-core potentials. It has been found that a variant of (M3)—i.e. (M4) involving one more parameter—gives phase-shift results which are generally in excellent agreement with the data up toq=2.5 fm−1 and the extrapolation of the results for the1S0 case in the higher wave number range not only follows the corresponding data qualitatively, but also reflects a behaviour similar to the Reid soft-core and Hamada-Johnston potentials together with a good agreement with the recent [4/3] Pade fits. A brief discussion regarding the features resulting from the variations in the ED parts of all the four models under consideration and their correlations with the inverse-scattering theory methodology concludes the paper.