Validity and accuracy of separable potentials in three-body calculations

Abstract

The three-body problem is reconsidered using separable potentials for the two-body interactions. Using the separable approximation, the Faddeev equations reduce to coupled integral equations in one continuous variable. The separable two-body interactions used are taken as consisting of two parts to include both attraction and repulsion. Each part of the potential is a spin-dependent central force together with tensor forces. Numerical calculations for the resulting integral equations are carried out to calculate the binding energies of the nuclei 'H, 'He, Li, 'Be, and "C, using separable potentials of the Yamaguchi, Tabakin, Mongan, and Reid forms, The present calculations show the validity of the separable approximation and that the separable potentials extract accurate binding energies, NUCLEAB STBUCTUBE H, 3He, Li,~ae, C; three-body model. Calculated binding energiea.

Superfluid Phase Transitions and Effects of Thermal Pairing Fluctuations in Asymmetric Nuclear Matter

“…( 5) is a separable approximation of the S-wave contribution, V (0,0) α (k, k ′ ). Such a separable potential has been successfully applied to various nuclear systems [14,[23][24][25][26][27][28][29][30][31][32][33].…”

Bound Three Alpha Particles Model for the 12C Nucleus as a Three‐Body Problem

“…The wave function method which is suggested by Mitra [3] and Eyges [14] has succeeded in extracting the binding energies for some cases as has been shown by Leung and Park [15]. The non-local separable potentials have been used successfully-in calculating the binding energy of the 12C nucleus by Harrington [5] and Osman [12]. The alpha-alpha interactions used by Osman [12] in his calculations are taken as composed of short-range repulsive potentials surrounded by long-range attractive potentials.…”

“…The non-local separable potentials have been used successfully-in calculating the binding energy of the 12C nucleus by Harrington [5] and Osman [12]. The alpha-alpha interactions used by Osman [12] in his calculations are taken as composed of short-range repulsive potentials surrounded by long-range attractive potentials. These potentials include as well the tensor forces.…”

Convergence of 2-Body Effective Range Expansions for $nd$ Quartet Scattering

“…Some recent work which has made use of separable potentials in 3-body calculations can be found in Refs. [19,33,34]. Following Waston and Nuttall [14] but using our sign conventions, the nd 4 S 3/2 T -matrix for the th partial wave is given by…”

“…Building on earlier work by Weinberg [31], E. Harms [13] developed a separable expansion for the 2-body potential which admits an algebraic matrix solution for the T -matrix. Several authors have studied the convergence of the separable expansion of the 2-body potential in 3-body applications [19,32,33,34]. The separable expansion truncated at leading order is historically referred to as the "Unitary Pole Approximation" (UPA).…”