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Three‐Body Problems with Separable Two‐Body Interactions
Author(s) -
Osman A.
Publication year - 1980
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19804920407
Subject(s) - separable space , faddeev equations , physics , three body problem , formalism (music) , classical mechanics , integral equation , many body problem , gaussian , two body problem , mathematical physics , quantum mechanics , mathematical analysis , mathematics , art , musical , visual arts
Faddeev equations for the three‐body problem are reconsidered using separable two‐body interactions. The separable potentials reduce the Faddeev equations to coupled integral equations in one continuous variable. Numerical calculations for the resulting integral equations are carried out using separable two‐body interactions which include both attraction and repulsion potentials. Each of the separable attraction and repulsion potentials used is taken as a spin‐dependent central force together with tensor forces. The potential functions of the different parts of the two‐body interactions are taken to be of the Yamaguchi, Gaussian, Tabakin, Mongan and Reid forms. Each of the nuclei 6 Li, 9 Be and 12 C is taken to be composed of three particles according to the cluster structure description of nuclei. The binding energies of the nuclei 6 Li, 9 Be and 12 C are calculated as a three‐body problem and in the framework of the Faddeev formalism.