Square-well solution to the three-body problem

Details Square-well solution to the three-body problem Square-well solution to the three-body problem

1996-08-15

arxiv.org/abs/nucl-th/9608034v1

Few Body Systems 22 (1997) 193-236

Physics

Nuclear Physics

Nuclear Theory

34 pages, LaTeX file, 9 postscript figures included using epsf.sty

Scientific paper

10.1007/s006010050060

The angular part of the Faddeev equations is solved analytically for s-states for two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We consider systems with three identical bosons, three non-identical particles and two identical spin-1/2 fermions plus a third particle with arbitrary spin. The angular wave functions are in general linear combinations of trigonometric and exponential functions. The Efimov conditions are obtained at large distances. General properties and applications to arbitrary potentials are discussed. Gaussian potentials are used for illustrations. The results are useful for numerical calculations, where for example large distances can be treated analytically and matched to the numerical solutions at smaller distances. The saving is substantial.

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