O(4) Expansion of the ladder Bethe-Salpeter equation

Details O(4) Expansion of the ladder Bethe-Salpeter equation O(4) Expansion of the ladder Bethe-Salpeter equation

1996-07-20

arxiv.org/abs/nucl-th/9607041v1

Few Body Syst.21:167-185,1996

Physics

Nuclear Physics

Nuclear Theory

21 pages, revtex

Scientific paper

10.1007/s006010050046

The Bethe-Salpeter amplitude is expanded on a hyperspherical basis, thereby reducing the original 4-dimensional integral equation into an infinite set of coupled 1-dimensional ones. It is shown that this representation offers a highly accurate method to determine numerically the bound state solutions. For generic cases only a few hyperspherical waves are needed to achieve convergence, both for the ground state as well as for radially or orbitally excited states. The wave function is reconstructed for several cases and in particular it is shown that it becomes independent of the relative time in the nonrelativistic regime.

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