Solving Potential Scattering Equations without Partial Wave Decomposition

Details Solving Potential Scattering Equations without Partial Wave Decomposition Solving Potential Scattering Equations without Partial Wave Decomposition

2003-12-08

arxiv.org/abs/nucl-th/0312023v2

Phys.Rev. C69 (2004) 034003

Physics

Nuclear Physics

Nuclear Theory

15 pages, 4 figures

Scientific paper

10.1103/PhysRevC.69.034003

Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a partial-wave expansion. We illustrate this procedure for the Bethe-Salpeter equation for pion-nucleon scattering and give explicit details for the one-nucleon-exchange term in the potential. Finally, we show how this method can be applied to pion photoproduction from the nucleon with $\pi N$ rescattering being treated so as to maintain unitarity to first order in the electromagnetic coupling. The procedure for removing the azimuthal angle dependence becomes increasingly complex as the spin of the particles involved increases.

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