Abstract
This paper investigates an energy-dependant finite rank approximation to the three-body amplitude at scattering energies both below and above the breakup threshold. The expansion method is one proposed by Adhikari and Sloan as an approximation method for solving few-body integral equations. Cubic spline functions are used to evaluate the expansion terms without contour rotation. Numerical results are obtained for a system of three identical bosons and the utility of this expansion method in a numerical treatment of the integral equations for four-body scattering is briefly discussed. Due to logarithmic singularities in the off-shell three-body amplitude at positive energies, no pointwise agreement is found between the separable expansion and the exact three-body amplitude at energies above the breakup threshold.
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