Asymptotic boundary conditions for three-body breakup: Probable nonutility of the standard approach

The coordinate space wave function describing three-body breakup behaves asymptotically like ${\rho }^{\mathrm{-}5/2}$, where ρ is the hyperspherical radius. It is concluded herein that the minimum ρ at which the asymptotic form is valid may be so large as to render impractical a position-space calculation of breakup using this form. This conclusion is based on tests of the accuracy of the stationary phase approximation, used to obtain the ${\rho }^{\mathrm{-}5/2}$ behavior. Significant errors are found in the stationary phase approximation for ρ=1000 fm and in one case for ρ=8300 fm at E=20 MeV.