Abstract
It is mathematically indicated that the widely used diabatic-by-sector recipe for solving coupled radial equations in the hyperspherical coordinate method causes non-negligible errors and these are revealed especially for extremely low-energy scattering. The intrinsic defects due to this method are illustrated for both bound state and the scattering states of $\mathrm{dt}\ensuremath{\mu}$. The calculated results are also compared with those obtained by the adiabatic expansion method.
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