Asymptotic normalization parameter of the triton

Abstract

On the basis of exact separable potential calculations, we show that there is a significant variation of the asymptotic normalization parameter ${{C}_{t}}^{2}$ of the triton with its binding energy. We present a partial wave dispersion relation technique for determining this parameter from the triton energy, the doublet $n\ensuremath{-}d$ scattering length, the doublet, $s$-wave, $n\ensuremath{-}d$ inelasticities, and the two-nucleon, on-shell scattering amplitudes. We test the method and find it to be accurate and stable with only low-energy information used as input. For a doublet scattering length of 0.65 fm we obtain ${{C}_{t}}^{2}=3.3\ifmmode\pm\else\textpm\fi{}0.1$, where the error limits are determined from uncertainties in the inelasticities and the analytic continuation of the two-nucleon amplitudes to negative energies.