Trinucleon system in a two-body model: Coulomb effect on bound and scattering states

Recently it has been suggested that as in the neutron deuteron problem the theoretically calculated spin-doublet S wave proton deuteron scattering length $^{2}\mathrm{a}_{\mathrm{pd}}$ is correlated with $^{3}\mathrm{He}$ binding energy. This strongly suggests that $^{2}\mathrm{a}_{\mathrm{pd}\mathrm{\ensuremath{\simeq}}0}$. In this paper we study various properties of the low energy trinucleon system including this correlation among scattering length and binding energy for the spin-doublet neutron deuteron and the proton deuteron systems in an ad hoc two-body model. The two-body potential models we employ have a long range tail of ${r}^{\mathrm{\ensuremath{-}}2}$ type and have been parametrized to produce the correct binding energies of $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ and the correct s wave spin-doublet neutron deuteron scattering lengths $^{2}\mathrm{a}_{\mathrm{nd}}$. The present study predicts the low energy nucleon deuteron phase shifts and predicts the proton deuteron scattering length to be $^{2}\mathrm{a}_{\mathrm{pd}\mathrm{\ensuremath{\simeq}}(0.15\ifmmode\pm\else\textpm\fi{}0.1}$) fm.

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