Analysis of $3N$ Parameters with $N-N$ Forces

This investigation has a twofold objective, (a) to examine in some detail the effects of various refinements in the input forces on the binding energy (BE) of the triton and the doublet neutron-deuteron scattering length ($a_{\frac{1}{2}}$), and (b) to compare the effects of shape variations in the potentials on the evaluation of the same quantities. For this purpose, we calculate the BE and $a_{\frac{1}{2}}$ with the inclusion of tensor and core effects individually and collectively and give a comprehensive comparison of these results along with those obtained in earlier investigations by various authors. For the second objective, we present the results for an entirely different shape of the separable potentials (viz., form factors of the type $\surd Q_0$ which fulfill certain analyticity requirements on the potentials), and compare these predictions with those based on potentials proposed by Yamaguchi and Yukawa. The effects of the shape variation on the results found from the comparison of these potentials, which agree only approximately on the energy shell, persist even with higher-ranked potentials which agree much more closely on the energy shell as a result of the inclusion of repulsive-core terms. The limitations that the effects of shape variations imply on the reliability of three-body calculations with input two-body forces are discussed.