Tensor force and zero-energy n-d scattering

Abstract

A three-body formalism with separable potentials is developed, with the inclusion of tensor forces in addition to the usual s-wave forces in triplet and singlet N-N states. For completeness, the formalism is generalized to include the effect of a hard core term in the singlet s-state, which is shown to require an extra spectator function, over and above three others already associated with the tensor and s-wave forces. Numerical results are presented for the doublet n-d scattering length, which, unlike its quartet counterpart, is rather sensitive to variations in the two-body potential parameters. While it has not yet been possible to obtain a quantitative estimate of the hard-core effect (because of the enormous computational problems associated with four spectators) the effect of the tensor force has been investigated in some detail with several sets of input parameters as are currently available. It is found that while the inclusion of tensor force greatly improves the magnitude of the scattering length, its sign is still negative, contrary to the experimental situation. The assumption of a smaller magnitude for the (negative) n-n scattering length, than its charge-independent value, (for which there is some recent evidence), yields a further improvement in the value of a_1/2, but not enough to flip its sign. This discrepancy is briefly discussed in the context of similar results obtained by other authors.