Pole inkcotδfor doublet,s-wave,n-dscattering

The position of the pole in $kcot\delta$, for doublet, $s$-wave, $n$-$d$ scattering, and its residue are shown to be correlated with the doublet scattering length. An approximate, analytic solution of the $\frac{N}{D}$ equations of Barton and Phillips indicates a linear dependence on the doublet scattering length for the pole position, and a quadratic dependence for the residue. These relationships are tested by means of exact numerical solutions of $\frac{N}{D}$ equations and three-particle equations with separable two-particle interactions, and found to be qualitatively correct. The approximate, analytic solution of the $\frac{N}{D}$ equations leads to a formula for $kcot\delta$, which is of the same form as the phenomenological formula used previously by other authors. A formalism is presented which makes it possible to parametrize the effect of the omitted portion of the left hand cut in an $\frac{N}{D}$ calculation.