Pole in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi><mml:mi/><mml:mrow><mml:mo>cot</mml:mo></mml:mrow><mml:mi>δ</mml:mi></mml:math>for doublet,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math>-wave,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>scattering

The position of the pole in $kcot\ensuremath{\delta}$, 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 $kcot\ensuremath{\delta}$, 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.NUCLEAR REACTIONS Pole in $n$-$d$, doublet, $s$-wave $kcot\ensuremath{\delta}$, $\frac{N}{D}$ calculations, solutions of three-particle equations with separable interactions.

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