One-Pole Approximation in the Elastic Scattering of Composite Particles

Abstract

We consider deuteron-alpha scattering, since it is a physical system in which the small separation between elastic and inelastic (breakup) thresholds can lead to observable consequences. Taking into account the three-body channel, we derive an approximate dispersion relation for the elastic amplitude and solve it in the one-pole approximation. We test its internal consistency by fitting the pole parameters to the ${\mathrm{Li}}^6$ binding energy and the $d-\alpha$ scattering length in the $J^{\pi }=1^{+}$ channel, and to the position and width of the ${\mathrm{Li}}^6$ resonance in the $3^{+}$ channel. We then calculated the corresponding phase shifts and compared them with the experimental values, obtaining good agreement. The good agreement of this fit gives us confidence in our subsequent assessment of the qualitative influence of the nearby three-particle inelastic channel on the (two-body) elastic scattering amplitude.