Solution for boson-diboson elastic scattering at zero energy in the shape-independent model

Abstract

We derive an exact analytic expression for the boson-diboson elastic scattering phase shift in the shape-independent model for positive two-body scattering lengths when the total energy vanishes. A three-body hard-core potential depending upon a hyperradial cutoff parameter R0 is introduced to obtain a finite result. The exact result is compared with adiabatic hyperspherical calculations of the phase shift, and a similar functional dependence on the cutoff parameter is found. The cutoff parameter plays the role of a renormalization constant in that it renormalizes the wave function at vanishing hyperradius.