Quasiparticle Calculations for a Three-Body Model with Local Potentials

The quasiparticle concept introduced by Weinberg for two-particle scattering has recently been applied to the three-body problem. It leads to an exact representation of the scattering matrix in terms of a modified Born series, the lowest order of which yields just the widely used separable-potential approximation. To test this method, the binding energies of three identical spinless particles interacting via Yukawa potentials, and the elastic scattering of one particle off a bound state of the other two, are calculated in zeroth- and first-order quasi-Born approximation. Our calculation shows that the inclusion of the first quasi-Born correction greatly improves the zeroth-order, i.e., the separable-potential, results. Comparison is also made with other calculations recently performed in this model.