Discretizing the three-body continuum: bound states and two-body amplitudes

In this paper, we use a soluble model to investigate the accuracy of a discretization approximation for calculating bound states and two-body collision parameters. The model is that of three identical particles interacting via short-range, separable, S-wave pair potentials. Both weakl;y (spin-quartet fermion) and strongly (boson) interacting systems are examined. Discretization is achieved by diagonalizing the Hamiltonian for the two-particle subsystems in a finite set of L2 functions, here chosen to be Laguerre polynomials. By requiring that the energy and eigenfunction of the lowest-lying member of the resulting set of pseudostates be in excellent agreement with the actual bound-state energy and eigenfunction of the two-particle Hamiltonian, this method discretizes the three-particle continuum, replacing it with a set of two-body continua corresponding to pseudo-inelastic scattering