Calculation of low-energy scattering parameters using artificial oscillator trap

Abstract

We introduce a recipe to estimate the low-energy scattering parameters of a quantum few-body system - scattering length, effective range, and shape parameter - by using only discrete state calculations. We place the system in an artificial oscillator trap of appropriate size and calculate the energies of the resulting discrete states close to the threshold of the system. The low-energy scattering parameters are then extracted - using a simple analytic formula - from the functional dependence of these energies upon the trap size. We first test the recipe against a simple model problem and then apply it to low-energy nucleon-nucleon scattering within the nuclear Model with Explicit Mesons in one sigma-meson approximation.