The dependence of the triton binding energy on the high-energy phase shift

Abstract

An investigation of the dependence of the binding energy of the model triton on the highenergy part of the phase shift has been made for an interaction consisting of a second-rank separable potential. For this investigation we used our previous exact solution of the inverse scattering problem for a second-rank separable potential. It is shown that for input phase shifts obtained from either a standard separable potential or a local potential with a repuslive core this high-energy dependence of the binding energy is rather small. However arbitrary modifications in the standard phase shift at high energies produce large effects in the binding energy, presumably resulting from the “unphysical” nature of such changes. It is also found that separable potentials reproducing the same two-body data as a local potential generally produce much higher triton binding energies than the local potential. The effect of the interaction between the high-energy on-shell phase shift and the off-shell behaviour of the potential on the triton binding energy is also discussed.