Validity of the unitary pole approximation at positive energies for hard-core exponential potentials

Exact analytic expressions for the S-wave phase shifts and half-shell functions have been obtained in the case of exponential potentials with and without hard core. The same quantities have also been computed in the unitary pole approximation to the same potential. A comparison of the exact and unitary pole approximation values shows that the unitary pole approximation is a fairly good approximation at positive energies too, particularly when the potential has an infinitely repulsive core