Accuracy of the unitary pole approximation at positive energies for local potentials containing a hard core

The accuracy of the unitary pole approximation (UPA) to the two-body t matrix at positve energies has been examined for the case of a local potential with a hard core. To this effect the S-wave phase shifts and the half-shell functions (Baranger, Giraud, Mukhopadhyaya, and Sauer), have been calculated for the Herzfeld potential as well as for its UPA. The agreement between the two sets, though satisfactory, is not as good as reported by Levinger and O'Donoghue who did similar calculations for various singlet potentials. This result may be attributed to the existence of a bound-state pole in the t matrix in the negative energy region in the case of the Herzfeld potential