We introduce a new separable expansion for local potentials. The expansion, called the unitary pole expansion, has real, energy-independent form factors, and satisfies the requirements of two-particle unitarity in all orders. The convergence of the expansion is investigated by comparing expanded and exact $T$ matrices for negative energies, and by performing three-body bound-state calculations. In the latter case, a one-term approximation gives energies accurate to within 2% for potentials containing repulsion of the magnitude indicated by two-nucleon data.

• Received 19 December 1969

DOI:https://doi.org/10.1103/PhysRevC.1.1667