New separable expansion for local potentials

A simple and practical method is given for constructing a rapidly convergent separable expansion, with simple form factors, for the $t$ matrix of a local potential. The requirement of two-particle unitarity is maintained for approximations of any rank. Unlike commonly used methods, the calculation of eigenfunctions and eigenvalues of the kernel of the Lippmann-Schwinger equation is not required. The method is illustrated for the two of the commonly used nucleon-nucleon potentials and the results compared with the unitary pole expansion and the exact results. Also in these cases our method yields an excellent rank-one approximation to the $t$ matrix.