Use of Analyticity in the Calculation of Nonrelativistic Scattering Amplitudes

A new method of calculating nonrelativistic scattering amplitudes is presented. The scattering amplitude is first calculated as a function of the complex energy below the scattering threshold, and the numerical results are then analytically continued to the physical region. The method is used to calculate two-body and two-channel scattering amplitudes. The numerical analytic continuation is accomplished by a rational-fraction representation similar to the Pad\'e method. Several techniques of numerical analytic continuation by rational fractions are described, and some examples are discussed.