Method of Calculating Phase Shifts for Spherically Symmetric Potentials

A method of calculating the phase shifts for spherically symmetric nonsingular potential is presented. The radial Schrödinger equation is reduced to a Ricatti's equation which is solved in the form of a continued fraction. Illustrative calculations of S‐wave phase shifts for an attractive exponential potential are made with the first and second approximants of the continued fraction in comparison with the exact and Born phase shifts. For the potential parameter chosen $\text{(Z\hspace{0.17em}=\hspace{0.17em}2}\mathrm{and}\text{2.6)}$ the agreement with the exact value and the over‐all behavior of the phase shifts as a function of the momentum is reasonably satisfactory in contrast to the Born phase shift. A brief discussion of the possible application of the method and its limitations are given along with a remark on the extension to singular potentials. The convergence of the continued fractions is discussed with an example of an exponential potential in the appendix.