Rapid accurate calculation of JWKB phase shifts

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Abstract
With a generalization of a procedure suggested by Pack, the JWKB phase shift has been evaluated using a number of Gauss–Mehler quadrature formulas. Extraordinary accuracy is obtained with convenient low‐order formulas employing the weight function (1−x)1/2 or (1−x)−1/2. The method has been tested with Lennard‐Jones (6–12), exponential, exp‐6, exp‐5, exp‐4, exp‐3, Morse, and Yukawa pontentials with excellent results in all cases. A change of variable is shown to make the method efficient even for high energies and small impact parameters. The present method is superior in speed and accuracy to the method proposed by Kennedy and Smith, which was formerly considered the best for numerical evaluation of JWKB phase shifts.