Evaluation of high-order JWKB phase integrals

Abstract

Two simple and reliable quadrature procedures for evaluating JWKB phase integrals of the form ∮dr f (r)/[E−U (r)]k+1/2 for integer k≳0 and any smooth potential U (r) are derived, tested, and compared. Their development allows calculations based on the higher-order JWKB quantization conditions to be done with virtually the same ease now associated with use of the first-order approximation. Applications to date include calculation of two-term and three-term (i.e., third- and fifth-order) JWKB eigenvalues and the direct calculation of diatomic molecule centrifugal distortion constants for both analytic and numerical potential energy functions.