The efficient computation of JWKB phase shifts

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Abstract
An exhaustive study of methods for computing the JWKB phase shift is reported. It is concluded that the integrals involved in the expression for the JWKB phase shift are best evaluated using a modification of the Clenshaw-Curtis method after the singularities have been removed by appropriate changes of variable. It is argued that the modified Clenshaw-Curtis quadrature method should be adopted generally for the numerical evaluation of integrals when the integrands are reasonably well behaved.