A quadrature procedure for the efficient computation of highhyphen;order semiclassical (or JWKB) scattering phase shifts for any smooth spherical potential is described and tested. In most situations this method yields phase shifts of rsquo;rsquo;quantum mechanical accuracyrsquo;rsquo; for almost the same computational effort associated with calculation of the familiar firsthyphen;order JWKB phase shifts. t t t
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