Abstract
An Ansatz based on an etalon function generated by the problem itself is used in order to obtain a uniform asymptotic approximation of the 3D wave function for the scattering by a non-central potential. The obtained uniform asymptotic approximation removes the singularities at the caustics that occur in the 3D WKB approximation. The scattering amplitude provided by the uniform asymptotic approximation contains the poles that are the fingerprints of the system. The comparison of the obtained uniform asymptotic approximation of the 3D scattering wave function with the exact scattering wave function shows the versatility of the Ansatz based on an etalon function generated by the problem itself.
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