A NEW UNIFORM ASYMPTOTIC APPROXIMATION OF 3D SCATTERING WAVE FUNCTION FOR A CENTRAL POTENTIAL

A new uniform asymptotic approximation of the 3D scattering wave function for a central potential is obtained by using an etalon function generated by the problem. The regular reduced radial wave function of zero orbital angular momentum is used as etalon function rather than a standard special function, as used in the Kravtsov-Ludwig uniform approximation. The method is applied to the scattering by a pure Coulomb potential. The obtained uniform asymptotic approximation of the 3D Coulomb scattering wave function has the same expression as the exact solution.