Computation of negative-energy Coulomb functions

Two new uniform semiclassical methods are presented for calculating negativ e-energy Coulomb functions, a highly accurate uniform Airy approximation in the vicinity of the outer classical turning point, and a parabolic uniform approximation to cover energy ranges close to and below the minimum in the ,centrifugally corrected Coulomb potential-energy curve. Test calculations at half-integer quantum numbers show excellent agreement with numerical sol utions of the radial equation, particularly for the uniform Airy approximat ion. A model problem, designed to test the parabolic approximation, gives e xcellent agreement for the eigenvalues, even those lying close to or below the centrifugally corrected Coulomb potential minimum.