Abstract
Rational approximants are introduced for expansions in orthogonal polynomials. They are proposed as a method to obtain fast convergent approximations. We investigate this possibility, by summing the partial wave expansion of the scattering amplitude in two cases, for which the exact phase shifts may be determined. In the first case, we consider the repulsive inverse square potential, as an example of the long range interactions usual in atomic collision processes. The results show, that when using this approximants, the knowledge of a few phase shifts is enough to obtain a degree of accuracy that requires several hundreds of them, when partial sums are used for the calculations. In the second case, we have considered the delta shell potential. Here the two approaches give similar results.
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Corbella, O.D., Garibotti, C.R. & Grinstein, F.F. Rational polynomial approximants and scattering amplitude for long range potentials. Z Physik A 277, 1–7 (1976). https://doi.org/10.1007/BF01547493
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DOI: https://doi.org/10.1007/BF01547493