K. HarttFollow

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Padé approximants to the scattering function F=k cot(δ0) are studied in terms of the variable x=k2, using four examples of potential models which possess features of thenpS01state. Strategies are thereby developed for analytically continuing F when only approximate partial knowledge of F is available. Results are characterized by high accuracy of interpolation. It is suggested that a physically realistic inverse scattering problem begins with such an analytically continued F. When it exists, the solution of this problem in terms of the Marchenko equation is a local potential of the Bargmann type. Some strategies for carrying out this program lead to a stably defined potential, while others do not. With hard core repulsions present, low order Padé approximants accurately describe F for Ec.m. ≤ 300 MeV. However, since the condition δ(∞)−δ(0)=0 is not satisfied in any of our examples containing hard core repulsions, the Marchenko method does not have a solution for them. A possible physical consequence of this result is discussed. Another inverse scattering method is proposed for application to hard core problems.

NUCLEAR REACTIONS Padé approximants used to calculate k cot(δ0)and to solve inverse scattering problem for models of np 1S0scattering; effects of hard cores.

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© 1980 The American Physical Society