Date of Original Version
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 the np 1S0 state. 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 1S0 scattering; effects of hard cores.
Hartt, K. (1980). Padé approximants, NN scattering, and hard core repulsions. Physical Review C, 22(4), 1377-1387. doi: 10.1103/PhysRevC.22.1377
Available at: http://dx.doi.org/10.1103/PhysRevC.22.1377