Inverse problem for potential scattering at fixed energy. II.

Abstract

The inverse problem for quantal potential scattering at fixed energy is solved for a class of scattering functions which represent nonrational modifications of the rational functions of angular momentum considered in the "Bargmann" method of previous work.The new scheme has a wider range of applicability. This is demonstrated by means of numerical examples.

Strong absorption model and its associated potential

“…False Regge poles and zeros are connected with singularities in the potential. As long as the false poles and zeros are far from the real axis one can overcome this difhculty by exploiting the similarity of the rational and a nonrational scheme [17] on the real axis. Usually the mixed procedure works rather well for higher energies.…”

“…These differences are displayed in Fig. 3 [17] that a I/r singularity ta.ken in the background potential implies the same singularity in the total potential. The SAM S matrix therefore corresponds to a singular potential.…”

Equivalent local potential for the fish bone optical potential by inversion of its phase shifts

“…We briefly outline the quantal inversion method (mixed scheme) and refer to [16,17,18] for a full description. The potential V(r) is determined iterately, V(r)=Vx(r), The LS~)-+(r) are the logarithmic derivatives* of the Jost solutions f;}")-+(r) to the potential V~(r) in the rational scheme (Im 2 % > 0, Im fi2 < 0), and of the regular functions ~b(~")(r), in the nonrational scheme (Ima2<0, Im/?2>0).…”

Algebraic and coordinate space potentials from heavy ion scattering

“…Such equations also occur in the more conventional Si(k)~V(r, k) inverse scattering at fixed energy, e.g. , in the method of [8] based on the Bargman-type rational S function in A (A = l+ 2) and its nonrational generalization [9]. They are a general feature of inverse scattering formalisms, and it is interesting that it is retained in this context.…”