On the inverse scattering problem for a class of spin–orbit and central potentials

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Abstract
The nonrelativistic scattering of spin‐1/2 particles by a certain class of central and spin–orbit potentials is considered. The potential coefficients associated with the phase shifts of all physical angular momenta at a fixed energy are deduced. It is shown that the construction does not lead to a unique solution and the found set of potential coefficients depend on two arbitrary constants. Finally the potential coefficients associated with transparent spin–orbit and central potentials are explicitly constructed.