Inverse potential scattering problem and its application to the Na–He system

We use the phase-integral approximation in the frame of the inverse scattering theory to reconstruct a potential of the type $v=v_{1}+v_{2}$ in which one component $v_{1}$ is assumed to be known a priori. We introduce an auxiliary potential with two adjustable parameters and show that the unattainable potential range (i.e., the range in which the potential cannot be reconstructed using this method) can be significantly reduced. An excellent agreement is obtained between the original potential and the current results in almost the entire range.