Relationship between the Scattering of High-Energy Dirac and Klein-Gordon Particles

Relationships have been found between the scattering of a high-energy relativistic particle that obeys the Dirac equation and one that obeys the Klein-Gordon equation. The phase shifts at high energies are related by ${\delta }_l=\frac{1}{2}({\eta }_l+{\eta }_{l+1\mathrm{}})$, where ${\delta }_l$ and ${\eta }_l$ are the Dirac and Klein-Gordon phase shifts, respectively; and the cross sections are related by ${\sigma }_D\left(\theta \right)={\sigma }_K\left(\theta \right){cos}^2\left(\frac{1}{2}\theta \right)$, where ${\sigma }_D$ and ${\sigma }_K$ are the Dirac and Klein-Gordon cross sections, respectively. The errors in these relations are discussed and the results of a numerical calculation using a square well potential are given to illustrate the accuracy of the above relations.