Abstract
A local momentum (LM) approximation applicable to semi-relativistic two-body repulsive interactions is presented. It assumes negligible variations in the (vector-type) potential. A Woods–Saxon barrier with a rectangular-like shape is studied in some detail. The LM-approximation gives exact results within the semi-relativistic framework for rectangular barrier interactions in (1+1) dimensions. Further approximations of the local momentum approach leads to the two-body approximation of Ikhdair & Sever, known since the early 90’s as the spinless Salpeter equation approximating the Bethe–Salpeter equation. LM- and GS-results indicate significant two-body effects. Results obtained from the (single-mass) Dirac equation are similar for certain two-body mass combinations.
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