Two-Body Local-Momentum Approximation of Spinless Particles Scattered by a (1+1)-D Woods-Saxon Barrier Potential

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Communications in Theoretical Physics ›› 2017, Vol. 67 ›› Issue (06) : 619-625.

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Two-Body Local-Momentum Approximation of Spinless Particles Scattered by a (1+1)-D Woods-Saxon Barrier Potential

Karl-Erik Thylwe

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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.

Key words

two-body effects / semi-relativistic / barrier transmission

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Karl-Erik Thylwe. Two-Body Local-Momentum Approximation of Spinless Particles Scattered by a (1+1)-D Woods-Saxon Barrier Potential[J]. Communications in Theoretical Physics, 2017, 67(06): 619-625

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