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Relativistic scattering with spatially-dependent effective mass in the Dirac equation

A. D. Alhaidari·H. Bahlouli·A. Al-Hasan·M. S. Abdelmonem
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Abstract

We formulate an algebraic relativistic method of scattering for systems with spatially dependent mass based on the J-matrix method. The reference Hamiltonian is the three-dimensional Dirac Hamiltonian but with a mass that is position-dependent and having a constant asymptotic limit. Additionally, this effective mass distribution is locally represented in a finite dimensional function subspace. The spinor couples to spherically symmetric vector and pseudo scalar potentials that are short-range such that they are accurately represented by their matrix elements in the same finite dimensional subspace. We calculate the relativistic phase shift as a function of energy for a given configuration and study the effect of spatial variation of the mass on the energy resonance structure.

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A. D. Alhaidari, H. Bahlouli, A. Al-Hasan, M. S. Abdelmonem. 2007-03-09. Relativistic scattering with spatially-dependent effective mass in the Dirac equation. https://doi.org/10.1103/physreva.75.062711

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