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

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.

24 pages, 5 figures

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• Dual kinetic balance approach to basis set expansions for the Dirac equation
• An extended class of L2-series solutions of the wave equation
• Relativistic extension of the complex scaling method
• Unified algebraic treatment of resonance
• Relativistic J-matrix method
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Cited by in corpus (11)

• New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case
• Effective-Mass Dirac Equation for Woods-Saxon Potential: Scattering, Bound States and Resonances
• Scattering of Woods-Saxon Potential in Schrodinger Equation
• Scattering of a spinless particle by an asymmetric Hulth{é}n potential within the effective mass formalism
• Scattering states of a particle, with position-dependent mass, in a double heterojunction
• On the singular position-dependent mass
• Correction to Solution of Dirac Equation
• Quantum Mechanics without an Equation of Motion
• Dirac fermions with electric dipole moment and position-dependent mass in the presence of a magnetic field generated by magnetic monopoles
• Solutions of the spatially-dependent mass Dirac equation with the spin and pseudo-spin symmetry for the Coulomb-like potential
• Scattering phase shift for relativistic separable potential with Laguerre-type form factors