# Low momentum scattering in the Dirac equation

@article{Dombey2001LowMS, title={Low momentum scattering in the Dirac equation}, author={Norman Dombey and Piers Kennedy}, journal={Journal of Physics A}, year={2001}, volume={35}, pages={6645-6657} }

It is shown that the amplitude for reflection of a Dirac particle with arbitrarily low momentum incident on a potential of finite range is −1 and hence the transmission coefficient T = 0 in general. If, however, the potential supports a half-bound state at momentum k = 0 this result does not hold. In the case of an asymmetric potential the transmission coefficient T will be nonzero whilst for a symmetric potential T = 1. Therefore in some circumstances a Dirac particle of arbitrarily small…

## 30 Citations

Low momentum scattering of the Dirac particlewith an asymmetric cusp potential

- Physics
- 2006

Abstract.We study the exact solutions of the bound and scattering states of the one-dimensional Dirac equation with an asymmetric cusp potential and derive the condition of the supercriticality for…

Scattering states of Dirac particle equation with position-dependent mass under the cusp potential

- Physics
- 2016

Abstract.We solved the one-dimensional position-dependent mass Dirac equation in the presence of the cusp potential and reported the solutions in terms of the Whittaker functions. We have derived the…

Strong Levinson theorem for the Dirac equation.

- Physics, MathematicsPhysical review letters
- 2004

This work connects the scattering phase shifts at E= +m and E= -m to the number of states that have left the positive energy continuum or joined the negative energy continuum, respectively, as the potential is turned on from zero.

Tunneling and transmission resonances of a Dirac particle by a double barrier

- Physics
- 2010

We calculate the tunneling process of a Dirac particle across two square barriers separated by a distance d, as well as the scattering by a double-cusp barrier, where the centers of the cusps are…

Scattering of a spinless particle by an asymmetric Hulthén potential within the effective mass formalism

- Physics
- 2012

Effective mass Klein-Gordon equation for the asymmetric Hulthen potential is solved in terms of hypergeometric functions. Results are obtained for the scattering and bound states with the position…

Energy-dependent one-dimensional potentials and scattering of relativistic particles

- Physics
- 2021

Scattering behaviors of spin-0 and spin-1/2 particles interacting with one-dimensional energy-dependent barrier-type potentials are investigated by considering the Klein–Gordon and Dirac equations.…

Full transmission within a wide energy range and supercriticality in relativistic barrier scattering

- Physics
- 2012

For potential barriers with scalar and vector coupling, we show that a Dirac particle could experience nearly full transmission within a wide sub-barrier energy band. Moreover, for certain potential…

Scattering and Bound State Solutions of the Yukawa Potential within the Dirac Equation

- Physics, Mathematics
- 2014

In the presence of spin symmetry case, we obtain bound and scattering states solutions of the Dirac equation for the equal scalar and vector Yukawa potentials for any spin-orbit quantum number . The…

Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances

- Physics
- 2012

Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions.…

Resonant states in an attractive one-dimensional cusp potential

- Physics
- 2007

We solve the two-component Dirac equation in the presence of a spatially one-dimensional symmetric attractive cusp potential. The components of the spinor solution are expressed in terms of Whittaker…

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