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… 
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References

SHOWING 1-10 OF 15 REFERENCES
Supercriticality and transmission resonances in the dirac equation
It is shown that a Dirac particle of mass m and arbitrarily small momentum will tunnel without reflection through a potential barrier V = U(c)(x) of finite range provided that the potential well V =
The Woods-Saxon potential in the Dirac equation
The two-component approach to the one-dimensional Dirac equation is applied to the Woods?Saxon potential. The scattering and bound state solutions are derived and the conditions for a transmission
Low-energy scattering and Levinson's theorem for a one-dimensional Dirac equation
For a Dirac system on the line, the scattering matrix is defined in terms of Lippmann-Schwinger type solutions, which are also used to express an eigenfunction expansion. The S-matrix is shown to be
Threshold anomalies in one‐dimensional scattering
In one‐dimensional scattering, the portion of particles that is transmitted in general vanishes as the kinetic energy of the incident particles approaches zero. Based upon published results from the
Klein Tunnelling and the Klein Paradox
The Klein paradox is reassessed by considering the properties of a finite square well or barrier in the Dirac equation. It is shown that spontaneous positron emission occurs for a well if the
Levinson’s theorem, zero‐energy resonances, and time delay in one‐dimensional scattering systems
The one‐dimensional Levinson’s theorem is derived and used to study zero‐energy resonances in a double‐potential system. The low energy behavior of time delay is also investigated. In particular, it
Scattering theory of waves and particles
Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to
Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac
ZusammenfassungEs wird die Reflexion von Elektronen an einem Potentialsprung nach der neuen Diracschen Dynamik untersucht. Bei sehr großen Werten des Potentialsprungs dringen der Theorie zufolge
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