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Low momentum scattering in the Dirac equation. (English) Zbl 1066.81040
Summary: 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 $T$ willbe nonzero whilst for a symmetric potential $T = 1$. Therefore in some circumstances a Dirac particle of arbitrarily small momentum can tunnel without reflection through a potential barrier.

81U05$2$-body potential scattering theory (quantum theory)
81U20$S$-matrix theory, etc. (quantum theory)
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