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

Abstract

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 configurations, including pseudo-spin symmetry where the scalar potential is the negative of the vector, full transmission occurs for arbitrarily small momentum.

Two-Body Local-Momentum Approximation of Spinless Particles Scattered by a (1+1)-D Woods–Saxon Barrier Potential

“…It corresponds to the strange two-body effect of the SRQ equation mentioned earlier, but apparently exists for smooth (but sharp) barriers. An increase of the potential strength to V 0 > 2µc 2 results in effects similar to single-mass phenomena discussed recently within the Dirac framework [14] (see Fig. 2).…”

“…The more important to compare these results with quantum field theory. Single-particle Dirac results, pointed out by Alhaidari et al, [14] Thomson [15] and others, indicate total transmission at low (non-relativistic) scattering energies. For equal masses the present study indicates non-existence of large low-energy transmissions.…”

“…1, relativistic differences occur at very low (non-relativistic) scattering energies and different masses. These are related to situations in the Dirac approach for single masses discussed by Alhaidari et al [14] However, this difference disappears for d = 0.1. Differences with respect to nonrelativistic results occur more generally at energies significantly above the barrier-top energies (see Tables 2-4).…”

“…As a final study, the Woods-Saxon potential is used to compare SRQ results with the results of the (singlemass) Dirac theory as the surface thickness is d = 0.01 (see Refs. [14][15]). For such potentials there are speculative investigations about zero-momentum resonances and low-energy (ϵ ≈ 0) total transmissions for very large barriers.…”

“…[11−13] Two potential models are considered: The rectangular barrier, which allows exact numerical SRQ comparisons, is given by V (x) = V 0 , −a < x < a, and V (x) = 0, |x| ≥ a . (1) Note that Alhaidari et al [14] studied transmission properties for a single fermion mass with scalar/vector-type rectangular barriers using Dirac theory.…”