Full transmission within a wide energy range and super-criticality in relativistic barrier scattering

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.Comment: 10 pages, 4 figures, 1 table, 1 video animatio