On the scattering of massive spinless bosons by a nonminimal vector smooth step potential

The Duffin-Kemmer-Petiau (DKP) equation for massive spinless bosons in the presence of a nonminimal vector smooth step potential is revised. The problem is mapped into a Sturm-Liouville equation. The reflection and transmission coefficients are obtained and discussed in detail. Furthermore, we show that Klein's paradox does not show its face in this sort of interaction.