  The problem of neutral fermions subject to a pseudoscalar potential is
investigated. Apart from the solutions for $E=\pm mc^{2}$, the problem is
mapped into the Sturm-Liouville equation. The case of a singular trigonometric
tangent potential ($\sim \mathrm{tan} \gamma x$) is exactly solved and the
complete set of solutions is discussed in some detail. It is revealed that this
intrinsically relativistic and true confining potential is able to localize
fermions into a region of space arbitrarily small without the menace of
particle-antiparticle production.

High Energy Physics - Theory;Quantum Physics