= Solution
The negative-kinetic-energy branch is interpreted as an <antiparticle> channel. In the overlap $mc^2<E<V_0-mc^2$, particles can escape to the left and oppositely charged <antiparticles> to the right. This interval exists only when $V_0>2mc^2$. The external electrostatic source supplies the <energy> for pair creation; the reflected particle <flux> can exceed the incident one because the outgoing state need not contain only the incident particle.
\b[The conserved quantity is signed charge current, not a positive one-particle <probability> in both regions.] Negative $\mathcal T$ denotes rightward transport of opposite charge, so it is consistent with $\mathcal R>1$ and $\mathcal R+\mathcal T=1$. A quantized charged field with particle and <antiparticle> creation operators gives the appropriate interpretation of this <Klein paradox>. This bosonic result must not be replaced by a fermionic reflection law or interpreted as a failure of charge conservation.<Klein Paradox for Spin-0 Particles by Douglas M. Gingrich>[Discussion after equation 4.155: pair creation and the oppositely signed transmitted current]{ref}
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