On the quantum behavior of a neutral fermion in a pseudoscalar potential barrier

In this Letter we have studied the quantum behavior of a spin half neutral fermion interacting with a pseudoscalar potential barrier in ( 1 + 1 )-dimensional spacetime. Exact solutions for the corresponding Dirac equation are obtained both for bound and scattering states. The exact energy levels are obtained from the solutions of Dirac equation. The validity of the quasi-classical quantization rule is examined. For the scattering process the transmission and reflection coefficients are exactly calculated. The absence of the Kleinʼs paradox is also discussed.