Scattering and Bound States of a Spin-1/2 Neutral Particle in the Cosmic String Spacetime

In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment in the cosmic string spacetime is reexamined by applying the von Neumann theory of self-adjoint extensions. Contrary to previous studies where the interaction between the spin and the line of charge is neglected, here we consider its effects. This interaction gives rise to a point interaction: . Due to the presence of the Dirac delta function, by applying an appropriated boundary condition provided by the theory of self-adjoint extensions, irregular solutions for the Hamiltonian are allowed. We address the scattering problem obtaining the phase shift, -matrix, and the scattering amplitude. The scattering amplitude obtained shows a dependency with energy which stems from the fact that the helicity is not conserved in this system. Examining the poles of the -matrix we obtain an expression for the bound states. The presence of bound states for this system has not been discussed before in the literature.

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