Scattering and Bound States of a Spin-12 Neutral Particle in the Cosmic String Spacetime

Abstract EN

In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment μ 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: ∇·E=(2λ/α)δ(r)/r.

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, S-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 S-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.