Particle with arbitrary spin in the magnetic field of a linear current

We investigated the bound-state spectrum of a particle with spin $F>~\frac{1}{2}$ in the magnetic field of a thin current-carrying wire. We prove the existence of infinitely many bound states for any $F$. The bound-state energies closely follow a Coulomb-like behavior with an effective angular momentum ${\ell }^{*}$, suggesting a high adiabaticity of the system. Numerical results ($F=\frac{1}{2}, \dots , 3$) are well approximated by a single simple formula for the quantum defect, which is more accurate than the approximations given in the literature. We find a qualitative disagreement with the result obtained by adiabatic approximation.