Exact Solution of the Dirac Equation in the Field of a 't Hooft-Polyakov Monopole

This paper presents an exact solution of the Dirac equation for an $I=\frac{1}{2}$ fermion in the field of a 't Hooft-Polyakov magnetic monopole (in the Prasad-Sommerfield limit), which is analytic at $\mathcal{r}=0\mathrm{}$. Helicity conservation restricts the $J=0\mathrm{}$ $S$ matrix to be pure charge exchange. Because of the long-range interaction, the scattering amplitude is enhanced at long wavelengths $\lambda \gg \frac{1}{M}$ (the monopole structure size). The relevance of the present results for the question of proton decay catalysis is briefly discussed.