Electromagnetic properties of the Δ(1232)

Abstract

We calculate the electromagnetic moments and radii of the $\ensuremath{\Delta}(1232)$ in the nonrelativistic quark model, including two-body exchange currents. We show that two-body exchange currents lead to nonvanishing $\ensuremath{\Delta}$ and $N\ensuremath{\rightarrow}\ensuremath{\Delta}$ transition quadrupole moments even if the wave functions have no $D$-state admixture. The usual explanation based on the single-quark transition model involves $D$-state admixtures but no exchange currents. We derive a parameter-free relation between the $N\ensuremath{\rightarrow}\ensuremath{\Delta}$ transition quadrupole moment and the neutron charge radius, namely ${Q}_{N\ensuremath{\rightarrow}\ensuremath{\Delta}}=(1/\sqrt{2}{)r}_{n}^{2}.$ Furthermore, we calculate the $M1$ and $E2$ amplitudes for the process $\ensuremath{\gamma}+N\ensuremath{\rightarrow}\ensuremath{\Delta}$. We find that the $E2$ amplitude receives sizable contributions from exchange currents. These are more important than the ones that result from $D$-state admixtures due to tensor forces between quarks if a reasonable quark core radius of about 0.6 fm is used. We obtain a ratio of $E2/M1=\ensuremath{-}3.5%$.