Exchange currents in nucleon electroexcitation

Abstract

We calculate the scalar and transverse helicity amplitudes for the electromagnetic excitation of nucleon resonances as a function of the photon four-momentum transfer. The helicity amplitudes are decomposed into electromagnetic multipoles and connected to the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{N}{N}^{*}$ transition form factors. The internal N and ${N}^{*}$ dynamics is described by a constituent quark model (CQM) Hamiltonian with gluon, pion, and $\ensuremath{\sigma}$-meson exchange potentials as residual interactions. The N and ${N}^{*}$-resonance wave functions are obtained by solving the Schr\odinger equation in a harmonic oscillator basis which contains up to $N=2$ excitation quanta. For the electromagnetic current we include, in addition to the one-body current, two-body exchange currents associated with the quark-quark potentials. Exchange currents provide an effective description of the cloud of $q\overline{q}$ pairs, which together with the valence quarks are important degrees of freedom in physical hadrons. We obtain sizable contributions of the two-body exchange currents for nearly all $\ensuremath{\gamma}{\mathrm{NN}}^{*}$ amplitudes. For some observables, e.g., the $C2/M1$ ratio in the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\Delta}(1232)$ transition, and the $M1$ transition to the ${N}^{*}(1440),$ exchange currents provide the most important contribution.