The generalized Gerasimov-Drell-Hearn sum rule for deuteron electrodisintegration

Abstract

The generalized Gerasimov-Drell-Hearn sum rule $I^{GDH}_{\gamma^*d}(Q^2)$ for deuteron electrodisintegration $d(e,e')np$ as function of the squared four-momentum transfer $Q^2$ is evaluated by explicit integration. The calculation is based on a conventional nonrelativistic framework using a realistic $NN$-potential and including contributions from meson exchange currents, isobar configurations and leading order relativistic terms. Good convergence is achieved. The prominent feature is a deep negative minimum, $I_{\gamma^* d}^{GDH}=-9.5$ mb, at low $Q^2\approx 0.2$ fm$^{-2}$ which is almost exclusively driven by the nucleon isovector anomalous magnetic moment contribution to the magnetic dipole transition to the $^1S_0$-state. Above $Q^2=20$ fm$^{-2}$ the integral $I^{GDH}_{\gamma^*}(Q^2)$ approaches zero rapidly.