Transverse electric form factors for electron scattering and violation of current conservation in nuclear models.

Abstract

Comparison is made between calculations of transverse electric form factors using the standard expression for the electric multipole operator and those obtained by invoking current conservation in the long wavelength limit and for arbitrary momentum transfer. In all cases, only the free-nucleon one-body current and charge operators are explicitly used. Results are presented for select E2 transitions in $^{12}\mathrm{C}$, $^{20}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, and $^{28}\mathrm{Si}$. It is found that the form factors yielded by the various operators differ significantly when the conventional 0\ensuremath{\Elzxh}\ensuremath{\omega} shell model wave functions are used, confirming that these do violate conservation of the usual free-nucleon current. For these cases, the data are best reproduced using the operator with current conservation invoked in the long-wavelength limit. However, the variation between results is much smaller when multishell models of nuclear structure are used, all three forms of the operator yielding good agreement with existing data, suggesting that the wave functions obtained from these still practicable models are significantly closer to being current conserving.