Current conservation and the transverse electric multipole field

Different prescriptions for imposing the constraints of current conservation on the Fourier transform of the electromagnetic current operator generate alternative forms for the electric multipole fields. These forms lead to quite different predictions for electromagnetic form factors in nuclear calculations that violate current conservation either by adopting an approximate current operator or by diagonalizing the nuclear Hamiltonian in a truncated Hilbert space. For typical shell model calculations of electron scattering form factors, it appears that no existing prescription for imposing the constraints of current conservation on electric multipole operators is entirely satisfactory. Numerical results are given for electric transitions in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$.