Sign of the L=4 Intrinsic Density Component from Electron Scattering Data

Ascertain the sign of the L=4 multipole component of the intrinsic rigid-body charge density of carbon-12 associated with the 0^+_1→4^+_2 electric transition, which cannot be determined from existing electron-scattering form factor data.

Background

When reconstructing intrinsic densities from electron-scattering form factors, the magnitude of the multipole components can be fitted, but the sign is not fixed by the data. The sign of the L=2 component can be inferred from the measured quadrupole moment of the 2^+_1 state, while the L=3 sign does not influence the reconstruction.

For L=4, the authors note that current experimental data do not allow determining the sign of the corresponding intrinsic density component. Although they argue its impact on the final reconstructed density is limited due to small amplitude, the sign remains an unresolved parameter.