The nth-order moment of the nuclear charge density and contribution from the neutrons

The relativistic expression for the nth-order moment of the nuclear charge density is presented. For the mean square radius (msr) of the nuclear charge density, the non-relativistic expression, which is equivalent to the relativistic one, is also derived consistently up to 1/M-2 with use of the Foldy-Wouthuysen transformation. The difference between the relativistic and non-relativistic expressions for the msr of the point proton density is also discussed. The n(>= 4)th-order moment of the nuclear charge density depends on the point neutron density. The fourth-order moment yields useful information on the msr of the point neutron density, and is expected to play an important role in electron scattering off neutron-rich nuclei.