Nonuniform Nuclear Charge Distributions and Measurements of Nuclear Electrical Radius

The dependence of three long wavelength electronic effects and of the nuclear Coulomb energy on the size and shape of the electrical charge distribution in heavy nuclei is examined. We note that the x-ray fine structure effect and the isotope shift effect measure the volume integral of r^2σ weighted by the nuclear charge density. [σ=1-(αZ)²1/2]. An earlier result of Feshbach---that medium-energy electron scattering measures the similarly weighted mean value of r²---is derived more simply. For these electronic effects, therefore, exact calculations for one shape of charge distribution may easily be scaled to other shapes. The nuclear Coulomb energy has no such simple dependence, but measures very roughly the weighted mean value of r0.8---nearly the same quantity as measured by the 2P→1S mu-mesonic transition in heavy nuclei.The nuclear Coulomb energy sheds no light on the shape of the nuclear charge distribution because of its inherent insensitivity to change of shape. The x-ray fine structure, and the atomic isotope shift, cannot give detailed information about the nuclear charge distribution because of uncertainty in the magnitude of radiative corrections, and of nuclear compressibility, respectively. Medium-energy electron scattering results, coupled with mu-mesonic x-ray results, will in principle be able to delineate shapes. Present evidence from this source suggests a charge distribution nearly uniform or somewhat peaked toward the edge of the nucleus.