Beyond the charge radius: the information content of the fourth radial moment

Measurements of atomic transitions in different isotopes offer key information on the nuclear charge radius. The anticipated high-precision experimental techniques, augmented by atomic calculations, will soon enable extraction of the higher-order radial moments of the charge density distribution. To assess the value of such measurements for nuclear structure research, we study the information content of the fourth radial moment $\rf$ by means of nuclear density functional theory and a multiple correlation analysis. We show that $\rf$ can be directly related to the surface thickness of nuclear density, a fundamental property of the atomic nucleus that is difficult to obtain for radioactive systems. Precise knowledge of these radial moments is essential to establish reliable constraints on the existence of new forces from precision isotope shift measurements.