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

TL;DR

This paper investigates the informational value of the fourth radial moment of nuclear charge density, showing its relation to surface thickness and its importance for constraining new forces via isotope shift measurements.

Contribution

It introduces a method to relate the fourth radial moment to nuclear surface thickness using nuclear density functional theory and correlation analysis.

Findings

The fourth radial moment correlates with nuclear surface thickness.

Precise measurement of this moment aids in constraining new fundamental forces.

It enhances understanding of nuclear structure beyond charge radius data.

Abstract

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 .