Garvey-Kelson Relations for Nuclear Charge Radii

TL;DR

This paper extends Garvey-Kelson relations to predict nuclear charge radii, achieving high accuracy and providing predictions for nuclei lacking experimental data, thus offering a simple yet effective alternative to complex microscopic models.

Contribution

The authors adapt Garvey-Kelson relations for nuclear charge radii, demonstrating their effectiveness and providing accurate predictions with uncertainties for unmeasured nuclei.

Findings

RMS deviation of 0.01 fm between predictions and experimental data.

Successful extension of GKRs beyond nuclear masses to charge radii.

Predictions for 116 nuclei with unknown charge radii.

Abstract

The Garvey-Kelson relations (GKRs) are algebraic expressions originally developed to predict nuclear masses. In this letter we show that the GKRs provide a fruitful framework for the prediction of other physical observables that also display a slowly-varying dynamics. Based on this concept, we extend the GKRs to the study of nuclear charge radii. The GKRs are tested on 455 out of the approximately 800 nuclei whose charge radius is experimentally known. We find a rms deviation between the GK predictions and the experimental values of only 0.01 fm. This should be contrasted against some of the most successful microscopic models that yield rms deviations almost three times as large. Predictions - with reliable uncertainties - are provided for 116 nuclei whose charge radius is presently unknown.