The Smoothness of Physical Observables

TL;DR

This paper demonstrates that Garvey-Kelson relations are universally valid for any smooth physical observable, independent of specific models, and can be systematically refined for better accuracy, with applications in nuclear and particle physics.

Contribution

It shows that GK relations are more general than previously thought, relying solely on the smoothness of the physical function, and are applicable to a wide range of observables.

Findings

GK relations are model independent.

Any slowly-varying observable satisfies GK relations.

The accuracy of GK relations can be systematically improved.

Abstract

The Garvey-Kelson (GK) relations are powerful algebraic expressions connecting the masses of neighboring atomic nuclei and derived under reasonable physical assumptions. In this contribution we show that these relations are even more general than originally assumed as their validity is conditioned by the smoothness of the underlying nuclear mass function and nothing else. Based on the assumed smoothness of the underlying physical function, the main conclusions from this study are: (1) the GK relations are model independent; (2) any slowly-varying physical observable satisfies the GK relations; and (3) the accuracy of the GK relations may be systematically improved. Examples from nuclear physics (charge radii) and from particle physics (baryon masses) are used to illustrate the flexibility of the approach.