Correlation Testing in Nuclear Density Functional Theory

TL;DR

This paper develops a mathematical foundation for correlation testing in nuclear density functional theory, demonstrating its utility and limitations in selecting terms for nuclear mass models.

Contribution

It provides the first rigorous justification for correlation testing, along with analytical examples, benchmarking, and discussion of potential improvements.

Findings

Correlation testing effectively discriminates potential terms.

The method has specific limitations and potential issues.

Future developments can enhance the method's reliability.

Abstract

Correlation testing provides a quick method of discriminating amongst potential terms to include in a nuclear mass formula or functional and is a necessary tool for further nuclear mass models; however a firm mathematical foundation of the method has not been previously set forth. Here, the necessary justification for correlation testing is developed and more detail of the motivation behind its use is give. Examples are provided to clarify the method analytically and for computational benchmarking. We provide a quantitative demonstration of the method's performance and short-comings, highlighting also potential issues a user may encounter. In concluding we suggest some possible future developments to improve the limitations of the method.