Basis Representation for Nuclear Densities from Principal Component Analysis

TL;DR

This paper introduces a PCA-based basis for nuclear density representation that outperforms traditional methods in accuracy and efficiency, facilitating improved analysis and modeling in nuclear physics.

Contribution

The paper presents a novel PCA-derived basis for nuclear densities, achieving high accuracy with fewer components and faster convergence than existing methods.

Findings

First five PCA basis functions capture over 99.999% of variance.

PCA basis outperforms Fourier-Bessel and Sum-of-Gaussians methods.

Provides a practical tool for experimental and theoretical nuclear density analysis.

Abstract

We develop an efficient method to represent nuclear densities using basis functions extracted via Principal Component Analysis (PCA). Applying PCA to densities of 75 nuclei calculated with the relativistic continuum Hartree-Bogoliubov (RCHB) theory yields an orthogonal set of components that efficiently capture the dominant features of nuclear density distributions, which can be used as basis functions for nuclear density representation. The first five basis functions account for more than 99.999\% of the total variance, demonstrating the efficiency of these PCA basis functions. The PCA basis achieves significantly higher accuracy and faster convergence than the Fourier-Bessel and Sum-of-Gaussians methods for reconstructing both theoretical and experimental densities. This approach provides an efficient and robust representation of nuclear densities, offering a practical tool for experimental density representation and for theories where densities play a central role, such as the orbital-free density functional theory, or the double folding model for nuclear reactions.