Data-Driven Energy Levels Calculation of Neutral Ytterbium ($Z$ = 70)

TL;DR

This paper introduces a novel data-driven approach combining HFR theory with ridge regression to accurately calculate energy levels of neutral ytterbium, overcoming challenges of high-Z element atomic structure calculations.

Contribution

The study presents a new method integrating HFR theory with ridge regression, improving the calculation of energy levels for high-Z elements like ytterbium.

Findings

Ridge regression outperforms Cowan's LSF in accuracy.

Calculated energy levels closely match experimental data.

Method demonstrates reliability for high-Z atomic structure calculations.

Abstract

In view of the difficulty in calculating the atomic structure parameters of high-$Z$ elements, the HFR (Hartree-Fock with relativistic corrections) theory in combination with the ridge regression (RR) algorithm rather than the Cowan code's least squares fitting (LSF) method is proposed and applied. By analyzing the energy level structure parameters of the HFR theory and using the fitting experimental energy level extrapolation method, some excited state energy levels of the {Yb~I} ($Z=70$) atom including the $4f$ open shell are calculated. The advantages of the ridge regression algorithm are demonstrated by comparing it with Cowan's least squares results. In addition, the results obtained by the new method are compared with the experimental results and other theoretical results to demonstrate the reliability and accuracy of our approach.