Approximating the nuclear binding energy using analytic continued fractions

Understanding nuclear behaviour is fundamental in nuclear physics. This paper introduces a data-driven approach, Continued Fraction Regression (cf-r), to analyze nuclear binding energy (B(A, Z)). Using a tailored loss function and analytic continued fractions, our method accurately approximates stable and experimentally confirmed unstable nuclides. We identify the best model for nuclides with A >= 200 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\ge 200$$\end{document} , achieving precise predictions with residuals smaller than 0.15 MeV. Our model's extrapolation capabilities are demonstrated as it converges with upper and lower bounds at the nuclear mass limit, reinforcing its accuracy and robustness. The results offer valuable insights into the current limitations of state-of-the-art data-driven approaches in approximating the nuclear binding energy. This work provides an illustration on the use of analytical continued fraction regression for a wide range of other possible applications.