Nuclear Mass Predictions Achieve Improved Accuracy with Quantum-inspired Bayesian Algorithm

Predicting the mass of atomic nuclei remains a fundamental challenge in nuclear physics, crucial for understanding the universe and developing technologies, and now, researchers are applying principles from quantum mechanics to improve these predictions. Kaizhong Tan, Jian Liu, and Chuan Wang, all from the College of Science at China University of Petroleum (East China), present a new algorithm that combines Bayesian probability with concepts from quantum dynamics. Their work effectively captures subtle patterns within existing theoretical models, leading to more reliable predictions of nuclear mass and offering a powerful new tool for exploring the landscape of atomic nuclei, with potential applications extending across nuclear physics. The team’s approach demonstrates the feasibility of leveraging quantum-inspired techniques to refine our understanding of nuclear structure and properties.

The method maps these residuals into wave functions within Hilbert space and solves the Schrödinger equation to obtain corresponding potentials. Assuming residuals follow a Boltzmann distribution, the algorithm derives prior and likelihood probability density functions (PDFs) from these potentials, ultimately applying Bayesian theorem to estimate target nuclear mass residuals. The QIBP algorithm defines a wave function, Ψ(δ), representing the dataset of nuclear mass residuals, calculated from numerous data points, and introduces a weighted coefficient to emphasize local features, capturing the influence of proton and neutron numbers.

This weighting refines the wave function, enabling a more accurate representation of the residual distribution. Additional wave functions are derived for isotopic and isotonic chains, considering nuclei with matching proton or neutron numbers. Treating these wave functions as eigenstates of the Schrödinger equation, the algorithm calculates potentials, demonstrating enhanced sensitivity and robustness in data processing. The minima of the potential function act as abstract gravitational sources, attracting the distribution of residuals toward more stable, lower-energy regions, effectively capturing quantum dynamical features. Finally, assuming a Boltzmann distribution, the algorithm derives the prior PDF and likelihood PDFs directly from the calculated potentials. This innovative approach allows for accurate predictions of nuclear masses, offering potential applications in nuclear reactions and astrophysics.

Quantum Algorithm Improves Nuclear Mass Prediction

This study presents a new algorithm, quantum-inspired Bayesian probability (QIBP), designed to improve predictions of nuclear mass through theoretical models. The method maps the differences between theoretical and experimental mass values into wave functions and uses principles from quantum dynamics, specifically solving the Schrödinger equation, to determine probability density functions. By assuming these differences follow a Boltzmann distribution, the algorithm derives accurate estimations of nuclear mass residuals, ultimately enhancing the reliability of theoretical predictions. The QIBP algorithm demonstrates an ability to capture subtle patterns and effects not fully accounted for in existing models, and its performance was validated through extrapolation analyses and predictions of decay energies for specific isotopes of radium and einsteinium.

The team successfully predicted nuclear masses, and analysis of einsteinium isotopes revealed details of subshell effects, demonstrating the algorithm’s capacity to describe complex nuclear structures. While the algorithm shows promise, the authors acknowledge that its performance relies on the initial assumption of a Boltzmann distribution for the residuals, which may not be universally applicable across all nuclei. Future research could focus on exploring alternative distributions or refining the quantum-inspired approach to better capture the nuances of nuclear structure. Nevertheless, this work establishes the feasibility of applying quantum-inspired methods to nuclear mass research, offering a potentially powerful tool for advancing our understanding of nuclear physics and its applications in fields like astrophysics and nuclear reactions.