Quantum Monte Carlo Calculates Helium Isotope Uncertainties with Fully Propagated Interactions up to Next-to-Next-to-Leading Order

Understanding the forces within atomic nuclei remains a fundamental challenge in physics, and recent work by Ryan Curry, Kai Hebeler, and Stefano Gandolfi, along with colleagues, represents a significant step forward. The team, spanning the University of Guelph, Technische Universität Darmstadt, and Los Alamos National Laboratory, has performed the first calculations of light helium isotopes that rigorously account for theoretical uncertainties throughout the entire process. By developing advanced computational techniques and employing a Bayesian approach, they propagate uncertainties from the underlying nuclear interactions all the way to observable properties, such as binding energies and charge radii. This achievement establishes a robust framework for future studies of atomic nuclei, allowing scientists to more accurately assess the reliability of theoretical predictions and deepen our understanding of nuclear structure.

Researchers report the first quantum Monte Carlo calculations of helium isotopes, fully propagating theoretical uncertainties from the interaction to the many-body observables. To achieve this, they construct emulators, computational tools that predict nuclear behaviour for various interaction parameters, for solutions to the equations describing few-body systems, specifically for the binding energy and Gamow-Teller matrix element of tritium. They also build emulators for auxiliary-field diffusion Monte Carlo calculations of the helium-4 charge radius, employing local two- and three-body interactions up to a high level of accuracy in chiral effective field theory. These emulators allow for efficient and accurate calculations of key nuclear properties, representing a significant advancement in the field of nuclear physics.

Ab Initio Calculations and Uncertainty Quantification

This collection of research papers focuses on ab initio calculations, uncertainty quantification, and the use of emulators to accelerate these calculations. These studies describe the fundamental methods used to solve the many-body problem in nuclear physics, starting from realistic interactions between nucleons. Several papers focus on neutron matter calculations, crucial for understanding neutron stars, and global sensitivity analyses, which identify the parameters in the nuclear force with the biggest impact. Other studies detail the Auxiliary Field Quantum Monte Carlo method, a powerful technique for solving complex nuclear problems.

These papers also address the critical issue of quantifying the uncertainties in nuclear calculations, stemming from both theoretical approximations and experimental inputs. Researchers have measured the alpha-particle charge radius with high precision, and performed global sensitivity analyses to understand the impact of uncertainties. Studies have also focused on quantifying uncertainties in tritium beta decay and neutrinoless double-beta decay, and developing methods for quantum Monte Carlo simulations. A major theme is the use of machine learning and emulation techniques to overcome the computational cost of ab initio calculations and perform uncertainty quantification more efficiently.

Researchers have developed BUQEYE, a projection-based emulator for nuclear physics, and emulated ab initio computations of infinite nucleonic matter. Other studies have focused on reduced-order scattering emulators and Bayesian inference, and emulators for neutron star observations. These studies demonstrate a clear trend towards using machine learning to accelerate calculations and improve the reliability of nuclear predictions. Several papers apply these methods to specific nuclear systems or phenomena, such as emulating ab initio computations of infinite nucleonic matter and inferring three-nucleon couplings from multi-messenger neutron-star observations. This research reflects the cutting edge of nuclear physics.

Quantifying Helium Isotope Uncertainties with Emulators

Scientists have achieved a breakthrough in calculating the properties of helium isotopes by systematically incorporating theoretical uncertainties into their models. This work represents the first Monte Carlo calculations of helium isotopes where theoretical uncertainties, stemming from the underlying interaction models, are fully propagated through to observable quantities. The team developed a novel framework utilizing emulators, computational tools that rapidly predict nuclear behaviour for various interaction parameters, to address the computational challenges of uncertainty quantification. Researchers employed these emulators to determine the range of plausible values for the parameters defining the nuclear interaction, up to a high level of accuracy in chiral effective field theory.

This involved fitting the model to experimental data for the energy and Gamow-Teller matrix element of tritium, as well as the charge radius of helium-4. The resulting ranges of plausible values were then propagated through auxiliary-field diffusion Monte Carlo calculations for the ground-state energies of helium-3, helium-4, and helium-6. Measurements demonstrate that the team successfully quantified uncertainties in the ground-state energies of these helium isotopes. For helium-4, the calculated ground-state energy falls within a range of -21. 0 to -24.

0 MeV, while for helium-3, the range is -8. 0 to -6. 0 MeV, and for helium-6, the range is -20. 0 to -24. 0 MeV. These calculations, incorporating full uncertainty propagation, provide a more realistic assessment of the predictive power of nuclear models and establish a systematic approach for future ab initio calculations.

Quantifying Helium Isotope Uncertainties with Monte Carlo

This research presents the first Monte Carlo calculations of helium isotopes that fully account for theoretical uncertainties originating from the underlying interactions and extending to observable quantities. Scientists developed computational emulators for key calculations, including those determining binding energies and charge radii, allowing for a comprehensive Bayesian analysis of the parameters defining the nuclear interaction up to a specific level of accuracy. By propagating these uncertainties through the calculations, the team successfully quantified the correlations between energies of different helium isotopes, finding a strong link between lighter isotopes but noting the distinct behaviour of the halo nucleus, helium-6. This achievement establishes a robust framework for future studies of atomic nuclei, enabling consistent treatment and correlation of theoretical uncertainties.

The researchers demonstrated the comparability of different emulator techniques, highlighting the necessity of certain methods when complete wave function information is unavailable. This work provides not only robust uncertainty estimates for predictions of nuclear energies, but also a pathway for incorporating and managing uncertainties in a wide range of nuclear calculations. Future research will extend these methods to further investigate halo nuclei and refine the understanding of nuclear structure.