Sign-Problem-Free Quantum Monte Carlo Predicts Nuclear Structure with High Accuracy.

Understanding the forces governing atomic nuclei remains a central challenge in nuclear physics, hampered by the inherent complexity of many-body quantum systems. Traditional computational methods, specifically Monte Carlo techniques, struggle with the ‘sign problem’, a computational obstacle that exponentially increases with system size and limits accurate predictions for heavier nuclei. Researchers at the Graduate School of China Academy of Engineering Physics, led by Zhong-Wang Niu and Bing-Nan Lu, alongside colleagues, present a solution in their work, ‘Sign-Problem-Free Nuclear Quantum Monte Carlo’. They detail a novel lattice nuclear force, rigorously designed to circumvent the sign problem for even-even nuclei, enabling scalable and predictive ab initio calculations – those derived from fundamental principles rather than empirical data – and offering a robust foundation for modelling nuclear structure across a wider range of isotopes.

Recent advances in nuclear physics demonstrate a significant improvement in modelling atomic nuclei, overcoming longstanding computational limitations and opening new avenues for predictive nuclear physics. Researchers have developed a novel lattice nuclear force that successfully mitigates the “sign problem” inherent in Monte Carlo (QMC) methods when applied to fermionic systems, such as atomic nuclei. QMC methods utilise random sampling to solve complex quantum mechanical problems, but the sign problem arises from the oscillating nature of the wave function, leading to cancellations and exponentially increasing computational cost. This innovative approach enables precise calculations for even-even nuclei, representing a substantial advancement towards performing ab initio calculations—those derived solely from fundamental physical constants—for increasingly complex nuclear systems.

The team validates the efficacy of this new lattice nuclear force through extensive calculations of binding energies for 76 even-even nuclei, ranging from helium to tin. Results demonstrate remarkable agreement with experimental data, achieving a standard deviation of approximately 1 MeV. This level of precision matches the performance of established phenomenological mean-field models, which rely on empirical parameters, but importantly, this new method offers the potential for predictive power beyond those models.

Crucially, the researchers achieve the first implementation of sign-problem-free spin-orbit coupling within a lattice framework. Spin-orbit coupling, the interaction between a particle’s intrinsic angular momentum (spin) and its orbital motion, plays a vital role in determining the energy levels and properties of nuclei. This breakthrough allows physicists to explore the effects of spin-orbit coupling on nuclear properties with unprecedented accuracy, and facilitates more realistic modelling of nuclear shell evolution—the arrangement of nucleons (protons and neutrons) into energy levels.

Furthermore, the team develops an efficient QMC-optimized framework that facilitates global parameter fitting, streamlining the computational process and enhancing the precision of the results. This framework automates the process of adjusting the parameters of the lattice nuclear force to achieve optimal agreement with experimental data, reducing computational demands.

Analysis reveals that this methodology provides a non-perturbative foundation for ab initio calculations, meaning it does not rely on approximations that can introduce errors. Traditional perturbative methods involve expanding a solution as a series, which can fail when interactions are strong. By providing a rigorous and accurate framework, scientists can gain a deeper understanding of the fundamental forces governing nuclear behaviour.

Researchers have demonstrated both accuracy and scalability, positioning this approach as a powerful complement to existing theoretical and experimental methods in nuclear physics. By combining the strengths of both theory and experiment, scientists can gain a more complete understanding of the atomic nucleus.

The implications of this research extend beyond nuclear physics, with potential applications in materials science, energy production, and medical imaging. Understanding the properties of nuclei is crucial for developing new materials, designing more efficient nuclear reactors, and improving medical imaging techniques such as Positron Emission Tomography (PET).

The team plans to make their computational tools and data publicly available, fostering collaboration and accelerating scientific progress. By sharing their resources, they hope to inspire the next generation of scientists.

Future research will focus on extending this methodology to odd-mass nuclei and exploring its potential for predicting nuclear properties relevant to astrophysics and nuclear technology. Scientists also plan to investigate the effects of different nuclear forces and interactions on nuclear structure and stability.