Complex-energy Eigenvector Continuation Efficiently Predicts Broad Resonances in H, He and Four-neutron Nuclei

Broad resonances present a significant challenge in nuclear physics, often causing computational instability and hindering theoretical studies of open nuclei. Rongzhe Hu, Nicolas Michel from the Chinese Academy of Sciences, and Zhicheng Xu, alongside Jianguo Li and Furong Xu, now address this problem with an extension of the eigenvector continuation method. Their innovative approach applies this technique to the complex-energy space, enabling efficient calculation of broad resonances using only a limited number of known bound and narrow resonance solutions as input. This advancement allows researchers to accurately model the behaviour of nuclei exhibiting broad resonances, including hydrogen, four-neutron systems, helium-6 and helium-8, and promises to unlock a deeper understanding of nuclear structure and reactions.

Broad resonances represent a unique phenomenon within nuclear many-body systems. Theoretical investigations typically require consideration of continuum degrees of freedom, which substantially increases the computational model space. This research presents an extension of the eigenvector continuation (EC) method to complex-energy space, specifically designed to address broad resonances in open quantum systems of nuclei. The EC method provides an efficient approach to predict solutions for large-scale many-body problems within a limited subspace, utilising only a few bound and narrow resonances.

Gamow Shell Model Calculations of Light Nuclei

Scientists are refining our understanding of the structure of atomic nuclei, particularly light nuclei, and the reactions occurring within them. This work focuses on the Gamow Shell Model, a theoretical framework crucial for describing nuclei far from stability. The research addresses the properties of halo nuclei, which possess loosely bound neutrons or protons forming a halo around a core, and other exotic nuclei, aiming to refine the understanding of the nuclear force that holds nuclei together. The team performs theoretical calculations and modeling using the Gamow Shell Model, involving complex many-body calculations to solve the Schrödinger equation for the nucleus and account for interactions between all protons and neutrons.

These calculations rely on effective interactions, simplified representations of the complex nuclear force tailored to specific nuclei and model spaces, including interactions based on chiral effective field theory. The theoretical results are compared with experimental data, such as energy levels and decay probabilities, to validate the models and refine the effective interactions. Researchers also explore ab initio methods, which aim to solve the nuclear many-body problem directly from fundamental interactions. This research has led to improved Gamow Shell Model calculations that more accurately predict the properties of exotic nuclei and validated the effective interactions used within the model.

The study contributes to a better understanding of halo nuclei, including their unusual decay modes, and has implications for understanding astrophysical processes where these nuclei are created. The work explores the convergence of different theoretical approaches, including the Gamow Shell Model and ab initio methods, to provide a more complete and accurate description of nuclear structure. This research is highly relevant to nuclear astrophysics, the field that studies nuclear reactions in stars and supernovae. It contributes to our fundamental understanding of the nuclear force and the structure of matter, driven by the increasing availability of exotic nuclei at rare isotope facilities worldwide. These facilities enable scientists to study previously inaccessible nuclei, pushing the boundaries of theoretical nuclear physics and refining methods for solving the complex many-body problem.

Complex Energy Extension Resolves Nuclear Resonances

Scientists have achieved a breakthrough in calculating broad resonances in nuclear physics, overcoming longstanding computational challenges. The research team extended the eigenvector continuation (EC) method to complex-energy space, enabling accurate predictions for the properties of open nuclei where traditional methods often fail. This advancement addresses a critical limitation in modeling nuclear systems, particularly those exhibiting broad resonances, which are difficult to treat due to the vast computational demands of including continuum effects. The team’s method begins with calculations performed using the Gamow shell model (GSM), incorporating a complex-energy Berggren basis that inherently accounts for continuum effects.

For lighter nuclei like helium and hydrogen, the no-core GSM was employed, while heavier nuclei utilized a core-based GSM approach. The core innovation lies in scaling the many-body Hamiltonian, initially using values greater than one, to ensure stable and converged calculations for bound and narrow resonance states. These solutions serve as “training points” and “snapshots” for the EC process. The researchers then project the target Hamiltonian, representing the physical system, onto a subspace defined by these training points, resulting in a generalized eigenvalue problem. This allows for the determination of eigenvalues and eigenvectors corresponding to broad resonances, even when direct calculations are unstable or non-convergent. Tests demonstrate the method’s ability to accurately predict resonance energies and widths, providing a crucial measure of particle emission half-life. The team successfully applied this technique to calculate broad resonances in hydrogen, helium, and four-neutron systems, establishing a powerful new tool for nuclear structure research.

Broad Resonance Properties Calculated With Eigenvector Continuation

Researchers have developed a method to accurately calculate the properties of broad resonances in atomic nuclei, a longstanding challenge in nuclear physics. These resonances, which represent unstable states of nuclei, are difficult to model because they involve interactions with a vast number of particles in the continuum, significantly increasing the complexity of calculations. The team extended the eigenvector continuation method, traditionally used for stable nuclear states, to the complex-energy domain, allowing them to effectively account for these interactions. This approach circumvents the computational difficulties by using a relatively small number of known stable and narrow resonance states to extrapolate the properties of the broad resonance.

The method was successfully tested on isotopes of hydrogen, helium, and four-neutron nuclei, demonstrating strong agreement with both experimental data and more computationally intensive calculations. The results provide a valuable tool for understanding the structure of unstable nuclei and interpreting experimental measurements. The accuracy of the method relies on the quality of the initial nuclear interactions used in the calculations, and uncertainties in these interactions contribute to the overall uncertainty in the predicted resonance properties. Future research will likely focus on refining these interactions and applying the method to a wider range of nuclei, potentially revealing new insights into the behaviour of matter under extreme conditions.